59 compared to 56

59 compared to 56 DEFAULT

National growth dynamics of wind and solar power compared to the growth required for global climate targets

Abstract

Climate mitigation scenarios envision considerable growth of wind and solar power, but scholars disagree on how this growth compares with historical trends. Here we fit growth models to wind and solar trajectories to identify countries in which growth has already stabilized after the initial acceleration. National growth has followed S-curves to reach maximum annual rates of 0.8% (interquartile range of 0.6–1.1%) of the total electricity supply for onshore wind and 0.6% (0.4–0.9%) for solar. In comparison, one-half of 1.5 °C-compatible scenarios envision global growth of wind power above 1.3% and of solar power above 1.4%, while one-quarter of these scenarios envision global growth of solar above 3.3% per year. Replicating or exceeding the fastest national growth globally may be challenging because, so far, countries that introduced wind and solar power later have not achieved higher maximum growth rates, despite their generally speedier progression through the technology adoption cycle.

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Data availability

We used data from IEA world energy balances53 for wind and solar power generation, data from refs. 53,78,79,80,81,82,83,84,85,86,87 for the independent variables used in the statistical analyses (see Supplementary Note 5 for details) and data from Huppmann et al.46 to calculate the growth rates in scenarios as reported in the Supplementary Data. Source data are provided with this paper.

Code availability

The code for curve fitting and the computational experiments is available at GitHub https://github.com/poletresearch/RES_article.

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Acknowledgements

The research that led to this publication received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 821471 (project Exploring National and Global Actions to Reduce Greenhouse Gas Emissions (ENGAGE)). V.V. received funding from the Norwegian Research Council no. 267528 Analysing past and future energy industry contractions: Towards a better understanding of the flip-side of energy transitions. J.J. received funding from the European Union’s Horizon 2020 ERC Starting Grant programme under grant agreement no. 950408 for Mechanisms and Actors of Feasible Energy Transitions (MANIFEST). The authors acknowledge G. Semieniuk for useful comments on the manuscript.

Author information

Author notes
  1. These authors contributed equally: Aleh Cherp, Vadim Vinichenko, Jessica Jewell.

Affiliations

  1. Department of Environmental Sciences and Policy, Central European University, Vienna, Austria

    Aleh Cherp & Joel A. Gordon

  2. International Institute for Industrial Environmental Economics, Lund University, Lund, Sweden

    Aleh Cherp

  3. Centre for Climate and Energy Transformation, University of Bergen, Bergen, Norway

    Vadim Vinichenko & Jessica Jewell

  4. Department of Geography, Faculty of Social Sciences, University of Bergen, Bergen, Norway

    Vadim Vinichenko & Jessica Jewell

  5. Institute of Political Science and Heidelberg Center for the Environment, Heidelberg University, Heidelberg, Germany

    Jale Tosun

  6. Department of Energy and Power, Cranfield University, Cranfield, UK

    Joel A. Gordon

  7. Division of Physical Resource Theory, Department of Space, Earth and Environment, Chalmers University of Technology, Gothenburg, Sweden

    Jessica Jewell

  8. Advancing Systems Analysis Program, International Institute for Applied Systems Analysis, Laxenburg, Austria

    Jessica Jewell

Contributions

A.C., V.V. and J.J. jointly conceived and designed the study. V.V. designed and implemented the statistical analysis, modelling growth curves and comparison with scenarios, which included acquisition of data. A.C., V.V. and J.J. jointly interpreted the results. V.V. and J.J. visualized the results with input from A.C. A.C. and J.J. led the literature review and writing with contributions from V.V., J.T. and J.A.G. J.A.G. conducted the literature review on technology diffusion and contributed to the analysis of offshore wind power with V.V. and to the comparison of solar and wind with J.J. and A.C. J.T. contributed to the design and implementation of the EHA of take-off and the literature review.

Corresponding author

Correspondence to Aleh Cherp.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review informationNature Energy thanks Nuno Bento and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Computational experiment for growth parameters of logistic and Gompertz growth models.

The vertical coordinates of each dot show the divergence in G (max growth rate) and horizontal – in ∆t (the duration of transition) for a single computational experiment. The divergence is the ratio between the ‘true’ growth parameter of a computer-generated logistic (a) and Gompertz (b) curve and the same parameter estimated by fitting the other model to the same data (Methods). The dashed line corresponds to equal divergence of G and ∆t. Experiments differ by the degree of curve ‘maturity’ (represented by different colors), that is to which extent the generated data approach the asymptote L of the curve (Methods). Large triangles show the relative differences between the ‘true’ curve and the fitted growth model. Dots show the divergence between the original curve with random noise added (up to 5% above or below the respective original value, uniformly distributed) and the fitted model (Methods). The data illustrate that estimates of the growth parameters converge across the two models with more complete data (high maturity), but that the max growth rate G becomes robust across the two models at lower levels of maturity than the duration of transition ∆t. See Supplementary Note 3 for more discussion on growth metrics.

Source data

Extended Data Fig. 2 Relative differences between parameters of logistic and Gompertz models fitted to empirical data (onshore wind and solar PV).

Panel (a) shows the divergence between parameters of logistic and Gompertz models for different maturity levels. Divergence is the ratio between the larger and the smaller value of the same parameter fitted to the same country data and estimated by two different models. Divergence is calculated for each country and then summary statistics – medians (dots) and full range (brackets) – are shown for sub-samples of countries with different maturity determined by the logistic fit. Median and maximum divergence for maturity <50% are beyond the vertical limits of the figure – see Supplementary Table 1. Panels (b) and (c) shows relative differences in G versus ∆t (panel b) and log(L)/∆t5,86 for all countries for maturity <50% and for all countries included in the analysis of G for maturity >50%. Maturity levels in panels (b) and (c) are depicted with colors. The dashed line in panels (b) and (c) shows the equal relative differences in G and ∆t and G and log(L)/∆t. Relative differences larger that 10 were limited to 10 to prevent the figure from being squeezed. See Supplementary Tables 17 and 18 for fitted values.

Source data

Extended Data Fig. 3 Takeoff years (1%) for onshore wind vs solar PV.

Each dot represents a country positioned according to its wind takeoff year on the horizontal axis and solar takeoff year on the vertical axis. The takeoff year is the year when the share of the given technology for the first time exceeds 1% of the total electricity supply. Countries where a particular technology has not taken off are placed in the grey bands on the top (no solar takeoff) and the right (no wind takeoff). The numbers in the top-right corner indicate the number of countries where neither wind nor solar takeoff has taken place. Colors indicate the country groups (Supplementary Table 5). See Supplementary Table 33 for country codes. The dashed line is based on a linear regression for the countries with both takeoff dates available (except for Denmark treated as an outlier with its very early wind takeoff). The regression coefficient is 0.33 (meaning that a country with wind takeoff three years earlier has, on average, solar takeoff one year earlier), R2 = 36%, p-value < 1%.

Source data

Extended Data Fig. 4 Historical deployment of wind power, growth models and maximum growth rates (G).

Gray dots show empirically observed electricity generation from onshore wind power, normalized to national electricity supply in the takeoff year to adjust for country size. The orange lines show Gompertz model fit and the dark blue lines show logistic model fit to these points (Methods). Stars indicate the takeoff year (T1%) and circles indicate the inflection points for each model (located in the future for accelerating growth). See Methods for definition of maturity and maximum growth rates (G) as well as the method for selecting countries for the analysis of G.

Source data

Extended Data Fig. 5 Historical deployment of wind power, growth models and maximum growth rates (G) for selected countries.

Gray dots show empirically observed electricity generation from solar PV power, normalized to national electricity supply in the takeoff year to adjust for country size. The orange lines show Gompertz model fit and the dark blue lines show logistic model fit to these points (Methods). Stars indicate the takeoff year (T1%) and circles indicate the inflection points for each model (located in the future for accelerating growth). See Methods for definition of maturity and maximum growth rates (G) as well as the method for selecting countries for the analysis of G.

Source data

Extended Data Fig. 6 Are wind and solar power on track to the Paris targets in 2030 and 2050? A comparison with an alternative approach.

The Figure contains the replication and analysis of ref’s8 assessment of whether wind and solar power are on track to attain Paris climate targets. On all panels, dashed lines replicate ref’s. 8 logistic curves fit to 2010 values and saturating at the ‘2050 Paris benchmarks’ defined by ref. 8 as median 2050 values for 1.5 °C scenarios (purple diamonds, also indicating median scenario values for 2030). For this replication we use the range of ‘emergence rates’ (year-on-year growth rates at the early stages) from ref. 8 of 15%, 20%, 25% for wind and 25%, 30%, 35% for solar. For each technology, we mark the central case in black and the high and low cases in grey. Panels (a) and (c) indicate yearly growth rates (G) at the inflection points of these curves normalised to the size of the global electricity system. The G’s for these considerably exceed the maximum growth rates we estimate for any large country so far (Supplementary Fig. 5). The orange and blue lines represent Gompertz and logistic model fits (with inflection points) to the empirical timeseries of global wind and solar power deployment using the approach in this paper (Methods). These models project much lower values for 2030 and 2050 than the models from ref. 8. Panels (b) and (d) zoom the same curves and data on 2010-2020 and indicate Residual Sum of Squares (RSS)74 for the replicated curves and our two model fits vs. 2010-2018 empirical data. The RSS for the replicated logistic curves are between 10 and 280 times larger than our best fit for wind and 400 and 1000 times larger than our best fit for solar, which indicate that the replicated curves from ref. 8 match the empirical data with considerably lower accuracy than our models.

Source data

Extended Data Fig. 7 Estimated vs. observed maximum growth rates.

Estimated growth rates (G) are for the maximum growth (inflection) year. Observed rates are the maximum 5-year moving average annual growth rates (panel a) or maximum observed growth 3-year moving average growth rates (panel b). Estimated maximum growth rates G are based on fitted growth models where the range depicts the difference between the logistic and the Gompertz models. All growth rates are expressed as % of the total electricity supply per year in which these rates are estimated or measured. 45° line depicts equal empirical and estimated rates. Only countries included in the analysis of G (Supplementary Table 18, Supplementary Table 19) are shown.

Source data

Supplementary information

Supplementary Information

Supplementary information includes Figs. 1–6, Tables 1–33 and Notes 1–6, as well as the references for these materials.

Supplementary Data 1

Wind and solar power growth rates in climate mitigation scenarios.

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Cherp, A., Vinichenko, V., Tosun, J. et al. National growth dynamics of wind and solar power compared to the growth required for global climate targets. Nat Energy6, 742–754 (2021). https://doi.org/10.1038/s41560-021-00863-0

