Frailty Models for Familial Risk With Application to Breast Cancer

Abstract

In evaluating familial risk for disease we have two main statistical tasks: assessing the probability of carrying an inherited genetic mutation conferring higher risk, and predicting the absolute risk of developing diseases over time for those individuals whose mutation status is known. Despite substantial progress, much remains unknown about the role of genetic and environmental risk factors, about the sources of variation in risk among families that carry high-risk mutations, and about the sources of familial aggregation beyond major Mendelian effects. These sources of heterogeneity contribute substantial variation in risk across families. In this article we present simple and efficient methods for accounting for this variation in familial risk assessment. Our methods are based on frailty models. We implemented them in the context of generalizing Mendelian models of cancer risk, and compared our approaches to others that do not consider heterogeneity across families. Our extensive simulation study demonstrates that when predicting the risk of developing a disease over time conditional on carrier status, accounting for heterogeneity results in a substantial improvement in the area under the curve of the receiver operating characteristic. On the other hand, the improvement for carriership probability estimation is more limited. We illustrate the utility of the proposed approach through the analysis of BRCA1 and BRCA2 mutation carriers in the Washington Ashkenazi Kin-Cohort Study of Breast Cancer. Supplementary materials for this article are available online.

KEY WORDS:

• Familial risk prediction
• Multivariate survival
• Risk index
• ROC analysis

Notes

*These authors contributed equally to this work. The authors thank Dr. Nilanjan Chatterjee for faciliating the access of the Washington Ashkenazi Jewish data. Work of Giovanni Parmigiani is supported by grant KG081303 from the Susan G Komen Breast Cancer Foundation and grants NIH/NCI 5P30 CA006516-46 and 1R21CA177233-01. Work of Li Hsu is supported by NIH grants P01CA53996, R01AG014358, and P50CA138293. Work of Malka Gorfine is supported by the Israel Science Foundation (ISF) grant 2012898. The R code for running our methods can be provided upon request by the first author.