Modeling left-truncated and right-censored survival data with longitudinal covariates

TL;DR

This paper develops a new statistical method to accurately analyze survival data with both left truncation and right censoring, incorporating longitudinal covariates, which are common in medical studies.

Contribution

It introduces an alternative likelihood approach that provides unbiased and efficient estimation of survival model parameters with complex truncation and longitudinal data.

Findings

The proposed method yields unbiased estimates in simulations.

It effectively handles biases caused by left truncation.

Application to AIDS data demonstrates practical utility.

Abstract

There is a surge in medical follow-up studies that include longitudinal covariates in the modeling of survival data. So far, the focus has been largely on right-censored survival data. We consider survival data that are subject to both left truncation and right censoring. Left truncation is well known to produce biased sample. The sampling bias issue has been resolved in the literature for the case which involves baseline or time-varying covariates that are observable. The problem remains open, however, for the important case where longitudinal covariates are present in survival models. A joint likelihood approach has been shown in the literature to provide an effective way to overcome those difficulties for right-censored data, but this approach faces substantial additional challenges in the presence of left truncation. Here we thus propose an alternative likelihood to overcome these difficulties and show that the regression coefficient in the survival component can be estimated unbiasedly and efficiently. Issues about the bias for the longitudinal component are discussed. The new approach is illustrated numerically through simulations and data from a multi-center AIDS cohort study.