Regression modeling of restricted mean survival time for left-truncated right-censored data

Abstract

The restricted mean survival time (RMST) is a clinically meaningful summary measure in studies with survival outcomes. Statistical methods have been developed for regression analysis of RMST to investigate impacts of covariates on RMST, which is a useful alternative to the Cox regression analysis. However, existing methods for regression modeling of RMST are not applicable to left-truncated right-censored data that arise frequently in prevalent cohort studies, for which the sampling bias due to left truncation and informative censoring induced by the prevalent sampling scheme must be properly addressed. The pseudo-observation (PO) approach has been used in regression modeling of RMST for right-censored data and competing-risks data. For left-truncated right-censored data, we propose to directly model RMST as a function of baseline covariates based on POs under general censoring mechanisms. We adjust for the potential covariate-dependent censoring or dependent censoring by the inverse probability of censoring weighting method. We establish large sample properties of the proposed estimators and assess their finite sample performances by simulation studies under various scenarios. We apply the proposed methods to a prevalent cohort of women diagnosed with stage IV breast cancer identified from surveillance, epidemiology, and end results-medicare linked database.

Keywords: general censoring mechanisms; inverse probability of censoring weighting; left-truncated right-censored data; pseudo-observations; restricted mean survival time.

FIGURE 1

Product-limit estimator of survival function (left panel) and the nonparametric RMST estimator (right panel) by receipt of chemotherapy (chemo = 1, receiving chemotherapy; chemo = 0, not receiving chemotherapy)

FIGURE 2

Product-limit estimator of survival function (left panel) and the nonparametric RMST estimator (right panel) for patients by ER/PR status (ER/PR = 1, positive; ER/PR = 0, negative)

FIGURE 3

Estimated RMST during the next five years post diagnosis ($\tau$= 5 years) against the age at diagnosis using two link functions. “Ref” represents the reference patients without chemotherapy and negative ER/PR status, and “chemo&ER/PR” represents patients with chemotherapy and positive ER/PR status

FIGURE 4

Estimated RMST by the combination of receipt of chemotherapy, ER/PR status, and age at diagnosis, using the nonparametric method, multivariable regression model of RMST with the linear link, multivariable regression model of RMST with the log link, and integrated multivariable Cox model survival curve. n is the number of patients in each combination