Longitudinal clinical trials with adaptive choice of follow-up time.

In longitudinal studies comparing two treatments with a maximum follow-up time there may be interest in examining treatment effects for intermediate follow-up times. One motivation may be to identify the time period with greatest treatment difference when there is a non-monotone treatment effect over time; another motivation may be to make the trial more efficient in terms of time to reach a decision on whether a new treatment is efficacious or not. Here, we test the composite null hypothesis of no difference at any follow-up time versus the alternative that there is a difference at at least one follow-up time. The methods are applicable when a few measurements are taken over time, such as in early longitudinal trials or in ancillary studies. Suppose the test statistic Z(t(k)) will be used to test the hypothesis of no treatment effect at a fixed follow-up time t(k). In this context a common approach is to perform a pilot study on N1 subjects, and evaluate the treatment effect at the fixed time points t1,…,t(K) and choose t* as the value of t(k) for which Z(t(k)) is maximized. Having chosen t* a second trial can be designed. In a setting with group sequential testing we consider several adaptive alternatives to this approach that treat the pilot and second trial as a seamless, combined entity and evaluate Type I error and power characteristics. The adaptive designs we consider typically have improved power over the common, separate trial approach.