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Through our vast driving experience and mechanical expertise, we have developed advanced rebuilding techniques that increase the transmission's durability, longevity, and performance. 1 A retrospective review of patients attending a uveitis clinic in the United Kingdom found that 70% of patients had visual impairment (visual acuity 6/18 or worse) and half of these patients had bilateral visual impairment. For added convenience, there is an optional protector case available for the W56P that makes the handset anti slid, crash proof, and waterproof. For example, referring to the fourth line of the table: The odds of dying from a motor-vehicle crash in 2019 were 1 in 8,393. For both tests, categorical outcomes (normal vs. 00, High: $2,850. Our packages can include match ticket-inclusive hospitality packages to the Semi-Finals and Finals matches, hotel accomodation, match day transport and more. I haven't gotten to the point I can confirm that yet. See full list on digit. See Details. The W59 is twice as strong as the W56, the R series transmissions are pretty close to twice as strong as the W59. Introduce film. Nd3t W56 Manual - Downloadily Docs Nhdt-w59 English Manual-. 89], respectively, although Psychologist-Delivered SASS did not). Change to local time. Click here to view current Fresno County C19 Metrics. W63-バンドリ! ガールズバンド. 01 Jul [1F] [2E] 21:30 [1H] [2G] Match 56. (P77) [prev. 43 - Pecked by turkey. 1985-2004 Ford Mustang LX GT 5. DG4092, 4OTM05, 040-1, 35TM03. 4L 4WD input shaft. Favorite Color:Oyster White. The 4cyl 8" diff '79-85 Trucks and 4Runners all have 4-cylinder engines and use what most call the 4cyl 8" diff in the front (the same one they use in the rear)- see "4cyl 8" diff" below. Auto defrost. 12 Victor von Gerdenheim 2 Introduced in Night Warriors 2. person changing tire on transport vehicle. BHW adapters are currently in production. Models: P110 1st generation Prius; P112 2nd. 05 Jul [W55] [W56] 21:30 [1B] [2A] Match 51. There are vast similarities between the 2. w56 question. Blood Type:B. To assist you Toyota has placed and identification plate on the fire wall of your. *links will take you to our ecommerce site. this TOYOTA W56 PARTS ILLUSTRATION transmission has an cast iron case that is end loaded with an aluminum extension housing. This is an amazing shade. FIFA World Cup 2018, the biggest sporting event is all set to kick off from June, 14 2018 to July, 15 2018 in Russia. This syndrome was initially designed to capture mental health related ED visits during and after disasters but can also be used for keyword-based monitoring of mental health concerns. 11 Sasquatch 1. A total of 36 teams will be participating in the event. Dimensions: Oven size H59. The W59 had a yield of 1 megaton, MT. 2 Acute anterior uveitis, which is the most common. JADWAL PIALA DUNIA 2010 AFRIKA SELATAN. The B57 was probably W25 derived,the W59 might have been the original W56 warhead and the W56 might have had a LASL primary stage. 5 Valley Stream South 183 (68). 3 swap in my 4runner, looking to use a toyota 5 speed i have been reading that the r150f's are the way to go because they are a much more beefier tranny then the. Allen Bradley Overload Relay Heater Tables For Bulletin 709 & 509. 8 h, with an upper limit of normal (2 SD from the mean) at 64. Part designations are given for standard items such as engines and transmissions. Alcohol Abuse and Dependence (ICD-9/10-CM) ICD-9-CM Codes: 291% OR 303. W56 5-speed truck; W57 5-speed; W58 5-speed; W59 5-speed truck; V-series. Karen Salzgeber) +602 (biggest upset!) Round 5: Sherry Shi Yuan Tian (vs Linda Shi) + 226 Round 6: Viktorija Zilajeva (vs Ioana Murgulet) + 292. 03 strike W58. Example Domain. 8L V6 T5 transmission main output shaft. One of the main causes of death beyond the first year after heart transplantation is cardiac allograft vasculopathy (CAV). download free Toyota Nh3t W56 english manual. Footnotes for server operating system comparison. 07/08(四) 04:30-05:00 賽後討論. Francis L35-56; 0:48 Natalia Ackerman's highlights Aptos vs. GM Dodge Jeep Getrag 290 NV3500 NV3550 input shaft pocket bearing. Hello dosto aaj me apko ant Audio w56 ka comparison wave 702 ke saath karne wala hu taaki aap sabhi ko pata chal sake ki dono me se konsa better haiAnt Audio. Single and double integrated ovens at Argos. 2 There were in company Simon Peter and Thomas, who was called The Twin,+ and Na·thanʹa·el+ from Caʹna of Galʹi·lee and the sons of Zebʹe·dee+ and two others of his disciples. With these safeguards in place, it is no wonder why the World Beverage Competition is accredited as the premier tasting event in the world of beverages, and why it is known as: "The Largest Beverage Competition in the World!"™. 866-552-0809. 19XS : W58 Contact with crocodile or alligator: W59. Add to Wishlist | Add to Compare. 14 oct 2020 — Hi? my NDCN W55 says please insert the correct map disc what can i do to correct the. 866-552-0809. Read more about this product. ini files as generated by the DOF config tool to control the cabinet outputs. There were a total of 175 W59 Mk-5 RVs manufactured and had an operational period from 1962 to 1969. If your transmission is not leaking we recommended that it be checked at each oil change and topped off. 1st and 2nd are low ratios like in the W56 for use to get a heavy vehicle moving. Reversible door to open the door from either side. Joined Jun 23, 2010 · 15 Posts. w55 w56 w58 w59 '78-'05 5-speed manual transmissions: overhaul kit. with abrasive wheel (metalworking) W31. 1997 Firebird Production Number Breakdown: Total: 30828: V6: V8: MT: AT: NOTE: Some discrepancies exist between the totals shown here and other data sources. Assessment of transmitral flow. Rebecca Giblon) +404 Round 2: Rachael Li (vs. Read more about this product. The Toyota "W" and "R" series transmissions were all manufactured by the Aisin-Warner company in Japan. 54 (95% confidence interval 0. All midweek home meetings 7. Built in design for eye level in a kitchen column. The r154 should be good for over 500whp. 8 Morrigan Aensland 1. Birmingham Edwards Plumbing Brummies Speedway: 2016 FIXTURES, RESULTS & REPORTS. Insert Correct Map disc/sd card NDDN W53/w54/w55/w56/w57/w58, NSDN W59/w60. The value of 30. Its been discussed that the W55 transmission can hold ABOUT 300/350whp. Echocardiographic evaluation of diastolic function has been traditionally performed by measurement of transmitral flow parameters including the early (E) and late (A) diastolic filling velocities, the E/A ratio, and the E deceleration time (DT) from an apical four chamber view with conventional pulsed wave Doppler (fig 1A 1A). ini files as generated by the DOF config tool to control the cabinet outputs. Please note that the fixtures and dates below are subject to change at short notice. 30pm (unless otherwise stated). ar5, jeep ax15 ba10 & toyota r151 l45 l52 w40 w46 w50 w55 w56 w58 w59 transmission rear seal fits 2wd (83503108) tpd pro-line. Hobbies:Listening to the Radio, Beach Combing. 416 Jefferson St, Burlington, IA 52601. The W56-A is listed for an 1985 application and the W56-B is listed for 1986-1988. A complete list of ICD-10 codes related to the animal kingdom. 15/06 | 19h00 | VTV6 | Egypt vs Uruguay. W55 W56 W58 5-SPEED … toyota w55 w56 w58 / w59 '78-'91 5-speed manual W55 W56 W58 Transmission rebuild kit fits '78-'91 toyota supra celica pickup Jan 30, 2010 · Page 1 of 2 - 4G63 + W58 - posted in Engine Swappers: I. I wanna go with either a W56 or a W59. View a trailer of the anime below:. Total load rating (electrical) 3. The clutch forks and pivots are the same as well, however 1981-89 applications (both 2WD and 4WD) used a two-piece release bearing with collar (see collar here ) and. Manual Transmission 2WD 5 Speed 4 Cylinder Engine Fits 05-15 TACOMA 390919 (Fits: Toyota Tacoma) $799. 07/08(四) 08:00-10:00 w49 vs w50 重播. 45pm (unless otherwise stated). I currently have an l50 I think. Height:159cm. 1 Anakaris 1. Below find a parts illustration for the Toyota W55, W56 and W58 5 speed manual transmission. 7L 4cyl engines. Example Domain. 코노미는 1학년 아래인 활기찬 후배로, 사키를 '언니'라 부르며 사모한다. Yuck!! But for transmissions, that is a good thing. Among others, our products include: adaptation sets for modernizing existing elevator systems with frequency-controlled motors and/or for installation of a hollow shaft rotary encoder, brake. 1st and 2nd are low ratios like in the W56 for use to get a heavy vehicle moving. Will the one I have now work with a w series trannie or would I need to get one that is made for a w series trannie?. We have fast shipping, great service and 6 month warranty on almost all our used car and truck parts, and we will surely find you the best. If your transmission is not leaking we recommended that it be checked at each oil change and topped off. you can use this to bolt a W56 to a 3rz-fe (2. Saturday 12 July. Interview: Advance Adapters and Cummins Discuss the 2. FIFA released the schedule for the first World Cup to be played in November and December on Wednesday, with kickoff times at 00:30 am IST, 3:30 pm. Click each picture for a larger version. Forged steel shipping plates are 0. Electronic: 1546-3141. 日本av女优中的乳神,波霸级av女优,性感火爆妩媚无边--泽井芽衣 三围:b88 w59 h86. LỊCH TRỰC TIẾP WORLD CUP 2018 TRÊN SÓNG VTV 💛 📟 01. 4 Felicia 1. L56" x W56" x H34" Add to Cart. Add to wishlist. Read the Bible to Understand It (‎36 occurrences) When a change in the meaning of a word dresses up falsehood in the garb of truth, the matter is indeed serious. A woman who is 36-24-36 at 5'2" tall, looks different from a woman who is 36-24-36 at 5'8" tall. 1881 W62-W63,W68-W69. Regular exercise helps to promote strong blood flow to the penis by temporarily disabling an enzyme known as phosphodiesterase-5, which is found at high levels in tomatoes, pink grapefruit, watermelon, guavas, red bell peppers, red cabbage, and papaya. Shimera Paxton) + 154 Round 3: Madison Ford-McKnight (vs. The Starting Point of Your Adventure. Karen Salzgeber) +602 (biggest upset!) Round 5: Sherry Shi Yuan Tian (vs Linda Shi) + 226 Round 6: Viktorija Zilajeva (vs Ioana Murgulet) + 292. To do the swap, you'll need an entire wire harness - the easiet route is to acquire the complete unit, and cut-and-cap the wires you don't need (IE, I plan on cutting out AC, power windows, ABS, airbags, electronics for 4WD) and lay the entire unit in. Connect to a server location, where your sports is running. A woman with 38-28-38 may have a bra size of 30H, 32F, 34DD and a 36 would be too large on her frame. Leading into the three minute film, all production students will introduce the film. Robert Johnston last updated 9 September 2008. Nd3t W56 Manual - Downloadily Docs Nhdt-w59 English Manual-. 01 Jul [1F] [2E] 21:30 [1H] [2G] Match 56. 4-liter 2RZ-FE. 89XS : W56 Contact with nonvenomous marine animal: W57. 各ECショップの売上や販売実績の分析が可能な「オークファンプロPlus」。ライバルの情報を丸裸にすることで、販売拡大や売れ筋商品が把握できる、セラー向けの販売戦略支援ツールです。Amazon、Yahoo!、eBay、楽天に対応. Best price for Ant Audio W56 Wired Headphone in India is sourced from trusted online stores like Flipkart, Amazon, Snapdeal & Tatacliq. The R series is DEFINITELY worth it. The W56-A is listed for an 1985 application and the W56-B is listed for 1986-1988. The Present on Admission Exempt (POA) indicator is used for diagnosis codes included in claims involving inpatient admissions to general acute care hospitals. 14,485 Posts. Includes transparent, vacuum, ubbelohde, cannon-fenske, asphalt and more. Please note that the fixtures and dates below are subject to change at short notice. This gearbox is mechanically similar to the Toyota W55/W56. For both tests, categorical outcomes (normal vs. Just send us an e-mail or contact us by phone. W56 5-speed truck; W57 5-speed; W58 5-speed; W59 5-speed truck; V-series. 4-liter 2RZ-FE. Read the Bible to Understand It (‎36 occurrences) When a change in the meaning of a word dresses up falsehood in the garb of truth, the matter is indeed serious. Information is provide for most vehicles. Santa Cruz Game 2 W 73-17; 0:31 Natalia Ackerman's highlights Aptos vs. Vandermeulen 2 1 132 L49 W37 W46 3 Roslyn 1 2 130 W34 L33 L63 4 Kellenberg Memorial 0 3 138 W56 W46 W67 4 Valley Stream South 3 0 152 W53 W58 W41 5 Plainview-Old Bethpage JFK 2 1 169 L51 W49 W69 6 4 vs. If your transmission is not leaking we recommended that it be checked at each oil change and topped off. Free shipping. All W55-59 are available in 2WD and the W56 and W59 are available in 4WD as well. 637 Me gusta · 2 personas están hablando de esto. R150 & R151. Mental Health. 2016 FIXTURES, RESULTS & REPORTS. Below find a parts illustration for the Toyota W55, W56 and W58 5 speed manual transmission. Best price and value when compared to PicClick similar items. Insert Correct Map disc sd card. Land Cruiser II, Land Cruiser Prado and Hilux Surf (1989-1993) 2L-T series and 1KZ series Turbo Diesel, V6 3VZE and 5VZ-FE ] (also Japan, UK and Europe 1KZ/TE 4Runners, 93-95). 07/08(四) 11:00-13:00 w58 vs w57 重播. A common truck transmission, this was the successor to the W56. It sounds like there are TWO options. 2015 FIXTURES, RESULTS & REPORTS. 3 Simon Peter said to them: "I am going fishing. The R151 came behind the 86 & 87 model 22RET (turbo trucks) 4x4's. 07/08(四) 19:30-21:30 w55 vs w56 重播. 02 amphibian W62. download free Toyota Nh3t W56 english manual. For more than 100 years the AJR has been recognized as one of the best specialty journals in the world. 