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Tractable Bayes of skew-elliptical link models for correlated binary data

BIOMETRICS 2023年第3期79卷 1788-1800页

作者： Zhang, Zhongwei Arellano-Valle, Reinaldo B. Genton, Marc G. Huser, Raphael King Abdullah Univ Sci & Technol KAUST Comp Elect & Math Sci & Engn Div Stat Program Thuwal 239556900 Saudi Arabia Pontificia Univ Catolica Chile Dept Estadist Santiago Chile

correlated binary response data with covariates are ubiquitous in longitudinal or spatial studies. Among the existing statistical models, the most well-known one for this type of data is the multivariate probit model, which uses a Gaussian link to model dependence at the latent level. However, a symmetric link may not be appropriate if the data are highly imbalanced. Here, we propose a multivariate skew-elliptical link model for correlated binary responses, which includes the multivariate probit model as a special case. Furthermore, we perform Bayesian inference for this new model and prove that the regression coefficients have a closed-form unified skew-elliptical posterior with an elliptical prior. The new methodology is illustrated by an application to COVID-19 data from three different counties of the state of California, USA. By jointly modeling extreme spikes in weekly new cases, our results show that the spatial dependence cannot be neglected. Furthermore, the results also show that the skewed latent structure of our proposed model improves the flexibility of the multivariate probit model and provides a better fit to our highly imbalanced dataset.

关键词： asymmetric link model correlated binary data COVID-19 pandemic Markov chain Monte Carlo tractable Bayes unified skew-elliptical distribution

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A genetic algorithm for simulating correlated binary data from biomedical research

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COMPUTERS IN BIOLOGY AND MEDICINE 2018年 92卷 1-8页

作者： Kruppa, Jochen Lepenies, Bernd Jung, Klaus Univ Vet Med Hannover Inst Anim Breeding & Genet Bunteweg 17p D-30559 Hannover Germany Univ Vet Med Hannover Immunol Unit Hannover Germany Univ Vet Med Hannover Res Ctr Emerging Infect & Zoonoses RIZ Hannover Germany

correlated binary data arise in a large variety of biomedical research. In order to evaluate methods for their analysis, computer simulations of such data are often required. Existing methods can often not cover the full range of possible correlations between the variables or are not available as implemented software. We propose a genetic algorithm that approaches the desired correlation structure under a given marginal distribution. The procedure generates a large representative matrix from which the probabilities of individual observations can be derived or from which samples can be drawn directly. Our genetic algorithm is evaluated under different specified marginal frequencies and correlation structures, and is compared against two existing approaches. The evaluation checks the speed and precision of the approach as well as its suitability for generating also high-dimensional data. In an example of high-throughput glycan array data, we demonstrate the usability of our approach to simulate the power of global test procedures. An implementation of our own and two other methods were added to the R package `RepeatedHighDim'. The presented algorithm is not restricted to certain correlation structures. In contrast to existing methods it is also evaluated for high-dimensional data.

关键词： correlated binary data Genetic algorithm High-dimensional data Random number generation Computer simulation

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GENERALIZED ESTIMATING EQUATIONS FOR correlated binary data - USING THE ODDS RATIO AS A MEASURE OF ASSOCIATION

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BIOMETRIKA 1991年第1期78卷 153-160页

作者： LIPSITZ, SR LAIRD, NM HARRINGTON, DP Department of Biostatistics Harvard School of Public Health677 Huntington Avenue Boston Massachusetts 02115 U.S.A.

Moment methods for analyzing repeated binary responses have been proposed by Liang & Zeger (1986), and extended by Prentice (1988). In their generalized estimating equations, both Liang & Zeger (1986) and Prentice (1988) estimate the parameters associated with the expected value of an individual's vector of binary responses as well as the correlations between pairs of binary responses. Because the odds ratio has many desirable properties, and some investigators may find the odds ratio is easier to interpret, we discuss modelling the association between binary responses at pairs of times with the odds ratio. We then modify the estimating equations of Prentice to estimate the odds ratios. In simulations, the parameter estimates for the logistic regression model for the marginal probabilities appear slightly more efficient when using the odds ratio parameterization.

