References

Akacha, M., Binkowitz, B., Bretz, F., Fritsch, A., Hougaard, P., Jahn-Eimermacher, A., & al., et. (2018). Request for CHMP qualification opinion: Clinically interpretable treatment effect measures based on recurrent event endpoints that allow for efficient statistical analyses. http://www.ema.europa.eu/documents/other/qualification-opinion-treatment-effect-measures-when-using-recurrent-event-endpoints-applicants_en.pdf.
Akacha, M., Bretz, F., Ohlssen, D., Rosenkranz, G., & Schmidli, H. (2017). Estimands and Their Role in Clinical Trials. Statistics in Biopharmaceutical Research, 9(3), 268–271. https://doi.org/10.1080/19466315.2017.1302358
Bebu, I., & Lachin, J. M. (2016). Large sample inference for a win ratio analysis of a composite outcome based on prioritized components. Biostatistics, 17(1), 178–187. https://doi.org/10.1093/biostatistics/kxv032
Bennett, S. (1983). Analysis of survival data by the proportional odds model. Statistics in Medicine, 2(2), 273–277. https://doi.org/10.1002/sim.4780020223
Brunner, E., Vandemeulebroecke, M., & Mütze, T. (2021). Win odds: An adaptation of the win ratio to include ties. Statistics in Medicine, 40(14), 3367–3384. https://doi.org/10.1002/sim.8967
Buyse, M. (2010). Generalized pairwise comparisons of prioritized outcomes in the two-sample problem. Statistics in Medicine, 29(30), 3245–3257. https://doi.org/10.1002/sim.3923
CHMP. (2020). Qualification opinion of clinically interpretable treatment effect measures based on recurrent event endpoints that allow for efficient statistical analyses. https://www.ema.europa.eu/en/documents/other/qualification-opinion-clinically-interpretable-treatment-effect-measures-based-recurrent-event_en.pdf.
Cui, Y., & Huang, B. (2023). WINS: The r WINS package. https://CRAN.R-project.org/package=WINS
Deltuvaite-Thomas, V., Verbeeck, J., Burzykowski, T., Buyse, M., Tournigand, C., Molenberghs, G., & Thas, O. (2022). Generalized pairwise comparisons for censored data: An overview. Biometrical Journal, 65(2). https://doi.org/10.1002/bimj.202100354
Dong, G., Hoaglin, D. C., Huang, B., Cui, Y., Wang, D., Cheng, Y., & Gamalo-Siebers, M. (2023). The stratified win statistics (win ratio, win odds, and net benefit). Pharmaceutical Statistics, 22(4), 748–756. https://doi.org/10.1002/pst.2293
Dong, G., Hoaglin, D. C., Qiu, J., Matsouaka, R. A., Chang, Y.-W., Wang, J., & Vandemeulebroecke, M. (2020). The Win Ratio: On Interpretation and Handling of Ties. Statistics in Biopharmaceutical Research, 12(1), 99–106. https://doi.org/10.1080/19466315.2019.1575279
Dong, G., Huang, B., Chang, Y.-W., Seifu, Y., Song, J., & Hoaglin, D. C. (2020a). The win ratio: Impact of censoring and follow-up time and use with nonproportional hazards. Pharmaceutical Statistics, 19(3), 168–177. https://doi.org/10.1002/pst.1977
Dong, G., Huang, B., Verbeeck, J., Cui, Y., Song, J., Gamalo-Siebers, M., Wang, D., Hoaglin, D. C., Seifu, Y., Mütze, T., & Kolassa, J. (2022). Win statistics (win ratio, win odds, and net benefit) can complement one another to show the strength of the treatment effect on time-to-event outcomes. Pharmaceutical Statistics, 22(1), 20–33. https://doi.org/10.1002/pst.2251
Dong, G., Huang, B., Wang, D., Verbeeck, J., Wang, J., & Hoaglin, D. C. (2021). Adjusting win statistics for dependent censoring. Pharmaceutical Statistics, 20(3), 440–450. https://doi.org/10.1002/pst.2086
Dong, G., Li, D., Ballerstedt, S., & Vandemeulebroecke, M. (2016). A generalized analytic solution to the win ratio to analyze a composite endpoint considering the clinical importance order among components. Pharmaceutical Statistics, 15(5), 430–437. https://doi.org/10.1002/pst.1763
