Sizing clinical trials with variable endpoint event rates.

Although many researchers in cardiovascular clinical trials have disciplined themselves to execute sample size calculations in the design of their studies, these computations become difficult in the presence of control group endpoint event rate uncertainty. Recent experience in cardiovascular clinical trials suggests that, although one may know the control group event rate during the design phase of the trial, it can decrease during the trial's execution. Its resultant overestimation can lead to a power reduction with serious consequences for the trial's interpretation. Although the investigators may acknowledge the likelihood that the control group event rate will decrease during the time course of the trial, there is no formal means to adjust the design phase estimate. In this paper, I first formulate the sample size as a function of the control group event rate theta and then I place a proper probability distribution on theta, allowing for the uncertainty in this parameter's value during the course of the study. From this assumption, the sample size itself becomes a random variable, whose expectation and variance are computed. I explore the implications for sample size for various reasonable proper probability distributions on the control group event rate.