Electronic Thesis and Dissertation Repository

Thesis Format



Master of Science




Choi, Yun-Hee


This thesis aims to develop a flexible approach for modelling time-dependent covariate effects on event risk using B-splines in the presence of correlated competing risks. The performance of the proposed model was evaluated via simulation in terms of the bias and precision of the estimation of the parameters and penetrance functions. In addition, we extended the concordance index to account for time-dependent effects and competing events simultaneously and demonstrated its inference procedures. We applied our proposed methods to data rising from the BRCA1 mutation families from the breast cancer family registry to evaluate the time-dependent effects of mammographic screening and prophylactic surgery on breast cancer risks, where ovarian cancer and death from other causes are competing events. Different time-dependent models were evaluated via time-dependent C-index and Brier scores.

Summary for Lay Audience

Hereditary breast and ovarian cancer syndrome families have significantly higher lifetime risks of developing breast and ovarian cancer than the general population. Preventive interventions such as mammographic screening (MS) and risk-reducing salpingo-oophorectomy (RRSO) can potentially reduce associated cancer risks. However, since the statuses and effects of these interventions vary over time and individuals may experience multiple cancers, the evaluation of these interventions is complicated.

To understand how the interventions affect the risk of developing breast cancer in the presence of other events, we used a statistical method called the correlated frailty competing risks model, which is applicable for family data with multiple events. To flexibly evaluate the effect of interventions, we incorporated a flexible approach, B-spline, instead of assuming the shape of the effect of RRSO on breast cancer. We further extended the concordance index, which is a common measure used to describe the predictive ability of a model to simultaneously account for the multiple events and changes in the interventions’ statuses. We applied our proposed method to BRCA1 mutation carrier families recruited through the Breast Cancer Family Registry to evaluate the time-dependent effects of MS and RRSO on breast cancer risks in the presence of ovarian cancer and death from the other causes as competing events. Then, the predictive abilities of the models were compared by using the extended concordance index.