Journal ArticleDOI
Checking the adequacy of the gamma frailty model for multivariate failure times
TLDR
In this article, the authors developed both graphical and numerical techniques for checking the adequacy of the gamma frailty model for multivariate failure time data, based on the posterior expectation of the frailty given the observable data.Abstract:
SUMMARY Multivariate failure time data arise when the sample consists of clusters and each cluster contains several dependent failure times. The semiparametric gamma frailty model (Vaupel, Manton & Stallard, 1979; Clayton, 1978; Oakes, 1982) for multivariate failure times characterises the intracluster dependence by the gamma frailty distribution while allowing the marginal distributions to be unspecified. This paper develops both graphical and numerical techniques for checking the adequacy of this model. The proposed techniques are based on the posterior expectation of the frailty given the observable data. Two examples from genetics are provided.read more
Citations
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Omnibus Goodness-of-Fit Tests for Copulas: A Review and a Power Study
TL;DR: In this paper, the authors present a critical review of blanket tests for goodness-of-fit testing of copula models and suggest new ones, and conclude with a number of practical recommendations.
Journal ArticleDOI
Goodness-of-fit tests for copulas: A review and a power study
TL;DR: In this paper, the authors present a critical review of the blanket test procedures and suggest new ones for goodness-of-fit testing of copula models, and describe and interpret the results of a large Monte Carlo experiment designed to assess the effect of the sample size and the strength of dependence on the level and power of blanket tests for various combinations of Copula models under the null hypothesis and the alternative.
Journal ArticleDOI
Goodness‐of‐fit Procedures for Copula Models Based on the Probability Integral Transformation
TL;DR: In this paper, a non-parametric approach for checking whether the dependence structure of a random sample of censored bivariate data is appropriately modelled by a given family of Archimedean copulas is described.
Book
Frailty Models in Survival Analysis
TL;DR: The concept of correlated frailty, a model for estimating covariates in proportional hazard models, and its applications to survival and hazard functions and frailty models are described.
Journal ArticleDOI
Shared Frailty Models for Recurrent Events and a Terminal Event
TL;DR: This model avoids the difficulties encountered in alternative approaches which attempt to specify a dependent joint distribution with marginal proportional hazards and yields an estimate of the degree of dependence.
References
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Book
Statistical Models Based on Counting Processes
TL;DR: Statistical Models Based on Counting Processes (SBP) as discussed by the authors is a monograph for mathematical statisticians and biostatisticians, although almost all methods are given in sufficient detail to be used in practice by other mathematically oriented researchers studying event histories.
Journal ArticleDOI
Statistical Models Based on Counting Processes
TL;DR: "Statistical Models Based on Counting Processes" may be viewed as a research monograph for mathematical statisticians and biostatisticians, although almost all methods are given in sufficient detail to be used in practice by other mathematically oriented researchers studying event histories.
Book
Empirical processes with applications to statistics
Galen R. Shorack,Jon A. Wellner +1 more
TL;DR: In this paper, a broad cross-section of the literature available on one-dimensional empirical processes is summarized, with emphasis on real random variable processes as well as a wide-ranging selection of applications in statistics.
Journal ArticleDOI
The impact of heterogeneity in individual frailty on the dynamics of mortality.
TL;DR: Calculations based on Swedish mortality data suggest that standard methods overestimate current life expectancy and potential gains in life expectancy from health and safety interventions, while underestimating rates of individual aging, past progress in reducing mortality, and mortality differentials between pairs of populations.
Journal ArticleDOI
A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence
TL;DR: In this article, a related model for association in bivariate survivorship time distributions is proposed for the analysis of familial tendency in disease incidence, which is related to more specifically epidemiological models.