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

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 (Formula presented.), 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 (Formula presented.). We express various well-known imputation rules as forms of the IDE. We model Y using mixed models and (Formula presented.) with the Royston-Parmar model. We build estimators for the marginal mean of Z given the estimated parameters for Y and T (Formula presented.). 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.