Parametric Overdispersed Frailty Models for Current Status Data

Abrams, Steven; Aerts, Marc; Molenberghs, Geert; Hens, Niel

doi:10.1111/biom.12692

Cited by 3 publications

(1 citation statement)

References 30 publications

(48 reference statements)

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“…Nonetheless, a simulation‐based empirical estimate of Kendall's tau can be calculated by looking at the concordance score of pairs of bivariate observations

[(Z_{1 j}, Z_{1 k}), (Z_{2 j}, Z_{2 k})]

generated based on the estimated frailty distributions. Hence, Kendall's tau can be obtained as the difference of the probability of concordance and discordance, that is:

τ_{S} = P [(Z_{1 j} - Z_{1 k}) (Z_{2 j} - Z_{2 k}) > 0] - P [(Z_{1 j} - Z_{1 k}) (Z_{2 j} - Z_{2 k}) < 0] .

Since the estimate of τ S is made over several simulations, the simulation‐based standard error can be calculated as well.…”

Section: Methodsmentioning

confidence: 99%

A general frailty model to accommodate individual heterogeneity in the acquisition of multiple infections: An application to bivariate current status data

Tran

Abrams

Braekers

2020

Statistics in Medicine

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The analysis of multivariate time-to-event (TTE) data can become complicated due to the presence of clustering, leading to dependence between multiple event times. For a long time, (conditional) frailty models and (marginal) copula models have been used to analyze clustered TTE data. In this article, we propose a general frailty model employing a copula function between the frailty terms to construct flexible (bivariate) frailty distributions with the application to current status data. The model has the advantage to impose a less restrictive correlation structure among latent frailty variables as compared to traditional frailty models. Specifically, our model uses a copula function to join the marginal distributions of the frailty vector. In this article, we considered different copula functions, and we relied on marginal gamma distributions due to their mathematical convenience. Based on a simulation study, our novel model outperformed the commonly used additive correlated gamma frailty model, especially in the case of a negative association between the frailties. At the end of the article, the new methodology is illustrated on real-life data applications entailing bivariate serological survey data. K E Y W O R D Sassociation, copula functions, frailty models, maximum likelihood inference, serological survey data 1 Statistics in Medicine. 2020;39:1695-1714.wileyonlinelibrary.com/journal/sim

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“…Nonetheless, a simulation‐based empirical estimate of Kendall's tau can be calculated by looking at the concordance score of pairs of bivariate observations

[(Z_{1 j}, Z_{1 k}), (Z_{2 j}, Z_{2 k})]

generated based on the estimated frailty distributions. Hence, Kendall's tau can be obtained as the difference of the probability of concordance and discordance, that is:

τ_{S} = P [(Z_{1 j} - Z_{1 k}) (Z_{2 j} - Z_{2 k}) > 0] - P [(Z_{1 j} - Z_{1 k}) (Z_{2 j} - Z_{2 k}) < 0] .

Since the estimate of τ S is made over several simulations, the simulation‐based standard error can be calculated as well.…”

Section: Methodsmentioning

confidence: 99%

A general frailty model to accommodate individual heterogeneity in the acquisition of multiple infections: An application to bivariate current status data

Tran

Abrams

Braekers

2020

Statistics in Medicine

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Sample size calculation for estimating key epidemiological parameters using serological data and mathematical modelling

Blaizot

Herzog

Abrams³

et al. 2018

Preprint

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Background. Our work was motivated by the need to, given serum availability and/or financial resources, decide on which samples to test for different pathogens in a serum bank. Simulationbased sample size calculations were performed to determine the age-based sampling structures and optimal allocation of a given number of samples for testing across various age groups best suited to estimate key epidemiological parameters (e.g., seroprevalence or force of infection) with acceptable precision levels in a cross-sectional seroprevalence survey.Methods. Statistical and mathematical models and three age-based sampling structures (surveybased structure, population-based structure, uniform structure) were used. Our calculations are based on Belgian serological survey data collected in 2002 where testing was done, amongst others, for the presence of IgG antibodies against measles, mumps, and rubella, for which a national mass immunisation programme was introduced in 1985 in Belgium, and against varicella-zoster virus and parvovirus B19 for which the endemic equilibrium assumption is tenable in Belgium.Results. The optimal age-based sampling structure to use in the sampling of a serological survey as well as the optimal allocation distribution varied depending on the epidemiological parameter of interest for a given infection and between infections. Conclusions.When estimating key epidemiological parameters with acceptable levels of precision within the context of a single cross-sectional serological survey, attention should be given to the age-based sampling structure. Simulation-based sample size calculations in combination with mathematical modelling can be utilised for choosing the optimal allocation of a given number of samples over various age groups. 4

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Sample size calculation for estimating key epidemiological parameters using serological data and mathematical modelling

Blaizot

Herzog

Abrams

et al. 2019

BMC Med Res Methodol

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Background Our work was motivated by the need to, given serum availability and/or financial resources, decide on which samples to test in a serum bank for different pathogens. Simulation-based sample size calculations were performed to determine the age-based sampling structures and optimal allocation of a given number of samples for testing across various age groups best suited to estimate key epidemiological parameters (e.g., seroprevalence or force of infection) with acceptable precision levels in a cross-sectional seroprevalence survey. Methods Statistical and mathematical models and three age-based sampling structures (survey-based structure, population-based structure, uniform structure) were used. Our calculations are based on Belgian serological survey data collected in 2001–2003 where testing was done, amongst others, for the presence of Immunoglobulin G antibodies against measles, mumps, and rubella, for which a national mass immunisation programme was introduced in 1985 in Belgium, and against varicella-zoster virus and parvovirus B19 for which the endemic equilibrium assumption is tenable in Belgium. Results The optimal age-based sampling structure to use in the sampling of a serological survey as well as the optimal allocation distribution varied depending on the epidemiological parameter of interest for a given infection and between infections. Conclusions When estimating epidemiological parameters with acceptable levels of precision within the context of a single cross-sectional serological survey, attention should be given to the age-based sampling structure. Simulation-based sample size calculations in combination with mathematical modelling can be utilised for choosing the optimal allocation of a given number of samples over various age groups. Electronic supplementary material The online version of this article (10.1186/s12874-019-0692-1) contains supplementary material, which is available to authorized users.

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Parametric Overdispersed Frailty Models for Current Status Data

Cited by 3 publications

References 30 publications

A general frailty model to accommodate individual heterogeneity in the acquisition of multiple infections: An application to bivariate current status data

A general frailty model to accommodate individual heterogeneity in the acquisition of multiple infections: An application to bivariate current status data

Sample size calculation for estimating key epidemiological parameters using serological data and mathematical modelling

Sample size calculation for estimating key epidemiological parameters using serological data and mathematical modelling

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