  In this article, we analyze perinatal data with birth weight (BW) as
primarily interesting response variable. Gestational age (GA) is usually an
important covariate and included in polynomial form. However, in opposition to
this univariate regression, bivariate modeling of BW and GA is recommended to
distinguish effects on each, on both, and between them. Rather than a
parametric bivariate distribution, we apply conditional copula regression,
where marginal distributions of BW and GA (not necessarily of the same form)
can be estimated independently, and where the dependence structure is modeled
conditional on the covariates separately from these marginals. In the resulting
distributional regression models, all parameters of the two marginals and the
copula parameter are observation-specific. Besides biometric and obstetric
information, data on drinking water contamination and maternal smoking are
included as environmental covariates. While the Gaussian distribution is
suitable for BW, the skewed GA data are better modeled by the three-parametric
Dagum distribution. The Clayton copula performs better than the Gumbel and the
symmetric Gaussian copula, indicating lower tail dependence (stronger
dependence when both variables are low), although this non-linear dependence
between BW and GA is surprisingly weak and only influenced by Cesarean section.
A non-linear trend of BW on GA is detected by a classical univariate model that
is polynomial with respect to the effect of GA. Linear effects on BW mean are
similar in both models, while our distributional copula regression also reveals
covariates' effects on all other parameters.
