The recently proposed proportional win-fractions (PW) model extends the two-sample win ratio analysis of prioritized composite endpoints to regression. Its proportionality assumption ensures that the covariate-specific win ratios are invariant to the follow-up time. However, this assumption is strong and may not be satisfied by every covariate in the model. We develop a stratified PW model that adjusts for certain prognostic factors without setting them as covariates, thus bypassing the proportionality requirement. We formulate the stratified model based on pairwise comparisons within each stratum, with a common win ratio across strata modeled as a multiplicative function of the covariates. Correspondingly, we construct an estimating function for the regression coefficients in the form of an incomplete -statistic consisting of within-stratum pairs. Two types of asymptotic variance estimators are developed depending on the number of strata relative to the sample size. This in particular allows valid inference even when the strata are extremely small, such as with matched pairs. Simulation studies in realistic settings show that the stratified model outperforms the unstratified version in robustness and efficiency. Finally, real data from a major cardiovascular trial are analyzed to illustrate the potential benefits of stratification. The proposed methods are implemented in the R package WR, publicly available on the Comprehensive R Archive Network (CRAN).
Trial registration: ClinicalTrials.gov NCT02787044.
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© 2022 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.