Hierarchical likelihood approach for the Weibull frailty model

Abstract

In this article, the proportional hazard model with Weibull frailty, which is outside the range of the exponential family, is used for analysing the right-censored longitudinal survival data. Complex multidimensional integrals are avoided by using hierarchical likelihood to estimate the regression parameters and to predict the realizations of random effects. The adjusted profile hierarchical likelihood is adopted to estimate the parameters in frailty distribution, during which the first-and second-order methods are used. The simulation studies indicate that the regression-parameter estimates in the Weibull frailty model are accurate, which is similar to the gamma frailty and lognormal frailty models. Two published data sets are used for illustration.

Survival Analysis of Premature Infants Admitted to Neonatal Int ensive Care Unit (NICU) in Northwest Ethiopia using Semi-Parametric Fr ailty Model

“…Model comparison and selection are among the most common problems of statistical practice, with numerous procedures for choosing among a set of models proposed in the literature [16][17][18][19][20][21], for recent reviews. Most selection methods are defined in terms of an appropriate information criterion, a mechanism that uses data to give each candidate model a certain score; this then leads to a fully ranked list of candidate models, from the best to the worst.…”

Mixed Models of Non-Proportional Hazard and Application in The Open Distance Education Students Retention Data

“…The estimation method used in the SEF model is hierarchical likelihood. The SEF model estimation method adopts the hierarchical probability (H-likelihood) introduced by Ha et al [24], Noh et al [42], Lee et al [34], Wang et al [59], Ha et al [28] and Christian et al [12] with frailty with normal log distribution. The hierarchical likelihood function is expressed as:…”