Determine the cause of bootstrap undercoverage

Determine the cause of the modest undercoverage observed for the 95% percentile bootstrap intervals of the withdrawal-referenced and treat-through durable-response contrasts, including the possible roles of plug-in bias, log-odds-scale skewness, finite-sample percentile-interval behavior, and Monte Carlo error from the inner bootstrap.

Background

The paper evaluates the full re-randomization-probability weighting and population-adjustment procedure through repeated finite-sample simulations and two-trial bootstrap intervals. Although the bootstrap standard errors track the empirical standard errors closely, coverage falls below the nominal 95% level for the withdrawal-referenced log-odds contrast and the comparison involving the treat-through trial, with reported coverages of 91.8% and 91.5%, respectively.

The authors list several plausible explanations—plug-in bias, skewness on the log-odds scale, ordinary finite-sample behavior of percentile intervals, and Monte Carlo error caused by using only 200 inner bootstrap draws—but explicitly state that the underlying cause has not been isolated. Establishing which mechanisms are responsible would clarify the reliability and appropriate implementation of the proposed interval procedure.