Blinded Sample Size Recalculation for Normally Distributed Outcomes Using Long‐ and Short‐term Data

Abstract

Clinical trials are often planned with high uncertainty about the variance of the primary outcome variable. A poor estimate of the variance, however, may lead to an over-or underpowered study. In the internal pilot study design, the sample variance is calculated at an interim step and the sample size can be adjusted if necessary. The available recalculation procedures use the data of those patients for sample size recalculation that have already completed the study. In this article, we consider a variance estimator that takes into account both the data at the endpoint and at an intermediate point of the treatment phase. We derive asymptotic properties of this estimator and the relating sample size recalculation procedure. In a simulation study, the performance of the proposed approach is evaluated and compared with the procedure that uses only long-term data. Simulation results demonstrate that the sample size resulting from the proposed procedure shows in general a smaller variability. At the same time, the Type I error rate is not inflated and the achieved power is close to the desired value.

Sample Size Recalculation in Internal Pilot Study Designs: A Review

“…; i ¼ 1; 2; are normally distributed with mean m Y;i and unknown common variance s 2 Y . Using maximum likelihood estimation techniques, the following result can be obtained (see Wçst and Kieser (2003) for more details). Note that estimation is based upon the data merged over the two treatment groups without identifying the treatment assignments.…”

“…The approach makes use only of the fact that the short-and long-term outcome may be correlated but does not assume that the association can be characterised by a specific model. The method was given by Wçst and Kieser (2003) who also proposed a related procedure for binary endpoints (Wçst and Kieser, 2005). Maschner and Becker (2001) and Galbraith and Maschner (2003) described an analogous approach for interim analyses in group sequential trials.…”

“…For example, for a correlation of q ¼ 0:8 between short-and long-term outcome, which is not uncommon in clinical trial applications, the reduction amounts to about 41 per cent times the fraction of patients with short-but no long-term information from those with short-term outcome data. A conjuncture for a formula describing the asymptotic variance reduction in the general situation of arbitrary D X and D Y is given without a proof in Wçst and Kieser (2003).…”

“…As both the correlation and h are increasing when the measurement visit of the short-term data is moved towards the end of the follow-up, the question arises as to how to choose an ''optimal" intermediate point for which the maximum variance reduction can be achieved. Some considerations on this topic are given in Wçst and Kieser (2003).…”

“…In Monte Carlo simulations, Wçst and Kieser (2003) investigated the accuracy of the asymptotic variance reduction forŝ s 2 X LS for finite sample sizes. They showed that the asymptotic result holds true for a wide range of parameters and that deviations from this approximation occur only for very small sample sizes of the internal pilot study.…”