Efficient Estimation For The Joint Model of Survival and Longitudinal Data

TL;DR

This paper introduces an efficient profile likelihood method for estimating parameters in joint models of survival and longitudinal data, demonstrating asymptotic normality and semi-parametric efficiency of the estimators.

Contribution

It develops a profile likelihood approach for joint survival and longitudinal models, providing explicit variance estimation and proving estimator efficiency.

Findings

Establishes asymptotic normality of the profile likelihood estimator.

Derives explicit variance estimator for the joint model parameters.

Shows the estimators are semi-parametric efficient.

Abstract

In survival studies it is important to record the values of key longitudinal covariates until the occurrence of event of a subject. For this reason, it is essential to study the association between longitudinal and time-to-event outcomes using the joint model. In this paper, profile likelihood approach has been used to estimate the cumulative hazard and regression parameters from the joint model of survival and longitudinal data. Moreover, we show the asymptotic normality of the profile likelihood estimator via asymptotic expansion of the profile likelihood and obtain the explicit form of the variance estimator. The estimators of the regression parameters from the joint model are shown to be semi-parametric efficient.