Abstract

Although longitudinal and survival data are collected in the same study, they are usually analyzed separately. Measurement errors and missing data problems arise because of separate analysis of these two data. Therefore, joint model should be used instead of separate analysis. The standard joint model frequently used in the literature is obtained by combining the linear mixed effect model of longitudinal data and Cox regression model with survival data. Nevertheless, to use the Cox regression model for survival data, the assumption of proportional hazards must be provided. Parametric survival sub-models should be used instead of the Cox regression model for the survival sub-model of the JM where the assumption is not provided. In this article, parametric joint modeling of longitudinal data and survival data that do not provide the assumption of proportional hazards are investigated. For the survival data, the model with Exponential, Weibull, Log-normal, Log-logistic, and Gamma accelerated failure time models and the linear mixed effect model are combined with random effects and the models were applied in primary biliary cirrhosis data set obtained from Mayo Clinic. After determining the best parametric joint model according to Akaike and Bayesian information criterions, the best available model was compared with standard joint model and of separate analysis of survival data and longitudinal data. As a results, in the studies where longitudinal and survival data are obtained together, it is seen that the parametric joint model gives more better results than the standard joint model when the proportional hazard assumption is not provided.

Highlights

  • The joint model (JM) is used to investigate the relationship between longitudinal and survival data and the effects of longitudinal data on survival

  • The standard joint model (JM), which is frequently used in the literature, is obtained by combining the linear mixed effect model of longitudinal measurement, and Cox regression model of survival data

  • Survival and longitudinal data obtained in the same study should be analyzed by JM in case there is a relationship between them

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Summary

Introduction

The JM is used to investigate the relationship between longitudinal and survival data and the effects of longitudinal data on survival. The standard joint model (JM), which is frequently used in the literature, is obtained by combining the linear mixed effect model of longitudinal measurement (longitudinal sub-model), and Cox regression model of survival data (survival sub-model). In studies where survival data for which this assumption is not provided, and longitudinal observation, parametric survival sub-models should be used for the survival sub-model of the JM. The JM was developed for the unbiased and effective estimates of the relationship between longitudinal and survival data after 1990s. JM was first applied in 1992 by Self and Pawitan to obtain the JM parameter estimates of the linear mixed effect (LME) model for longitudinal data and Cox regression model for survival data (Self and Pawitan, 1992)

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