Comparing the survival of two groups with an intermediate clinical event

Consider a subject entered on a clinical trial in which the major endpoint is a time metric such as death or time to reach a well defined event. During the observational period the subject may experience an intermediate clinical event. The intermediate clinical event may induce a change in the survival distribution. We consider models for the one and two sample problem. The model for the one sample problem enables one to test if the occurrence of the intermediate event changed the survival distribution. This models provides a way of carrying out non-randomized clinical trial to determine if a therapy has benefit. The two sample problem considers testing if the probability distributions, with and without an intermediate event, are the same. Statistical tests are derived using a semi-Markov or a time dependent mixture model. Simulation studies are carried out to compare these new procedures with the log rank, stratified log rank and landmark tests. The new tests appear to have uniformly greater power than these competitor tests. The methods are applied to a randomized clinical trial carried out by the Aids Clinical Trial Group (ACTG) which compared low versus high doses of zidovudine (AZT).