Modeling restricted mean survival time under general censoring mechanisms

Abstract

Restricted mean survival time (RMST) is often of great clinical interest in practice. Several existing methods involve explicitly projecting out patient-specific survival curves using parameters estimated through Cox regression. However, it would often be preferable to directly model the restricted mean for convenience and to yield more directly interpretable covariate effects. We propose generalized estimating equation methods to model RMST as a function of baseline covariates. The proposed methods avoid potentially problematic distributional assumptions pertaining to restricted survival time. Unlike existing methods, we allow censoring to depend on both baseline and time-dependent factors. Large sample properties of the proposed estimators are derived and simulation studies are conducted to assess their finite sample performance. We apply the proposed methods to model RMST in the absence of liver transplantation among end-stage liver disease patients. This analysis requires accommodation for dependent censoring since pre-transplant mortality is dependently censored by the receipt of a liver transplant.

Keywords: Dependent censoring; Generalized linear model; Inverse weighting; Pre-treatment survival; Restricted mean lifetime; Transplantation.

Fig. 1

Bias of [β_D0, β_D1, β_D2, β_D3]′ when censoring models are mis-specified

Fig. 2

Bias comparison between our and Tian’s methods in presence of dependent censoring

Fig. 3

Fitted RMST (L = 36 months) by MELD score for a reference patient: white, male, age=50, Region=5, year=2005, not hospitalized, not on dialysis, blood Type=O, BMI ∈ (20, 25], sodium=130