Bayesian modeling of multivariate spatial binary data with applications to dental caries

Bandyopadhyay, Dipankar; Reich, Brian J.; Slate, Elizabeth H.

doi:10.1002/sim.3647

Cited by 21 publications

(20 citation statements)

References 45 publications

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“…The ALR case discussed in the theorem is exactly the same, but with φ ≡ Xγ and α ≡ Xβ. Writing Equation (18) in terms of these regression parameters gives system (17). Model equivalence is the same as consistency of that system.…”

Section: Non-equivalence Of Alr Modelsmentioning

confidence: 99%

“…Under the ALR model, the responses follow an autologistic distribution, and the distribution's parameters are written in terms of a linear predictor involving the covariates. The ALR model has been used in a variety of fields, including ecology [14,15], dentistry [16,17], anthropology [18], materials science [19] and computer vision [20,21].…”

Section: Introductionmentioning

confidence: 99%

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Better Autologistic Regression

Wolters

2017

Front. Appl. Math. Stat.

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Autologistic regression is an important probability model for dichotomous random variables observed along with covariate information. It has been used in various fields for analyzing binary data possessing spatial or network structure. The model can be viewed as an extension of the autologistic model (also known as the Ising model, quadratic exponential binary distribution, or Boltzmann machine) to include covariates. It can also be viewed as an extension of logistic regression to handle responses that are not independent. Not all authors use exactly the same form of the autologistic regression model. Variations of the model differ in two respects. First, the variable coding-the two numbers used to represent the two possible states of the variables-might differ. Common coding choices are (zero, one) and (minus one, plus one). Second, the model might appear in either of two algebraic forms: a standard form, or a recently proposed centered form. Little attention has been paid to the effect of these differences, and the literature shows ambiguity about their importance. It is shown here that changes to either coding or centering in fact produce distinct, non-nested probability models. Theoretical results, numerical studies, and analysis of an ecological data set all show that the differences among the models can be large and practically significant. Understanding the nature of the differences and making appropriate modeling choices can lead to significantly improved autologistic regression analyses. The results strongly suggest that the standard model with plus/minus coding, which we call the symmetric autologistic model, is the most natural choice among the autologistic variants.

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Section: Non-equivalence Of Alr Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Better Autologistic Regression

Wolters

2017

Front. Appl. Math. Stat.

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“…Zhu et al [8] pre-selected the spatial and temporal neighborhood structure without including covariates using the AIC and then, once the neighborhood structure was specified, chose covariates for their analysis of the mountain pine beetle outbreak in British Columbia, Canada. Using pre-selected covariates, Bandyopadhyay et al [9] employed a Bayesian paradigm to compare several different spatial dependence structures for dental caries data. As these examples suggest, covariates and neighborhood structure are usually not selected simultaneously, since examining all possible combinations of covariates and neighborhood structure may be prohibitively time-consuming.…”

Section: Model Selectionmentioning

confidence: 99%

“…Spatial-temporal models are important tools for the analysis of spatial data collected repeatedly over time and have been applied to a wide range of problems, including modeling patterns in lung cancer [1], breast cancer [2], birth defects [3], and West Nile virus [4]; see also Cressie [5], Rue and Held [6], and Schabenberger and Gotway [7]. In particular, for binary data that are observed on a spatial lattice over time, spatial-temporal autologistic regression models relate binary responses to covariates while accounting for spatial and temporal dependence simultaneously [8,9]. …”

Section: Introductionmentioning

confidence: 99%

On Selecting Spatial-Temporal Autologistic Regression Models for Binary Lattice Data

Zheng¹,

Charnigo²

2012

J Biom Biostat

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“…Its operational effectiveness was attributed to the use of the Bayesian net. Another system using the Bayesian net was designed to detect the presence/absence of dental caries [29]. It demonstrated accurate predictions indicating the higher efficiency of the Bayesian net.…”

Section: Current State Of Artmentioning

confidence: 99%

Application of Bayesian Classifier for the Diagnosis of Dental Pain

et al. 2010

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Toothache is the most common symptom encountered in dental practice. It is subjective and hence, there is a possibility of under or over diagnosis of oral pathologies where patients present with only toothache. Addressing the issue, the paper proposes a methodology to develop a Bayesian classifier for diagnosing some common dental diseases (D = 10) using a set of 14 pain parameters (P = 14). A questionnaire is developed using these variables and filled up by ten dentists (n = 10) with various levels of expertise. Each questionnaire is consisted of 40 real-world cases. Total 14*10*10 combinations of data are hence collected. The reliability of the data (P and D sets) has been tested by measuring (Cronbach's alpha). One-way ANOVA has been used to note the intra and intergroup mean differences. Multiple linear regressions are used for extracting the significant predictors among P and D sets as well as finding the goodness of the model fit. A naïve Bayesian classifier (NBC) is then designed initially that predicts either presence/absence of diseases given a set of pain parameters. The most informative and highest quality datasheet is used for training of NBC and the remaining sheets are used for testing the performance of the classifier. Hill climbing algorithm is used to design a Learned Bayes' classifier (LBC), which learns the conditional probability table (CPT) entries optimally. The developed LBC showed an average accuracy of 72%, which is clinically encouraging to the dentists.

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Bayesian modeling of multivariate spatial binary data with applications to dental caries

Cited by 21 publications

References 45 publications

Better Autologistic Regression

Better Autologistic Regression

On Selecting Spatial-Temporal Autologistic Regression Models for Binary Lattice Data

Application of Bayesian Classifier for the Diagnosis of Dental Pain

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