Bayesian modelling of Dupuytren disease by using Gaussian copula graphical models

Cross-sectional survey and Bayesian network model analysis of traditional Chinese medicine in Austria: investigating public awareness, usage determinants and perception of scientific support

OBJECTIVES

Despite the paucity of evidence verifying its efficacy and safety, traditional Chinese medicine (TCM) is expanding in popularity and political support. Decisions to include TCM diagnoses in the International Classification of Diseases 11th Revision and campaigns to integrate TCM into national healthcare systems have occurred while public perception and usage of TCM, especially in Europe, remains undetermined. Accordingly, this study investigates TCM's popularity, usage and perceived scientific support, as well as its relationship to homeopathy and vaccinations.

DESIGN/SETTING

We performed a cross-sectional survey of the Austrian population. Participants were either recruited on the street (in-person) or online (web-link) via a popular Austrian newspaper.

PARTICIPANTS

1382 individuals completed our survey. The sample was poststratified according to data derived from Austria's Federal Statistical Office.

OUTCOME MEASURES

Associations between sociodemographic factors, opinion towards TCM and usage of complementary medicine (CAM) were investigated using a Bayesian graphical model.

RESULTS

Within our poststratified sample, TCM was broadly known (89.9% of women, 90.6% of men), with 58.9% of women and 39.5% of men using TCM between 2016 and 2019. Moreover, 66.4% of women and 49.7% of men agreed with TCM being supported by science. We found a positive relationship between perceived scientific support for TCM and trust in TCM-certified medical doctors (ρ=0.59, 95% CI 0.46 to 0.73). Moreover, perceived scientific support for TCM was negatively correlated with proclivity to get vaccinated (ρ=-0.26, 95% CI -0.43 to -0.08). Additionally, our network model yielded associations between TCM-related, homeopathy-related and vaccination-related variables.

CONCLUSIONS

TCM is widely known within the Austrian general population and used by a substantial proportion. However, a disparity exists between the commonly held public perception that TCM is scientific and findings from evidence-based studies. Emphasis should be placed on supporting the distribution of unbiased, science-driven information.

Bayesian Estimation of Single-Test Reliability Coefficients

Popular measures of reliability for a single-test administration include coefficient α, coefficient λ₂, the greatest lower bound (glb), and coefficient ω. First, we show how these measures can be easily estimated within a Bayesian framework. Specifically, the posterior distribution for these measures can be obtained through Gibbs sampling - for coefficients α, λ₂, and the glb one can sample the covariance matrix from an inverse Wishart distribution; for coefficient ω one samples the conditional posterior distributions from a single-factor CFA-model. Simulations show that - under relatively uninformative priors - the 95% Bayesian credible intervals are highly similar to the 95% frequentist bootstrap confidence intervals. In addition, the posterior distribution can be used to address practically relevant questions, such as "what is the probability that the reliability of this test is between .70 and .90?", or, "how likely is it that the reliability of this test is higher than .80?" In general, the use of a posterior distribution highlights the inherent uncertainty with respect to the estimation of reliability measures.

Regression‐based Bayesian estimation and structure learning for nonparanormal graphical models

A nonparanormal graphical model is a semiparametric generalization of a Gaussian graphical model for continuous variables in which it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone transformations. We consider a Bayesian approach to inference in a nonparanormal graphical model in which we put priors on the unknown transformations through a random series based on B‐splines. We use a regression formulation to construct the likelihood through the Cholesky decomposition on the underlying precision matrix of the transformed variables and put shrinkage priors on the regression coefficients. We apply a plug‐in variational Bayesian algorithm for learning the sparse precision matrix and compare the performance to a posterior Gibbs sampling scheme in a simulation study. We finally apply the proposed methods to a microarray dataset. The proposed methods have better performance as the dimension increases, and in particular, the variational Bayesian approach has the potential to speed up the estimation in the Bayesian nonparanormal graphical model without the Gaussianity assumption while retaining the information to construct the graph.