Dong, G., Mao, L., Huang, B., Gamalo-Siebers, M., Wang, J., Yu, G., & Hoaglin, D. C. (2020b). The inverse-probability-of-censoring weighting (IPCW) adjusted win ratio statistic: an unbiased estimator in the presence of independent censoring. Journal of Biopharmaceutical Statistics, 30(5), 882–899. https://doi.org/10.1080/10543406.2020.1757692
Dong, G., Qiu, J., Wang, D., & Vandemeulebroecke, M. (2017). The stratified win ratio. Journal of Biopharmaceutical Statistics, 28(4), 778–796. https://doi.org/10.1080/10543406.2017.1397007
EUnetHTA. (2015). Guidance for industry: Multiple endpoints in clinical trials. https://www.eunethta.eu/wp-content/uploads/2018/01/Endpoints-used-for-Relative-Effectiveness-Assessment-Composite-endpoints_Amended-JA1-Guideline_Final-Nov-2015_0.pdf
Fay, M. P., Brittain, E. H., Shih, J. H., Follmann, D. A., & Gabriel, E. E. (2018). Causal estimands and confidence intervals associated with Wilcoxon-Mann-Whitney tests in randomized experiments. Statistics in Medicine, 37(20), 2923–2937. https://doi.org/10.1002/sim.7799
FDA. (2022). Guidance for industry: Multiple endpoints in clinical trials. https://www.fda.gov/regulatory-information/search-fda-guidance-documents/multiple-endpoints-clinical-trials-guidance-industry
FDA. (2023). Guidance document: Adjusting for covariates in randomized clinical trials for drugs and biological products. US Food and Drug Adminstration. https://www.fda.gov/regulatory-information/search-fda-guidance-documents/adjusting-covariates-randomized-clinical-trials-drugs-and-biological-products
Fine, J. P., & Gray, R. J. (1999). A Proportional Hazards Model for the Subdistribution of a Competing Risk. Journal of the American Statistical Association, 94(446), 496–509. https://doi.org/10.1080/01621459.1999.10474144
Finkelstein, D. M., & Schoenfeld, D. A. (1999). Combining mortality and longitudinal measures in clinical trials. Statistics in Medicine, 18(11), 1341–1354. https://doi.org/10.1002/(sici)1097-0258(19990615)18:11<1341::aid-sim129>3.0.co;2-7
Follmann, D., Fay, M. P., Hamasaki, T., & Evans, S. (2019). Analysis of ordered composite endpoints. Statistics in Medicine, 39(5), 602–616. https://doi.org/10.1002/sim.8431
Freemantle, N., Calvert, M., Wood, J., Eastaugh, J., & Griffin, C. (2003). Composite Outcomes in Randomized Trials. JAMA, 289(19), 2554. https://doi.org/10.1001/jama.289.19.2554
Fritsch, A., Schlömer, P., Mendolia, F., Mütze, T., & Jahn-Eimermacher, A. (2023). Efficiency Comparison of Analysis Methods for Recurrent Event and Time-to-First Event Endpoints in the Presence of Terminal EventsApplication to Clinical Trials in Chronic Heart Failure. Statistics in Biopharmaceutical Research, 15(2), 268–279. https://doi.org/10.1080/19466315.2021.1945488
Gasparyan, S. B., Folkvaljon, F., Bengtsson, O., Buenconsejo, J., & Koch, G. G. (2020). Adjusted win ratio with stratification: Calculation methods and interpretation. Statistical Methods in Medical Research, 30(2), 580–611. https://doi.org/10.1177/0962280220942558
Gasparyan, S. B., Kowalewski, E. K., Folkvaljon, F., Bengtsson, O., Buenconsejo, J., Adler, J., & Koch, G. G. (2021). Power and sample size calculation for the win odds test: application to an ordinal endpoint in COVID-19 trials. Journal of Biopharmaceutical Statistics, 31(6), 765–787. https://doi.org/10.1080/10543406.2021.1968893
Gehan, E. A. (1965). A generalized Wilcoxon test for comparing arbitrarily singly-censored samples. Biometrika, 52(1-2), 203–224. https://doi.org/10.1093/biomet/52.1-2.203
Ghosh, D., & Lin, D. Y. (2000). Nonparametric Analysis of Recurrent Events and Death. Biometrics, 56(2), 554–562. https://doi.org/10.1111/j.0006-341x.2000.00554.x
Gray, R. J. (1988). A class of K-sample tests for comparing the cumulative incidence of a competing risk. The Annals of Statistics, 16(3). https://doi.org/10.1214/aos/1176350951
ICH. (1998). Statistical principles for clinical trials. London: European Medicines Evaluation Agency.
