Exemplary data: sample size and power in the design of event-time clinical trials

In planning a complex clinical trial with time to event as the outcome, it is difficult to derive the power of the test statistic analytically. In this paper we describe an algorithm for generating exemplary data from an alternative hypothesis that can be used to compute the expected value of a logrank test statistic and its power under that alternative. Exemplary data are nonrandomly computer-generated data that are constructed from a complex stochastic process and have desirable characteristics such as distributional moments similar to those of the process. An algorithm for generating exemplary timed events data is presented and its use in evaluating power for the planning of clinical trials demonstrated. These data represent "expectations" of outcome, data censoring, and censoring event times. A test statistic, z, such as the logrank can be computed from the data. It is distributed asymptotically, N(mu A, 1), under the alternative hypothesis and its value is used to estimate mu A and the power of the test for a given trial scenario. The results compare favorably to results from analytical methods and Monte Carlo simulations published in the literature. The advantages of the method lie in the degree of flexibility in study design, choice of models that describe the timing of events, and the range of testing methods that can be used. Although Monte Carlo methods may appear to have similar flexibility, the exemplary algorithm is more practical because only one data set need be analyzed and the modifications can be achieved without reprogramming.