Flexible Modeling of Time‐Dependent Covariate Effects in Survival Models With Correlated Competing Risks: Application to the Evaluation of Risk‐Reducing Salpingo‐Oophorectomy in Women With <scp> <i>BRCA1</i> </scp> Pathogenic Variants

Modeling of medical interventions, such as preventive surgeries, on a survival outcome necessitates an accurate and flexible representation of the time-dependent effect of the intervention. We propose using B-splines to model the time-dependent effect of a binary time-dependent covariate on a survival outcome in the presence of correlated competing risks. The proposed B-splines can also help choose the best functional form for the time-dependent effect. Our simulation studies demonstrate that the proposed competing risks model with B-splines performs well in estimating the time-dependent effect of the intervention and the penetrance function in all scenarios considered. We applied our proposed method to families carrying a pathogenic variant in BRCA1 recruited through the Breast Cancer Family Registry and evaluated the time-dependent effects of risk-reducing salpingo-oophorectomy on breast cancer risk in the presence of ovarian cancer and death from other causes as competing events. We found that the B-splines model better captured the changes in the association between the intervention and breast cancer over time and provided better predictive ability than alternative parametric models, such as the permanent exposure model and the Cox and Oakes model. Our results indicate that risk-reducing salpingo-oophorectomy has a significant protective effect on breast cancer incidence over the follow-up period.