ICH. (2020). ICH E9 (R1) addendum on estimands and sensitivity analysis in clinical trials to the guideline on statistical principles for clinical trials, step 5. London: European Medicines Evaluation Agency.
Ionan, A. C., Paterniti, M., Mehrotra, D. V., Scott, J., Ratitch, B., Collins, S., Gomatam, S., Nie, L., Rufibach, K., & Bretz, F. (2022). Clinical and Statistical Perspectives on the ICH E9(R1) Estimand Framework Implementation. Statistics in Biopharmaceutical Research, 15(3), 554–559. https://doi.org/10.1080/19466315.2022.2081601
Li, H., Chen, W.-C., Lu, N., Tang, R., & Zhao, Y. (2024). The elusiveness of the win ratio parameter in the presence of missing data. Therapeutic Innovation & Regulatory Science, 1–2.
Lin, D. Y., Wei, L. J., & Ying, Z. (1993). Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika, 80(3), 557–572. https://doi.org/10.1093/biomet/80.3.557
Lu, Y., & Tian, L. (2021). Statistical Considerations for Sequential Analysis of the Restricted Mean Survival Time for Randomized Clinical Trials. Statistics in Biopharmaceutical Research, 13(2), 210–218. https://doi.org/10.1080/19466315.2020.1816491
Luo, X., Huang, B., & Quan, H. (2019). Design and monitoring of survival trials based on restricted mean survival times. Clinical Trials, 16(6), 616–625. https://doi.org/10.1177/1740774519871447
Luo, X., Qiu, J., Bai, S., & Tian, H. (2017). Weighted win loss approach for analyzing prioritized outcomes. Statistics in Medicine, 36(15), 2452–2465. https://doi.org/10.1002/sim.7284
Luo, X., Tian, H., Mohanty, S., & Tsai, W. Y. (2015). An Alternative Approach to Confidence Interval Estimation for the Win Ratio Statistic. Biometrics, 71(1), 139–145. https://doi.org/10.1111/biom.12225
Mao, L. (2018). On causal estimation using U-statistics. Biometrika, 105(1), 215–220. https://doi.org/10.1093/biomet/asx071
Mao, L. (2019). On the Alternative Hypotheses for the Win Ratio. Biometrics, 75(1), 347–351. https://doi.org/10.1111/biom.12954
Mao, L. (2023a). Nonparametric Inference of General While-Alive Estimands for Recurrent Events. Biometrics, 79(3), 1749–1760. https://doi.org/10.1111/biom.13709
Mao, L. (2023b). On restricted mean time in favor of treatment. Biometrics, 79(1), 61–72. https://doi.org/10.1111/biom.13570
Mao, L. (2023c). Power and Sample Size Calculations for the Restricted Mean Time Analysis of Prioritized Composite Endpoints. Statistics in Biopharmaceutical Research, 15(3), 540–548. https://doi.org/10.1080/19466315.2022.2110936
Mao, L. (2023d). Study Design for Restricted Mean Time Analysis of Recurrent Events and Death. Biometrics, 79(4), 3701–3714. https://doi.org/10.1111/biom.13923
Mao, L. (2024). Defining estimand for the win ratio: separate the true effect from censoring. Clinical Trials, In press.
