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A study of variable selection using g-prior distribution with ridge parameter

COMPUTATIONAL STATISTICS & DATA ANALYSIS 2012年第6期56卷 1920-1934页

作者： Baragatti, M. Pommeret, D. CNRS Inst Math Luminy F-13288 Marseille 9 France Ipsogen SA Luminy Biotech Entreprises F-13288 Marseille 9 France

In the Bayesian stochastic search variable selection framework, a common prior distribution for the regression coefficients is the g-prior of Zellner. However there are two standard cases where the associated covariance matrix does not exist and the conventional prior of Zellner cannot be used: if the number of observations is lower than the number of variables (large p and small n paradigm), or if some variables are linear combinations of others. In such situations, a prior distribution derived from the prior of Zellner can be considered by introducing a ridge parameter. This prior is a flexible and simple adaptation of the g-prior and its influence on the selection of variables is studied. A simple way to choose the associated hyper-parameters is proposed. The method is valid for any generalized linear mixed model and particular attention is paid to the study of probit mixed models when some variables are linear combinations of others. The method is applied to both simulated and real datasets obtained from Affymetrix microarray experiments. Results are compared to those obtained with the Bayesian Lasso. (c) 2011 Elsevier B.V. All rights reserved.

关键词： Bayesian Lasso generalized linear mixed model Metropolis-within-Gibbs algorithm Probit mixed regression model Ridge parameter Stochastic search variable selection Zellner prior

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Detection of Significant Disease Risks Using a Spatial Conditional Autoregressive model

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BIOMETRICS 2008年第4期64卷 1043-1053页

作者： Escaramis, Georgia Carrasco, Josep L. Ascaso, Carlos Univ Barcelona Dept Salut Publ Barcelona 08035 Spain

The conditional autoregressive (CAR) model is widely used to describe the geographical distribution of a specific disease risk in lattice mapping. Successful developments based on frequentist and Bayesian procedures have been extensively applied to obtain two-stage disease risk predictions at the subregional level. Bayesian procedures are preferred for making inferences, as the posterior standard errors (SE) of the two-stage prediction account for the variability in the variance component estimates;however, some recent work based on frequentist procedures and the use of bootstrap adjustments for the SE has been undertaken. In this article we investigate the suitability of an analytical adjustment for disease risk inference that provides accurate interval predictions by using the penalized quasilikelihood (PQL) technique to obtain model parameter estimates. The method is a first-order approximation of the naive SE based on a Taylor expansion and is interpreted as a conditional measure of variability providing conditional calibrated prediction intervals, given the data. We conduct a simulation study to demonstrate how the method can be used to estimate the specific subregion risk by interval. We evaluate the proposed methodology by analyzing the commonly used example data set of lip cancer incidence in the 56 counties of Scotland for the period 1975-1980. This evaluation reveals a close similarity between the solutions provided by the method proposed here and those of its fully Bayesian counterpart.

关键词： Best linear unbiased predictors Conditional autoregressive model Disease mapping generalized linear mixed model Penalized quasilikelihood Variance components

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Laplace approximation in measurement error models

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BIOMETRICAL JOURNAL 2011年第3期53卷 411-425页

作者： Battauz, Michela Univ Udine Dept Econ & Stat I-33100 Udine Italy

Likelihood analysis for regression models with measurement errors in explanatory variables typically involves integrals that do not have a closed-form solution. In this case, numerical methods such as Gaussian quadrature are generally employed. However, when the dimension of the integral is large, these methods become computationally demanding or even unfeasible. This paper proposes the use of the Laplace approximation to deal with measurement error problems when the likelihood function involves high-dimensional integrals. The cases considered are generalized linear models with multiple covariates measured with error and generalized linear mixed models with measurement error in the covariates. The asymptotic order of the approximation and the asymptotic properties of the Laplace-based estimator for these models are derived. The method is illustrated using simulations and real-data analysis.

关键词： generalized linear mixed model generalized linear model Laplace approximation Measurement error Random effect

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Computational techniques for spatial logistic regression with large data sets

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2007年第8期51卷 3631-3653页

作者： Paciorek, Christopher J. Harvard Univ Sch Publ Hlth Boston MA 02115 USA

In epidemiological research, outcomes are frequently non-normal, sample sizes may be large, and effect sizes are often small. To relate health outcomes to geographic risk factors, fast and powerful methods for fitting spatial models, particularly for non-normal data, are required. I focus on binary outcomes, with the risk surface a smooth function of space, but the development herein is relevant for non-normal data in general. I compare penalized likelihood (PL) models, including the penalized quasi-likelihood (PQL) approach, and Bayesian models based on fit, speed, and ease of implementation. A Bayesian model using a spectral basis (SB) representation of the spatial surface via the Fourier basis provides the best tradeoff of sensitivity and specificity in simulations, detecting real spatial features while limiting overfitting and being reasonably computationally efficient. One of the contributions of this work is further development of this underused representation. The SB model outperforms the PL methods, which are prone to overfitting, but is slower to fit and not as easily implemented. A Bayesian Markov random field model performs less well statistically than the SB model, but is very computationally efficient. We illustrate the methods on a real data set of cancer cases in Taiwan. The success of the SB with binary data and similar results with count data suggest that it may be generally useful in spatial models and more complicated hierarchical models. (c) 2006 Elsevier B.V. All rights reserved.

