Design and analysis of group sequential logrank tests in maximum duration versus information trials

When monitoring a clinical trial with failure time data using the logrank test and the type I error spending function approach, the information time has to be estimated as a fraction of the maximum number of failures. In maximum duration trials, the denominator of this fraction is a random quantity and has to be estimated; besides, there are two candidates for the denominator, one under the null hypothesis of no treatment difference and the other under the specified alternative hypothesis. Either way, some adjustments are necessary in determining group sequential boundaries in order to maintain type I error at a desired significance level. As a consequence, the type I error spending function will be altered from the one chosen for the design, thus affecting the operating characteristics of the subsequent group sequential logrank tests. In maximum information trials, however, the maximum amount of information is fixed, and thus the estimate of the information time is always unbiased. The net effect is that computation of group sequential boundaries becomes straightforward, with a potential saving in study durations as compared to maximum duration trials. We will illustrate how adjustments are made in maximum duration trials to maintain type I error when the information times are estimated with the information horizons under the null and alternative hypotheses and present numerical explorations to compare robustness of two different estimates of the information times. We then propose a design procedure for maximum information trials and investigate the properties of maximum information trials for different group sequential boundaries. We also compare maximum information trials and maximum duration trials based on an example.