Mao, L., & Kim, K. (2021). Statistical Models for Composite Endpoints of Death and Nonfatal Events: A Review. Statistics in Biopharmaceutical Research, 13(3), 260–269. https://doi.org/10.1080/19466315.2021.1927824
Mao, L., Kim, K., & Li, Y. (2022). On recurrent-event win ratio. Statistical Methods in Medical Research, 31(6), 1120–1134. https://doi.org/10.1177/09622802221084134
Mao, L., Kim, K., & Miao, X. (2022). Sample size formula for general win ratio analysis. Biometrics, 78(3), 1257–1268. https://doi.org/10.1111/biom.13501
Mao, L., & Lin, D. Y. (2016). Semiparametric regression for the weighted composite endpoint of recurrent and terminal events. Biostatistics, 17(2), 390–403. https://doi.org/10.1093/biostatistics/kxv050
Mao, L., & Wang, T. (2021). A class of proportional win-fractions regression models for composite outcomes. Biometrics, 77(4), 1265–1275. https://doi.org/10.1111/biom.13382
Mao, L., & Wang, T. (2024). Dissecting the restricted mean time in favor of treatment. Journal of Biopharmaceutical Statistics, 34(1), 111–126. https://doi.org/10.1080/10543406.2023.2210658
Moertel, C. G., Fleming, T. R., Macdonald, J. S., Haller, D. G., Laurie, J. A., Goodman, P. J., Ungerleider, J. S., Emerson, W. A., Tormey, D. C., Glick, J. H., Veeder, M. H., & Mailliard, J. A. (1990). Levamisole and Fluorouracil for Adjuvant Therapy of Resected Colon Carcinoma. New England Journal of Medicine, 322(6), 352–358. https://doi.org/10.1056/nejm199002083220602
Murphy, S. A., Rossini, A. J., & Vaart, A. W. van der. (1997). Maximum Likelihood Estimation in the Proportional Odds Model. Journal of the American Statistical Association, 92(439), 968–976. https://doi.org/10.1080/01621459.1997.10474051
O’Connor, C. M., Whellan, D. J., Lee, K. L., Keteyian, S. J., Cooper, L. S., Ellis, S. J., Leifer, E. S., Kraus, W. E., Kitzman, D. W., Blumenthal, J. A., Rendall, D. S., Miller, N. H., Fleg, J. L., Schulman, K. A., McKelvie, R. S., Zannad, F., Piña, I. L., & HF-ACTION Investigators, for the. (2009). Efficacy and Safety of Exercise Training in Patients With Chronic Heart Failure. JAMA, 301(14), 1439. https://doi.org/10.1001/jama.2009.454
Oakes, D. (1989). Bivariate Survival Models Induced by Frailties. Journal of the American Statistical Association, 84(406), 487–493. https://doi.org/10.1080/01621459.1989.10478795
Oakes, D. (2016). On the win-ratio statistic in clinical trials with multiple types of event. Biometrika, 103(3), 742–745. https://doi.org/10.1093/biomet/asw026
Péron, J., Buyse, M., Ozenne, B., Roche, L., & Roy, P. (2016). An extension of generalized pairwise comparisons for prioritized outcomes in the presence of censoring. Statistical Methods in Medical Research, 27(4), 1230–1239. https://doi.org/10.1177/0962280216658320
Pocock, S. J., Ariti, C. A., Collier, T. J., & Wang, D. (2012). The win ratio: a new approach to the analysis of composite endpoints in clinical trials based on clinical priorities. European Heart Journal, 33(2), 176–182. https://doi.org/10.1093/eurheartj/ehr352
Qu, Y., & Lipkovich, I. (2021). Implementation of ICH E9 (R1): A Few Points Learned During the COVID-19 Pandemic. Therapeutic Innovation & Regulatory Science, 55(5), 984–988. https://doi.org/10.1007/s43441-021-00297-6
