Sample size re-estimation in a superiority clinical trial using a hybrid classical and Bayesian procedure

When designing studies involving a continuous endpoint, the hypothesized difference in means ( ${\theta }_A$ ) and the assumed variability of the endpoint ( ${\sigma }^2$ ) play an important role in sample size and power calculations. Traditional methods of sample size re-estimation often update one or both of these parameters using statistics observed from an internal pilot study. However, the uncertainty in these estimates is rarely addressed. We propose a hybrid classical and Bayesian method to formally integrate prior beliefs about the study parameters and the results observed from an internal pilot study into the sample size re-estimation of a two-stage study design. The proposed method is based on a measure of power called conditional expected power (CEP), which averages the traditional power curve using the prior distributions of θ and ${\sigma }^2$ as the averaging weight, conditional on the presence of a positive treatment effect. The proposed sample size re-estimation procedure finds the second stage per-group sample size necessary to achieve the desired level of conditional expected interim power, an updated CEP calculation that conditions on the observed first-stage results. The CEP re-estimation method retains the assumption that the parameters are not known with certainty at an interim point in the trial. Notional scenarios are evaluated to compare the behavior of the proposed method of sample size re-estimation to three traditional methods.