Class Of Frailty Models Research Articles

Goodness-of-fit tests for the frailty distribution in proportional hazards models with shared frailty

Frailty models account for the clustering present in event time data. A proportional hazards model with shared frailties expresses the hazard for each subject. Often a one-parameter gamma distribution is assumed for the frailties. In this paper, we construct formal goodness-of-fit tests to test for gamma frailties. We construct a new class of frailty models that extend the gamma frailty model by using certain polynomial expansions that are orthogonal with respect to the gamma density. For this extended family, we obtain an explicit expression for the marginal likelihood of the data. The order selection test is based on finding the best fitting model in such a series of expanded models. A bootstrap is used to obtain p-values for the tests. Simulations and data examples illustrate the test's performance.

The Cox shared frailty model with log-skew-normal frailties

Clustered survival data arise when groups of failure times share a common ingredient; typically, they refer to the same individual or individuals with a common factor. When the association between failure times within the same cluster is of interest, statistical methods called frailty models have been used. The frailty is an unobserved random component which affects the risk level, changing from cluster to cluster but shared by all observations within the same cluster. Various probability distributions have been proposed for the frailty term, with special emphasis on the gamma and log-normal distribution. Since adequate modelling of the frailty distribution is essential to properly investigate the dependence structure, we introduce a new class of frailty models with a flexible distribution form. Specifically, we adopt the skew-normal distribution for the log-transformed frailty, leading to an extension of the log-normal model. After presenting the methodology connected to this choice, we illustrate it with a case study of multiple myeloma patients with autologous stem cells transplantation.

Goodness-of-Fit Tests for the Frailty Distribution in Proportional Hazards Models with Shared Frailty

Frailty models account for the clustering present in grouped event time data. A proportional hazards model with shared frailties expresses the hazard for each subject. Often a one-parameter gamma distribution is assumed for the frailties. In this paper we construct formal goodness-of-fit tests to test for gamma frailties. We construct a new class of frailty models that extend the gamma frailty model by using certain polynomial expansions that are orthogonal with respect to the gamma density. For this extended family we obtain an explicit expression for the marginal likelihood of the data. The order selection test is based on finding the best fitting model in such a series of expanded models. A bootstrap is used to obtain p-values for the tests. Simulations and data examples illustrate the test's performance.

Random effects Weibull regression model for occupational lifetime

Abstract With great interest we read the recent publication of Sohn et al. [Sohn, S.Y., Chang, I.S., Moon, T.H., 2007. Random effects Weibull regression model for occupational lifetime. European Journal of Operational Research 179, 124–131] on a Weibull regression model with random effects for modelling occupational lifetime. We congratulate Sohn and colleagues on their comprehensive and clearly written paper. Nevertheless, we would like to comment on two points, the first regarding the moments of the underlying Weibull distribution, the second regarding the relations of Sohn’s model to the class of frailty models.

Bayesian frailty models based on Box-Cox transformed hazards

Due to natural or articial clustering, multivariate failure time data of- ten arise in biomedical research. To account for the intracluster correlation, we propose a novel class of frailty models by imposing the Box-Cox transformation on the hazard functions. This class of models generalizes the relationships between the baseline hazard and the hazard functions, which includes the proportional and the additive hazards frailty models as two special cases. Since hazards cannot be negative, complex multidimensional nonlinear parameter constraints must be im- posed in the model formulation. To facilitate a tractable computational algorithm, the joint priors are constructed through a conditional-marginal specication. The conditional distribution of the prior specication is univariate and absorbs the pa- rameter constraints, while the marginal part is free of constraints. We propose a Markov chain Monte Carlo (MCMC) computational scheme for sampling from the posterior distribution of the parameters. We derive an MCMC approximation for the conditional predictive ordinate to assess model adequacy, and illustrate the proposed method with a dataset.