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

Keywords:

• Clinical trials
• Estimands
• Missing data

Supplementary Materials

1) Guidance to fit the Royston-Parmar model in SAS; 2) SAS script to fit the model of Section 4.1; 3) Simulations study: results by arm; 4) PREMIER dataset: estimated model parameters.

Acknowledgments

The authors thank the anonymous reviewers for their constructive comments. The authors also report there are no competing interests to declare.

Data Availability

SAS scripts are available as Supporting Materials. The PREMIER dataset is a property of the Biologic Specimen and Data Repositories Information Coordinating Center (BioLINCC) — an initiative of the National Heart, Lung, and Blood Institute (NHLBI). The authors are not allowed to release or distribute this database further and therefore refer to the PREMIER clinical trial website at BioLINCC (https://biolincc.nhlbi.nih.gov/studies/premier/).

Additional information

Funding

This work was partially supported by the Spanish Ministry of Science and Innovation under Grant PID2019-104681RBI00.