Mid‐course sample size modification in clinical trials based on the observed treatment effect

Abstract

It is not uncommon to set the sample size in a clinical trial to attain specified power at a value for the treatment effect deemed likely by the experimenters, even though a smaller treatment effect would still be clinically important. Recent papers have addressed the situation where such a study produces only weak evidence of a positive treatment effect at an interim stage and the organizers wish to modify the design in order to increase the power to detect a smaller treatment effect than originally expected. Raising the power at a small treatment effect usually leads to considerably higher power than was first specified at the original alternative. Several authors have proposed methods which are not based on sufficient statistics of the data after the adaptive redesign of the trial. We discuss these proposals and show in an example how the same objectives can be met while maintaining the sufficiency principle, as long as the eventuality that the treatment effect may be small is considered at the design stage. The group sequential designs we suggest are quite standard in many ways but unusual in that they place emphasis on reducing the expected sample size at a parameter value under which extremely high power is to be achieved. Comparisons of power and expected sample size show that our proposed methods can out-perform L. Fisher's 'variance spending' procedure. Although the flexibility to redesign an experiment in mid-course may be appealing, the cost in terms of the number of observations needed to correct an initial design may be substantial.

Adaptive and nonadaptive group sequential tests

“…t o under which it may be decided later that higher power is desirable. In our experience, adaptations which make a noticeable change to a test's power curve are liable to introduce inefficiency at least as great as that seen in our two examples and often much larger; see Jennison & Turnbull (2003) for an example of a two-stage adaptive design with much higher efficiency loss. In the following sections we complement this empirical evidence with theory and numerical evaluation of optimal tests within well-defined adaptive and non-adaptive classes.…”

“…More recently, Cui et al (1999), L. D. Fisher (1998), Shen & Fisher (1999) and Müller & Schäfer (2001), among others, have proposed a variety of methods that preserve the type I error rate despite completely unplanned design changes. Although differing in appearance and derivation, these methods are closely related in that each preserves the conditional type I error probability whenever the design is modified; Jennison & Turnbull (2003) prove this must be the case for any unplanned re-design that preserves the overall type I error rate.…”

“…2.3) raises questions both about the statistical efficiency of the experimental designs and the credibility results will have when reported to a wider audience. In an analysis of selected examples, Jennison & Turnbull (2003) show that adaptive sampling rules can be highly inefficient in comparison with standard group sequential tests. Tsiatis & Mehta (2003) give a formal proof that any adaptive test using a non-sufficient statistic can be out-performed by a sequential test using the sufficient statistic;…”

Choosing inclusion criteria that minimize the time and cost of clinical trials

“…Adaptive sample size reestimation avoids these pitfalls and can reduce the expected sample size, and in turn the cost of the study, under a range of treatment effects. Protocols and procedures for re-specification of sample size are well described in the literature [4,[17][18][19][20][21] . This type of adaptive design can arguably reduce time and cost, but does not specifically deal with optimizing inclusion/exclusion criteria.…”

A 25‐year review of sequential methodology in clinical studies

“…Statistics in Medicine has published articles on the subject throughout the 25 years of the journal. In the early years, the emphasis was perhaps more on the application of techniques described elsewhere (for example [11][12][13][14]), but more recently the focus has shifted, with authors submitting more methodological manuscripts to the journal (for example [15][16][17][18]). …”