关键词： correlated binary data GENERALIZED ESTIMATING EQUATION MARGINAL MODEL REPEATED MEASURES

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Sample sizes for designed studies with correlated binary data

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES D-THE STATISTICIAN 2003年第4期52卷 539-551页

作者： Brooks, RJ Cottenden, AM Fader, MJ UCL Dept Stat Sci London WC1E 6BT England

The paper considers comparative studies in which subjects use more than one product or receive more than one treatment. The paper is focused mainly on the comparison of products, including the possibility of a large number of products. The data to be analysed are on a binary variable that is observed by each subject for each product used. The calculation of the number of subjects or sample size is illustrated for a variety of basic study designs, assuming that the data may be correlated and the analysis of the data uses generalized estimating equations methodology. The sample sizes use asymptotic theory developed by Liu and Liang. A simulation study that evaluates some of the resulting sample sizes suggests that these need to be increased slightly to achieve the nominal power.

关键词： correlated binary data generalized estimating equation power sample size study design

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Shrinkage estimation analysis of correlated binary data with a diverging number of parameters

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Science China Mathematics 2013年第2期56卷 359-377页

作者： XU PeiRong FU WenJiang ZHU LiXing School of Finance and Statistics East China Normal University Department of Epidemiology and Biostatistics Michigan State University Department of Mathematics Hong Kong Baptist University

For analyzing correlated binary data with high-dimensional covariates,we,in this paper,propose a two-stage shrinkage ***,we construct a weighted least-squares(WLS) type function using a special weighting scheme on the non-conservative vector field of the generalized estimating equations(GEE) ***,we define a penalized WLS in the spirit of the adaptive LASSO for simultaneous variable selection and parameter *** proposed procedure enjoys the oracle properties in high-dimensional framework where the number of parameters grows to infinity with the number of ***,we prove the consistency of the sandwich formula of the covariance matrix even when the working correlation matrix is *** the selection of tuning parameter,we develop a consistent penalized quadratic form(PQF) function *** performance of the proposed method is assessed through a comparison with the existing methods and through an application to a crossover trial in a pain relief study.

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Parameter-expandeddata augmentation for analyzing correlated binary data using multivariate probit models

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STATISTICS IN MEDICINE 2020年第25期39卷 3637-3652页

作者： Zhang, Xiao Michigan Technol Univ Math Sci 1400 Townsend Dr Houghton MI 49931 USA

data augmentation has been commonly utilized to analyze correlated binary data using multivariate probit models in Bayesian analysis. However, the identification issue in the multivariate probit models necessitates a rigorous Metropolis-Hastings algorithm for sampling a correlation matrix, which may cause slow convergence and inefficiency of Markov chains. It is well-known that the parameter-expanded data augmentation, by introducing a working/artificial parameter or parameter vector, makes an identifiable model be non-identifiable and improves the mixing and convergence of data augmentation components. Therefore, we motivate to develop efficient parameter-expanded data augmentations to analyze correlated binary data using multivariate probit models. We investigate both the identifiable and non-identifiable multivariate probit models and develop the corresponding parameter-expanded data augmentation algorithms. We point out that the approaches, based on one non-identifiable model, circumvent a Metropolis-Hastings algorithm for sampling a correlation matrix and improve the convergence and mixing of correlation parameters;the identifiable model may produce the estimated regression parameters with smaller standard errors than the non-identifiable model does. We illustrate our proposed approaches using simulation studies and through the application to a longitudinal dataset from the Six Cities study.