关键词： Bayesian statistics disease mapping Fourier basis generalized linear mixed model geostatistics risk surface spatial statistics spectral basis

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Measures of single arm outcome in meta-analyses of rare events in the presence of competing risks

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BIOMETRICAL JOURNAL 2015年第4期57卷 649-660页

作者： Andreano, Anita Rebora, Paola Valsecchi, Maria Grazia Univ Milano Bicocca Dept Hlth Sci Ctr Biostat Clin Epidemiol I-20900 Monza Italy

When performing single arm meta-analyses of rare events in small populations, if the outcome of interest is incidence, it is not uncommon to have at least one study with zero events, especially in the presence of competing risks. In this paper, we address the problem of how to include studies with zero events in inverse variance meta-analyses when individual patient data are not available, going beyond the naive approach of not including the study or the use of a continuity correction. The proposed solution is the arcsine transformation of the crude cumulative incidence as its approximate variance, which is inversely proportional to the sample size, can be calculated also for studies with a zero estimate. As an alternative, generalized linear mixed models (GLMM) can be used. Simulations were performed to compare the results from inverse variance method meta-analyses of the arcsine transformed cumulative incidence to those obtained from meta-analyses of the cumulative incidence itself and of the logit transformation of the cumulative incidence. The comparisons have been carried out for different scenarios of heterogeneity, incidence, and censoring and for competing and not competing risks. The arcsine transformation showed the smallest bias and the highest coverage among models assuming within study normality. At the same time, the GLMM model had the best performance at very low incidences. The proposed method was applied to the clinical context that motivated this work, i.e. a meta-analysis of 5-year crude cumulative incidence of central nervous system recurrences in children treated for acute lymphoblastic leukemia.

关键词： Arcsine transformation Competing risks generalized linear mixed model Meta-analysis Rare events Survival

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A Joint modelling of socio-professional trajectories and cause-specific mortality

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2018年 119卷 39-54页

作者： Karimi, M. Rey, G. Latouche, A. CepiDc Inserm 80 Rue Gen Leclerc F-94270 Le Kremlin Bicetre France Imperial Coll London Sch Publ Hlth MRC PHE Ctr Environm & Health Dept Epidemiol & Biostat Norfolk Pl London W2 1PG England Conservatoire Natl Arts & Metiers Cnam EA4629 Paris France Inst Curie Inserm U900 St Cloud France

The association between life-course socio-professional trajectories and mortality has already been discussed in the literature. However, these socio-professional trajectories may be subject to informative censoring due to death. This loss to follow-up which is related to an individual's survival, should not be ignored and thus, it is of interest to model jointly these professional trajectories and their survival. The main focus has been made on continuous, binary or ordinal variables while much less attention has been paid to nominal categorical data. Therefore, an extension to the joint modelling of longitudinal nominal data and survival under a likelihood-based approach is proposed. A generalized linear mixed model is considered for modelling the longitudinal nominal data, in addition to two cause-specific proportional hazards model for the survival competing risks data. The association between longitudinal and survival outcomes is captured by assuming a multivariate Gaussian distribution for the joint distribution of the random effects of two sub-models. The proposed joint model provides a robust framework for estimating longitudinal membership probabilities, accounting for informative censoring caused by individual's death. Simulations are carried out to assess the performance of this joint model comparing with the results of the separate longitudinal and competing risks analysis. A disadvantage of joint models is that they are computationally intensive. To overcome this problem, an approach mimicking a meta-analysis strategy of individual participant data is suggested. The relevance of this approach is then illustrated on a large sample of the French salaried population, which contains all employment records between 1976 and 2002. (C) 2017 Elsevier B.V. All rights reserved,

关键词： generalized linear mixed model Cause-specific hazards Joint model Membership probability Large-scale data

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Detection of outliers in longitudinal count data via overdispersion

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2014年 79卷 192-202页

作者： Gumedze, Freedom N. Chatora, Tinashe D. Univ Cape Town Dept Stat Sci ZA-7701 Rondebosch South Africa

Count data are usually modeled using the Poisson generalized linear model. The Poisson model requires that the variance be a deterministic function of the mean. This assumption may not be met for a particular data set, that is, the model may not adequately capture the variability in the data. The extra-variability in the data may be accommodated using overdispersion models, such as the negative binomial distribution. In addition to the overdispersion outliers may be present in the data as indicated by the model residuals or some functions of the model residuals. A variance shift outlier model (VSOM) for count data is introduced. The model is used to detect potential outliers in the data, and to down-weight them in the analysis if desired. In this model the overdispersion is modeled using an observation-specific random effect. The status of a given observation as an outlier is indicated by the size of the associated shift in variance for that observation. The model is then extended to longitudinal count data for the detection of outliers at the subject level. We illustrate the methodology using a real data set taken from the literature. Extensions of the VSOM for count data to other non-normal responses are discussed. (C) 2014 Elsevier B.V. All rights reserved.

