Analysis of Covariance (ANCOVA) in Randomized Trials: More Precision and Valid Confidence Intervals, Without Model Assumptions

• Activity Number: 610 - Power, Sample Size, and Applications to Time-To-Event
• Type: Contributed
• Date/Time: Thursday, August 1, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Bingkai Wang* and Michael Rosenblum and Elizabeth Ogburn
• Companies: Johns Hopkins Bloomberg School of Public Health and Johns Hopkins Bloomberg School of Public Health and Johns Hopkins Bloomberg School of Public Health
• Keywords: Imbalance; Relative Efficiency; Robustness

Abstract

According to two surveys of clinical trial reports, there is confusion about the statistical properties of covariate adjustment. We focus on the ANCOVA estimator and trials with equal probability of assignment to treatment and control. We prove the following new robustness property of ANCOVA to arbitrary model misspecification: Not only is the ANCOVA point estimate consistent (as proved by Yang and Tsiatis (2001)) but so is its standard error. This implies that confidence intervals and hypothesis tests conducted as if the linear model were correct are still valid even when the linear model is arbitrarily misspecified, e.g., when the baseline variables are nonlinearly related to the outcome or there is treatment effect heterogeneity. We also give a simple, robust formula for the variance reduction (equivalently, sample size reduction) from using ANCOVA. By re-analyzing completed randomized trials for mild cognitive impairment, schizophrenia, and depression, we demonstrate how ANCOVA can achieve variance reductions of 4% to 32% and increase power even by chance there is perfect balance across arms in the baseline variables.