Sequential analysis of censored survival data from three treatment groups

In this paper, we propose a simple means of designing and analyzing a sequential procedure for comparing survival data from three treatments with the goal of eventually identifying the best treatment. Our procedure consists of the concatenation of two sequential tests, as is suggested by Siegmund (1993, Annals of Statistics 21, 464-483) for instantaneous normal responses. The first sequential test is a global test that attempts to detect an overall treatment effect. If one is found, the least promising treatment is eliminated and a second sequential test attempts to identify the better of the two remaining treatments. Although there are three different information time scales to consider corresponding to each pairwise comparison, we show that under certain conditions they may be approximated by a single time scale. This enables us to gain insight into the problem of censored survival data from the more easily understood case of instantaneous normal data. Also, it eliminates the need for intensive computations and simulations for the design and analysis of the procedure.