Three influential design quantities on the power of Wald-type tests for treatment comparisons in clinical trials

Abstract

In clinical trials, efficient statistical inference is critical to the well-being of future patients. We therefore construct Wald-type tests for the hypothesis of treatment-by-covariate interaction when treatments are assigned to patients by an adaptive design and the true model is a generalized linear model. Our measure of efficiency is the power of the test while ethics of a trial or well-being of participating patients is measured by the success rate of treatments. We demonstrate that the power of the test depends on the target allocation proportion, the bias of the randomization procedure from the target, and the variability induced by the randomization process (design variability) for adaptive designs. We prove that these quantities influence the power when the trial involves two treatments and a single covariate. We also show that, in this case, as design variability decreases the power increases. Due to the complexity of the problem, we demonstrate by simulation that this result still holds when more than one covariate is present in the model. In simulation studies, we compare the measures of efficiency and ethics under response-adaptive (RA), covariate-adjusted responseadaptive (CARA), and completely randomized (CR) designs. The methods are applied to data from a clinical trial on stroke prevention in atrial fibrillation (SPAF).

Journal of Statistical Research 2022, Vol. 56, No. 1, pp. 11-36