3RU 3RU Lo 3RU Hi 2RU 4RU Lo Steel. All midweek home meetings 7. XXXS : W57 Bitten or stung by nonvenomous insect and other nonvenomous arthropods: W58. 1881 W62-W63,W68-W69. 0 V6) is a passenger side drop t-case. 12XD - Struck by macaw, subsequent encounter. W59] View PDF; Download PDF of final working paper version. Models: V160; V161; Hybrid P-series (HSD) The P-series (HSD) are Hybrid Synergy Drive transmissions used in Toyota and Lexus hybrids for FWD-based platforms. in order to run a gear drive t case behind a w59 trans, you must use an adapter( which marlin sells), hope that clarifies some issues. Read more about this product. Add to Wishlist | Add to Compare. 12 Victor von Gerdenheim 2 Introduced in Night Warriors 2. The lifetime odds of dying in a motor-vehicle crash for a person born in 2019 were 1 in 107. a control IP condition (with scrambled images as primes) was associated with reduced high-calorie food preference. 1 animal (nonvenomous) NEC W64 marine W56. 9 TDI to W56 Adapter Kit will mate your VW 1. Insert Correct Map disc/sd card NDDN W53/w54/w55/w56/w57/w58, NSDN W59/w60. TECHNICAL SUPPORT • EXCEPTIONAL CUSTOMER SERVICE • CUSTOM PRODUCTS • SUPPLY CHAIN SOLUTIONS • QUALITY ASSURANCE. Click here to view current Fresno County C19 Metrics. Hobbies:Listening to the Radio, Beach Combing. Our innovative line of luxury whirlpool bathtubs offer the best in therapeutic massage leaving you relaxed and refreshed even after the most stressful day. 2015 FIXTURES, RESULTS & REPORTS. 637 Me gusta · 2 personas están hablando de esto. I would definitely purchase again for other windows if needed. Touch control. W56 5-speed truck; W57 5-speed; W58 5-speed; W59 5-speed truck; V-series. Size W59, D52cm. The B57 was probably W25 derived,the W59 might have been the original W56 warhead and the W56 might have had a LASL primary stage. Next, you need to start the car again and look for an option in the navigation systems menu, which says English. New(to me):. person examining engine of vehicle broken down in (on side of) road. 3 Proverbs 19:8 speaks of life as soul when it says: "He that is acquiring heart is loving his own soul. Configure FT-19RS. The B57 was probably W25 derived,the W59 might have been the original W56 warhead and the W56 might have had a LASL primary stage. Fresno has declared a Shelter In Place but as an essential business we remain OPEN. Just send us an e-mail or contact us by phone. Maanasi Limaye) + 338 Round 4: Viktorija Zilajeva (vs. All midweek home meetings 7. Also that the cruising range for an ALH in that swap is 2700 to 3000 rpm @70mph. 4L 4WD input shaft. Welcome to 4x4Wire! You, your 4x4, and Access Below are the specifications for different parts used on Toyota pickups and 4Runners. The W59 warhead was designed and developed by Los Alamos National Laboratory, LANL. Diamond tools may be used in forward or reverse modes. This is the most. 7L 4cyl engines. We have fast shipping, great service and 6 month warranty on almost all our used car and truck parts, and we will surely find you the best. Residual heat indicator. Some Japanese car models come with the option. Our packages can include match ticket-inclusive hospitality packages to the Semi-Finals and Finals matches, hotel accomodation, match day transport and more. 4-liter 2RZ-FE. The W56P features a 3. A common truck transmission, this was the successor to the W56. All midweek home meetings 7. LỊCH TRỰC TIẾP WORLD CUP 2018 TRÊN SÓNG VTV 💛 📟 01. Contact with nonvenomous marine animal (W56) Bit/stung by nonvenom insect and oth nonvenomous arthropods (W57) Contact with crocodile or alligator (W58) Contact with other nonvenomous reptiles (W59) Contact w nonvenom plant thorns and spines and sharp leaves (W60) Contact with birds (domestic) (wild) (W61) Contact with nonvenomous amphibians (W62). 如龙0角色与女优原型对比. Play-off for. Works on transmission from a Toyota aged between 1978 and 2005. Saturday 12 July. LaB Coffee, Da Nang, Vietnam. The B57 was probably W25 derived,the W59 might have been the original W56 warhead and the W56 might have had a LASL primary stage. It will be held from14th June, 2018 to 15th July, 2018 in Russia. Connect to a server location, where your sports is running. 코노미는 1학년 아래인 활기찬 후배로, 사키를 '언니'라 부르며 사모한다. The IS300 W55 has an 11mm longer input shaft, while all other W-series transmissions I am aware of share the shorter shaft. With all the write ups online I think I'll tackle wiring myself with plug and play harness. Customers who bought this also. W56 - Blankets: W57 - Textile end products: W58 - Threads, straps and ropes: W59 - Other textile articles: W60 - Knitted fabric in general: W61 - Knitting yarns and threads: W62 - Knitted grey fabrics: W63 - Knit articles: W70 - Printed and dyed articles: W71 - Printed and dyed cotton and cotton-blended fabric articles. 7-liter 3RZ-FE. Round 1: Shimera Paxton (vs. 8 h, with an upper limit of normal (2 SD from the mean) at 64. Our transmissions far exceed Toyota OEM standards. W59 A common truck transmission, this was the successor to the W56. Jan 31, 2020. 7 x 54 x 57. This is a list of characters from the Darkstalkers series of fighting games by Capcom. Round 1: Shimera Paxton (vs. Physically, these transmissions have much in common (like the bell housing-to-body bolt pattern) with other Aisin-built transmissions, like the Jeep AX-5 and the Toyota G-series. 3 Proverbs 19:8 speaks of life as soul when it says: "He that is acquiring heart is loving his own soul. A MATCHING PART FOR EVERY REQUIREMENT. View Offer. XXXS : W57 Bitten or stung by nonvenomous insect and other nonvenomous arthropods: W58. The W59 warhead was designed and developed by Los Alamos National Laboratory, LANL. Blood Type:B. 01 Jul [1H] [W59] [W60] 01:30 +1d. DG4092, 4OTM05, 040-1, 35TM03. There were a total of 175 W59 Mk-5 RVs manufactured and had an operational period from 1962 to 1969. 如龙最新作《如龙ZERO 誓言之地》(简称《如龙0》)此前沿袭系列传统,曾举办了人气女优投票评选活动. This series transmission fit Toyota Pickup, Tundra, Tacoma, T100 trucks, Cailica, Corona, Crown, MarkII, Cressida, Lexus and Supra. This 5-speed manual transmission was only used in trucks that had the Toyota 2RZ-FE 2. Hello dosto aaj me apko ant Audio w56 ka comparison wave 702 ke saath karne wala hu taaki aap sabhi ko pata chal sake ki dono me se konsa better haiAnt Audio. This model appears to have a combination of ratios used in older models of the W-series. Age:19 Years Old. 4-liter 2RZ-FE. 1985-2004 Ford Mustang LX GT 5. Customers who bought this also. The first South American World Cup since 1978 promises to provide one of the tightest competitions in years. Echocardiographic evaluation of diastolic function has been traditionally performed by measurement of transmitral flow parameters including the early (E) and late (A) diastolic filling velocities, the E/A ratio, and the E deceleration time (DT) from an apical four chamber view with conventional pulsed wave Doppler (fig 1A 1A). The old style type N heater elements are used with Bulletin 709 motor starters and Overload Relay Blocks. a W59 will not bolt to a 22re. Shimera Paxton) + 154 Round 3: Madison Ford-McKnight (vs. 07/08(四) 19:30-21:30 w55 vs w56 重播. 2005-2010 Mustang Gt/V6 5 speed manual bronze transmission shift bushing kit. 43 - Pecked by turkey. Th "W" family consists of the W55, W56, W57, W58. Comparison pics below. We have fast shipping, great service and 6 month warranty on almost all our used car and truck parts, and we will surely find you the best. 1984-95 Toyota W56 W58 W59 5 speed 2. Rebecca Giblon) +404 Round 2: Rachael Li (vs. This series transmission fit Toyota Pickup, Tundra, Tacoma, T100 trucks, Cailica, Corona, Crown, MarkII, Cressida, Lexus and Supra. Manual Transmission 2WD 5 Speed 4 Cylinder Engine Fits 05-15 TACOMA 390919 (Fits: Toyota Tacoma) $799. A woman who is 36-24-36 at 5'2" tall, looks different from a woman who is 36-24-36 at 5'8" tall. Part designations are given for standard items such as engines and transmissions. The Starting Point of Your Adventure. 코노미는 1학년 아래인 활기찬 후배로, 사키를 '언니'라 부르며 사모한다. The W55, W56, W57, W58, and W59 are very similar aside from the gear ratios. The lifetime odds of dying in a motor-vehicle crash for a person born in 2019 were 1 in 107. 6 months credit when you spend over £99 on all large kitchen appliances. View Offer. w59 code 62 w60 w72 code 61 w91 flat socket weld tube o-ring pressure rating flat face w6 code 61 w62 w58 code 62 w63 w71 code 61 w90 blanking o-ring pressure rating flat face w36 code 61 w37 w38 code 62 w39 size of port in flange dash number nominal size thread or socket specification nptf sae st. FIFA World Cup 2018, the biggest sporting event is all set to kick off from June, 14 2018 to July, 15 2018 in Russia. 8L diesel crate engine conversion. Color: WhiteSize: W59"x H64" Verified Purchase. W59 W58 2 Earl L. The W59 warhead was designed and developed by Los Alamos National Laboratory, LANL. Our payment security system encrypts your information during transmission. Measurements:B85 / W56 / H86. With all the write ups online I think I'll tackle wiring myself with plug and play harness. W50 SHIFTER HOUSING LID 18" INCH + REPAIR KIT FOR TOYOTA CELICA STEELCASE TRANS. The old style type N heater elements are used with Bulletin 709 motor starters and Overload Relay Blocks. Fits in eye level worktop. DISCOUNT CODE - £100 off your order when you spend over £1000 on 2 or more large kitchen appliances. Since this framework supports the use of more than one output controller/LedWiz, the use of more than one such file can be used. Echocardiographic evaluation of diastolic function has been traditionally performed by measurement of transmitral flow parameters including the early (E) and late (A) diastolic filling velocities, the E/A ratio, and the E deceleration time (DT) from an apical four chamber view with conventional pulsed wave Doppler (fig 1A 1A). 45pm (unless otherwise stated). W55 W56 W58 5-SPEED … toyota w55 w56 w58 / w59 '78-'91 5-speed manual W55 W56 W58 Transmission rebuild kit fits '78-'91 toyota supra celica pickup Jan 30, 2010 · Page 1 of 2 - 4G63 + W58 - posted in Engine Swappers: I. The W59 had a yield of 1 megaton, MT. 89 bite W56. Anchor Fluid Power has developed a low cost solution to leaky, gasketless port covers. Height will also affect the presentation of the figure. From speakers to earphones or headphones, all our products feature excellent quality at a competitive price. Several other prognostic scores are available. 98 Buy It Now 19d 4h. But even with a 4. 2011 FIXTURES & RESULTS. 8L diesel crate engine conversion. 00 L59"x W59"x H25" Add to Cart. 日本av女优中的乳神,波霸级av女优,性感火爆妩媚无边--西田麻衣 三围:95-58-81. 1881 W62-W63,W68-W69. Sample order. #13 · Apr 21, 2013. 日本av女优中的乳神,波霸级av女优,性感火爆妩媚无边--河野麻奈 三围:b85 w56 h87cm. I now have a G58-5 spd trans when I need the W56 5-spd (8 bolt vs 6 bolt top plate) My question is what is the difference between the two. A MATCHING PART FOR EVERY REQUIREMENT. Please note that the fixtures and dates below are subject to change at short notice. The old style type N heater elements are used with Bulletin 709 motor starters and Overload Relay Blocks. The largest amount of requests we receive about engine conversions are for V8s. w56 question. 1st and 2nd are low ratios like in the W56 for use to get a heavy vehicle moving. Play-off for third place. We kept a broad perspective by applying wide eligibility criteria to. Its been discussed that the W55 transmission can hold ABOUT 300/350whp. 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W55 W56 W57 W58 W59 TRANSMISSION RUBBER MOUNT FOR TOYOTA SUPRA GEARBOX. b) use a R150 from a V6 and use a turbo bell housing and a v6 adapter. Birthday:July 7. Play-off for third place. This model appears to have a combination of ratios used in older models of the W-series. 5,991 likes · 7,106 were here. Occupation:Unknown. by William D'Angelo, posted on 01 August 2019 / 1,671 Views. 46, Low: $30. 8L Diesel Engine Conversion for Jeep® At the 2016 SEMA Show, Steve Roberts from Advance Adapters and Stephen "Steve" Sanders of Cummins Repower program share in-depth details on the Cummins 2. View All Packages. Here you will find out each and every updates about FIFA World Cup 2018. Price - Front & Rear Seals For W40 W50 W55 W56 W57 W58 G52 G56 Toyota Gearbox. Francis L35-56; 0:48 Natalia Ackerman's highlights Aptos vs. I got a tranny from someone here, and it turns out to be the wrong one. 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Contact with nonvenomous marine animal (W56) Bit/stung by nonvenom insect and oth nonvenomous arthropods (W57) Contact with crocodile or alligator (W58) Contact with other nonvenomous reptiles (W59) Contact w nonvenom plant thorns and spines and sharp leaves (W60) Contact with birds (domestic) (wild) (W61) Contact with nonvenomous amphibians (W62). The opposite side has a machined flat-face for capping off hose ends. 8L V6 T5 transmission main output shaft. The monthly American Journal of Roentgenology is a highly respected peer-reviewed journal with a worldwide circulation of close to 25,000. This model appears to have a combination of ratios used in older models of the W-series. 1882 W58-W59 1900 W85 1901 W94,W101 1902 W102 1904 W116 1906 W119-W121 Soquel 1901 W96-W97 See also: Water Rights Agriculture See: Farms and Agriculture Alfalfa See: Hay Allardt, George F. 45pm (unless otherwise stated). W69], Emerging Markets Review 2002, 429-448. 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Open Access

