Evaluating the Impact of Outcome Delay on the Efficiency of Sample Size Re-Estimation

Sample size re-estimation (SSR) can be a powerful tool to ensure that a clinical trial meets its pre-specified power requirements when uncertainty regarding a design parameter exists at the planning stage. However, long-term primary endpoints can be harmful to the efficiency of this trial design. If recruitment is continued while treatment outcomes are awaited, long delays can potentially lead to a large number of 'pipeline' participants being recruited in the trial that do not contribute to the interim analysis. This may lead to a larger number of recruited participants than are actually deemed required, resulting in an over-powered trial with high cost. This paper studies the exact impact of such outcome delay on the efficiency of 'internal pilot' type SSR designs. The distribution of the final sample size post SSR is obtained under various delay lengths for both continuous and binary outcome data; how delay impacts the precision of the final sample size estimate is then discussed. Precisely, the impact of delay on this precision is assessed through RMSE, as well as two more novel metrics, termed the delay impact and cost. The results indicate that with an increase in delay length, the delay impact increases, inflating average sample size and power. However, the severity of the effect of delayed outcomes depends highly on the exact trial setting. Trials where the re-estimated sample size is smaller than originally planned suffer the most from delayed outcomes, often leading to an over-powered trial. However, the impact of delay is substantially less if the originally planned sample size remains smaller than the re-estimated sample size.