Analysis of clinical trials with delayed treatment effects

For biological reasons, there are often significant differences between the time a treatment is administered and a measurable clinical response is observed. Understanding the delayed effect is of great practical importance. Although there is a growing body of literature criticizing the wide-spread practice of ignoring the delayed treatment effect, and although multiple statistical methods that would take such effects into account have been proposed when comparing two treatments on time to response, there is little in terms of a consistent evaluation of current methods.;We evaluate the applicability of the log-rank test, weighted log-rank test and proportional hazards (PH) regression to the problem of comparing an experimental treatment to a control with respect to time to delayed beneficial effect. For PH, anticipated treatment effect is modeled as a time-dependent covariate. As another approach to test the null hypothesis H0: no differences between survival curves, we propose a new permutation test based on comparing difference in the area under survival curves. Since area under survival curves corresponds to mean survival time, this method allows testing null hypothesis and allows measuring the treatment effect as difference in mean survival times.;Using large-scale simulations we find that the proportional hazard model treatment effect modeled as a time-dependent covariate has numerous benefits as compared to log-rank test in testing the null hypothesis in the presence of delayed effect: it performs best in terms of power, does not inflate Type I error, and allows easy addition of important prognostic covariates. In addition, it allows measuring the treatment effect as a hazard ratio. However, application of this method requires knowledge of expected time to delay to benefit. Based on simulation, we evaluate impact on hazard ratio, power and alpha of the test and analyze situations where the delayed time is mis-specified. Applying the analysis to a recent renal cell carcinoma (RCC) study, we illustrate the proposed methods. This leads to the practical recommendation that for the late stage clinical trials the use of the proportional hazard model with treatment effect modeled as time-dependent covariate is both feasible and accurate. However, we conclude that in earlier stages of clinical trials the effort should be made to scientifically evaluate the presence of delayed effect and the time to delay. In summary, we provide a thorough overview of existing tests that take the delay effect into account and also evaluate a new test to yield insight into this important problem.