Peer-reviewed

  • Ella Salgó,
  • Liliána Szeghalmi,
  • Bettina Bajzát,
  • Eszter Berán,
  • Zsolt Unoka
  • Ella Salgó, 
  • Liliána Szeghalmi, 
  • Bettina Bajzát, 
  • Eszter Berán, 
  • Zsolt Unoka
PLOS

x

Abstract

Objectives

Emotion regulation difficulties are a major characteristic of personality disorders. Our study investigated emotion regulation difficulties that are characteristic of borderline personality disorder (BPD), compared to a healthy control group.

Methods

Patients with BPD (N = 59) and healthy participants (N = 70) filled out four self-report questionnaires (Cognitive Emotion Regulation Questionnaire, Difficulties in Emotion Regulation Scale, Five Facet Mindfulness Questionnaire, Self-Compassion Scale) that measured the presence or lack of different emotion-regulation strategies. Differences between the BPD and the healthy control group were investigated by Multivariate Analysis of Variance (MANOVA) and univariate post-hoc F-test statistics.

Results

People suffering from BPD had statistically significantly (p<0.05) higher levels of emotional dysregulation and used more maladaptive emotion-regulation strategies, as well as lower levels of mindfulness and self-compassion compared to the HC group.

Conclusion

In comparison to a healthy control group, BPD patients show deficits in the following areas: mindfulness, self-compassion and adaptive emotion-regulation strategies. Based on these results, we suggest that teaching emotion-regulation, mindfulness, and self-compassion skills to patients can be crucial in the treatment of borderline personality disorder.

Citation: Salgó E, Szeghalmi L, Bajzát B, Berán E, Unoka Z (2021) Emotion regulation, mindfulness, and self-compassion among patients with borderline personality disorder, compared to healthy control subjects. PLoS ONE 16(3): e0248409. https://doi.org/10.1371/journal.pone.0248409

Editor: Stephan Doering, Medical University of Vienna, AUSTRIA

Received: June 16, 2020; Accepted: February 26, 2021; Published: March 17, 2021

Copyright: © 2021 Salgó et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the manuscript and its Supporting information files.

Funding: This work was supported by the Hungarian National Research, Development and Innovation Fund [grant numbers NKFI-132546]. PI is Zsolt Unoka.

Competing interests: The authors have declared that no competing interests exist.

1. Introduction

Emotion regulation consists of the capabilities to process and modulate affective experience. Difficulties with these abilities are often present in people suffering from borderline personality disorder (BPD); moreover, emotion dysregulation is considered a core attribute of this mental disorder [1, 2]. BPD patients are frequently experiencing overwhelming negative emotions such as abandonment, loneliness, jealousy, feeling rejected, hatred, envy, anger, shame and guilt [3–5]. They often report aversive tension, a diffuse, highly aroused state with negative valence [6], and they have difficulties with identifying, naming, or putting into context these emotional states [7–10]. Their reactions to their emotions are often inappropriate: they can be impulsive and have angry outbursts, impulsive behavioral reactions and labile affect. The way they respond to their negative emotions influences the frequency or intensity with which negative affect arises. Their emotion and affect regulation strategies are dysfunctional; for example, they have a tendency towards clinginess [11], dissociation [12], emptiness [13], self-harming behavior [14], alcohol and substance use [15], impulsive sexual behaviors [16], binging, purging [17], and rumination [18]. We hypothesized that they are less able to use functional emotion regulation, such as being mindfully aware of one’s emotions, to label, accept and validate emotions, and to tolerate negative or positive emotion-related distress [2].

In the current study, we aimed to investigate whether a broad range of emotion regulation difficulties are characteristic to BPD patients compared to a healthy control group. We also wanted to examine emotion regulation difficulties, adaptive and maladaptive cognitive emotion regulation strategies, mindfulness, and self-compassion in the two groups. Our study is partly a replication and partly an extension of previous studies.

1.1 Difficulties in emotion regulation in BPD

Emotion regulation difficulties are a significant characteristic of BPD [1], such that BPD symptoms and interpersonal problems in BPD are found to be mediated by emotion regulation difficulties [19, 20]. The results of a study suggest that emotion dysregulation, particularly lack of access to emotion regulation strategies and lack of emotional clarity, mediate the relationship between BPD symptoms and poor physical health symptoms (e.g., “headaches,” “dizziness,” “stomach pain”) measured eight months later [21]. A study of 100 adults diagnosed with BPD demonstrated significant reductions in emotion dysregulation (measured by DERS) after a six-month-long dialectical behavior therapy intervention [22]. Emotion dysregulation assessed by DERS explained unique variance in BPD symptoms, showing that impulse control difficulties and limited access to emotion regulation strategies have the strongest relationship to BPD [23, 24]. As a consequence of emotion dysregulation, people suffering from BPD show deficits in action planning and emotion regulation functioning as a mechanism of effective and goal-directed behavior [25]. In our study, we would like to compare emotional dysregulation in the BPD and HC groups in an adult sample by using DERS as a measurement tool for emotion dysregulation. The only previous study [26] that compared BPD and HC groups by using DERS analyzed differences in its "acceptance" subscale only. Our study complements these findings by analyzing all subscales of DERS.

1.2 Cognitive emotion regulation in BPD measured by CERQ

Cognitive strategies have a crucial role in emotion regulation. In order to measure adaptive and non-adaptive cognitive emotion regulation strategies, the Cognitive Emotion Regulation Questionnaire (CERQ) [27] has been developed, using the following nine subscales: self-blame, other-blame, rumination or focus on thought, catastrophizing, putting into perspective, positive refocusing, positive reappraisal, acceptance and refocus on planning.

Using CERQ, it has been shown that people with BPD tend to practice maladaptive emotion regulation strategies. A study showed [26] that BPD patients have more frequent use of maladaptive cognitive emotion regulation strategies (suppression, rumination, avoidance) and less frequent use of adaptive strategies (acceptance, cognitive reappraisal, problem-solving) relative to HC. Using CERQ, Wijk-Herbrink, and colleagues [28] identified three higher-order factors; adaptive coping, non-adaptive coping, and external attribution style in people with personality disorders. They found that they used more non-adaptive coping and less adaptive coping strategies as compared to a general population sample. This study suggests that dysfunctional cognitive emotion regulation can be a characteristic of personality disorders in general. Another study, however, shows no significant differences between people of cluster B personality disorders and healthy control in the nine cognitive emotion regulation strategies measured by CERQ [29]. Research found [30] that the use of maladaptive cognitive emotion regulation strategies (self-blame, blaming others, rumination, and catastrophizing) were related to high levels of negative affectivity and increased psychological problems in people with PDs. Another study compared BPD and schizotypal PD, where the participants scored similarly on CERQ, except for the catastrophizing subscale that had higher scores in BPD patients [31]. Our study will have added value to the previous studies comparing BPD and HC groups by using CERQ [26, 29, 32], in as much as our research analyzes all the subscales of CERQ and determines effect sizes as well.

1.3 BPD and mindfulness

Mindfulness is a non-judgmental, present-focused state of mind characterized by present-moment awareness, where thoughts, perceptions, and feelings are accepted and purposefully brought into attention [33]. Low levels of mindfulness have been proven to play a significant role in personality psychopathology, and specifically in BPD [34]. Mindfulness is inversely associated with BPD features and core areas of dysfunctionality, such as interpersonal ineffectiveness, impulsive, passive emotion regulation, and neuroticism [35, 36]. In a study exploring differences in the five mindfulness facets (measured by FFMQ) among patients diagnosed with either obsessive-compulsive disorder, major depressive disorder or borderline personality disorder and HC, BPD patients scored lower on all mindfulness facets compared to the HC group [37]. In a study conducted by Nicastro et al. [38] fewer mindfulness skills were found in BPD patients than in control participants. Findings demonstrate that dispositional mindfulness is negatively associated with BPD features and suicidal thinking among patients in substance use treatment [39]. The inverse relation between BPD and mindfulness can be explained by the difficulties of BPD patients to be consciously aware of their experiences in the present moment instead of focusing on general concepts. The latter may impair their ability to effectively regulate their emotions [40].

Mindfulness is a multidimensional construct. Yu and Clark [36] investigated the relationship between mindfulness (assessed by FFMQ) and borderline personality traits in a non-clinical sample and found that mindfulness facets relate differentially to BPD symptoms, among them "non-judging" is the facet most strongly related to BPD traits. Research suggests that for BPD patients, mindful self-observation can be an adaptive alternative to rumination when feeling angry [32].

Conceptual integration of mindfulness and emotion regulation was proposed by Chambers, Gullone, and Allen [41]. According to their review, cognitive emotion regulation strategies and mindfulness fundamentally differ in that according to the concept of emotion regulation, unpleasant thoughts/appraisals need to be acted upon or manipulated in some way to make them less distressing. In contrast, mindfulness considers all mental phenomena as mere mental events that do not need to be transformed. Their proposed "mindful emotion regulation" is the capacity to remain mindfully aware of the experienced emotions, irrespective of their valence, intensity, and without attempting to reappraise or modify them. Based on this proposition, in our study, we consider mindfulness a potential form of emotion regulation. Our study’s additional value to the previous research comparing BPD and HC groups by exploring the five mindfulness facets [37] is that it evaluates the effect sizes in terms of the magnitude of the difference between the two groups.

1.4 BPD and self-compassion

Self-compassion is a self-regulation strategy that counters self-criticism and related negative self-directed emotions, such as shame [42]. Neff [43] conceptualized self-compassion with the following three dimensions: a) self-kindness vs. self-judgment, b) common humanity vs. isolation, and c) mindfulness vs. over-identification. Based on a quantitative meta-analytic study, each of these factors are suggested to assist adaptive self-regulatory processes [44]. One may reason that such self-regulatory processes in general—including emotion-regulation—are impaired in BPD since BPD is frequently associated with childhood trauma and abuse [45–47], and childhood trauma exposure and emotional dysregulation are suggested to have a complex and bidirectional relationship [48]. Linehan’s biosocial theory [49] suggests that what she calls "invalidating environments" during childhood may play an important role in the subsequent development of BPD in adolescence, by hindering the development of self-compassion and emotion-regulation. However, a study [50] found that even though childhood parental invalidation and lack of self-compassion are both strongly associated with BPD symptoms, their associations with BPD symptoms are independent of each other. In contrast, traumatic experiences may contribute to a self-invalidating and self-critical cognitive style [49]. Other studies suggest that self-criticism is a diagnostic element [51] and a frequent characteristic of BPD [52–54].

Research shows that loving-kindness and compassion meditation based on self-compassion lowers self-criticism and improves self-kindness and acceptance in BPD patients [53]. Moreover, self-compassion seems to mediate between mindfulness and BPD symptoms, and between mindfulness and emotion dysregulation as well [55]. Self-compassion is also considered the outcome of mindfulness practice [56].

The above studies suggest that the lack of self-compassion is associated with BPD symptoms and that improved self-compassion can ease the emotional pain experienced in BPD. Some research has already been conducted on comparing BPD population to HC in the context of self-compassion, although with a different aim. Scheibner and colleagues [55] used the Self Compassion Scale (SCS) to compare BPD patients with HC, and found significant differences between these two groups in terms of self-compassion. A study found that BPD patients had significantly higher fears and resistances to all forms of compassion (fears of self-compassion, fears of being open to compassion of others, fears of being compassionate to others) compared to the control group [57]. The current study is an extension of the previous one that compared BPD and HC groups by using SCS [55] since it investigates group differences in the SCS subscales as well.

1.5 Mini review of the literature of the studies that compared BPD and HC on one of the following scales: CERQ, DERS, FFMQ, and SCS

Why do we need one further study? As outlined in the Introduction, there are several studies examining emotion regulation difficulties in BPD. However, there are only a few studies comparing adult BPD groups to healthy control participants, and those that exist do not examine CERQ, DERS, FFMQ and SCS simultaneously by analyzing all of their subscales. We prepared a summary of the literature that compares adult BPD and HC groups by using CERQ, DERS, FFMQ and/or SCS (see Table 1). By administering these four questionnaires in the two groups in the current study, we cover a more comprehensive array of emotion regulation strategies than previous studies.

1.6 Hypothesis

We hypothesized that the BPD and HC groups would show significant differences in terms of emotion regulation, mindfulness, and self-compassion. Furthermore, dysfunctional emotion regulation strategies and lack of self-compassion would be predominant among BPD patients. We also hypothesized that adaptive emotion regulation strategies, mindfulness skills, and self-compassion techniques would score higher in the HC group.

2. Method

2.1 Subjects and procedure

Subjects participated in a four-week-long inpatient psychotherapy program at Semmelweis University’s Department of Psychiatry and Psychotherapy between 2017 and 2019. Psychiatrists and clinical psychologists made the diagnoses during intake interviews. Data has been gathered from 59 subjects diagnosed with borderline personality disorder and from 70 healthy control subjects. Medical students recruited age, gender, and education matched healthy control volunteers who were acquaintances and relatives of university students with no known psychiatric disorders. There were 104 female (80.6%) and 25 male (19.4%) participants, with a mean age of 30.7 years (SD = 11.1, range = 18–57). Regarding educational level, 0% completed just the first six years of primary school, 28.7% passed A-level exams, 24.8% did not obtain A-level exams, 3.8% dropped out of college, 9.3% completed vocational studies, 11.6% obtained a college degree, 8.5% dropped out of the university while 13.1% obtained university degree. (To see the distribution of clinical diagnosis, see Table 2).

Subjects had been provided with sufficient information about the research and signed an informed consent sheet. Their anonymity was guaranteed. Participants were diagnosed with SCID II interviews and filled out questionnaires online. The Regional and Institutional Committee of Science and Research Ethics of Semmelweis University approved the research procedure.

2.2 Self-reported questionnaires measuring emotion regulation strategies

The Cognitive Emotion Regulation Questionnaire (CERQ) is a 36-item questionnaire measuring cognitive emotion regulation strategies applied after having experienced negative life events or situations [27]. It assesses nine cognitive emotion regulation strategies: self-blame, other-blame, rumination, or focus on thought, catastrophizing, putting into perspective, positive refocusing, positive reappraisal, acceptance, and refocus on planning. Cronbach’s α coefficients of the subscales in this study ranged between.60 (acceptance) and.89 (positive refocusing). Cognitive emotion regulation strategies were measured on a 5-point Likert scale ranging from 1 (almost never) to 5 (almost always). The Hungarian version of the questionnaire had been validated by Miklósi and colleagues [58].

