Incorporating delayed entry into the joint frailty model for recurrent events and a terminal event

TL;DR

This paper introduces a method to estimate joint frailty models for recurrent and terminal events with delayed entry, addressing left-truncated data in survival analysis.

Contribution

It extends joint frailty modeling to account for delayed entry, providing a way to handle left-truncated data in recurrent event studies.

Findings

Method accurately estimates rates in simulations.

Application to urinary tract infections and mortality data.

Adjusts for dependent censoring due to delayed entry.

Abstract

In studies of recurrent events, joint modeling approaches are often needed to allow for potential dependent censoring by a terminal event such as death. Joint frailty models for recurrent events and death with an additional dependence parameter have been studied for cases in which individuals are observed from the start of the event processes. However, the samples are often selected at a later time, which results in delayed entry. Thus, only individuals who have not yet experienced the terminal event will be included in the study. We propose a method for estimating the joint frailty model from such left-truncated data. The frailty distribution among the selected survivors differs from the frailty distribution in the underlying population if the recurrence process and the terminal event are associated. The correctly adjusted marginal likelihood can be expressed as a ratio of two integrals over the frailty distribution, which may be approximated using Gaussian quadrature. The baseline rates are specified as piecewise constant functions, and the covariates are assumed to have multiplicative effects on the event rates. We assess the performance of the estimation procedure in a simulation study, and apply the method to estimate age-specific rates of recurrent urinary tract infections and mortality in an older population.