关键词： generalized linear model generalized linear mixed model Hierarchical generalized linear model Likelihood ratio test Negative binomial model Outlier detection Overdispersion Poisson model Variance shift outlier model

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model-based geostatistics

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS 1998年第3期47卷 299-326页

作者： Diggle, PJ Tawn, JA Moyeed, RA Univ Lancaster Dept Math & Stat Lancaster LA1 4YF England Univ Plymouth Plymouth Devon England

Conventional geostatistical methodology solves the problem of predicting the realized value of a linear functional of a Gaussian spatial stochastic process S(x) based on observations Y(i) = S(x(i))+Z(i) at sampling locations x(i), where the Z(i) are mutually independent, zero-mean Gaussian random variables. We describe two spatial applications for which Gaussian distributional assumptions are clearly inappropriate. The first concerns the assessment of residual contamination from nuclear weapons testing on a South Pacific island, in which the sampling method generates spatially indexed Poisson counts conditional on an unobserved spatially varying intensity of radioactivity;we conclude that a conventional geostatistical analysis oversmooths the data and underestimates the spatial extremes of the intensity. The second application provides a description of spatial variation in the risk of campylobacter infections relative to other enteric infections in part of north Lancashire and south Cumbria. For this application, we treat the data as binomial counts at unit postcode locations, conditionally on an unobserved relative risk surface which we estimate. The theoretical framework for our extension of geostatistical methods is that, conditionally on the unobserved process S(x), observations at sample locations x(i) form a generalized linear model with the corresponding values of S(x(i)) appearing as an offset term in the linear predictor. We use a Bayesian inferential framework, implemented via the Markov chain Monte Carte method, to solve the prediction problem for non-linear functionals of S(x), making a proper allowance for the uncertainty in the estimation of any model parameters.

关键词： generalized linear mixed model geostatistics kriging Markov chain Monte Carlo method spatial prediction

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Group Testing Regression models with Fixed and Random Effects

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BIOMETRICS 2009年第4期65卷 1270-1278页

作者： Chen, Peng Tebbs, Joshua M. Bilder, Christopher R. Univ S Carolina Dept Stat Columbia SC 29208 USA Univ Nebraska Dept Stat Lincoln NE 68583 USA

P>Group testing, where subjects are tested in pools rather than individually, has a long history of successful application in infectious disease screening. In this article, we develop group testing regression models to include covariate effects that are best regarded as random. We present approaches to fit mixed effects models using maximum likelihood, investigate likelihood ratio and score tests for variance components, and evaluate small sample performance using simulation. We illustrate our methods using chlamydia and gonorrhea data collected by the state of Nebraska as part of the Infertility Prevention Project.

关键词： generalized linear mixed model Latent binary response Likelihood ratio test Monte Carlo EM algorithm Pooled testing Score test

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Extreme climate conditions limit seed availability to successfully attain natural regeneration of Pinus pinaster in sandy areas of central Spain

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CANADIAN JOURNAL OF FOREST RESEARCH 2015年第12期45卷 1795-1802页

作者： Ruano, Irene Manso, Ruben Fortin, Mathieu Bravo, Felipe Univ Valladolid Sustainable Forest Management Res Inst Palencia 34004 Spain INIA Palencia 34004 Spain Univ Valladolid Dept Prod Vegetal & Recursos Forestales ETS Ingn Agr Palencia 34004 Spain INRA UMR LERFoB 1092 F-54280 Champenoux France AgroParisTech UMR LERFoB 1092 F-54042 Nancy France

Natural regeneration comprises different subprocesses, each of them driven by specific climatic and stand-related factors, which determine the success of natural regeneration. The objective of this study was to investigate the seed availability of maritime pine (Pinus pinaster Aiton). To meet this objective, seed rain was monitored for four different levels of stand density at the experimental site of Cuellar, Spain, during a 10-year period. A generalized linear mixed-effects model was fitted to test the effects of climatic variables and stand density on the annual seed production and seed rain. The climatic covariates were chosen among those that are thought to affect the key physiological phases governing these subprocesses: minimum temperature in October 2 years before dispersal (cone growing), April precipitation 1 year before dispersal (cone growing), and October-November precipitation 1 year before dispersal (cone maturation). No climate variable related to flowering or seed rain process was significant. Moreover, stand density was considered through a spatially explicit index called the seed-source index. Primary cone growth was limited by extreme cold events. Absence of precipitation limits secondary growth and hinders final cone ripening. It turns out that seed production and seed rain may be a bottleneck for natural regeneration of P. pinaster under low stand densities, especially under extreme climatic scenarios.

关键词： climate change generalized linear mixed model Mediterranean ecosystem natural regeneration seed limitation

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