The Difficulties in Emotion Regulation Scale (DERS) [59], was created based on four main aspects of emotion regulation, as defined by the authors:

  1. “(a) awareness and understanding of emotions,
  2. (b) acceptance of emotions,
  3. (c) ability to control impulsive behaviors and behave in accordance with desired goals when experiencing negative emotions,
  4. (d) ability to use situationally appropriate emotion regulation strategies flexibly to modulate emotional responses as desired, in order to meet individual goals and situational demands.” (pp42).

Higher scores on the measure indicate greater dysfunctionality or dysregulation. DERS was implemented [59] in its Hungarian version [60] in order to determine the degree of difficulty in emotion regulation. The 36 items of DERS are organized into a 6-factor structure: non-acceptance of emotional responses, difficulty engaging in goal-directed behavior, impulse control difficulties, lack of emotional awareness, limited access to emotion regulation strategies and lack of emotional clarity. Cronbach’s α coefficients of the DERS subscales in this research ranged between.67 (impulse control difficulties) and.91 (limited access to emotion regulation strategies). DERS’s scales are rated on a 5-point Likert scale.

The Self-Compassion Scale (SCS), developed by Dr. Kristine Neff [43], is applied to measure self-compassion, which is defined as compassion turned inward and refers to how we relate to ourselves in instances of perceived failure, inadequacy or personal suffering [61]. The scale consists of 26 items rated on a 5-point Likert scale. Its three subscales are self-kindness versus self-judgment, a sense of common humanity versus isolation, and mindfulness versus over-identification. Cronbach’s α coefficients of the subscales in this study ranged between.56 (self-judgment) and.84 (self-kindness). The Hungarian version of SCS was implemented by Sági and co-workers [62]. In our study, we interpret our findings according to the two-factor model of SCS, which collapses self-kindness, common humanity, and mindfulness items into a positive, "self-compassion" factor and self-judgment, isolation, and over-identification items into a negative, "self-criticism" factor [61].

The Five Facet Mindfulness Questionnaire includes 39 items that examine the five major aspects of mindfulness on a 5-point Likert scale: observation, description, mindful actions, non-judgmental inner experience and non-reactivity [63]. Cronbach’s α coefficients of the subscales in this study ranged between.70 (non-reactivity) and.88 (description). The Hungarian adaptation of the scale was carried out by Józsa (unpublished work).

2.3 Statistical analysis

Our statistical analyses tested the hypothesis that difficulty of emotion regulation scores are higher in patients with borderline personality disorder than in healthy participants against the null-hypothesis of no difference. The differences between the BPD and HC groups in terms of their DERS, CERQ, FFMQ and SCS sub-scales were investigated by Multivariate Analysis of Variance (MANOVA), and subsequently by post-hoc univariate F-test statistics determined from the MANOVA analysis.

The analyses were conducted based on a hierarchical approach. Specifically, first, in our primary analysis, the total score on each of the four scales of interest was tested. Study group (BPD or HC) was used as the independent variable in the MANOVA, whereas DERS-total, CERQ adaptive emotion regulation total, CERQ maladaptive emotion regulation total, FFMS-total, and SCS-total scales served as dependent variables. Second, in case the primary analyses yielded a significant difference, we conducted post-hoc analyses by determining the univariate F-statistics to examine the differences between the two groups in the subscales of the four scales mentioned above. In the post-univariate analyses, we used the Hochberg correction to adjust for the inflation of alpha error as a result of multiple testing. We added an asterisk to those results that remained statistically significant after correction for multiple testing in the tables.

Because of different sample sizes, effect sizes were measured by Hedges’ g [64], which provides a measure of effect size weighted according to the relative size of each sample (small effect = 0.2, medium effect = 0.5, large effect = 0.8, [65]). In order to assess the homogeneity of variances, Levene’s test was performed. Where Levene’s test indicated unequal variances, a Welch test was performed.

Based on the adopted statistical approach (MANOVA), we conducted a statistical power analysis for our primary comparisons to determine the assay sensitivity (i.e., the statistical effect size for a detectable group difference) in the study The power analysis followed the procedure described in the literature [66, 67]. The input parameters for the computation were the available sample size (n = 59 and 70 in the two groups, respectively), and the required alpha threshold level (= 0.05) and level of correlation in terms of Pearson’r among the individual variables used in the MANOVA analysis. Since the individual measures used in the MANOVA are expected to be correlated for Pearson’s we conservatively we adopted a value of 0.5 (i.e., 25% in terms of overlapping variance). Our results indicated that the available sample size provides >80% power to detect a standardized group difference of 0.3 on the variables entered in the MANOVA analysis; this value is considered a small effect size, and was deemed to provide sufficient assay sensitivity for the study.

3. Results

3.1. Demographic, descriptive and clinical characteristics

The current study included a sample of 129 participants (BPD = 59 (9 males), HC = 70 (16 males)). The two groups did not differ significantly on gender (chi-square test: χ2 = 1.2, p = 0.27) in levels of education (chi-square test: χ2 = 9.9, p = 0.12) or in age (ANOVA: (F (1,127) = 0.2; p = 0.62). See Table 2.

3.2 MANOVA for the total scores

We conducted MANOVA multivariate statistics to determine whether differences between the means of the BPD and HC groups are statistically significant based on the scales’ total scores. The primary MANOVA of the total scores of DERS, CERQ Adaptive, CERQ Non-Adaptive, FFMQ, and SCS found statistically significant differences between the BPD and the HC groups: Multivariate F (5,123) = 61.24, p < .0001; Wilk’s Λ = 0.29. Results of the post-hoc univariate comparisons are presented in Table 3.

3.3 MANOVA of the two groups based on the difficulty of emotion regulation

Since the primary analyses of DERS total score yielded a significant difference, we conducted post-hoc analyses to examine the differences between the two groups in the subscales of the DERS. In every subscale of DERS, patients with BPD had higher scores than healthy participants (DERS total F(1,127) = 187.90, p < 0.001). Effect sizes between the BPD and the HC groups are large, except for one medium effect size in the lack of emotional awareness subscale. Results are presented in Table 4.

Both the primary analyses of “adaptive emotion regulation total” and “maladaptive emotion regulation total” scores yielded a significant difference; we conducted post-hoc analyses to examine the differences between the two groups in the subscales of the CERQ. Only its two subscales, “other-blame” and “acceptance,” did not show significant differences between the two groups. Maladaptive emotion regulation strategies scored higher in the BPD group, while adaptive strategies scored higher in the HC group. (CERQ adaptive total F(1,127) = 92.02, p< 0.001, CERQ maladaptive total F(1,127) = 79.54, p< 0.001). Large effect sizes were found between the BPD and HC groups, with the exception of the other-blame and acceptance scales. Negative effect sizes indicate poorer results on the given subscale in the BPD group, e.g., putting into perspective. Results are presented in Table 5.

The FFMQ total score’s primary analyses yielded a significant difference (FFMQ total F(1,127) = 125.40, p < 0.001), so we conducted post-hoc analyses to examine the differences between the two groups in its subscales. Four subscales; "mindful actions", "non-judgmental inner experience", "non-reactivity" and "description" had higher scores in the HC group than in the BPD group. Only the "observation" subscale did not present significant differences between the two groups. Effect sizes are medium to large between the two groups, with the exception of the observation subscale that yielded very small effect sizes among the groups. Results are presented in Table 6.

The primary analyses of SCS total score yielded a significant difference, so we conducted post-hoc analyses to examine the differences between the two groups in its subscales. The relevant subscale-pairs in SCS present opposing trends in their mean scores; “self-kindness,” “common humanity,” and “mindfulness” scored higher in the HC group, while “self-judgment,” “isolation,” and “over-identification” have higher scores in the BPD group. (SCS positive subscales total F(1,127) = 82.55, p< 0.001, SCS negative subscales total F(1,127) = 234.00, p< 0.001). Effect sizes are large between the BPD and HC groups. Results are presented in Table 7.

4. Discussion

Our study has investigated emotion-regulation, mindfulness, and self-compassion abilities in BPD, compared to HC. Results confirmed our hypothesis that people suffering from BPD had a higher level of emotional dysregulation and used more maladaptive emotion-regulation strategies and less adaptive emotion regulation strategies, lower mindfulness and self-compassion levels than HC participants. We are going to discuss each result in detail below.

4.1 DERS

In agreement with our hypothesis, results revealed that BPD patients had higher overall emotion dysregulation compared to the HC group. All the six subscales of DERS presented significant differences between the two groups. This result is different from Ibraheim and co-worker’s findings in an adolescent sample, where only two subscales ("limited access to strategies" and "impulse control difficulties") differed significantly [24]. The finding is also in agreement with the results of a meta-analysis by Daros and Williams [2]. In this study, results are based on 93 unique studies indicating that symptoms of BPD were associated with less frequent use of adaptive emotion regulation strategies (i.e., problem solving and cognitive reappraisal) and more frequent use of strategies that are less effective in reducing negative affect (i.e. suppression, rumination, and avoidance).

4.2 CERQ

Our results show that the BPD and HC populations have significant differences in almost all CERQ subscales-except for "other-blame" and "acceptance". These results are in harmony with a study [68] examining people with BP features after negative mood and rumination induction. Those participants who scored higher on BP features (measured by Morey’s Personality Assessment Inventory-Borderline Features Scale [69]) reported higher levels of self-blame. Moreover, self-blame, as well as other-blame seemed to be an indicator of impulsive behavior as well [70]. Social exclusion was also associated with self-blame in BPD patients [71]. Another study shows that self-blame partially mediates the relationship between child maltreatment and later non-suicidal self-injury [72].

Our results demonstrate that the inability to put an unpleasant event into perspective is characteristic of the BPD group. This finding is affirmed by the alternative DSM-5 Model of personality disorders [73] which characterized PDs by impairments in personality functioning and pathological personality traits. The incapability of considering and understanding different perspectives is a defining component of the "empathy" factor of the Levels of Personality Functioning Scale, and a proposed diagnostic criteria for BPD.

4.3 Mindfulness

Our findings show impaired mindfulness abilities on four mindfulness facets among BPD patients compared to HC; mindful actions, description, non-reactivity and non-judgmental inner experience. The latter subscale presented the largest difference between the BPD and the HC groups. These results are in agreement with previous studies [42, 74, 75]. The result that the "observing" subscale was not significantly different among the three groups is similar to the finding of Didonna and co-worker’s study [37]. Results are in line with the theoretical assumptions that mindfulness practice promotes adaptive emotion regulation strategies [76, 77].

4.4 Self-compassion

According to our study, BPD patients scored lower on the adaptive, and higher on the maladaptive dimensions of the self-compassion scale than the healthy control group. Self-compassion has already been examined in BPD in contrast to a healthy population [55, 57]; their findings were similar to our results. A study, where self-compassion was examined in cluster C personality disorders before and after a short-term dynamic psychotherapy, showed that levels of self-compassion increased due to therapy, and this in turn predicted decrease in psychiatric symptoms, and personality pathology [78]. The study of Castilho and co-workers [79] found similar results about self-compassion when examining different clinical samples with diagnoses associated with difficulties in emotion- regulation (e.g. personality disorders).

4.5 Limitations

One of the limitations of our study is that self-administered questionnaires might have distorted the data, because self-awareness and self-reflection are impaired functions in BPD [80]. Furthermore, our BPD sample consists of patients participating in a 4 week-long psychotherapy program, suffering from severe symptoms and dysfunctionality; this limits our findings’ generalizability to BPD patients who are functioning better or less motivated to seek help. In both of our samples, the number of female participants is much higher than the number of men. This difference reflects a general observation that BPD is diagnosed predominantly (75%) in females in the clinical sample [81], although Grant et al. did not find gender differences in their epidemiologic survey [82]. The differential gender prevalence of BPD in our clinical setting may be the result of clinical sampling bias. In addition, our sample represents BPD patients who seek pharmaco- and psychotherapeutic help, and this is more characteristic to female BPD patients [83].

5. Conclusion

In summary, we can conclude that BPD features have a strong association with emotion dysregulation, and that this manifests in emotion regulation strategies—an increased number of maladaptive ones and a decreased number of adaptive ones—as well as in low levels of mindfulness and self-compassion as compared to an HC group. Based on these results, we suggest that teaching emotion-regulation, mindfulness, and self-compassion skills to patients can be crucial in the treatment of borderline personality disorder.

Acknowledgments

We thank Pál Czobor, Ph.D., who is a biostatistician, for his advice on solving statistical questions posed by our reviewers.

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Sours: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0248409

Screening for colorectal neoplasia with faecal occult blood testing compared with flexible sigmoidoscopy directly in a 55-56 years' old population

Reduced mortality from colorectal cancer may be achieved by screening with faecal occult blood testing. Screening for neoplasia in the rectum and sigmoid colon with flexible sigmoidoscopy is suggested to be more effective, particular among persons between 50 and 60 years of age. A cohort of 6367 persons 55-56 years of age were randomised to screening with rehydrated Hemoccult II tests (HII group) or with flexible videosigmoidoscopy directly (FS group). In the HII group 59% (1893/3183) attended, compared to 49% (1353/3184) in the FS group. Of the 1893 persons who attended in the HII group, 4% had a positive HII test and in 13% (10/78) of them a neoplasm > or = 1 cm in the rectum or sigmoid colon was diagnosed by endoscopy. The corresponding rate in the FS group was 2.3%. Overall the number of persons with a neoplasm > or = 1 cm diagnosed in the HII group was 10 and in the FS group 31. A subgroup in the flexible sigmoidoscopy group, who also performed rehydrated HII tests, showed a sensitivity of the HII test for neoplasia > or = 1 cm of 26% and a specificity of 95.6%. To find a neoplasm > or = 1 cm in the rectum or sigmoid colon, 44 examinations were needed when using flexible sigmoidoscopy directly and 7 examinations when only those with positive HII tests were examined. In mass screening for neoplasia in the rectum and sigmoid colon, the relatively low prevalence of colorectal neoplasia at 55-56 years of age makes primary selection with rehydrated Hemoccult testing an alternative to the resource-consuming endoscopy of all invited persons.

