Sample Size Determination for Survival Studies

Abstract

Deciding how many subjects to include in a randomized clinical trial is a key component of its design. In the classical hypothesis testing framework, for any type of outcome, one must specify the effect change one is aiming for, the inherent variability in the test statistic, the significance level of the test, and the desired power of the test to detect the effect change. In survival analysis, there are additional factors that one must specify regarding the censoring mechanism and the particular survival distributions in the null and alternative hypotheses. First, one needs either to specify what parametric survival model one is using, or that the test will be semi-parametric, e.g., the log-rank test. This allows for determining the number of deaths (or events) required to meet the power and other design specifications. Second, one must, for administrative reasons, provide an estimate of the number of patients that need to be entered into the trial to produce the required number of deaths. We shall assume that the clinical trial is run as described in Chap. 1, where patients enter a trial over a certain accrual period of length a, and then followed for an additional period of time f known as the follow-up time. Patients still alive at the end of follow-up are censored. We will describe sample size methods for single arm clinical trials and then for two arm clinical trials.