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.

中文翻译：

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SMIM：使用多重插补和鞅的生存敏感性分析的统一框架

截尾生存数据在临床试验研究中很常见。我们提出了一个统一的敏感性分析框架，用于使用多重插补和鞅随机审查生存数据，称为 SMIM。所提出的框架采用 δ 调整和基于控制的模型，以灵敏度参数为索引，需要随机审查和广泛的审查而不是随机假设。此外，它还针对一大类治疗效果估计值，定义为特定治疗生存函数的函数，同时考虑到由于审查导致的缺失数据。多重插补有助于使用简单的全样本估计；然而，标准鲁宾的组合规则可能高估了敏感性分析框架中推理的方差。我们基于估计器的顺序构造将多重插补估计器分解为一个鞅序列，并通过对鞅序列进行重采样提出了野引导推理。新的自举推理从理论上保证了一致性，并且与非参数自举推理相比计算效率更高。我们通过模拟和在 HIV 临床试验中的应用来评估所提出的 SMIM 的有限样本性能。