Sours: https://pubmed.ncbi.nlm.nih.gov/9401844/

Compared to 56 59

Neutralizing antibody levels are highly predictive of immune protection from symptomatic SARS-CoV-2 infection

Abstract

Predictive models of immune protection from COVID-19 are urgently needed to identify correlates of protection to assist in the future deployment of vaccines. To address this, we analyzed the relationship between in vitro neutralization levels and the observed protection from severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection using data from seven current vaccines and from convalescent cohorts. We estimated the neutralization level for 50% protection against detectable SARS-CoV-2 infection to be 20.2% of the mean convalescent level (95% confidence interval (CI) = 14.4–28.4%). The estimated neutralization level required for 50% protection from severe infection was significantly lower (3% of the mean convalescent level; 95% CI = 0.7–13%, P = 0.0004). Modeling of the decay of the neutralization titer over the first 250 d after immunization predicts that a significant loss in protection from SARS-CoV-2 infection will occur, although protection from severe disease should be largely retained. Neutralization titers against some SARS-CoV-2 variants of concern are reduced compared with the vaccine strain, and our model predicts the relationship between neutralization and efficacy against viral variants. Here, we show that neutralization level is highly predictive of immune protection, and provide an evidence-based model of SARS-CoV-2 immune protection that will assist in developing vaccine strategies to control the future trajectory of the pandemic.

Main

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has spread globally over the past year, infecting an immunologically naive population and causing significant morbidity and mortality. Immunity to SARS-CoV-2 induced either through natural infection or vaccination has been shown to afford a degree of protection against reinfection and/or reduce the risk of clinically significant outcomes. Seropositive recovered subjects have been estimated to have 89% protection from reinfection1, and vaccine efficacies from 50 to 95% have been reported2. However, the duration of protective immunity is presently unclear, primary immune responses are inevitably waning3,4,5, and there is ongoing transmission of increasingly concerning viral variants that may escape control by both vaccine-induced and convalescent immune responses6.

A critical challenge at present is to identify the immune correlate(s) of protection from SARS-CoV-2 infection and thereby predict how changes in immunity will be reflected in clinical outcomes. A defined correlate of protection will permit both confidence in opening up economies and facilitate rapid improvements in vaccines and immunotherapies. In influenza infection, for example, a hemagglutination inhibition (HAI) titer of 1:40 is thought to provide 50% protection from influenza infection7 (although estimates range from 1:17 to 1:110, refs. 8,9). This level was established over many years using data from a standardized HAI assay10 applied to serological samples from human challenge and cohort studies. This assay is used to predict vaccine efficacy and to assist in the annual reformulation of seasonal influenza vaccines. At present, however, there are few standardized assays for assessing SARS-CoV-2 immunity, little data comparing immune levels in susceptible versus resistant individuals, and no human challenge model11.

The data currently available for SARS-CoV-2 infection include immunogenicity data from phase 1 and 2 studies of vaccines, and data on protection from preliminary reports from phase 3 studies and from seropositive convalescent individuals (Supplementary Tables 1 and 2). Although antiviral T and B cell memory certainly contribute some degree of protection, strong evidence of a protective role for neutralizing serum antibodies exists. For example, passive transfer of neutralizing antibodies can prevent severe SARS-CoV-2 infection in multiple animal models,12,13 and Regeneron has recently reported similar data in humans14. We therefore focus our studies on in vitro virus neutralization titers reported in studies of vaccinated and convalescent cohorts. Unfortunately, the phase 1 and 2 studies all use different assays for measuring neutralization. Normalization of responses against a convalescent serum standard has been suggested to provide greater comparability between the results from different assays15. Although all studies compare immune responses after vaccination against the responses in convalescent individuals, the definition of convalescence is not standardized across studies. Similarly, among phase 3 studies, the timeframes of study and the case definitions of infection also vary (Supplementary Table 2). Recognizing these limitations, our aim was to investigate the relationship between vaccine immunogenicity and protection.

Results

Identification of neutralization titer as a correlate of immune protection

To compare neutralization titers across studies, we determined the mean and standard deviation (on a log scale) of the neutralization titer in published data from seven vaccine studies (mRNA-1273, NVX-CoV2373, BNT162b2, rAd26-S+rAd5-S, ChAdOx1 nCoV-19, Ad26.COV2.S and CoronaVac) and one convalescent study3,16,17,18,19,20,21,22 (Supplementary Table 1). Because of the different assays used in each study, neutralization titers were normalized to the mean convalescent titer using the same assay in the same study (noting that the definition of convalescence was also not standardized across studies and a variable number of convalescent samples are analyzed in each study). We then compared this normalized neutralization level in each study against the corresponding protective efficacy reported from the seven phase 3 clinical trials19,23,24,25,26,27,28,29 (detailed in Supplementary Table 2). Despite the known inconsistencies between studies, comparison of normalized neutralization levels and vaccine efficacy demonstrates a remarkably strong non-linear relationship between mean neutralization level and the reported protection across different vaccines (Spearman r = 0.905; P = 0.0046) (Fig. 1a).

a, Relationship between neutralization level and protection from SARS-CoV-2 infection. The reported mean neutralization level from phase 1 and 2 trials and the protective efficacy from phase 3 trials for seven vaccines, as well as the protection observed in a seropositive convalescent cohort, are shown (details of data sources are given in Supplementary Tables 1 and 2). The 95% CIs are indicated as vertical and as horizontal whiskers. The red solid line indicates the best fit of the logistic model and the red shading indicates the 95% predictive interval of the model. The mean neutralization level and protective efficacy of the Covaxin vaccine are indicated as a green circle (data from this study were available only after modeling was complete and did not contribute to fitting). b, Schematic illustration of the logistic approach to identifying the protective neutralization level. The data for each study include the distribution of the measured in vitro neutralization titer against SARS-CoV-2 in vaccinated or convalescent subjects (as a proportion of the mean titer in convalescent subjects (dashed line)) (blue/red bell curve), accompanied by a level of protective efficacy for the same regimen. The efficacy is illustrated by the proportions of the bell curve ‘protected’ (blue) and ‘susceptible’ (red) for individual studies. The modeling fits the optimal 50% protective neutralization level (blue solid line, the shaded area indicates the 95% CI) that best estimates the correct levels of protection observed across the different studies. c, Predictions of the leave-one-out analysis. Modeling was repeated multiple times using all potential sets of the seven vaccination studies and the convalescent study to predict the efficacy of the eighth study. The diagonal dashed line indicates the position of a 1:1 correlation (i.e., the relationship if the model were completely accurate). The horizontal whiskers indicate 95% CIs and the vertical whiskers indicate 95% predictive intervals.

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Estimation of the protective neutralization level against COVID-19

To further dissect the relationship between immunogenicity and protection in SARS-CoV-2 we considered the parallels with previous approaches to estimating a ‘50% protective titer’ in influenza infection. These historic studies in influenza involved comparison of HAI titers in infected versus uninfected subjects (in either natural infection or human challenge studies) and used logistic or receiver operating characteristic approaches to identify an HAI titer that provided protection7,8,9,30,31. We adapted these approaches to analyze the existing data on reported ‘mean neutralization level’ in different studies and the observed level of protection from infection (details of statistical methods are provided in the Methods).

We first fitted a logistic model to estimate the ‘50% protective neutralization level’ (across all studies) that best predicted the protective effect observed in each study (consistent with the use of a logistic function to model protection in influenza serological studies30,31). We found that this model provided a good explanation of the relationship between mean neutralization level and protection across the studies, and determined that the estimated 50% protective neutralization level was 20.2% (95% confidence interval (CI) = 14.4–28.4%) of the mean convalescent level (Fig. 1a,b). Given that different neutralization assays were used for each study11 (see above and Supplementary Table 1), a 50% protective neutralization level equivalent to 20% of the mean titer in the convalescent subjects equates to a measured in vitro neutralization titer of between 1:10 and 1:30 in most of the assays reported (although up to 1:200 in one assay), or we estimate approximately 54 international units (IU)/ml (95% CI 30–96 IU/ml) (Supplementary Table 4). Given that the model is dependent on the mean and distribution of neutralization levels, we also estimated these using different approaches, which led to similar estimates (see Methods and Extended Data Fig. 1).

To relax the assumption that neutralization levels are normally distributed in the above model, we also estimated the protective level using a distribution-free approach and applied this to the raw data for individual neutralization levels reported in the studies. We refer to this as the ‘protective neutralization classification model’. Although this approach may be slightly unrealistic in applying a protected or unprotected cut-off in a binary fashion (unlike the logistic approach), it has the advantage of being independent of any assumptions of the distribution of neutralization titers. Using this classification approach the estimated protective threshold was 28.6% (95% CI = 19.2–29.2%) of the mean convalescent level. As expected, the estimated protective level using the classification method was slightly higher than the 50% protective level estimated using the logistic method, given that the classification method essentially estimates a level of 100% protection instead of 50% protection.

This analysis suggests that the mean in vitro neutralization level of a vaccine measured early after vaccination is predictive of the subsequent protective efficacy measured in phase 3 trials, and estimates that the 50% neutralization level for SARS-CoV-2 is approximately 20% of the mean convalescent titer. To test the potential utility of this in predicting the protective efficacy of an unknown vaccine, we repeated our analysis using a leave-one-out approach. That is, we repeated our analysis by removing one of the datasets and fitting the model to the remaining seven vaccine or convalescent studies. We then used the parameters obtained from this fitting to predict the efficacy of the eighth (removed) dataset. We repeated this by removing each dataset one at a time. Figure 1c shows the results of using the logistic model of protection to predict the efficacy of each vaccine from the results of the other seven. In addition, after fitting the model to the data for eight vaccine or convalescent studies, the phase 3 efficacy results of another vaccine (BBV152) were released in a press release on 3 March 2021 (ref. 32). Using the observed neutralization level (a mean of 79.2% of the convalescent titer in that study33 (Supplementary Table 1), the predicted efficacy of the new vaccine was 79.6% (95% predictive interval: 76.2–83.0%), which is in very close agreement with the reported efficacy of 80.6% (ref. 32) and suggests good predictive value of the model (Fig. 1a).

Modeling of the duration of immune protection after vaccination

Recent studies have identified a decline in neutralization titer with time for up to 8 months after SARS-CoV-2 infection3,4,5. A major question is whether vaccine-induced responses may be more durable than those measured following infection. Limited studies have analyzed the trajectory of neutralization titer after vaccination34. To compare decay in neutralization titer we fitted a model of exponential decay to equivalent time periods in data from either convalescent3 or messenger RNA vaccination34 cohorts. Comparing neutralization titers measured between 26 and 115 d (the longest time period available for vaccination) after either mRNA-based vaccination34 or symptom onset for post-infection sera3, we found similar half-lives (65 d versus 58 d, respectively; P = 0.88, likelihood ratio test; Extended Data Fig. 2a). Although this comparison relies on limited data, it suggests that decay of vaccine-induced neutralization is similar to that observed after natural SARS-CoV-2 infection.

If the relationship between neutralization level and protection that we observe cross-sectionally between different vaccines is maintained over time, we can use the observed relationship between neutralization and protection to predict how the observed waning of neutralization titers might affect vaccine effectiveness. Important caveats to this modeling are that (1) it assumes that neutralization is a major mechanism of protection (or that the mechanism of protection remains correlated with neutralization over time), although B cell memory and T cell responses may be more durable3,4,5,35 and may play a larger role later after infection or vaccination; (2) it applies the decay of neutralization observed in convalescence to the vaccine data; and (3) it assumes that the decay in titer is the same regardless of the initial starting titer (whereas others have suggested either faster36 or slower37 decay for higher initial levels). These limitations notwithstanding, we analyzed the half-life of neutralization titer using published data from a study of convalescent subjects up to 8 months after infection (using a mixed-effects model with censoring) and estimated that neutralization titer decayed with a half-life of 108 d over this period (Extended Data Fig. 2b)5. We also tried alternative models of decay such as bi-exponential decay (consistent with rapid early decay slowing over time), but found that these did not provide a better fit to the available data. We then used this half-life of 108 d to model the decay of neutralization and protection over the first 250 d after vaccination (Fig. 2a). Our model predicts that even if the waning of neutralization titer over time is the same for different vaccines, this decay will have non-linear effects on the level of protection from SARS-CoV-2 infection, depending on initial vaccine efficacy. For example, a vaccine starting with an initial efficacy of 95% would be expected to maintain 77% efficacy by 250 d. However, a response starting with an initial efficacy of 70% would be predicted to drop to 33% efficacy after 250 d. This analysis can also be used to estimate how long it would take a response of a given initial efficacy to drop to 50% (or 70%) efficacy, which may be useful in predicting the time until boosting is required to maintain a minimum level of efficacy (Fig. 2b). Clearly, data generated from standardized assays are needed to track the long-term decay of post-vaccination immune responses and their relationship to clinical protection. However, this model provides a framework that can be adapted to predict outcomes as further immune and protection data become available. Indeed, if a disconnect between the decay of neutralization titer and protection is observed, this may be a direct pointer to the role of non-neutralizing responses in protection.

a, Prediction of the effects of declining neutralization titer. Assuming that the observed relationship between neutralization level and protection is consistent over time, we estimate the decline in efficacy for vaccines with different levels of initial efficacy. The model assumes a half-life of the neutralization titer of 108 d over the first 250 d (as observed in a convalescent cohort5). b, Modeling of the time for efficacy to drop to 70% (red line) or 50% (blue line) for scenarios with different initial efficacy. For example, for a group starting with an initial protective efficacy of 90%, the model predicts that 70% efficacy will be reached after 201 d and 50% efficacy will not be reached before 250 d. c, Estimation of the impact of viral antigenic variation on vaccine efficacy. In vitro studies have shown that neutralization titers against some SARS-CoV-2 variants are reduced compared with titers against wild-type virus. If the relationship between neutralization and protection remains constant, we can predict the difference in protective efficacy against wild-type and variant viruses from the difference in neutralization level. The dashed line indicates equal protection against wild-type and variant strains. Details of the data and modeling are provided in the Methods.

