Semicontinuous Regression Models with Skew Distributions

Abstract

In applied studies, researchers are often confronted with semicontinuous response models. These are models with a semicontinuous response variable, i.e. a continuous variable that has a lower bound, that we here consider to be zero, and such that a sizable fraction of the observations takes value on this boundary. Semicontinuous response models are common in pharmacovigilance, pharmacoepidemiological and pharmacoeconomic studies, where it can be sometimes useful to evaluate and monitor the doses of a certain drug substance consumed by the general population. The preponderant number of observations taking value zero corresponds to the part of the population which is not actually consuming the medicine, either because they do not need it or because, even if they need it, they are not taking it in a given interval of time. Another interesting field of application concerns goods or drugs consumption to be studied for economic or social purposes. We here explore the use of several asymmetric distributions to address the fact that the continuous part of the data distribution shows skewness in most cases. As an illustration, the proposal is applied to model alcohol expenditure in Italian households.