Sequentially randomized designs are becoming common in biomedical research, particularlyin clinical trials. These trials are usually designed to evaluate and compare the effect ofdifferent treatment regimes. In such designs, eligible patients are first randomly assignedto receive one of the initial treatments. Patients meeting some criteria (e.g. no progressive diseases) are then randomized to receive one of the maintenance treatments. Usually, the procedure continues until all treatment options are exhausted. Such multistage treatment assignment results in dynamic treatment regimes consisting of initial treatment, intermediate response and second stage treatment. However, methods for effcient analysis of sequentially randomized trials have only been developed very recently. As a result, earlier clinical trials reported results based only on the comparison of stage-specific treatments.We first propose to use accelerated failure time and proportional hazards models for estimating the effects of treatment regimes from sequentially randomized designs. Based onthe proposed models, differences between treatment regimes in terms of their hazards aretested. We investigate the properties of these methods and tests in a Monte Carlo simulationstudy. Finally the proposed models are applied to the long-term outcome of the high riskneuroblastoma study.We then extend the proportional hazards model to a generalized Cox proportional hazards model that applies to comparisons of any combination of any number of treatment regimes regardless of the number of stages of treatment. Contrasts of dynamic treatment regimes are tested using the Wald chi-square method. Both the model and Wald chi-square tests of contrasts are illustrated through a simulation study and an application to a high risk neuroblastoma study to complement the earlier results reported on this study.Chronic diseases such as cancer and cardiovascular diseases are major causes of mortality and morbidity in the United States and in the world. Sequentially randomized designs arecommonly used in clinical studies investigating treatments of chronic diseases such as cancer,AIDS, and depression. The public health significance of the methodologies proposed in thisresearch is to allow efficient analysis of data from such studies and thereby enhance thediscovery of efficient maintenance and eradication strategies for chronic diseases
