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12
Accounting for Model Uncertainty in Survival Analysis Improves Predictive Performance
 In Bayesian Statistics 5
, 1995
"... Survival analysis is concerned with finding models to predict the survival of patients or to assess the efficacy of a clinical treatment. A key part of the modelbuilding process is the selection of the predictor variables. It is standard to use a stepwise procedure guided by a series of significanc ..."
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Cited by 56 (12 self)
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Survival analysis is concerned with finding models to predict the survival of patients or to assess the efficacy of a clinical treatment. A key part of the modelbuilding process is the selection of the predictor variables. It is standard to use a stepwise procedure guided by a series of significance tests to select a single model, and then to make inference conditionally on the selected model. However, this ignores model uncertainty, which can be substantial. We review the standard Bayesian model averaging solution to this problem and extend it to survival analysis, introducing partial Bayes factors to do so for the Cox proportional hazards model. In two examples, taking account of model uncertainty enhances predictive performance, to an extent that could be clinically useful. 1 Introduction From 1974 to 1984 the Mayo Clinic conducted a doubleblinded randomized clinical trial involving 312 patients to compare the drug DPCA with a placebo in the treatment of primary biliary cirrhosis...
Bayesian covariance selection in generalized linear mixed models
 Biometrics
, 2006
"... SUMMARY. The generalized linear mixed model (GLMM), which extends the generalized linear model (GLM) to incorporate random effects characterizing heterogeneity among subjects, is widely used in analyzing correlated and longitudinal data. Although there is often interest in identifying the subset of ..."
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Cited by 16 (3 self)
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SUMMARY. The generalized linear mixed model (GLMM), which extends the generalized linear model (GLM) to incorporate random effects characterizing heterogeneity among subjects, is widely used in analyzing correlated and longitudinal data. Although there is often interest in identifying the subset of predictors that have random effects, random effects selection can be challenging, particularly when outcome distributions are nonnormal. This article proposes a fully Bayesian approach to the problem of simultaneous selection of fixed and random effects in GLMMs. Integrating out the random effects induces a covariance structure on the multivariate outcome data, and an important problem which we also consider is that of covariance selection. Our approach relies on variable selectiontype mixture priors for the components in a special LDU decomposition of the random effects covariance. A stochastic search MCMC algorithm is developed, which relies on Gibbs sampling, with Taylor series expansions used to approximate intractable integrals. Simulated data examples are presented for different exponential family distributions, and the approach is applied to discrete survival data from a timetopregnancy study.
Enhancing the Predictive Performance of Bayesian Graphical Models
 Communications in Statistics – Theory and Methods
, 1995
"... Both knowledgebased systems and statistical models are typically concerned with making predictions about future observables. Here we focus on assessment of predictive performance and provide two techniques for improving the predictive performance of Bayesian graphical models. First, we present Baye ..."
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Cited by 8 (4 self)
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Both knowledgebased systems and statistical models are typically concerned with making predictions about future observables. Here we focus on assessment of predictive performance and provide two techniques for improving the predictive performance of Bayesian graphical models. First, we present Bayesian model averaging, a technique for accounting for model uncertainty. Second, we describe a technique for eliciting a prior distribution for competing models from domain experts. We explore the predictive performance of both techniques in the context of a urological diagnostic problem. KEYWORDS: Prediction; Bayesian graphical model; Bayesian network; Decomposable model; Model uncertainty; Elicitation. 1 Introduction Both statistical methods and knowledgebased systems are typically concerned with combining information from various sources to make inferences about prospective measurements. Inevitably, to combine information, we must make modeling assumptions. It follows that we should car...
ADAPTIVE BAYESIAN CRITERIA IN VARIABLE SELECTION FOR GENERALIZED LINEAR MODELS
"... Abstract: For the problem of variable selection in generalized linear models, we develop various adaptive Bayesian criteria. Using a hierarchical mixture setup for model uncertainty, combined with an integrated Laplace approximation, we derive Empirical Bayes and Fully Bayes criteria that can be com ..."
