In mixed company: Bayesian inference for bivariate conditional copula models with discrete and continuous outcomes

Boosting distributional copula regression

Capturing complex dependence structures between outcome variables (e.g., study endpoints) is of high relevance in contemporary biomedical data problems and medical research. Distributional copula regression provides a flexible tool to model the joint distribution of multiple outcome variables by disentangling the marginal response distributions and their dependence structure. In a regression setup, each parameter of the copula model, that is, the marginal distribution parameters and the copula dependence parameters, can be related to covariates via structured additive predictors. We propose a framework to fit distributional copula regression via model-based boosting, which is a modern estimation technique that incorporates useful features like an intrinsic variable selection mechanism, parameter shrinkage and the capability to fit regression models in high-dimensional data setting, that is, situations with more covariates than observations. Thus, model-based boosting does not only complement existing Bayesian and maximum-likelihood based estimation frameworks for this model class but rather enables unique intrinsic mechanisms that can be helpful in many applied problems. The performance of our boosting algorithm for copula regression models with continuous margins is evaluated in simulation studies that cover low- and high-dimensional data settings and situations with and without dependence between the responses. Moreover, distributional copula boosting is used to jointly analyze and predict the length and the weight of newborns conditional on sonographic measurements of the fetus before delivery together with other clinical variables.

A flexible copula-based approach for the analysis of secondary phenotypes in ascertained samples

Data collected for a genome-wide association study of a primary phenotype are often used for additional genome-wide association analyses of secondary phenotypes. However, when the primary and secondary traits are dependent, naïve analyses of secondary phenotypes may induce spurious associations in non-randomly ascertained samples. Previously, retrospective likelihood-based methods have been proposed to correct for sampling biases arising in secondary trait association analyses. However, most methods have been introduced to handle studies featuring a case-control design based on a binary primary phenotype. As such, these methods are not directly applicable to more complicated study designs such as multiple-trait studies, where the sampling mechanism also depends on the secondary phenotype, or extreme-trait studies, where individuals with extreme primary phenotype values are selected. To accommodate these more complicated sampling mechanisms, only a few prospective likelihood approaches have been proposed. These approaches assume a normal distribution for the secondary phenotype (or the latent secondary phenotype) and a bivariate normal distribution for the primary-secondary phenotype dependence. In this paper, we propose a unified copula-based approach to appropriately detect genetic variant/secondary phenotype association in the presence of selected samples. Primary phenotype is either binary or continuous and the secondary phenotype is continuous although not necessary normal. We use both prospective and retrospective likelihoods to account for the sampling mechanism and use a copula model to allow for potentially different dependence structures between the primary and secondary phenotypes. We demonstrate the effectiveness of our approach through simulation studies and by analyzing data from the Avon Longitudinal Study of Parents and Children cohort.

Analysis of paediatric visual acuity using Bayesian copula models with sinh-arcsinh marginal densities

We analyse paediatric ophthalmic data from a large sample of children aged between 3 and 8 years. We use a Bayesian additive conditional bivariate copula regression model with sinh-arcsinh marginal densities with location, scale, and shape parameters that depend smoothly on a covariate. We perform Bayesian inference about the unknown quantities of our model using a specially tailored Markov chain Monte Carlo algorithm. We gain new insights about the processes, which determine transformations in visual acuity with respect to age, including the nature of joint changes in both eyes as modelled with the age-related copula dependence parameter. We analyse posterior predictive distributions to identify children with unusual sight characteristics, distinguishing those who are bivariate, but not univariate outliers. In this way, we provide an innovative tool that enables clinicians to identify children with unusual sight who may otherwise be missed. We compare our simultaneous Bayesian method with a two-step frequentist generalised additive modelling approach.

Risk Measurement of Stock Markets in BRICS, G7, and G20: Vine Copulas versus Factor Copulas

Multivariate copulas have been widely used to handle risk in the financial market. This paper aimed to adopt two novel multivariate copulas, Vine copulas and Factor copulas, to measure and compare the financial risks of the emerging economy, developed economy, and global economy. In this paper, we used data from three groups (BRICS, which stands for emerging markets, specifically, those of Brazil, Russia, India, China, and South Africa; G7, which refers to developed countries; and G20, which represents the global market), separated into three periods (pre-crisis, crisis, and post-crisis) and weighed Value at Risk (VaR) and Expected Shortfall (ES) (based on their market capitalization) to compare among three copulas, C-Vine, D-Vine, and Factor copulas. Also, real financial data demonstrated that Factor copulas have stronger stability and perform better than the other two copulas in high-dimensional data. Moreover, we showed that BRICS has the highest risk and G20 has the lowest risk of the three groups.