The correlated and shared gamma frailty model for bivariate current status data: An illustration for cross‐sectional serological data

Abstract

SUMMARYFrailty models are often used to study the individual heterogeneity in multivariate survival analysis. Whereas the shared frailty model is widely applied, the correlated frailty model has gained attention because it elevates the restriction of unobserved factors to act similar within clusters. Estimating frailty models is not straightforward due to various types of censoring. In this paper, we study the behavior of the bivariate-correlated gamma frailty model for type I interval-censored data, better known as current status data. We show that applying a shared rather than a correlated frailty model to cross-sectionally collected serological data on hepatitis A and B leads to biased estimates for the baseline hazard and variance parameters.

Estimating the force of infection for HCV in injecting drug users using interval-censored data

“…The frailty could be shared when one latent variable is considered per individual or correlated when a joint latent distribution for both infections is assumed. An illustration of the use of shared frailty models on current status data for hepatitis B and C has been reported [10] ; and also for hepatitis B and C and HIV infection in [11] and for hepatitis A and B with correlated frailties [27].…”

Parametric Overdispersed Frailty Models for Current Status Data

“…A flexible alternative to these distributions is the Gompertz distribution encompassing both monotonic increasing and decreasing hazards. The Gompertz distribution has been used by Hens et al (2009) to analyse the serological data introduced in Section 2. The Gompertz model T * ijk ∼ G (ξ i , ν i ) can be formulated as follows:…”

“…As individuals differ in social contact behaviour, susceptibility to infection and infectiousness upon infection, frailty models are of importance to quantify unobserved variability in the time to the acquisition of infections. Furthermore, the use of bivariate frailty models in infectious disease epidemiology was popularized by the seminal work of Farrington et al (2001) and the work by Hens et al (2009) on shared and correlated frailty models, respectively, applied to serological data on immunizing infections. Recently, several extensions have been proposed focusing on, but not limited to, recurrent infection processes (Abrams and Hens, 2015) and time-varying individual heterogeneity (Farrington et al, 2012;Unkel et al, 2014).…”

“…In addition to dependence among individual infection times, overdispersion can arise when the observed variability in the data exceeds the one implied by the model. In this article, we discuss parametric overdispersed frailty models for time-to-event data under Type I interval-censoring, building upon the work by Molenberghs et al (2010) and Hens et al (2009). The proposed methodology is illustrated using bivariate serological data on hepatitis A and B from Flanders, Belgium anno 1993-1994.…”

Statistical Analysis of Bivariate Current Status Data with Informative Censoring Using Frailty Effects

“…Dunson and Dinse (2002) considered informative censoring for multivariate current status data and developed a MCMC method under conditional independence using frailty effect. Chen et al (2009) and Hens et al (2009) applied a univariate frailty effect for multivariate current status data without death. In this paper, we extend the three state model to analyze bivariate current status data with informative censoring and assume the occurrence of two events are conditionally independent given a bivariate frailty.…”