Joint Modeling of Longitudinal and Cure-Survival Data

Abstract

This article presents semiparametric joint models to analyze longitudinal measurements and survival data with a cure fraction. We consider a broad class of transformations for the cure-survival model, which includes the popular proportional hazards structure and the proportional odds structure as special cases. We propose to estimate all the parameters using the nonparametric maximum likelihood estimators (NPMLE). We provide the simple and efficient EM algorithms to implement the proposed inference procedure. Asymptotic properties of the estimators are shown to be asymptotically normal and semiparametrically efficient. Finally, we demonstrate the good performance of the method through extensive simulation studies and a real-data application.

Inclusion of Time-Varying Covariates in Cure Survival Models with an Application in Fertility Studies

“…() and Kim et al . () developed joint models for longitudinal and cure survival data in the context of the promotion time model. Brown and Ibrahim () proposed a longitudinal model for the immunologic response to vaccination over time, specified the latent hazard as a function of the trajectory of the immunologic marker and modelled the probability of observing the monitored event by using baseline covariates only.…”

“…() and Kim et al . () suggested that the (continuous) longitudinal biomarker has an effect on the probability of being cured only through the random effect of the longitudinal model.…”

“…Brown and Ibrahim (2003) proposed a longitudinal model for the immunologic response to vaccination over time, specified the latent hazard as a function of the trajectory of the immunologic marker and modelled the probability of observing the monitored event by using baseline covariates only. Chen et al (2004) and Kim et al (2013) suggested that the (continuous) longitudinal biomarker has an effect on the probability of being cured only through the random effect of the longitudinal model.…”

A novel approach to estimate the Cox model with temporal covariates and application to medical cost data

“…Our procedure is based on joint modelling the longitudinal process that generates the time-dependent covariates and the time to event. The topic of joint model has been widely discussed (Henderson et al (2000); Song et al (2002); Hsieh et al (2006); Ye et al (2008); Rizopoulos (2011); Kim et al (2013); Lawrence Gould et al (2015)). A comprehensive review is also available in Tsiatis and Davidian (2004); Sousa (2011);Ibrahim et al (2010).…”

Vertical modeling: analysis of competing risks data with a cure fraction

“…In the analysis of single outcome survival data with a cured fraction, cure models address the problem of cure rate estimation, as well as the estimation of the probability of failure due to the disease of interest. They have received a lot of attention both in terms of methodological developments Farewell (1986); Sy and Taylor (2000); Li and Taylor (2002); Yu et al (2004); Kim et al (2013) and applications Andersson et al (2011); Andrae et al (2012). These cure models are mixture models which specify a conditional model for the survival component, given that failure may occur, and a marginal distribution of the binary indicator for whether or not cure can occur.…”