Quantitative Decision Under Unequal Covariances and Post-Treatment Variances: A Kidney Disease Application

Abstract

Proof-of-concept (PoC) trials enable sponsors decide whether to continue or discontinue a compound’s development based on preliminary evidence of safety and efficacy. Many accounts exist on using quantitative approaches for this decision. Still, these accounts are devoid of quantitative decisions under unequal covariances and post-treatment variances for continuous endpoints. Filling this void is important because randomization to treatment groups only guarantees equal variances before treatment initiation. In this article, I show how unequal covariances and post-treatment variances affect the consider zone when using a three-outcome frequentist decision framework. Results herein suggest that the consider zone decreases with increase in correlation between baseline and post-baseline measurements for any sample size. Compared to decrease in consider zone under equal covariances and post-treatment variances, decrease in consider zone was greater under unequal covariances and post-treatment variances. The results suggest that ignoring a baseline covariate correlated with an outcome robs the study team of an opportunity to effectively minimize uncertain decision in PoC trial scoped to support quantitative decisions. Used for illustration is design of a PoC trial in kidney disease.