Semicontinuous regression models with Skew distributions

In many studies on drug consumption in a given population, researchers are often confronted with models for a semicontinuous outcome variable. A semicontinuous variable has a lower (or upper) bound, that we here consider to be zero, and is such that the probability of observing a value on this boundary is non negligible. In the framework of pharmacovigilance, pharmacoepidemiological and pharmacoeconomic studies, for instance, it can be sometimes useful to evaluate and monitor the consumption of a certain drug in the general public, i.e. outside of a clinical trial. The preponderant presence of observed zeros corresponds to the part of the population which is not consuming the medicine, either because they do not need it or because they do not actually take it.We here explore the use of several skew distributions to address the fact that often (a) the excess of zero may be due to an underlying skewed distribution function and (b) the continuous part of the data is often skewed