Restricted mean survival time as a function of restriction time

Abstract

Restricted mean survival time (RMST) is a clinically interpretable and meaningful survival metric that has gained popularity in recent years. Several methods are available for regression modeling of RMST, most based on pseudo-observations or what is essentially an inverse-weighted complete-case analysis. No existing RMST regression method allows for the covariate effects to be expressed as functions over time. This is a considerable limitation, in light of the many hazard regression methods that do accommodate such effects. To address this void in the literature, we propose RMST methods that permit estimating time-varying effects. In particular, we propose an inference framework for directly modeling RMST as a continuous function of L. Large-sample properties are derived. Simulation studies are performed to evaluate the performance of the methods in finite sample sizes. The proposed framework is applied to kidney transplant data obtained from the Scientific Registry of Transplant Recipients (SRTR).

Restricted mean survival time regression model with time‐dependent covariates

“…The existence of extreme values may lead to weights that are too large or too small, leading to extreme values of the regression coefficients and their variances, resulting in the stability of the predicted RMST values; however, the weights can be stabilized by setting an appropriate $$$ \tau $$$ . 10 In addition, the T‐RMST model is not capable of processing endogenous time‐dependent covariates, but the dynamic RMST model can do this 29 . Also, the choice of $$$ \tau $$$ requires careful consideration.…”

“…According to Tian 11 and Zhong, 10 we have $$$ \sqrt{n}\left(\hat{\boldsymbol{\eta}}\hbox{-} \boldsymbol{\eta} \right)\sim N\left(0,{\boldsymbol{A}}^{-1}{\boldsymbol{BA}}^{-1}\right) $$$; therefore, $$$ \hat{V}\left(\hat{\boldsymbol{\eta}}\right)={\hat{\boldsymbol{A}}}^{-1}{\hat{\boldsymbol{B}}\hat{\boldsymbol{A}}}^{-1} $$$, where $$$$ \hat{\boldsymbol{A}}=E\left[{\boldsymbol{Z}}_i{\left({t}_i\right)}^{\otimes 2}{\dot{g}}^{-1}\left({\hat{\boldsymbol{\eta}}}^T{\boldsymbol{Z}}_i\left({t}_i\right)\right)\right], $$$$ $$$$ \hat{\boldsymbol{B}}=E\left[{\boldsymbol{\varepsilon}}_i{\left(\hat{\boldsymbol{\eta}}\right)}^{\otimes 2}\right], $$$$ …”

“…Authors, including Kerrison, 6 Zucker, 7 Chen, 8 and Zhang, 9 all use different regression models based on hazards to indirectly estimate the RMST. However, this method is computationally intensive and cumbersome; it relies on the proportional hazard assumption through the use of the Cox model, which, if untrue, can lead to bias 10 . Hence, several authors have suggested direct methods to model the RMST itself, which mainly include the ANCOVA‐type method, pseudo‐observation type method, and inverse probability weight (IPW)‐type method 4 .…”

“…However, this method is computationally intensive and cumbersome; it relies on the proportional hazard assumption through the use of the Cox model, which, if untrue, can lead to bias. 10 Hence, several authors have suggested direct methods to model the RMST itself, which mainly include the ANCOVA-type method, pseudo-observation type method, and inverse probability weight (IPW)-type method. 4 Tian's ANCOVA-type method 11 constructed estimating equations for the RMST based on the inverse probability of censoring weighting (IPCW), and the weight function was the inverse of the Kaplan-Meier estimator.…”

Clustered restricted mean survival time regression

“…Theorem 1 is an extension of Zhong and Schaubel (2022) from independent and identically distributed (i.i.d.) survival data to clustered survival data.…”