Optimal timing for interim analyses in clinical trials

In clinical trials, interim analyses are often performed before the completion of the trial. The intention is to possibly terminate the trial early or adjust the sample size. The time of conducting an interim analysis affects the probability of the early termination and the number of subjects enrolled until the interim analysis. This influences the expected total number of subjects. In this study, we examine the optimal time for conducting interim analyses with a view to minimizing the expected total sample size. It is found that regardless of the effect size, the optimal time of one interim analysis for the early termination is approximately two-thirds of the planned observations for the O'Brien-Fleming type of spending function and approximately half of the planned observations for the Pocock type when the subject enrollment is halted for the interim analysis. When the subject enrollment is continuous throughout the trial, the optimal time for the interim analysis varies according to the follow-up duration. We also consider the time for one interim analysis including the sample size adjustment in terms of minimizing the expected total sample size.