Partially Linear Additive Quantile Regression: Theory and Applications to Breast Cancer Patients' Survival

Accurate prediction of the breast cancer patient's life expectancy is essential for treatment decisions. This study aims to develop a novel model estimation and variable selection method for the partially linear additive quantile regression model when the survival times are subject to right censoring. Rather than most of the existing methods using the formulation of synthetic data points or weighting schemes to tackle censoring, we use an adapted loss function to solve censoring. Moreover, we adopt the B-spline to approximate the nonparametric additive components. To further improve the prediction accuracy, we use the group smoothly clipped absolute deviation (SCAD) penalty to select significant variables in the nonparametric additive components. To implement the proposed method, we develop an effective block-wise majorize-minimize (MM) algorithm. Furthermore, we establish the asymptotic properties for the resultant estimators. Numerical simulations illustrate that the finite sample performance of the proposed method outperforms alternative methods. Finally, we apply our method for the personalized treatment of female malignant metastatic breast cancer patients, using the Surveillance, Epidemiology, and End Results (SEER) research data.