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Modeling of the effect of viral variation on immune protection

In addition to the effect of declining neutralization titer over time, reduced neutralization titers and reduced vaccine efficacy to different viral variants have also been observed6,38,39,40,41. For example, it has been reported that the neutralization titer against the B.1.351 variant in vaccinated individuals is between 7.6-fold and 9-fold lower compared with the early Wuhan-related Victoria variant42. Our model predicts that a lower neutralization titer against a variant of concern will have a larger effect on vaccines for which protective efficacy against the wild-type virus was lower (Fig. 2c). For example, a fivefold lower neutralization titer is predicted to reduce efficacy from 95% to 77% in a high efficacy vaccine, but from 70% to 32% for a vaccine with lower initial efficacy.

Estimation of the 50% protective level against severe infection

The analysis above investigates vaccine (and convalescent) protection against symptomatic SARS-CoV-2 infection (using the definitions provided in the different phase 3 and convalescent studies, Supplementary Table 2). However, it is thought that the immune response may provide greater protection from severe infection than from mild infection. To investigate this, we also analyzed data on the observed level of protection from severe infection when these were available. It is important to note that as with symptomatic infection, the definition of severe infection was not consistent across studies (the definitions for each study are detailed in Supplementary Table 3). Given that there have been under 100 severe infections reported across all the phase 3 trials combined, the 95% confidence intervals on the level of protection from severe infection are broad. The neutralization level for 50% protection from severe infection was 3.0% of the mean convalescent level (95% CI = 0.71–13%), which was significantly lower than the 20% level required for protection from any symptomatic infection (P = 0.00039, likelihood ratio test, Supplementary Table 5) (Fig. 3a). An important caveat to this analysis is the implicit assumption that neutralization titer itself confers protection from severe infection. However, it is possible that T cell responses or recall of memory B cell responses may also be important in protection from severe disease43,44,45,46.

a, The predicted relationship between efficacy against any symptomatic SARS-CoV-2 infection and the efficacy against severe infection. The black line indicates the best fit model for the relationship between protection against any versus severe SARS-CoV-2 infection. The shaded areas indicate the 95% CIs. Efficacy against severe infection was calculated using a threshold that was 0.15 times lower than that for mild infection (95% CI = 0.036–0.65) (see Methods and Supplementary Table 5). b, Extrapolation of the decay of neutralization titers over time. This model uses the estimated half-life of SARS-CoV-2 neutralization titer in convalescent subjects of 108 d over the first 250 d5, after which the decay decreases linearly until it achieves a 10-year half-life (consistent with the long-term stability of antibody responses seen after other vaccines47,48). We simulate three scenarios, with decay of neutralization taking 1 year (blue dashed line), 1.5 years (purple dashed line) or 2 years (red dashed line) to slow to a 10-year half-life. For different initial starting levels the model projects the decay in neutralization titer over the subsequent 1,000 d (the gray shaded area indicates projections beyond the currently available data). The purple shaded region indicates being below the 50% protective titer for any symptomatic SARS-CoV-2 infection, and the orange shaded region indicates being below the 50% protective titer for severe SARS-CoV-2 infection. The model illustrates that, depending on the initial neutralization level, individuals may maintain protection from severe infection while becoming susceptible to mild infection (that is, with neutralization levels remaining in the purple shaded region). c, Extrapolation of the trajectory of protection for groups with different starting levels of protection. The model uses the same assumptions for the rate of immune decay as discussed in b. The projections beyond 250 d (gray shaded region) rely on an assumption of how the decay in SARS-CoV-2 neutralization titer will slow over time. In addition, the modeling projects only how decay in neutralization is predicted to affect protection. Other mechanisms of immune protection may play important roles in providing long-term protection that are not captured in this simulation.

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Prediction of the potential for long-term protection

The estimated neutralization level for protection from severe infection is approximately sixfold lower than the level required to protect from any symptomatic infection. Thus, a higher level of protection against severe infection is expected for any given level of vaccine efficacy against mild SARS-CoV-2 infection. Assuming that this relationship remains constant over time, it appears probable that immunity to severe infection may be much more durable than overall immunity to any infection. Long-term studies of antibody responses to vaccinia, measles, mumps or rubella suggest that these responses generally stabilize with half-lives of >10 years47,48. We therefore projected beyond the reported decay of SARS-CoV-2 responses (out to 8 months after infection5), assuming that after 8 months following the infection the decay rate will slow down. We modeled the decay rate of the neutralization titer, assuming that it slowed linearly to a 10-year half-life over 1, 1.5 or 2 years (details in Methods). This analysis predicts that even without immune boosting, a significant proportion of individuals may maintain long-term protection from severe infection by an antigenically similar strain, even though they may become susceptible to mild infection (Fig. 3b,c).

Discussion

Understanding the relationship between measured immunity and clinical protection from SARS-CoV-2 infection is urgently needed to plan the next steps in the COVID-19 vaccine program. Placebo-controlled vaccine studies are unlikely to be possible in the development of next-generation vaccines, and therefore correlates of immunity will become increasingly important in planning booster doses of vaccine, prioritizing next-generation vaccine development, and powering efficacy studies49. Our work uses available data on immune responses and protection to model both the protective titer and the long-term behavior of SARS-CoV-2 immunity. It suggests that neutralization titer will be an important predictor of vaccine efficacy in the future as new vaccines emerge. The model also predicts that immune protection from infection may wane with time as neutralization levels decline, and that booster immunization may be required within a year. However, protection from severe infection may be considerably more durable given that lower levels of response may be required or alternative responses (such as cellular immune responses) may play a more prominent role.

As discussed above, a major caveat of our estimate of the relative protective level of antibodies in SARS-CoV-2 infection is that it includes aggregation of data collected from diverse neutralization assays and clinical trial designs (Supplementary Tables 1 and 2). It is hoped that in the future a standardized neutralization assay may be developed and utilized, which will allow direct comparison of neutralization titers and further refinement of these analyses11. In addition, the development of standardized trials and case definitions is necessary, given that differences in classification (particularly of severe disease) may prove to be important (Supplementary Table 3). The association of neutralization with protection across these studies does not prove that neutralizing antibodies are necessarily mechanistic in mediating protection. It is possible that neutralization is correlated with other immune responses, leading to an apparent association (as has been suggested for the use of HAI titer in influenza50,51,52). Thus, it will be important to study other responses such as T cell responses or B cell memory responses as additional potential correlates of protection. Another important refinement of this approach would be to have standardized measures of other serological and cellular responses to infection, to identify if any of these provide a better predictive value than neutralization. However, despite these limitations, our work identifies neutralizing antibodies as an immune correlate of protection and provides a quantitative prediction of the link between neutralizing antibody levels and clinical protection based on evidence from clinical trials and convalescent cohort studies. An important factor that is not explored in this analysis is the role of age in immunogenicity, in the durability of neutralizing responses, and in clinical protection, given that vaccine studies tend to exclude older individuals.

Our method for estimating protective neutralization titer for COVID-19 uses a very similar modeling approach to that previously used to estimate the protective titer for influenza infection7,8,9,30,31. However, a major difference is the data used in the models. Our approach utilizes the wide range of immunogenicity and protective efficacy across different vaccines to estimate the 50% protective titer. By contrast, studies in influenza infection use data from the HAI titer of individual subjects and their subsequent risk of infection in either cohort or human challenge studies to estimate protection7,8,9,30,31. It will be important to prospectively validate our results using a similar analysis of individual risk of COVID-19 infection in future studies.

Our results are consistent with studies of both influenza and seasonal coronavirus infection, for which reinfection is possible 1 year after the initial infection, although it usually results in mild infection53,54. Similarly, after influenza virus vaccination, protective efficacy is thought to decline by around 7% per month55. Our modeling and predictions are based on a number of assumptions regarding the mechanisms and rate of loss of immunity. Important priorities for the field are the development of standardized assays to measure neutralization and other immune responses, as well as standardized clinical trial protocols. These data will allow further testing and validation of other potential immune correlates of protection. However, our study develops a modeling framework for integrating available, if imperfect, data from vaccination and convalescent studies to provide a tool for predicting the uncertain future of SARS-CoV-2 immunity.

Methods

Data extraction

When possible, data values were used as directly stated in publications. In addition, when necessary, raw data were directly extracted from the original publications using an online digitizer tool (https://automeris.io/WebPlotDigitizer/, version 4.4). All sources of data are described in Supplementary Tables 1–3.

Statistical methods

Estimation of the standard deviation of neutralization titers

Neutralization titers were extracted for each study (as above) and used to determine the standard deviation of the log10-transformed neutralization titers for each study. The standard deviation for each study had to consider that some measurements of neutralization titer fell below the limit of detection (LOD) of that study assay (LOD varied for each study, Supplementary Table 4). To remove the effect of LOD censoring on estimates of the standard deviation of neutralization titers we used a censored regression model to fit the distribution of the neutralization titers for each study. The likelihood function is given by

$${\cal{L}}({\boldsymbol{D}}_{\boldsymbol{s}}|\mu _{cens},\sigma _{cens},L_s) = \mathop {\prod }\limits_{n_i \in {\boldsymbol{D}}_{\boldsymbol{s}}} f\left( {n_i|\mu _{cens},\sigma _{cens}} \right)^{1 - I_i}F\left( {L_s|\mu _{cens},\sigma _{cens}} \right)^{I_i}$$

(1)

where Ds is a vector of all of the log10-neutralization titers, ni, for the study s. The function f is the probability function of a normal distribution with mean μcens and standard deviation σcens, and F is the cumulative density function of the same distribution. The LOD of the assay for study s is given by Ls. The index variable Ii is 1 when ni ≤ Ls and 0 otherwise. The negative log of this likelihood function was minimized in R using the built-in optimizer nlm to estimate the mean and standard deviation of the log10-transformed neutralization titers after factoring in the LOD. When no LOD was reported or when all of the values were above the LOD, Ls was set to negative infinity (−Inf).

Pooled standard deviation

Given the differing sample size of the neutralization data for each study, the accuracy of estimations of the standard deviation for each study varied considerably. Therefore, despite finding some limited evidence of a difference in the standard deviation between each study (P = 0.049, Fligner–Killeen test), we combined all extracted data and calculated the standard deviation of the pooled data. A test of normality showed that the pooled neutralization data were consistent with a normal distribution (P = 0.26, Shapiro–Wilk test). To estimate a pooled standard deviation, we first centered the neutralization data for each study at the reported mean of the neutralization titers for that study. The LOD given for each study was also adjusted in the same way. This provided a combined dataset of neutralization titers from all studies, which was fitted, using the likelihood model in equation (1), to the pooled data to produce an estimate of the standard deviation of the pooled data. All estimated standard deviations are reported in Supplementary Table 4.

Modeling of the relationship between neutralization and protection

In the above sections we used neutralization titer information from each vaccine and from convalescent individuals to estimate the distribution of the neutralization titers for each study. However, as discussed in the main text, owing to the diversity of assays used to assess neutralization in each study (Supplementary Table 1), from this point forward we normalized the neutralization titers in each study by the mean of the neutralization titer in the corresponding convalescent individuals from the same study. Also, in all of the analyses below we use the log10 transform of the normalized neutralization titers. For simplicity, in the remainder of this paper we refer to these log10-transformed normalized neutralization titers as the ‘neutralization levels’.

Logistic method

To model the relationship between the neutralization level of antibodies collected from individuals after vaccination (or during convalescence) and the protection from COVID-19 we assumed a logistic relationship between neutralization level and protective efficacy, such that,

$$E_I\left( {n|n_{50},k} \right) = \frac{1}{{1 + e^{ - k(n - n_{50})}}},$$

(2)

where EI is the protective efficacy of an individual given the neutralization level n (note the definition of neutralization level above). The parameter n50 is the neutralization level at which an individual will have a 50% protective efficacy (that is, half the chance of being infected compared with an unvaccinated person). The steepness of this relationship between protective efficacy and neutralization level is determined by the parameter k.

