A semiparametric 2-part mixed-effects heteroscedastic transformation model for correlated right-skewed semicontinuous data.

In longitudinal or hierarchical structure studies, we often encounter a semicontinuous variable that has a certain proportion of a single value and a continuous and skewed distribution among the rest of values. In this paper, we propose a new semiparametric 2-part mixed-effects transformation model to fit correlated skewed semicontinuous data. In our model, we allow the transformation to be nonparametric. Fitting the proposed model faces computational challenges due to intractable numerical integrations. We derive the estimates for the parameter and the transformation function based on an approximate likelihood, which has high-order accuracy but less computational burden. We also propose an estimator for the expected value of the semicontinuous outcome on the original scale. Finally, we apply the proposed methods to a clinical study on effectiveness of a collaborative care treatment on late-life depression on health care costs.