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Cited by 6 (0 self)
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Abstract: For the problem of variable selection in generalized linear models, we develop various adaptive Bayesian criteria. Using a hierarchical mixture setup for model uncertainty, combined with an integrated Laplace approximation, we derive Empirical Bayes and Fully Bayes criteria that can be computed easily and quickly. The performance of these criteria is assessed via simulation and compared to other criteria such as AIC and BIC on normal, logistic and Poisson regression model classes. A Fully Bayes criterion based on a restricted region hyperprior seems to be the most promising. Finally, our criteria are illustrated and compared with competitors on a data example.
Improved Bayesian Logistic Supervised Topic Models with Data Augmentation
"... Supervised topic models with a logistic likelihood have two issues that potentially limit their practical use: 1) response variables are usually overweighted by document word counts; and 2) existing variational inference methods make strict meanfield assumptions. We address these issues by: 1) int ..."
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Cited by 3 (2 self)
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Supervised topic models with a logistic likelihood have two issues that potentially limit their practical use: 1) response variables are usually overweighted by document word counts; and 2) existing variational inference methods make strict meanfield assumptions. We address these issues by: 1) introducing a regularization constant to better balance the two parts based on an optimization formulation of Bayesian inference; and 2) developing a simple Gibbs sampling algorithm by introducing auxiliary PolyaGamma variables and collapsing out Dirichlet variables. Our augmentandcollapse sampling algorithm has analytical forms of each conditional distribution without making any restricting assumptions and can be easily parallelized. Empirical results demonstrate significant improvements on prediction performance and time efficiency. 1
A Hierarchical Bayes Approach to Variable Selection for Generalized Linear Models
, 2004
"... For the problem of variable selection in generalized linear models, we develop various adaptive Bayesian criteria. Using a hierarchical mixture setup for model uncertainty, combined with an integrated Laplace approximation, we derive Empirical Bayes and Fully Bayes criteria that can be computed easi ..."
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Cited by 2 (0 self)
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For the problem of variable selection in generalized linear models, we develop various adaptive Bayesian criteria. Using a hierarchical mixture setup for model uncertainty, combined with an integrated Laplace approximation, we derive Empirical Bayes and Fully Bayes criteria that can be computed easily and quickly. The performance of these criteria is assessed via simulation and compared to other criteria such as AIC and BIC on normal, logistic and Poisson regression model classes. A Fully Bayes criterion based on a restricted region hyperprior seems to be the most promising.
Directed Walk Designs for Dose Response Problems with Competing Failure Modes
"... this paper, we have focused on two aspects of the design of phase I/II clinical trials. The first relates to rules for movement of an adaptive sampling design on a discrete dose set. Along with the basic walk, there are a number of factors such as starting sequence, endpoint conventions and explorat ..."
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Cited by 1 (1 self)
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this paper, we have focused on two aspects of the design of phase I/II clinical trials. The first relates to rules for movement of an adaptive sampling design on a discrete dose set. Along with the basic walk, there are a number of factors such as starting sequence, endpoint conventions and exploration rules, that play an important role in design performance. Ignoring these factors can lead to highly flawed designs
Forming Poststrata Via Bayesian Treed CaptureRecapture Models
, 2004
"... For the problem of dual system estimation, we propose a treed Capture Recapture Model (CRM) to account for heterogeneity of capture probabilities where individual auxiliary information is available. A treed CRM uses a binary tree to partition the covariate space into “homogeneous ” regions, within e ..."
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For the problem of dual system estimation, we propose a treed Capture Recapture Model (CRM) to account for heterogeneity of capture probabilities where individual auxiliary information is available. A treed CRM uses a binary tree to partition the covariate space into “homogeneous ” regions, within each of which the capture response can be described adequately by a simple model that assumes equal catchability. In this paper, a Bayesian approach is presented to fit and search promising treed CRMs. We compare the performance of estimators based on this approach to those of alternative models in three examples. The attractive features of the proposed models include reduction of correlation bias, robustness, practical flexibility as well as simplicity and interpretability. In addition, they provide a systematic and effective way to form poststrata for the Sekar and Deming estimator of population size.
Printed in Great Britain
"... Forming poststrata via Bayesian treed capturerecapture ..."
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