Analysis of interval censored survival data in sequential multiple assignment randomized trials

Data analysis methods have been well developed for analyzing data to make inferences about adaptive treatment strategies in sequential multiple assignment randomized trials (SMART), when data are continuous or right-censored. However, in some clinical studies, time-to-event outcomes are interval censored, meaning that, for example, the time of interest is only observed between two random visit times to the clinic, which is common in some areas such as psychology studies. In this case, the appropriate analysis methods in SMART studies have not been considered in the literature. This article tries to fill this gap by developing methods for this purpose. Based on a proportional hazards model, we propose to use a weighted spline-based sieve maximum likelihood method to make inference about the group differences using a Wald test. Asymptotic properties of the estimator for the hazard ratio are derived, and variance estimation is considered. We conduct a simulation to assess its finite sample performance, and then analyze data from the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) trial.