Hypothesis Testing with Paired Partly Interval Censored Data

Partly interval censored data frequently occur in many areas including clinical trials, epidemiology research, and medical follow-up studies. When data come from observational studies, we need to carefully adjust for the confounding bias in order to estimate the true treatment effect. Pair matching designs are popular for removing confounding bias without parametric assumptions. With time-to-event outcomes, there are some literature for hypothesis testing with paired right censored data, but not for interval censored data. O’Brien and Fleming extended the Prentice Wilcoxon test to right censored paired data by making use of the Prentice-Wilcoxon scores. Akritas proposed the Akritas test and established its asymptotic properties. We extend Akritas test to partly interval censored data. We estimate the survival distribution function by nonparametric maximum likelihood estimation (NPMLE), and prove the asymptotic validity of the new test. To improve our test under small sample size or extreme distributions, we also propose a modified version using the rank of the score difference. Simulation results indicate that our proposed methods have very good performance.