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.
Missing data is inevitable in longitudinal clinical trials. Conventionally, the missing at random assumption is assumed to handle missingness, which however is unverifiable empirically. Thus, sensitivity analyses are critically important to assess the robustness of the study conclusions against untestable assumptions. Toward this end, regulatory agencies and the pharmaceutical industry use sensitivity models such as return-to-baseline, control-based, and washout imputation, following the ICH E9(R1) guidance. Multiple imputation is popular in sensitivity analyses; however, it may be inefficient and result in an unsatisfying interval estimation by Rubin’s combining rule. We propose distributional imputation in sensitivity analysis, which imputes each missing value by samples from its target imputation model given the observed data. Drawn on the idea of Monte Carlo integration, the distributional imputation estimator solves the mean estimating equations of the imputed dataset. It is fully efficient with theoretical guarantees. Moreover, we propose weighted bootstrap to obtain a consistent variance estimator, taking into account the variabilities due to model parameter estimation and target parameter estimation. The superiority of the distributional imputation framework is validated in the simulation study and an antidepressant longitudinal clinical trial.
more » « less- NSF-PAR ID:
- 10379076
- Publisher / Repository:
- SAGE Publications
- Date Published:
- Journal Name:
- Statistical Methods in Medical Research
- Volume:
- 32
- Issue:
- 1
- ISSN:
- 0962-2802
- Format(s):
- Medium: X Size: p. 181-194
- Size(s):
- ["p. 181-194"]
- Sponsoring Org:
- National Science Foundation
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