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

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 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 over estimate 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

Doubly robust estimators for generalizing treatment effects on survival outcomes from randomized controlled trials to a target population

“…Alternatively, we define the average treatment effect (ATE) measure θ τ as a function of treatmentspecific survival curves, θ τ = Ψ τ (S 1 (t), S 0 (t)) where τ is a pre-specified constant. This formulation of the ATE includes a broad class of estimands that are favored in survival analysis (Yang et al, 2020). For example, θ τ = S 1 (τ ) − S 0 (τ ) is a simple survival difference at a fixed time τ , and…”

“…Similar to Yang et al (2020), we consider an asymptotic linear characterization of the ATE estimator θ ACW τ = Ψ τ S ACW 1 (t), S ACW 0 (t) for both ACW1 and ACW2 estimators. That is, under mild regularity conditions,…”

“…Let S a (t) be a estimator of a treatment-specific survival curve S a (t) such that S a (t) − S a (t) = o p (N −1/2 ) for a ∈ {0, 1}. Following Yang et al (2020), under mild regularity conditions, all survival estimands mentioned in the main paper have the following asymptotic linear characterizations,…”