We assume that a vaccine (or prior exposure) will induce a (normal) distribution of neutralization levels (n) in a population with some mean μs and standard deviation σs. The mean neutralization level for each study, μs, is the difference between the log10-transformed mean neutralization titers for vaccinated and for convalescent individuals in that study. The standard deviation, σs, is the standard deviation for vaccinated individuals in that study only. (Note that the distribution of neutralization level for convalescent individuals has a mean of zero by definition (that is, the log of the mean of neutralization titers for convalescent individuals normalized by itself).) Therefore the proportion of the vaccinated population for a study, s, that will be protected will be given by

$$P\left( {n_{50},k,\mu _s,\sigma _s} \right) = \mathop {\smallint }\limits_{ - \infty }^\infty E_I\left( {n|n_{50},k} \right)f(n|\mu _s,\sigma _s)dn,$$

(3)

where f is the probability density function of a normal distribution and EI is the logistic function in equation (2). The above integral is the so-called logistic-normal integral and the mean of the logit-normal distribution, which has no analytical solution56. Therefore, we use a simple numerical approximation (left Riemann sum).

Fitting of the logistic model and confidence intervals

The above model of protection was fitted to data on the protective efficacy of vaccines from phase 3 (and another large cohort study of convalescent individuals). For each vaccine and convalescence study the number of control (unvaccinated, or placebo or naive) individuals enrolled (\(N_s^c\)), the number of control individuals infected (\(I_s^c\)), the number of vaccinated (previously exposed) individuals enrolled (\(N_s^v\)), and the number of vaccinated individuals infected (\(I_s^v\)) were used in the fitting of the model. The likelihood of observing the number of infected individuals in the control and vaccinated groups for each study, given some parameters, is

$$\begin{array}{l}{\cal{L}}_s\left( {N_s^c,I_s^c,N_s^v,I_s^v,\mu _s,\sigma _s|n_{50},k,b_s} \right) = Bi\left( {N_s^c,I_s^c,b_s} \right)\\Bi\left( {N_s^v,I_s^v,b_s\left( {1 - P(n_{50},k,\mu _s,\sigma _s)} \right)} \right),\end{array}$$

(4)

where bs is the probability of an unvaccinated control individual becoming infected in study s (baseline risk), \(b_s\left( {1 - P(n_{50},k,\mu _s,\sigma _s)} \right)\) is the probability of infection in the vaccination group (see equation 3) and Bi(N, K, p) is the binomial probability mass function of the probability of K events from a sample size of N, for which each event has a probability p of occurring. However, we wish to fit all studies simultaneously, and so the total likelihood of observing the data in all studies, given some parameters, is

$$\begin{array}{l}{\cal{L}}\left( {{\boldsymbol{N}}^{\boldsymbol{c}},{\boldsymbol{I}}^{\boldsymbol{c}},{\boldsymbol{N}}^{\boldsymbol{v}},{\boldsymbol{I}}^{\boldsymbol{v}},{\boldsymbol{\mu }},{\boldsymbol{\sigma }}|n_{50},k,{\boldsymbol{b}}} \right) = \mathop {\prod }\limits_{\forall s} Bi\left( {N_s^c,I_s^c,b_s} \right)\\ Bi\left( {N_s^v,I_s^v,b_s\left( {1 - P(n_{50},k,\mu _s,\sigma _s)} \right)} \right),\end{array}$$

(5)

where Nc, Ic, Nv, Iv, μ, σ are vectors containing the data \(N_s^c,I_s^c,N_s^v,I_s^v,\mu _s,\sigma _s\) for each study s, and b is a vector of the baseline risk parameters bs for each study. The best-fitting parameters n50, k and b were found using the nlm optimizer in R by minimizing \(- \log \left( {\cal{L}} \right)\). The standard error (s.e.) of these estimates was estimated using the hessian H output from this function and the formula \({\mathrm{s.e.}} = \sqrt {{\mathrm{diag}}(H^{ - 1})}\). The 95% CIs were taken as ±1.95 × s.e. of the estimated parameters.

The variable μs is the mean neutralization level, which can be calculated in two ways; first, by dividing the geometric mean of the neutralization titers in vaccinated individuals by the geometric mean of the neutralization titer in convalescent individuals in the same study. This is, in most cases, the ratio of two values directly reported in the immunogenicity studies. However, this approach does not account for situations in which the neutralization assay had neutralization titers below the LOD, therefore we also used a second method, in which we estimated this value by extracting the neutralization titers from the figures in each immunogenicity study (Supplementary Table 1) and computing the mean neutralization titer for vaccinated and convalescent individuals in each study using censoring regression (equation 1). Additionally, although it was in principle possible to compute the standard deviation of neutralization levels for each study (as above), these appeared somewhat confounded by the varying numbers of individuals between studies, hence we fitted the above model using (1) the standard deviation estimates for each study, (2) one standard deviation from one larger study to which we had direct access to raw data3 (that is, no manual data extraction required), and (3) an estimate of the standard deviation for all studies pooled together. The two different methods of estimating the mean neutralization level for each study and the three methods of estimating the standard deviation of the neutralization levels give rise to six versions of the above model. All of these versions of the model were fitted, and the estimated protective levels were very similar (Extended Data Fig. 1).

Protective neutralization classification model

The above modeling approach assumed that neutralization levels were normally distributed. Here, we present a method for determining a protective threshold that is free of assumptions regarding the distribution of neutralization levels. This model assumes that there is a protective neutralization level, T, above which individuals will be protected from infection and below which individuals will be susceptible. The protective efficacies observed in phase 3 clinical trials of vaccinated individuals (and another large cohort study of convalescent individuals1; Supplementary Table 2) are denoted by Es. These represent the proportion of individuals in each study, s, who should possess a neutralization level above the protective threshold. It follows then that the number of individuals above the protective threshold in study s is a function of T, which we denote Ks(T). Therefore, the probability of observing Ks(T) individuals above the protective threshold, given that there were Ns individuals in the immunogenicity study (which are much smaller than the phase 3 studies), is given by

$$P(K_s(T)|N_s,T) = Bi(N_s,K_s(T),E_s),$$

(6)

where Bi is a binomial distribution. Note that

$$K_s\left( T \right) = \mathop {\sum }\limits_{n_i \in {\boldsymbol{D}}_s} H(n_i - T),$$

(7)

and Ns = |Ds|, such that H is the heavy-side step function taking the value 1 when ni − T > 0, or 0 otherwise, and |Ds| denotes the size of set Ds (that is, the number of neutralization levels measured). To determine one protective threshold using the results of all efficacy studies in this paper, we construct a likelihood function

$${\cal{L}}\left( {{\boldsymbol{D}}|T} \right) = \mathop {\prod }\limits_{{\boldsymbol{D}}_{\boldsymbol{s}} \in {\boldsymbol{D}}} Bi(N_s,K_s(T),E_s),$$

(8)

where D is the set of vectors of the neutralization levels from each study. Note that this likelihood function is discontinuous as the threshold T is varied. Therefore, we evaluate this likelihood function with the threshold T set equal to all observed neutralization levels ni across all studies, and find the value of T that maximizes this likelihood (Extended Data Fig. 3). This method determines a protective level at which the proportion of individuals with neutralization levels above the threshold is in greatest agreement with the observed protective efficacy of that vaccine.

Equation (8) is the likelihood function that should be adopted when neutralization measurements are not affected by an LOD. In the case that some neutralization levels are below the LOD, the likelihood function is adjusted as follows:

$${\cal{L}}\left( {{\boldsymbol{D}}|T} \right) = \mathop {\prod }\limits_{{\boldsymbol{D}}_{\boldsymbol{s}} \in {\boldsymbol{D}}} Bi\left( {N_s,K_s\left( T \right),E_s} \right)^{1 - J_s} \times Q\left( {N_s,C_s,1 - E_s} \right)^{J_s},$$

(9)

where Js is an index that takes the value 1 when the LOD of study s is above the threshold T and at least one value is censored, or 0 otherwise. Cs is the number of censored values in study s and Q is the cumulative binomial distribution function. This later term considers the probability that as many as all of the censored values were below the threshold T given the protective efficacy of the study Es.

To determine the 95% CIs for the estimated protective neutralization level, a bootstrapping approach was used in which the neutralization levels were resampled 1,000 times at random with replacement. Resampling was performed so as to preserve the total number of neutralization levels in each study. These randomly generated samples of the original data were then fitted in the same way as described above, which generated 1,000 corresponding estimates of the protective neutralization level. The 95% CI was calculated as the 2.5 and 97.5 percentiles of these 1,000 estimates of the protective neutralization level.

Assessment of the predictive ability of the model

To determine the ability of the model to predict the efficacy of a vaccine, we performed a leave-one-out analysis in which we systematically excluded one of the vaccine studies (or the convalescent study) and performed the same model-fitting procedure described above. Using the model fitted on the subset of the studies we then estimated the efficacy of the vaccine that was left out from the fitted model. This leave-one-out analysis was performed for all versions of the logistic model (that is, using the six methods of estimating the mean neutralization level and standard deviation outlined above). The predicted efficacy for each vaccine and convalescence obtained while leaving the study out are plotted against the reported efficacy in Fig. 1c. Also, the 50% protective level that was estimated each time a study was left out of the analysis provides a metric of the sensitivity of the model to the inclusion of each study. Note that the exclusion of any of the studies did not greatly influence the estimate of the 50% protective level (Extended Data Fig. 1).

Error bars and regions in efficacy and neutralization

In Fig. 1a there are both horizontal and vertical error bars as well a 95% predictive interval for the fitted model. The vertical error bars indicate the 95% CIs for the efficacy estimates for each study, these were calculated using the Katz-log method specified in supplementary table 1 of ref. 57. The horizontal error bars indicate 95% CIs in the difference of the mean of the (log10) neutralization titers for vaccinated and convalescent individuals in each study. That is, these represent

$$\pm 1.96 \times \sqrt {\frac{{\sigma _v^2}}{{n_v}} + \frac{{\sigma _c^2}}{{n_c}}},$$

(10)

where σv and σc are the standard deviation in the log10 of the neutralization titers for vaccinated and convalescent individuals, respectively, and were estimated as described in the section on estimating the standard deviation of neutralization titers above. nv and nc are the number of vaccinated and convalescent individuals who were included for each study, respectively. The 95% predictive interval in Fig. 1a was calculated using the delta method58.

Comparison of the protective level in mild and severe infection

We also tested if the protective neutralization level was different between mild and severe infection by fitting the combined dataset with two different mathematical models. The simplest model assumes that we could use the same protective level in both severe and mild infection (that is, the shared steepness parameter (k) and 50% protective level (n50) in the logistic model (above)); and the alternative model uses different protective level parameters while we constrained the model to have the same k in severe and mild infection (equation 3). We used both the Akaike information criterion and a likelihood ratio test to determine which model provided the best fit of the dataset for both severe COVID-19 cases and all COVID-19 cases reported (Supplementary Table 5).

Modeling of the decay of neutralization and the effects of antigenic variation

Comparison of decay in convalescence and vaccination

A number of studies have analyzed the decay in neutralization titer in convalescent subjects. These studies have generally shown a rapid early decay that slows with time3,4,5,59,60. We identified one study by Widge et al.34 in which the time course of neutralization titer after mRNA vaccination was able to be analyzed. That study measured the decay of neutralization titer out to 115 d. To compare the half-life of decay of the neutralization titer in vaccinated versus convalescent cohorts we analyzed the decay in that vaccination study compared with a previously published study of convalescent neutralization titer3, restricting the convalescent data to data collected within 115 d (Extended Data Fig. 2a).

We compared the decay rates using linear mixed-effects modeling and censoring values below the LOD61, by treating ‘vaccination group’ (vaccinated or convalescent) as a binary variable. The statistical significance of ‘vaccination group’ as a covariate (whether it was significantly different from zero) was calculated using the likelihood ratio test. Note that this restricted convalescent time course was used only so that we could compare decay in vaccination and convalescence over a similar time course (time-limited by the vaccination data).

The half-life of neutralization titers in convalescent subjects was estimated over a longer time course of 240 d using the same mixed-effects modeling approach described above, but applied to the neutralization data reported by Dan et al.5 in supplementary data file 1 of their paper. This is the estimate that was used in the predictive model presented in Figs. 2 and 3.

Predicting the loss of efficacy as neutralization wanes and that due to variants

The decay in efficacy with time (Fig. 2a,b) was modeled by reducing the neutralization levels at a rate corresponding to a half-life of 108 d and recalculating the efficacy given this new distribution of neutralization levels, using equation (3). The efficacy against a SARS-CoV-2 variant, given an associated decrease in neutralization (Fig. 2c), was calculated by reducing the mean neutralization level by a factor of 2, 5 or 10 and using equation (3). Efficacy against severe infection was similarly calculated using the same approach as above, but using the 50% protective level associated with the severe threshold (Supplementary Table 5), which was a factor of 0.15 lower than that for mild infection (95% CI = 0.036–0.65) (Fig. 3a,b). We also extrapolated the decay of the neutralization level beyond the current data, assuming that neutralization levels decay with a half-life of 108 d up until d 250 and that this decay rate slows linearly to a 10-year half-life over 1, 1.5 or 2 years (Fig. 3c).

Ethics statement

This work was approved by the University of NSW Sydney Human Research Ethics Committee (approval HC200242).

Reporting Summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability

All data are freely available from the corresponding author upon request.

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