Inference on Competing Risks in Breast Cancer Data

While nonparametric methods have been well established for inference on competing risks data, parametric methods for such data have not been developed as much. Because the cumulative incidence functions are improper by their nature, flexible distribution families accommodating improperness are needed for modeling competing data more accurately. Additionally, different types of events present in a competing risks setting may be correlated, yet current inference methods do not permit inferring such data taking into account the correlation between failure time distributions. This work first presents two new distributions which are well-suited for modeling competing risks data. In existing inference procedures for competing risks data, it appears that the correlation between failure time distributions of competing events are fixed as a constant. In the second part of this dissertation, a novel approach is proposed which allows researchers to model competing risks data by taking the correlation into account by estimating it. The methods are illustrated by analyzing survival data from a breast cancer trial of the National Surgical Adjuvant Breast and Bowel Project. Simulation studies are also presented for each of the proposed new distributions.Public Health Significance: Competing risks occur often in many clinical studies, and must be accounted for whenever researchers are interested in only one type of event. For example, researchers may be interested in investigating only local recurrences of breast cancer, but must also take into account all other possible types of events as competing. Parametric methods are not currently as well established as other methods for competing risks data. Development of flexible parametric inference procedures suitable for modeling competing risks data would provide more accurate information, which will serve to improve patient care in clinical settings