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In multi‐season clinical trials with a randomize‐once strategy, patients enrolled from previous seasons who stay alive and remain in the study will be treated according to the initial randomization in subsequent seasons. To address the potentially selective attrition from earlier seasons for the non‐randomized cohorts, we develop an inverse probability of treatment weighting method using season‐specific propensity scores to produce unbiased estimates of survival functions or hazard ratios. Bootstrap variance estimators are used to account for the randomness in the estimated weights and the potential correlations in repeated events within each patient from season to season. Simulation studies show that the weighting procedure and bootstrap variance estimator provide unbiased estimates and valid inferences in Kaplan‐Meier estimates and Cox proportional hazard models. Finally, data from the INVESTED trial are analyzed to illustrate the proposed method. 

Summary A general framework is set up to study the asymptotic properties of the intent-to-treat Wilcoxon–Mann–Whitney test in randomized experiments with nonignorable noncompliance. Under location-shift alternatives, the Pitman efficiencies of the intent-to-treat Wilcoxon–Mann–Whitney and $$t$$ tests are derived. It is shown that the former is superior if the compliers are more likely to be found in high-density regions of the outcome distribution or, equivalently, if the noncompliers tend to reside in the tails. By logical extension, the relative efficiency of the two tests is sharply bounded by least and most favourable scenarios in which the compliers are segregated into regions of lowest and highest density, respectively. Such bounds can be derived analytically as a function of the compliance rate for common location families such as Gaussian, Laplace, logistic and $$t$$ distributions. These results can help empirical researchers choose the more efficient test for existing data, and calculate sample size for future trials in anticipation of noncompliance. Results for nonadditive alternatives and other tests follow along similar lines.