Bayesian Accelerated Failure Time Model With Multivariate Doubly Interval-Censored Data and Flexible Distributional Assumptions

Abstract

A Bayesian approach is proposed for an accelerated failure time model with interval-censored data. The model allows for structured correlated data by inclusion of a random effect part that might depend on covariates, as in a linear mixed model. The error distribution is modelled as a normal mixture with an unknown number of components. Also, the means and variances of the components are not prespecified so as to accommodate most continuous distributions. This results, among other things, in a nearly correct estimation of the shape of the hazard and survivor curves. A Markov chain Monte Carlo algorithm is described that samples from the posterior distribution. The approach is evaluated using a simulation study, and is illustrated by modeling the emergence times of eight permanent teeth using data from the Signal Tandmobiel study.

Accelerated failure time model for multivariate two-stage current-status data with parallel and longitudinal correlated random effects

“…Our approach is also compared to an existing method proposed by Komarek and Lesaffre (2008). The parametric AFT formulation in their Bayesian approach is very similar to that in our proposed model, and the estimation procedure for both of our methods mainly rely on the MCMC iterations.…”

“…Since Current-status data is a special case of interval censoring, the application is straightforward for most cases. (Komarek and Lesaffre, 2008) However, when both events have not happened by the time of each observation (I 1 = 0 and I 2 = 0), distinction needs to be made whether the first event has already happened or not by the time of the second observation. This is a very natural observation in a dental example, but not necessarily so in other cases when measurement of one event does not come along with measurement of the other event.…”

“…We were mainly concerned with the situation when observation is rather difficult or expensive, and only one observation is made for each event which results in the current-status data. With the exact same simulation setting of small sample size (n = 50), we applied the Bayesian AFT model in Komarek and Lesaffre (2008) using the R BayesSurv package. Since Current-status data is a special case of interval censoring, the application is straightforward for most cases.…”

“…Association between two subjects of the same cluster is captured by a semi-parametric bivariate error distribution, inspired by the penalized smoothing technique where the shape is partially driven by the data. Komarek and Lesaffre (2008) extended the discussion to a situation when the number of subjects within each cluster can be arbitrarily more than two. A shared random effect term is introduced to the AFT model for the association of the subjects in the same cluster, and a univariate version of the same smoothing technique is used for the random effect and error distribution.…”

Inferential Procedures for Log Logistic Distribution with Doubly Interval Censored Data

“…Authors who have contributed include Bacchetti (1990); Bacchetti & Jewell (1991); Kim, et al (1993); Jewell (1994); Jewell et al (1994); Gómez & Lagakos (1994); Sun (1995Sun ( , 1997; Tu (1995); Gómez & Calle (1999) ;Goggins, et al (1999) ;Sun, et al (1999); Fang & Sun (2001); Pan (2001); and Lim, et al (2002). The Bayesian approach has gained some attention in analysis of DIC data in recent years for severe acute respiratory syndrome (SARS) disease incubation time (McBryde, et al, 2006) and time to caries development in children (Komárek, et al, 2005;Komárek & Lesaffre, 2006, 2008Jara, et al, 2010). Brookmeyer & Goedart (1989) proposed a two-stage parametric regression model for jointly estimating the effects of covariates on risk of HIV infection as well as risk of progression to AIDS disease once infected.…”