An Instrumental Variable Approach to Learning the Causal Exposure–Response Relationship in a Randomized Dose Comparison Trial

Abstract

We consider the problem of estimating the causal effect of drug exposure on clinical response in a randomized dose comparison trial where each group receives a different dose. Because exposure is not randomized, the exposure–response relationship is subject to confounding in this setting. Conventional statistical methods for confounding adjustment with a continuous exposure typically assume that there are no unmeasured confounders. This article provides an instrumental variable approach that does not require the assumption of no unmeasured confounders. Specifically, we use randomized dose assignment as an instrumental variable and characterize the causal exposure–response relationship using a control variable under a mild monotonicity assumption on individual dose–exposure profiles. Based on this characterization, we derive partial identification bounds for the causal exposure–response relationship, which are model-free but may be too wide to be useful in practice. For practicality, we further develop a simple estimation method based on a regression model for the mean response conditional on exposure and the control variable. Simulation results show that, in the presence of unmeasured confounding, the model-based estimation method reduces estimation bias effectively at the expense of increased variability, as compared to existing methods. The method is illustrated with real data from a study of chimeric antigen receptor T cell therapy for treating chronic lymphocytic leukemia.