Comparing adaptive treatment strategies in two-stage randomized trials with grouped survival data.

Two-stage randomized trials, or the more general sequential multiple assignment randomized trials (SMART), have been increasingly used in studying adaptive treatment strategies for treating chronic diseases or conditions where treatments need to be adjusted during the treatment course. Methods for analyzing two-stage randomized trials with continuous, longitudinal or right-censored survival endpoints have been developed. However, no method exists for data analysis for two-stage randomized trials with grouped survival endpoints, which are frequently encountered in practice. In this article, we propose methods for analyzing grouped survival data from two-stage randomized trials. We first extend the methods in Prentice and Gloeckler (1978) to allow for patient missing pre-specified visits, and use an efficient score test to make inferences on treatment effects with grouped data in traditional randomized trials. Based on this, we propose a weighted efficient score test to compare two adaptive treatment strategies with grouped survival data in two-stage randomized trials with missing visits. Asymptotic properties are formulated, and simulation studies are conducted to evaluate the performances of the proposed methods. We also apply the weighted score test in analyzing data from the sequenced treatment alternatives to relieve depression (STAR*D) trial.