Ratitch, B., Bell, J., Mallinckrodt, C., Bartlett, J. W., Goel, N., Molenberghs, G., O’Kelly, M., Singh, P., & Lipkovich, I. (2020). Choosing Estimands in Clinical Trials: Putting the ICH E9(R1) Into Practice. Therapeutic Innovation & Regulatory Science, 54(2), 324–341. https://doi.org/10.1007/s43441-019-00061-x
Redfors, B., Gregson, J., Crowley, A., McAndrew, T., Ben-Yehuda, O., Stone, G. W., & Pocock, S. J. (2020). The win ratio approach for composite endpoints: practical guidance based on previous experience. European Heart Journal, 41(46), 4391–4399. https://doi.org/10.1093/eurheartj/ehaa665
Royston, P., & Parmar, M. K. B. (2011). The use of restricted mean survival time to estimate the treatment effect in randomized clinical trials when the proportional hazards assumption is in doubt. Statistics in Medicine, 30(19), 2409–2421. https://doi.org/10.1002/sim.4274
Schmidli, H., Roger, J. H., & Akacha, M. (2023a). Estimands for Recurrent Event Endpoints in the Presence of a Terminal Event. Statistics in Biopharmaceutical Research, 15(2), 238–248. https://doi.org/10.1080/19466315.2021.1895883
Schmidli, H., Roger, J. H., & Akacha, M. (2023b). Rejoinder to Commentaries on Estimands for Recurrent Event Endpoints in the Presence of a Terminal Event. Statistics in Biopharmaceutical Research, 15(2), 255–256. https://doi.org/10.1080/19466315.2023.2166098
Seifu, Y., Mt-Isa, S., Duke, K., Gamalo-Siebers, M., Wang, W., Dong, G., & Kolassa, J. (2022). Design of paediatric trials with benefit-risk endpoints using a composite score of adverse events of interest (AEI) and win-statistics. Journal of Biopharmaceutical Statistics, 33(6), 696–707. https://doi.org/10.1080/10543406.2022.2153202
Song, J., Verbeeck, J., Huang, B., Hoaglin, D. C., Gamalo-Siebers, M., Seifu, Y., Wang, D., Cooner, F., & Dong, G. (2022). The win odds: statistical inference and regression. Journal of Biopharmaceutical Statistics, 33(2), 140–150. https://doi.org/10.1080/10543406.2022.2089156
Tian, L., Jin, H., Uno, H., Lu, Y., Huang, B., Anderson, K. M., & Wei, L. (2020). On the empirical choice of the time window for restricted mean survival time. Biometrics, 76(4), 1157–1166. https://doi.org/10.1111/biom.13237
Troendle, J. F., Leifer, E. S., Yang, S., Jeffries, N., Kim, D.-Y., Joo, J., & O’Connor, C. M. (2024). Use of win time for ordered composite endpoints in clinical trials. Statistics in Medicine, 43(10), 1920–1932. https://doi.org/10.1002/sim.10045
Tsiatis, A. A., Davidian, M., Zhang, M., & Lu, X. (2008). Covariate adjustment for two-sample treatment comparisons in randomized clinical trials: A principled yet flexible approach. Statistics in Medicine, 27(23), 4658–4677. https://doi.org/10.1002/sim.3113
Uno, H., & Horiguchi, M. (2023). Ratio and difference of average hazard with survival weight: New measures to quantify survival benefit of new therapy. Statistics in Medicine, 42(7), 936–952. https://doi.org/10.1002/sim.9651
Verbeeck, J., De Backer, M., Verwerft, J., Salvaggio, S., Valgimigli, M., Vranckx, P., Buyse, M., & Brunner, E. (2023). Generalized Pairwise Comparisons to Assess Treatment Effects. Journal of the American College of Cardiology, 82(13), 1360–1372. https://doi.org/10.1016/j.jacc.2023.06.047
