Semiparametric Accelerated Failure Time Partial Linear Model and Its Application to Breast Cancer.

Breast cancer is the most common non-skin cancer in women and the second most common cause of cancer-related death in U.S. women. It is well known that the breast cancer survival varies by age at diagnosis. For most cancers, the relative survival decreases with age but breast cancer may have the unusual age pattern. In order to reveal the stage risk and age effects pattern, we propose the semiparametric accelerated failure time partial linear model and develop its estimation method based on the P-spline and the rank estimation approach. The simulation studies demonstrate that the proposed method is comparable to the parametric approach when data is not contaminated, and more stable than the parametric methods when data is contaminated. By applying the proposed model and method to the breast cancer data set of Atlantic county, New Jersey from SEER program, we successfully reveal the significant effects of stage, and show that women diagnosed around 38s have consistently higher survival rates than either younger or older women.