Designed Extension of Studies Based on Conditional Power

Abstract

We propose a flexible method of extending a study based on conditional power. The possibility for extension when the p value at the planned end is small but not statistically significant is built in to the design of the study. The significance of the treatment difference at the planned end is used to determine the number of additional observations needed and the critical value necessary for use after accruing those additional observations. It may therefore be thought of as a two-stage procedure. Even though the observed treatment difference at stage 1 is used to make decisions, the Type I error rate is protected.

Maximum inflation of the type 1 error rate when sample size and allocation rate are adapted in a pre‐planned interim look

“…Large differences between the solutions are only found for very low and very large values of r (1) . The case of r (1) = 0 is discussed in Section 5 below.…”

“…Note that in this region I the maximization of the conditional error in (1) with r (1) ≠ 1 leads to the same solution since for and or and the conditional error function does not depend on r (1) .…”

“…This is the only part of the sample space where the calculations differ for different values of the first stage allocation rate r (1) . For example, the boundary for early rejection changes to and is not anymore symmetric around in this area.…”

“…For example, the boundary for early rejection changes to and is not anymore symmetric around in this area. Figure 2 shows for varying values of r (1) and different α.…”

“…Adaptive combination tests (see [2], [3], [4], [5]) and tests based on the conditional error function (see [1], [6], [7]) have been proposed which allow for such interim design modifications without inflating the type 1 error rate. For a short review of sample size reestimation in clinical trials see e.g.…”