关键词： correlated binary data data augmentation multivariate probit model parameter-expanded data augmentation

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Interval estimation of proportion ratios for stratified bilateral correlated binary data

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STATISTICAL METHODS IN MEDICAL RESEARCH 2020年第7期29卷 1987-2014页

作者： Xue, Yuqing Ma, Chang-Xing Univ Buffalo Dept Biostat Buffalo NY 14214 USA

Confidence interval (CI) methods for the ratio of two proportions in the presence of correlated bilateral binary data are constructed for comparative clinical trials with stratified design. Simulations are conducted to evaluate the performance of the presented CIs with respect to mean coverage probability (MCP), mean interval width (MIW), and the ratio of mesial non-coverage probability to the distal non-coverage probability (RMNCP). Based on the empirical results, we suggest the use of the proposed CI method based on the complete score statistics (CS) for general applications. An example from a rheumatology study is used to demonstrate the proposed methodologies.

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A comparison of analysis procedures for correlated binary data in dedicated multi-rater imaging trials

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PHARMACEUTICAL STATISTICS 2015年第1期14卷 34-43页

作者： Kunz, Michael Bayer Pharma AG Global Res & Clin Dev Stat D-13342 Berlin Germany

In this paper, three analysis procedures for repeated correlated binary data with no a priori ordering of the measurements are described and subsequently investigated. Examples for correlated binary data could be the binary assessments of subjects obtained by several raters in the framework of a clinical trial. This topic is especially of relevance when success criteria have to be defined for dedicated imaging trials involving several raters conducted for regulatory purposes. First, an analytical result on the expectation of the Majority rater' is presented when only the marginal distributions of the single raters are given. The paper provides a simulation study where all three analysis procedures are compared for a particular setting. It turns out that in many cases, Average rater' is associated with a gain in power. Settings were identified where Majority significant' has favorable properties. Majority rater' is in many cases difficult to interpret. Copyright (c) 2014 John Wiley & Sons, Ltd.

关键词： multi-rater trial multiplicity correlated binary data imaging trial clinical trial

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Generalized linear mixed models for correlated binary data with t-link

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STATISTICS AND COMPUTING 2014年第6期24卷 1111-1123页

作者： Prates, Marcos O. Costa, Denise R. Lachos, Victor H. Univ Fed Minas Gerais Dept Stat Belo Horizonte MG Brazil Univ Estadual Campinas Dept Stat Campinas SP Brazil

A critical issue in modeling binary response data is the choice of the links. We introduce a new link based on the Student's t-distribution (t-link) for correlated binary data. The t-link relates to the common probit-normal link adding one additional parameter which controls the heaviness of the tails of the link. We propose an interesting EM algorithm for computing the maximum likelihood for generalized linear mixed t-link models for correlated binary data. In contrast with recent developments (Tan et al. in J. Stat. Comput. Simul. 77:929-943, 2007;Meza et al. in Comput. Stat. data Anal. 53:1350-1360, 2009), this algorithm uses closed-form expressions at the E-step, as opposed to Monte Carlo simulation. Our proposed algorithm relies on available formulas for the mean and variance of a truncated multivariate t-distribution. To illustrate the new method, a real data set on respiratory infection in children and a simulation study are presented.

关键词： correlated binary data EM-algorithm Generalized linear mixed models Truncated multivariate t-distribution

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Regression models for correlated binary data with random effects assuming a mixture of normal distributions

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COMPUTATIONAL STATISTICS 2003年第1期18卷 39-55页

作者： Achcar, JA Janeiro, V Mazucheli, J Univ Sao Paulo ICMC BR-13560970 Sao Carlos SP Brazil State Univ Maringa Dept Stat BR-87020900 Maringa Parana Brazil

binary responses are correlated when the sampling units are clustered or when repeated binary responses are taken on the same experiment unit. In this paper we present a Bayesian analysis of logistic regression models for correlated binary data with random effects. We assume that the random effects, namely alpha(i), i = 1,..., n are draw from a mixture of normal distributions. This assumption gives a great flexibility of fit by correlated binary data. Considering Gibbs sampling with Metropolis-Hastings algorithms, we obtain Monte Carlo estimates for the posterior quantities of interest.

关键词： correlated binary data logistic regression model random effects mixture of normal distributions

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