Bayes and Empirical Bayes Methods for Data Analysis, Second Edition

Carlin, Bradley P.; Louis, Thomas A.

doi:10.1201/9781420057669

Cited by 1,581 publications

(1,593 citation statements)

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“…We pursued a random-effects approach which would allow the computation of a posterior distribution for the center effects given the observed effects [an Empirical Bayes (EB) approach]. A full Bayes (B) approach was also applied in order to evaluate the between-center differences (8). To do this, we proceeded as in a meta analysis and used information from the total data to derive a more accurate reflection of performance in specific centers.…”

Section: Random Center Effectmentioning

confidence: 99%

Predictors of Lung Transplant Survival in Eurotransplant

Smits

Mertens

Houwelingen

et al. 2003

American Journal of Transplantation

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This study was undertaken to assess the influence of patient/donor and center factors on lung transplantation outcome. Outcomes of all consecutive first cadaveric lung transplants performed at 21 Eurotransplant centers in 1997-99 were analyzed. The risk-adjusted center effect on mortality was estimated. A Cox model was built including donor and recipient age and gender, primary disease, HLA mismatches, patient's residence, cold ischemic time, donor's cause of death, serum creatinine, type of lung transplant, respiratory support status, clinical condition and percentage predicted FEV 1 . The center effect was calculated (expressed as the standardized difference between the observed and expected survival rates), and empirical and full Bayes methods were applied to evaluate between-center differences. A total of 590 adults underwent lung transplantation. The primary disease (p = = 0.01), HLA-mismatches (p = = 0.02), clinical condition (p < 0.0001) and the patient's respiratory support status (p = = 0.05) were significantly associated with survival. After adjusting for case-mix, no betweencenter differences could be found. An in-depth empirical Bayes analysis showed the between-center variation to be zero. Similar results were obtained from the full Bayes analysis. Based on these data, there is no scientific basis to support a hypothesis of possible association between center volume and lung survival rates.

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Section: Random Center Effectmentioning

confidence: 99%

Predictors of Lung Transplant Survival in Eurotransplant

Smits

Mertens

Houwelingen

et al. 2003

American Journal of Transplantation

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“…The central posterior density (CPD) regions [6] defined by 2.5% and 97.5% percentiles covered well the parameter values used in the simulation of data (Tab. I).…”

Section: Simulation Studymentioning

confidence: 58%

A bivariate quantitative genetic model for a threshold trait and a survival trait

Damgaard¹,

Korsgaard²

2006

Genet. Sel. Evol.

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-Many of the functional traits considered in animal breeding can be analyzed as threshold traits or survival traits with examples including disease traits, conformation scores, calving difficulty and longevity. In this paper we derive and implement a bivariate quantitative genetic model for a threshold character and a survival trait that are genetically and environmentally correlated. For the survival trait, we considered the Weibull log-normal animal frailty model. A Bayesian approach using Gibbs sampling was adopted in which model parameters were augmented with unobserved liabilities associated with the threshold trait. The fully conditional posterior distributions associated with parameters of the threshold trait reduced to well known distributions. For the survival trait the two baseline Weibull parameters were updated jointly by a Metropolis-Hastings step. The remaining model parameters with non-normalized fully conditional distributions were updated univariately using adaptive rejection sampling. The Gibbs sampler was tested in a simulation study and illustrated in a joint analysis of calving difficulty and longevity of dairy cattle. The simulation study showed that the estimated marginal posterior distributions covered well and placed high density to the true values used in the simulation of data. The data analysis of calving difficulty and longevity showed that genetic variation exists for both traits. The additive genetic correlation was moderately favorable with marginal posterior mean equal to 0.37 and 95% central posterior credibility interval ranging between 0.11 and 0.61. Therefore, this study suggests that selection for improving one of the two traits will be beneficial for the other trait as well.bivariate genetic model / survival trait / ordered categorical trait / Bayesian analysis

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“…Although the EB priors performed best in terms of MSE, they did not perform well in terms of bias, coverage rates, quantiles, and Type 1 error rates. Several studies have found that EB priors can result in an underestimation of the posterior variance (Carlin & Louis, 2000a;Darnieder, 2011;Efron, 1996), which can partly explain the low coverage rates. Furthermore, the EB priors considered in this paper were developed to be generally applicable.…”

Section: Discussionmentioning

confidence: 99%

“…As will be shown the proposed EB prior generally contains less information than the information of one observation. For this reason, the double use of the data and the resulting underestimation of the posterior variance, a known problem of EB methodology (e.g., Darnieder, 2011;Carlin & Louis, 2000a;Efron, 1996), is expected to be negligible.…”

Section: Vague Proper Priorsmentioning

confidence: 99%

Prior sensitivity analysis in default Bayesian structural equation modeling.

Erp

Mulder

Oberski

2018

Psychological Methods

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Bayesian structural equation modeling (BSEM) has recently gained popularity because it enables researchers to fit complex models while solving some of the issues often encountered in classical maximum likelihood (ML) estimation, such as nonconvergence and inadmissible solutions. An important component of any Bayesian analysis is the prior distribution of the unknown model parameters. Often, researchers rely on default priors, which are constructed in an automatic fashion without requiring substantive prior information. However, the prior can have a serious influence on the estimation of the model parameters, which affects the mean squared error (MSE), bias, coverage rates, and quantiles of the estimates.In this paper, we investigate the performance of three different default priors: noninformative improper priors, vague proper priors, and empirical Bayes priors, with the latter being novel in the BSEM literature. Based on a simulation study, we find that these three default BSEM methods may perform very differently, especially with small samples. A careful prior sensitivity analysis is therefore needed when performing a default BSEM analysis. For this purpose, we provide a practical step-by-step guide for practitioners to conducting a prior sensitivity analysis in default BSEM. Our recommendations are illustrated using a well-known case study from the structural equation modeling literature and all code for conducting the prior sensitivity analysis is made available in the online supplemental material.

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Bayes and Empirical Bayes Methods for Data Analysis, Second Edition

Cited by 1,581 publications

References 0 publications

Predictors of Lung Transplant Survival in Eurotransplant

Predictors of Lung Transplant Survival in Eurotransplant

A bivariate quantitative genetic model for a threshold trait and a survival trait

Prior sensitivity analysis in default Bayesian structural equation modeling.

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