Sample size calculation for studies with grouped survival data

Grouped survival data arise often in studies where the disease status is assessed at regular visits to clinic. The time to the event of interest can only be determined to be between two adjacent visits or is right censored at one visit. In data analysis, replacing the survival time with the endpoint or midpoint of the grouping interval leads to biased estimators of the effect size in group comparisons. Prentice and Gloeckler developed a maximum likelihood estimator for the proportional hazards model with grouped survival data and the method has been widely applied. Previous work on sample size calculation for designing studies with grouped data is based on either the exponential distribution assumption or the approximation of variance under the alternative with variance under the null. Motivated by studies in HIV trials, cancer trials and in vitro experiments to study drug toxicity, we develop a sample size formula for studies with grouped survival endpoints that use the method of Prentice and Gloeckler for comparing two arms under the proportional hazards assumption. We do not impose any distributional assumptions, nor do we use any approximation of variance of the test statistic. The sample size formula only requires estimates of the hazard ratio and survival probabilities of the event time of interest and the censoring time at the endpoints of the grouping intervals for one of the two arms. The formula is shown to perform well in a simulation study and its application is illustrated in the three motivating examples.