A Bayesian analysis of doubly censored data using a hierarchical Cox model

Abstract

Two common statistical problems in pooling survival data from several studies are addressed. The first problem is that the data are doubly censored in that the origin is interval censored and the endpoint event may be right censored. Two approaches to incorporate the uncertainty of interval-censored origins are developed, and then compared with more usual analyses using imputation of a single fixed value for each origin. The second problem is that the data are collected from multiple studies and it is likely that heterogeneity exists among the study populations. A random-effects hierarchical Cox proportional hazards model is therefore used. The scientific problem motivating this work is a pooled survival analysis of data sets from three studies to examine the effect of GB virus type C (GBV-C) coinfection on survival of HIV-infected individuals. The time of HIV infection is the origin and for each subject this time is unknown, but is known to lie later than the last time at which the subject was known to be HIV negative, and earlier than the first time the subject was known to be HIV positive. The use of an approximate Bayesian approach using the partial likelihood as the likelihood is recommended because it more appropriately incorporates the uncertainty of interval-censored HIV infection times.

Imputation methods for doubly censored HIV data

“…The bootstrap inference procedure is recommended, however, since the computational demand with imputation methods is not excessive. Zhang et al [30] propose a Bayesian approach to analyse doubly censored data by making a parametric assumption for the interval-censored origin and treating it as an unknown quantity. This approach could be used as an alternative to the bootstrap inference procedure.…”

A flexible semiparametric modeling approach for doubly censored data with an application to prostate cancer

“…Moreover, Zhang et al 20 also proposed another imputation method for doubly censored data under the PH model. Assuming that the terminating event S is right-censored, Sun et al 15 and Zhang et al 21 have developed new modeling strategies. In the Bayesian analysis framework, Komarek et al 22,23 considered frailty versions of the PH model and accelerated failure time (AFT) models, respectively.…”

A Bayesian MCMC approach to survival analysis with doubly-censored data

“…The Bayesian Markov chain Monte Carlo (MCMC) method is an alternative to the full likelihood method and is especially appropriate for doubly-censored data. Kneib (2006) proposed additive and geoadditive regression models for interval-censored data and Zhang et al (2008) used a hierarchical Cox model for doubly censored data from multiple studies.…”