A Monotonic Single-Index Model Powered by Deep Neural Networks for Non-Gaussian Periodontal Data

Music City Center 

Periodontal pocket depth is a widely used biomarker for diagnosing risk of periodontal disease. However, pocket depth typically exhibits skewness and heavy-tailedness, and its relationship with clinical risk factors is often nonlinear. Motivated by periodontal studies, this paper develops a robust single-index modal regression framework for analyzing skewed and heavy-tailed data. Our method has the following novel features: (1) a flexible two-piece scale Student-t error distribution that generalizes both normal and two-piece scale normal distributions; (2) a deep neural network with guaranteed monotonicity constraints to estimate the unknown single-index function; and (3) theoretical guarantees, including model identifiability and a universal approximation theorem. Our single-index model combines the flexibility of neural networks and the two-piece scale Student-t distribution, delivering robust mode-based estimation that is resistant to outliers, while retaining clinical interpretability through parametric index coefficients. We demonstrate the performance of our method through simulation studies and an application to periodontal disease data from the HealthPartners Institute of Minnesota. The proposed methodology is implemented in the R package DNNSIM.

deep neural network

single index model

skewness

heavy-tailed

modal regression 

Section on Statistical Learning and Data Science