Wang, B., Susukida, R., Mojtabai, R., Amin-Esmaeili, M., & Rosenblum, M. (2021). Model-Robust Inference for Clinical Trials that Improve Precision by Stratified Randomization and Covariate Adjustment. Journal of the American Statistical Association, 118(542), 1152–1163. https://doi.org/10.1080/01621459.2021.1981338
Wang, B., Zhou, D., Zhang, J., Kim, Y., Chen, L.-W., Dunnmon, P., Bai, S., Liu, Q., & Ishida, E. (2023). Statistical power considerations in the use of win ratio in cardiovascular outcome trials. Contemporary Clinical Trials, 124, 107040. https://doi.org/10.1016/j.cct.2022.107040
Wang, T., Li, Y., & Qu, Y. (2024). Restricted time win ratio: from estimands to estimation. Statistics in Biopharmaceutical Research, 1–18. https://doi.org/10.1080/19466315.2024.2332675
Wang, T., & Mao, L. (2022). Stratified proportional win-fractions regression analysis. Statistics in Medicine, 41(26), 5305–5318. https://doi.org/10.1002/sim.9570
Wang, T., Zilinskas, R., Li, Y., & Qu, Y. (2023). Missing Data Imputation for a Multivariate Outcome of Mixed Variable Types. Statistics in Biopharmaceutical Research, 15(4), 826–837. https://doi.org/10.1080/19466315.2023.2169753
Wei, J., Mütze, T., Jahn-Eimermacher, A., & Roger, J. (2023). Properties of Two While-Alive Estimands for Recurrent Events and Their Potential Estimators. Statistics in Biopharmaceutical Research, 15(2), 257–267. https://doi.org/10.1080/19466315.2021.1994457
Wu, P., Han, Y., Chen, T., & Tu, X. M. (2013). Causal inference for Mann-Whitney-Wilcoxon rank sum and other nonparametric statistics. Statistics in Medicine, 33(8), 1261–1271. https://doi.org/10.1002/sim.6026
Yang, S., & Troendle, J. (2020). Event-specific win ratios and testing with terminal and non-terminal events. Clinical Trials, 18(2), 180–187. https://doi.org/10.1177/1740774520972408
Yang, S., Troendle, J., Pak, D., & Leifer, E. (2022). Event-specific win ratios for inference with terminal and non-terminal events. Statistics in Medicine, 41(7), 1225–1241. https://doi.org/10.1002/sim.9266
Ye, T., Shao, J., Yi, Y., & Zhao, Q. (2023). Toward Better Practice of Covariate Adjustment in Analyzing Randomized Clinical Trials. Journal of the American Statistical Association, 118(544), 2370–2382. https://doi.org/10.1080/01621459.2022.2049278
Yu, R. X., & Ganju, J. (2022). Sample size formula for a win ratio endpoint. Statistics in Medicine, 41(6), 950–963. https://doi.org/10.1002/sim.9297
Zhou, T. J., LaValley, M. P., Nelson, K. P., Cabral, H. J., & Massaro, J. M. (2022). Calculating power for the Finkelstein and Schoenfeld test statistic for a composite endpoint with two components. Statistics in Medicine, 41(17), 3321–3335. https://doi.org/10.1002/sim.9419
Zinman, B., Wanner, C., Lachin, J. M., Fitchett, D., Bluhmki, E., Hantel, S., Mattheus, M., Devins, T., Johansen, O. E., Woerle, H. J., Broedl, U. C., & Inzucchi, S. E. (2015). Empagliflozin, Cardiovascular Outcomes, and Mortality in Type 2 Diabetes. New England Journal of Medicine, 373(22), 2117–2128. https://doi.org/10.1056/nejmoa1504720