Bayesian Semiparametric Frailty Selection in Multivariate Event Time Data

Abstract

Biomedical studies often collect multivariate event time data from multiple clusters (either subjects or groups) within each of which event times for individuals are correlated and the correlation may vary in different classes. In such survival analyses, heterogeneity among clusters for shared and specific classes can be accommodated by incorporating parametric frailty terms into the model. In this article, we propose a Bayesian approach to relax the parametric distribution assumption for shared and specific-class frailties by using a Dirichlet process prior while also allowing for the uncertainty of heterogeneity for different classes. Multiple cluster-specific frailty selections rely on variable selection-type mixture priors by applying mixtures of point masses at zero and inverse gamma distributions to the variance of log frailties. This selection allows frailties with zero variance to effectively drop out of the model. A reparameterization of log-frailty terms is performed to reduce the potential bias of fixed effects due to variation of the random distribution and dependence among the parameters resulting in easy interpretation and faster Markov chain Monte Carlo convergence. Simulated data examples and an application to a lung cancer clinical trial are used for illustration.

Evaluation of Estimation Methods and Power of Tests of Discrete Covariates in Repeated Time-to-Event Parametric Models: Application to Gaucher Patients Treated by Imiglucerase

“…The advantage of a full parametric model is that the clinical trial simulation can be performed. Various methods of estimation for parametric frailty models exist: the likelihood estimation using the Newton-Raphson algorithm, the expectation-maximization (EM) algorithm (10), the penalized likelihood method (11)(12)(13), or Bayesian methods (14). Liu et al (15) proposed a novel adaptive Gaussian quadrature (AGQ) which is implemented in PROC NLMIXED of SAS.…”

Bayesian variable selection under the proportional hazards mixed-effects model

“…From the point of view of model selection, it then depends on the criterion that is important to the question of concern according to which one chooses to model the random treatment effect or not. We also note that Cai (2010) analyzed this data set using Dirichlet process prior for the frailty distribution, and reached a conclusion that was somewhat a compromise between Dunson and Chen (2004) and Gray (1995).…”

Birnbaum–Saunders frailty regression models: Diagnostics and application to medical data

“…Fan and Li () considered variable selection in frailty models. Cai () analyzed Bayesian semiparametric frailty selection in multivariate event time data. Mazroui et al.…”

“…Fan and Li (2002) considered variable selection in frailty models. Cai (2010) analyzed Bayesian semiparametric frailty selection in multivariate event time data. Mazroui et al (2013) proposed a multivariate frailty model that jointly assumes two types of recurrent events with a dependent terminal event.…”