Bayesian Modelling of Dupuytren Disease by Using Gaussian Copula Graphical Models

Abstract

Summary. Dupuytren disease is a fibroproliferative disorder with unknown aetiology that often progresses and eventually can cause permanent contractures of the fingers affected. We provide a computationally efficient Bayesian framework to discover potential risk factors and investigate which fingers are jointly affected. Our Bayesian approach is based on Gaussian copula graphical models, which provide a way to discover the underlying conditional independence structure of variables in multivariate data of mixed types. In particular, we combine the semiparametric Gaussian copula with extended rank likelihood to analyse multivariate data of mixed types with arbitrary marginal distributions. For structural learning, we construct a computationally efficient search algorithm by using a transdimensional Markov chain Monte Carlo algorithm based on a birth-death process. In addition, to make our statistical method easily accessible to other researchers, we have implemented our method in C++ and provide an interface with R software as an R package BDgraph, which is freely available from http://CRAN.Rproject.org/package=BDgraph.

BDgraph: An R Package for Bayesian Structure Learning in Graphical Models

“…We have presented the BDgraph package which was designed for Bayesian structure learning in general -decomposable and non-decomposable -undirected graphical models. The package implements recent improvements in computation, sampling and inference of Gaussian graphical models (Mohammadi and Wit 2015; for Gaussian data and Gaussian copula graphical models (Mohammadi et al 2017a; for non-Gaussian, discrete and mixed data.…”

“…In Section 3.2, we briefly describe the Gaussian copula graphical model , which can deal with non-Gaussian, discrete or mixed data. Then we explain the birth-death MCMC algorithm which is designed for the Gaussian copula graphical models; for more details see Mohammadi et al (2017a).…”

“…In recent years, significant progress has been made in designing efficient algorithms to discover arXiv:1501.05108v6 [stat.ML] 13 May 2019 graph structures from multivariate data (Dobra, Lenkoski, and Rodriguez 2011;Jones, Carvalho, Dobra, Hans, Carter, and West 2005;Dobra and Mohammadi 2018;Mohammadi and Wit 2015;Mohammadi, Abegaz Yazew, van den Heuvel, and Wit 2017a;Friedman, Hastie, and Tibshirani 2008;Meinshausen and Buhlmann 2006;Murray and Ghahramani 2004;Pensar, Nyman, Niiranen, Corander et al 2017;Rolfs, Rajaratnam, Guillot, Wong, and Maleki 2012;Wit and Abbruzzo 2015a,b;Dyrba, Grothe, Mohammadi, Binder, Kirste, Teipel, Initiative et al 2018;Behrouzi and Wit 2019). Bayesian approaches provide a principled alternative to various penalized approaches.…”

Loglinear model selection and human mobility

“…A third key computational improvement comes from allowing multiple edge updates at each iteration. The vast majority of the MCMC and stochastic search algorithms that have been developed in the Bayesian graphical models literature are based on adding or removing one edge at each iteration [43,48,72,48,87,60,61,58,14]. These single edge updates are in part responsible for making these structural learning algorithms quite slow for datasets that comprise a larger number of variables p. Multiple birth-death sampling approaches have been used to address image processing problems that aim to detect a configuration of objects from a digital image, and have been found to outperform the convergence speed of competing reversible jump MCMC algorithms [18,29,35,34].…”

Detecting Epistatic Selection with Partially Observed Genotype Data by Using Copula Graphical Models

“…Sklar's theorem shows that any p-dimensional joint distribution can be decomposed into its p marginal distributions and a copula, which describes the dependence structure between p-dimensional multivariate random variables (Nelsen, 1999). Various statistical network modelling approaches have been proposed for inferring high dimensional associations between non-Gaussian variables (Liu et al, 2009(Liu et al, , 2012Dobra and Lenkoski, 2011;Mohammadi et al, 2017). The above-mentioned models have some limitations; the first two methods cannot deal with missing data, and the last two are computationally expensive since their inference is based on a Bayesian approach.…”