  Mammographic screening and prophylactic surgery such as risk-reducing
salpingo oophorectomy (RRSO) can potentially reduce breast cancer risks among
mutation carriers of BRCA families. The evaluation of these interventions is
usually complicated by the fact that their effects on breast cancer may change
over time and by the presence of competing risks. We introduce a correlated
competing risks model to model breast and ovarian cancer risks within BRCA1
families that accounts for time-varying covariates (TVCs). Different parametric
forms for these TVCs are proposed for more flexibility and a correlated gamma
frailty model is specified to account for the correlated competing events. We
also introduced a new ascertainment correction approach that accounts for the
selection of families through probands affected with either breast or ovarian
cancer, or unaffected. Our simulation studies demonstrate the good performances
of our proposed approach in terms of bias and precision of the estimators of
model parameters and cause-specific penetrances over different levels of
familial correlations. We apply our new approach to 498 BRCA1 mutation carrier
families recruited through the Breast Cancer Family Registry. Our results
demonstrate the importance of the functional form of the TVC when assessing the
role of RRSO on breast cancer. In particular, under the best fitting TVC model,
the overall effect of RRSO on breast cancer risk was statistically significant
in women with BRCA1.
