Bayesian Semiparametric Dynamic Frailty Models for Multiple Event Time Data

Abstract

Many biomedical studies collect data on times of occurrence for a health event that can occur repeatedly, such as infection, hospitalization, recurrence of disease, or tumor onset. To analyze such data, it is necessary to account for within-subject dependency in the multiple event times. Motivated by data from studies of palpable tumors, this article proposes a dynamic frailty model and Bayesian semiparametric approach to inference. The widely used shared frailty proportional hazards model is generalized to allow subject-specific frailties to change dynamically with age while also accommodating nonproportional hazards. Parametric assumptions on the frailty distribution are avoided by using Dirichlet process priors for a shared frailty and for multiplicative innovations on this frailty. By centering the semiparametric model on a conditionally conjugate dynamic gamma model, we facilitate posterior computation and lack-of-fit assessments of the parametric model. Our proposed method is demonstrated using data from a cancer chemoprevention study.

Looking for a needle in a haystack: inference about individual fitness components in a heterogeneous population

“…1) Because survival, breeding, and success events were accounted for by a first‐order Markov process, Tuljapurkar et al (2009) and Steiner et al (2010) called the resulting heterogeneity among life histories ‘dynamic heterogeneity’: heterogeneity caused by the stochastic movement of individuals among homo geneous strata in a population stratified according to a small number of observable criteria. 2) This observable ‘dynamic heterogeneity’ should be distinguished from ‘dynamic frailty’ of the statistical, medical and economical literature (Yue and Chan 1997, Pennel and Dunson 2005), which corresponds to models with individual‐specific parameters (unobserved heterogeneity) that change over life. 3) Alternatively, variation among individual life histories can be accounted for by models incorporating unobserved heterogeneity among individuals where the baseline individual vital rate doesn't change after birth or recruitment (depending on the type of data used): fixed heterogeneity (Link and Barker 2009).…”

Bayesian nonparametric functional data analysis through density estimation

“…Most extensions of the Dirichlet process achieve dependence either by forming convex combinations of independent processes (Müller et al, 2004; Dunson, 2006; Pennell & Dunson, 2006; Dunson et al, 2007), or by introducing dependence in the elements of the stick-breaking representation of the distribution (MacEachern, 1999; Teh et al, 2006; DeIorio et al, 2004; Gelfand et al, 2005; Griffin & Steel, 2006; Rodriguez et al, 2008). For example, given a set D , let {η (t), t ∈ D } and { z (t) , t ∈ D } be stochastic processes on D such that z (t) ~ Be {1, α( t )} for all t ∈ D and define $$H_t(·)={\displaystyle \sum _{l=1}^{\infty }{w}_l^{*}(t){\delta }_{{\eta }_l^{*}(t)}(·),}$$ where ${\{{\eta }_l^{*}(t)\}}_{l=1}^{\infty }\text{and}{\{z_l^{*}(t)\}}_{l=1}^{\infty }$ are collections of independent realizations of the stochastic processes {η( t ) ∈ D } and { z ( t ), t ∈ D }, and $w_l^{*}(t)=z_l^{*}(t){\displaystyle {\prod }_{s=1}^{l-1}\{1-z_s^{*}}(t)\}$.…”

Bayesian local influence for survival models

“…Ibrahim et al (2001) give a comprehensive review of Bayesian survival analysis methods up to 2001 and we refer the reader to their book for more details. More recent work includes methods for multivariate survival data (Dunson and Dinse 2002; Yin and Ibrahim 2005a), mixtures of Polya tree priors for accelerated failure time models (Hanson and Johnson 2002), order restricted Bayesian survival analysis (Dunson and Herring 2003; Chen and Dunson 2004), Bayesian model selection and model averaging in survival analysis (Dunson and Herring 2005), methods for missing data in survival models (Chen et al 2002b, 2006; Ibrahim et al 2008), Bayesian transformation survival models (Yin and Ibrahim 2005b), cure rate models (Kim et al 2009; Yin and Ibrahim 2005c,d; Cooner et al 2007; Chen et al 2002a,b,c), methods for recurrent events and panel count data (Sinha et al 2008; Sinha and Maiti 2004), additive hazards models (Sinha et al 2009), dynamic frailty models for multivariate survival data (Pennell and Dunson 2006), and dependent Dirichlet process models for survival data (De Iorio et al 2009). Although not specifically mentioned in their papers, applications of kernel stick-breaking processes (Dunson and Park 2008) and nested Dirichlet processes (Rodriguez et al 2008) to models for survival data are also potentially promising.…”