A Deep Neural Network Two-part Model and Feature Importance Test for Semi-continuous Data

Semi-continuous data frequently arise in clinical practice. For example, while many surgical patients suffer from varying degrees of acute postoperative pain (POP) post surgery (i.e., POP score > 0), others experience none (i.e., POP score = 0), indicating the existence of two distinct data processes at play. Existing parametric or semi-parametric two-part modeling methods for this type of semicontinuous data can fail to appropriately model these two underlying data processes as such methods rely heavily on (generalized) linear additive assumptions. However, many factors may interact to jointly influence the experience of POP non-additively and non-linearly. Motivated by this challenge and inspired by the flexibility of deep neural networks (DNN) to accurately approximate complex functions universally, we derive a DNN-based two-part model by adapting the conventional DNN methods by adding two additional components: a bootstrapping procedure along with a filtering algorithm to boost the stability of the conventional DNN, an approach we denote as sDNN. To improve the interpretability and transparency of sDNN, we further derive a feature importance testing procedure to identify important features contributing to the outcome measurements of the two data processes, denoting this approach fsDNN. We show that fsDNN not only offers a valid feature importance test but also that using the identified features can further improve the predictive performance of sDNN. The proposed sDNN- and fsDNN-based twopart models are applied to the analysis of real data from a POP study, in which application they clearly demonstrate advantages over the existing parametric and semi-parametric two-part models. Further, we conduct extensive numerical studies to demonstrate that sDNN and fsDNN consistently outperform the existing two-part models regardless of the data complexity. An R package implementing the proposed methods has been developed and deposited on GitHub (https://github.com/SkadiEye/fsDNN).