A two-stage design for evaluating induction and maintenance therapies for a time to event endpoint

For chronic disease and oncology new drug developments, it is crucial to demonstrate whether the experimental drugs are effective induction therapies and maintenance therapies. Many designs have been proposed for trials with binary and continuous endpoints. For these endpoints, the evaluation of an induction therapy can be based on only the data of the induction phase. Nonetheless, for time to event endpoint (e.g., mortality) treatment may need time to manifest effect and the assessment of an induction therapy may need long-term data beyond data of only the induction phase. A two-stage re-randomized design has been advocated for time to event endpoint to address this in the literature. For this design, patients are initially randomized to one of two induction therapies. Then induction responders are re-randomized to one of the two maintenance therapies. An inverse probability weighting approach is used for the analysis. To simplify trial operation, we propose the use of a one-randomization, two-stage and four-treatment-regimen design. As maintenance therapies are not administrated and have no effects during the induction phase, a time dependent covariate proportional hazards model is applied to data analysis. To increase power, a weighted combination test is used for overall between-treatment assessment. A multiple imputation tipping point sensitivity analysis is considered for handling informative censoring issue. Simulations are conducted to evaluate the performances of the methods, and an example is used to illustrate the applications of the methods.