A Flexible Analytical Framework for Reference-Based Imputation, Delta Adjustment and Tipping-Point Stress-Testing

Abstract

This article addresses the challenge of implementing the treatment policy strategy when subjects are not followed up after treatment discontinuation. This problem can be addressed using reference-based imputation, delta adjustment, and tipping-point analysis. Our new framework tackles this problem analytically. We characterize the process that measures the response regardless of drug discontinuation, Z(t), using its association with two observable processes: time to drug dropout , and the variable representing the response in a hypothetical world without drug discontinuation Y(t). We define the intervention discontinuation effect (IDE) as the unobservable process that quantifies the difference between Y(t) and Z(t) after . We express various well-known imputation rules as forms of the IDE. We model Y using mixed models and with the Royston-Parmar model. We build estimators for the marginal mean of Z given the estimated parameters for Y and T. We demonstrate that this simple estimator building suits all studied rules and provide guidance to extend this methodology. With the proposed framework, we can analytically resolve a broad range of imputation rules and have right-censored treatment discontinuation. This methodology is more efficient and computationally faster than multiple imputation and, unlike Rubin’s variance estimator, presents no standard error over-estimation.