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Title: Bayesian nonparametric approach for vine copula modelling: An application to preterm birth data in repeated pregnancies Authors:  Rosario Barone - Sapienza University of Rome (Italy) [presenting]
Luciana Dalla Valle - University of Plymouth (United Kingdom)
Abstract: Preterm births represent a serious medical issue since they can affect the health of the mother and the fetus. Since women tend to be affected by adverse outcomes in repeated pregnancies, we focus on the study of the dependence between preterm births in repeated pregnancies using a vine copula approach. Our dataset includes 164 women with gestational ages lower than 37 weeks, each of whom has had at least three pregnancies. Since we are working with truncated data, distributional assumptions on the margins might be restrictive: we model the gestational age of each pregnancy as a GAMLSS (more specifically as a truncated Weibull), choosing as covariates information about smoking, history of preterm birth, parity and type of preterm birth. Then, we follow a Bayesian nonparametric method to estimate the pair copulas in the vine, extending the approach presented by Wu et. al (2015), which used an infinite mixture of Gaussian copula densities to define a nonparametric copula for modelling any dependence structure between the marginals, to the vine copula setting. Therefore, we assume a Dirichlet process prior on each pair copula. Our approach has two main advantages compared to the traditional methods: on the one hand it is extremely flexible, due to the vine structure, and on the other hand it overcomes the need of specify the families of each pair copula.