Assessing heterogeneity of treatment effect in a clinical trial with the proportional interactions model

Understanding how individuals vary in their response to treatment is an important task of clinical research. For standard regression models, a proportional interactions model first described by Follmann and Proschan (1999) offers a powerful approach for identifying effect modification in a randomized clinical trial when multiple variables influence treatment response. In this paper, we present a framework for using the proportional interactions model in the context of a parallel-arm clinical trial with multiple prespecified candidate effect modifiers. To protect against model misspecification, we propose a selection strategy that considers all possible proportional interactions models. We develop a modified Bonferroni correction for multiple testing that accounts for the positive correlation among candidate models. We describe methods for constructing a confidence interval for the proportionality parameter. In simulation studies, we show that our modified Bonferroni adjustment controls familywise error and has greater power to detect proportional interactions compared with multiplcity-corrected subgroup analyses. We demonstrate our methodology by using the Studies of Left Ventricular Dysfunction Treatment trial, a placebo-controlled randomized clinical trial of the efficacy of enalapril to reduce the risk of death or hospitalization in chronic heart failure patients. An R package called anoint is available for implementing the proportional interactions methodology.