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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 δ‐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 a broad class of treatment effect estimands defined as functionals of treatment‐specific survival functions, taking into account 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 nonparametric bootstrap counterpart. We evaluate the finite‐sample performance of the proposed SMIM through simulation and an application on an HIV clinical trial.
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This content will become publicly available on June 15, 2025
Distributional imputation for the analysis of censored recurrent events
Longitudinal clinical trials for which recurrent events endpoints are of interest are commonly subject to missing event data. Primary analyses in such trials are often performed assuming events are missing at random, and sensitivity analyses are necessary to assess robustness of primary analysis conclusions to missing data assumptions. Control‐based imputation is an attractive approach in superiority trials for imposing conservative assumptions on how data may be missing not at random. A popular approach to implementing control‐based assumptions for recurrent events is multiple imputation (MI), but Rubin's variance estimator is often biased for the true sampling variability of the point estimator in the control‐based setting. We propose distributional imputation (DI) with corresponding wild bootstrap variance estimation procedure for control‐based sensitivity analyses of recurrent events. We apply control‐based DI to a type I diabetes trial. In the application and simulation studies, DI produced more reasonable standard error estimates than MI with Rubin's combining rules in control‐based sensitivity analyses of recurrent events.
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- Award ID(s):
- 2242776
- PAR ID:
- 10511449
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Statistics in Medicine
- Volume:
- 43
- Issue:
- 13
- ISSN:
- 0277-6715
- Page Range / eLocation ID:
- 2622 to 2640
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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