Hierarchical models for multicentre binary response studies

Skene, A. M.; Wakefield, John C.

doi:10.1002/sim.4780090808

Cited by 63 publications

(46 citation statements)

References 8 publications

(2 reference statements)

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“…Examples include models for the analysis of longitudinal data (Gilks et al, 1993), spatial data (Breslow and Clayton, 1993) and health care utilization data (Normand et al, 1997). Other modelling strategies for combining information in a Bayesian perspective are provided by Du Mouchel (1990), Skene and Wake®eld (1990), Smith et al (1995) andSilliman (1997). Recently, spatiotemporal statistical models with applications to environmental epidemiology have been proposed by Wikle et al (1997) and Wake®eld and Morris (1998).…”

Section: Pooling Results Across Citiesmentioning

confidence: 99%

Combining Evidence on Air Pollution and Daily Mortality from the 20 Largest US Cities: A Hierarchical Modelling Strategy

Dominici

Samet

Zeger

2000

Journal of the Royal Statistical Society Series A: Statistics in Society

239

217

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Summary. Reports over the last decade of association between levels of particles in outdoor air and daily mortality counts have raised concern that air pollution shortens life, even at concentrations within current regulatory limits. Criticisms of these reports have focused on the statistical techniques that are used to estimate the pollution±mortality relationship and the inconsistency in ®ndings between cities. We have developed analytical methods that address these concerns and combine evidence from multiple locations to gain a uni®ed analysis of the data. The paper presents log-linear regression analyses of daily time series data from the largest 20 US cities and introduces hierarchical regression models for combining estimates of the pollution±mortality relationship across cities. We illustrate this method by focusing on mortality effects of PM 10 (particulate matter less than 10 m in aerodynamic diameter) and by performing univariate and bivariate analyses with PM 10 and ozone (O 3 ) level. In the ®rst stage of the hierarchical model, we estimate the relative mortality rate associated with PM 10 for each of the 20 cities by using semiparametric log-linear models. The second stage of the model describes between-city variation in the true relative rates as a function of selected city-speci®c covariates. We also ®t two variations of a spatial model with the goal of exploring the spatial correlation of the pollutant-speci®c coef®cients among cities. Finally, to explore the results of considering the two pollutants jointly, we ®t and compare univariate and bivariate models. All posterior distributions from the second stage are estimated by using Markov chain Monte Carlo techniques. In univariate analyses using concurrent day pollution values to predict mortality, we ®nd that an increase of 10 g m À3 in PM 10 on average in the USA is associated with a 0.48% increase in mortality (95% interval: 0.05, 0.92). With adjustment for the O 3 level the PM 10 -coef®cient is slightly higher. The results are largely insensitive to the speci®c choice of vague but proper prior distribution. The models and estimation methods are general and can be used for any number of locations and pollutant measurements and have potential applications to other environmental agents.

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Section: Pooling Results Across Citiesmentioning

confidence: 99%

Combining Evidence on Air Pollution and Daily Mortality from the 20 Largest US Cities: A Hierarchical Modelling Strategy

Dominici

Samet

Zeger

2000

Journal of the Royal Statistical Society Series A: Statistics in Society

239

217

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“…This yields, after some algebra, a simple Gibbs sampler that iterates between two sets of conditional distributions: Figure 5 shows the results of applying this Gibbs sampler to the data from Skene and Wakefield (1990).…”

Section: S61 2 × 2 × N Tablesmentioning

confidence: 99%

Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables

Polson

Scott

Windle

2013

Journal of the American Statistical Association

715

1,070

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We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of Pólya-Gamma distributions, which are constructed in detail. A variety of examples are presented to show the versatility of the method, including logistic regression, negative binomial regression, nonlinear mixed-effects models, and spatial models for count data. In each case, our data-augmentation strategy leads to simple, effective methods for posterior inference that: (1) circumvent the need for analytic approximations, numerical integration, or Metropolis-Hastings; and (2) outperform other known data-augmentation strategies, both in ease of use and in computational efficiency. All methods, including an efficient sampler for the Pólya-Gamma distribution, are implemented in the R package BayesLogit.In the technical supplement appended to the end of the paper, we provide further details regarding the generation of Pólya-Gamma random variables; the empirical benchmarks reported in the main manuscript; and the extension of the basic dataaugmentation framework to contingency tables and multinomial outcomes.

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“…In a Bayesian analysis, a joint prior is put on the pair (µ, τ ). Bayesian approaches are developed in a number of papers, including Skene and Wakefield (1990), DuMouchel (1990), Morris and Normand (1992), Carlin (1992), and Smith et al (1995). As is discussed in these papers, a key advantage of the Bayesian approach is that inference concerning the center-specific effects ψ i is carried out in a natural manner through consideration of the posterior distributions of these parameters.…”

Section: Introductionmentioning

confidence: 99%

A Bayesian Semiparametric Model for Random-Effects Meta-Analysis

Burr

Doss

2005

Journal of the American Statistical Association

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In meta-analysis there is an increasing trend to explicitly acknowledge the presence of study variability through random effects models. That is, one assumes that for each study, there is a study-specific effect and one is observing an estimate of this latent variable. In a random effects model, one assumes that these study-specific effects come from some distribution, and one can estimate the parameters of this distribution, as well as the studyspecific effects themselves. This distribution is most often modelled through a parametric family, usually a family of normal distributions. The advantage of using a normal distribution is that the mean parameter plays an important role, and much of the focus is on determining whether or not this mean is 0. For example, it may be easier to justify funding further studies if it is determined that this mean is not 0. Typically, this normality assumption is made for the sake of convenience, rather than from some theoretical justification, and may not actually hold. We present a Bayesian model in which the distribution of the study-specific effects is modelled through a certain class of nonparametric priors. These priors can be designed to concentrate most of their mass around the family of normal distributions, but still allow for any other distribution. The priors involve a univariate parameter that plays the role of the mean parameter in the normal model, and they give rise to robust inference about this parameter. We present a Markov chain algorithm for estimating the posterior distributions under the model. Finally, we give two illustrations of the use of the model.

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Hierarchical models for multicentre binary response studies

Cited by 63 publications

References 8 publications

Combining Evidence on Air Pollution and Daily Mortality from the 20 Largest US Cities: A Hierarchical Modelling Strategy

Combining Evidence on Air Pollution and Daily Mortality from the 20 Largest US Cities: A Hierarchical Modelling Strategy

Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables

A Bayesian Semiparametric Model for Random-Effects Meta-Analysis

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