Maximum type I error rate inflation from sample size reassessment when investigators are blind to treatment labels

Abstract

Consider a parallel group trial for the comparison of an experimental treatment to a control, where the second-stage sample size may depend on the blinded primary endpoint data as well as on additional blinded data from a secondary endpoint. For the setting of normally distributed endpoints, we demonstrate that this may lead to an inflation of the type I error rate if the null hypothesis holds for the primary but not the secondary endpoint. We derive upper bounds for the inflation of the type I error rate, both for trials that employ random allocation and for those that use block randomization. We illustrate the worst-case sample size reassessment rule in a case study. For both randomization strategies, the maximum type I error rate increases with the effect size in the secondary endpoint and the correlation between endpoints. The maximum inflation increases with smaller block sizes if information on the block size is used in the reassessment rule. Based on our findings, we do not question the well-established use of blinded sample size reassessment methods with nuisance parameter estimates computed from the blinded interim data of the primary endpoint. However, we demonstrate that the type I error rate control of these methods relies on the application of specific, binding, pre-planned and fully algorithmic sample size reassessment rules and does not extend to general or unplanned sample size adjustments based on blinded data. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Keywords: adaptive clinical trials; blinded interim analysis; block randomization; random allocation; sample size reassessment; type I error rate control.

Figure 1

Comparing the asymptotic results with MCMC output for an example data set.

Figure 2

Maximum type I error rate as a function of the secondary endpoint effect size with and without restrictions for the second stage sample size. Here, the first stage sample size n ₁=144 and σ = 1. (Black) solid lines denote unrestricted results, and (red) dashed lines results for restricted case with $n_2^{\min }=n_1/2$ and $n_2^{\max }=4n_1$. ρ∈{0,0.5,0.8,0.9,1} and the larger the ρ the thicker the line.

Figure 3

Maximum type I error rate without restrictions for the second stage sample size and for blocked randomization with block sizes 2, 4, 6 and the unblocked design (n ₁=144,ρ = 0,σ = 1, and 2.5·10⁵ (2·10⁵) simulation runs for block size 2 (4, 6, unblocked design)).