In this paper, we proposed a semi-parametric single-index two-part regression model to weaken assumptions in parametric regression methods that were frequently used in the analysis of skewed data with additional zero values. The estimation procedure for the parameters of interest in the model was easily implemented. The proposed estimators were shown to be consistent and asymptotically normal. Through a simulation study, we showed that the proposed estimators have reasonable finite-sample performance. We illustrated the application of the proposed method in one real study on the analysis of health care costs
