Bayesian Inference in a Joint Model for Longitudinal and Time to Event Data with Gompertz Baseline Hazards

Abstract

Longitudinal and time to event data are frequently encountered in many medical studies. Clinicians are more interested in how longitudinal outcomes influences the time to an event of i nterest. To study the association between longitudinal and time to event data, joint modeling approaches were found to be the most appropriate techniques for such data. The approaches involves the choice of the distribution of the survival times which in most cases authors prefer either exponential or Weibull distribution. However, these distributions have some shortcomings. In this paper, we propose an alternative joint model approach under Bayesian prospective. We assumed that survival times follow a Gompertz distribution. One of the advantages of Gompertz distribution is that its cumulative distribution function has a closed form solution and it accommodates time varying covariates. A Bayesian approach through Gibbs sampling procedure was developed for parameter estimation and inferences. We evaluate the finite samples performance of the joint model through an extensive simulation study and apply the model to a real dataset to determine the association between markers(tumor sizes) and time to death among cancer patients without recurrence. Our analysis suggested that the proposed joint modeling approach perform well in terms of parameter estimations when correlation between random intercepts and slopes is considered.

A Semiparametric Bayesian Joint Modelling of Skewed Longitudinal and Competing Risks Failure Time Data: With Application to Chronic Kidney Disease

“…See, for example, Refs. [2][3][4][5][6][7][8] among others. The most popular submodels proposed in the joint modelling method include mixed-effects submodels e.g., [6,9] for longitudinal data, a Cox regression submodel [4] or a Weibull survival submodel [6,9] for time-to-event data.…”

“…Furthermore, various parameterization (association structure) approaches have been utilized in the literature to formulate joint models and evaluate the association between time-toevent(s) and longitudinal outcome(s) processes. These include current value parameterization; see, e.g., [7,23,[34][35][36][37], shared random-effects parameterization [8,10,12,21,22,26], a special type of shared random-effects parameterization with associated fixed parameters of timedependent covariates [38][39][40][41], and correlated random-effects parameterization [42][43][44]. The choice of the association structure, however, may also need careful consideration because the statistical results from various parametrizations may differ.…”