Bayesian analysis of multivariate crash counts using copulas

There has been growing interest in jointly modeling correlated multivariate crash counts in road safety research over the past decade. To assess the effects of roadway characteristics or environmental factors on crash counts by severity level or by collision type, various models including multivariate Poisson regression models, multivariate negative binomial regression models, and multivariate Poisson-Lognormal regression models have been suggested. We introduce more general copula-based multivariate count regression models with correlated random effects within a Bayesian framework. Our models incorporate the dependence among the multivariate crash counts by modeling multivariate random effects using copulas. Copulas provide a flexible way to construct valid multivariate distributions by decomposing any joint distribution into a copula and the marginal distributions. Overdispersion as well as general correlation structures including both positive and negative correlations in multivariate crash counts can easily be accounted for by this approach. Our copular-based models can also encompass previously suggested multivariate count regression models including multivariate Poisson-Gamma mixture models and multivariate Poisson-Lognormal regression models. The proposed method is illustrated with crash count data of five different severity levels collected from 451 three-leg unsignalized intersections in California.

Using Bayesian Latent Gaussian Graphical Models to Infer Symptom Associations in Verbal Autopsies

Learning dependence relationships among variables of mixed types provides insights in a variety of scientific settings and is a well-studied problem in statistics. Existing methods, however, typically rely on copious, high quality data to accurately learn associations. In this paper, we develop a method for scientific settings where learning dependence structure is essential, but data are sparse and have a high fraction of missing values. Specifically, our work is motivated by survey-based cause of death assessments known as verbal autopsies (VAs). We propose a Bayesian approach to characterize dependence relationships using a latent Gaussian graphical model that incorporates informative priors on the marginal distributions of the variables. We demonstrate such information can improve estimation of the dependence structure, especially in settings with little training data. We show that our method can be integrated into existing probabilistic cause-of-death assignment algorithms and improves model performance while recovering dependence patterns between symptoms that can inform efficient questionnaire design in future data collection.

Dietary Intakes of Vegetable Protein, Folate, and Vitamins B-6 and B-12 Are Partially Correlated with Physical Functioning of Dutch Older Adults Using Copula Graphical Models

BACKGROUND

In nutritional epidemiology, dealing with confounding and complex internutrient relations are major challenges. An often-used approach is dietary pattern analyses, such as principal component analysis, to deal with internutrient correlations, and to more closely resemble the true way nutrients are consumed. However, despite these improvements, these approaches still require subjective decisions in the preselection of food groups. Moreover, they do not make efficient use of multivariate dietary data, because they detect only marginal associations. We propose the use of copula graphical models (CGMs) to model and make statistical inferences regarding complex associations among variables in multivariate data, where associations between all variables can be learned simultaneously.

OBJECTIVE

We aimed to reconstruct nutritional intake and physical functioning networks in Dutch older adults by applying a CGM.

METHODS

We addressed this issue by uncovering the pairwise associations between variables while correcting for the effect of remaining variables. More specifically, we used a CGM to infer the precision matrix, which contains all the conditional independence relations between nodes in the graph. The nonzero elements of the precision matrix indicate the presence of a direct association. We applied this method to reconstruct nutrient-physical functioning networks from the combined data of 4 studies (Nu-Age, ProMuscle, ProMO, and V-Fit, total n = 662, mean ± SD age = 75 ± 7 y). The method was implemented in the R package nutriNetwork which is freely available at https://cran.r-project.org/web/packages/nutriNetwork.

RESULTS

Greater intakes of vegetable protein and vitamin B-6 were partially correlated with higher scores on the total Short Physical Performance Battery (SPPB) and the chair rise test. Greater intakes of vitamin B-12 and folate were partially correlated with higher scores on the chair rise test and the total SPPB, respectively.

CONCLUSIONS

We determined that vegetable protein, vitamin B-6, folate, and vitamin B-12 intakes are partially correlated with improved functional outcome measurements in Dutch older adults.

An Expectation Conditional Maximization approach for Gaussian graphical models

Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes enormous, rendering even state-of-the-art Bayesian stochastic search computationally infeasible. We propose a deterministic alternative to estimate Gaussian and Gaussian copula graphical models using an Expectation Conditional Maximization (ECM) algorithm, extending the EM approach from Bayesian variable selection to graphical model estimation. We show that the ECM approach enables fast posterior exploration under a sequence of mixture priors, and can incorporate multiple sources of information.