SMIM: a unified framework of Survival sensitivity analysis using Multiple Imputation and Martingale

TL;DR

This paper introduces SMIM, a comprehensive framework for sensitivity analysis of censored survival data using multiple imputation and martingale methods, accommodating various assumptions about censoring mechanisms.

Contribution

The paper develops a unified approach combining multiple imputation and martingale techniques for sensitivity analysis in survival data, with a novel bootstrap inference method.

Findings

SMIM effectively handles a broad class of censoring assumptions.

The wild bootstrap provides consistent and efficient inference.

Simulation and HIV trial data demonstrate SMIM's practical utility.

Abstract

Censored survival data are common in clinical trial studies. We propose a unified framework for sensitivity analysis to censoring at random in survival data using multiple imputation and martingale, called SMIM. The proposed framework adopts the \delta-adjusted and control-based models, indexed by the sensitivity parameter, entailing censoring at random and a wide collection of censoring not at random assumptions. Also, it targets for a broad class of treatment effect estimands defined as functionals of treatment-specific survival functions, taking into account of missing data due to censoring. Multiple imputation facilitates the use of simple full-sample estimation; however, the standard Rubin's combining rule may overestimate the variance for inference in the sensitivity analysis framework. We decompose the multiple imputation estimator into a martingale series based on the sequential construction of the estimator and propose the wild bootstrap inference by resampling the martingale series. The new bootstrap inference has a theoretical guarantee for consistency and is computationally efficient compared to the non-parametric bootstrap counterpart. We evaluate the finite-sample performance of the proposed SMIM through simulation and an application on a HIV clinical trial.