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 paper 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.

Calibrated predictions for multivariate competing risks models

“…Our main concern is estimating the probability of a counselee developing a disease of type r by age t, t > T 0 , given the observed information ℱ = { T 0 , R 0 = 0, G 0 , Z 0 , T, R, Z, G }. The risk prediction methods presented below are in the spirit of Gorfine et al (2013), with the required modifications to accommodate competing risks. In addition, each method is contrasted with its counterpart in the case where competing risks are wrongly considered as independent right censoring.…”

“…Since the variance of the proposed estimators of the survival probability, cannot be derived analytically in a closed form, the simple resampling-based procedure of Gorfine et al (2013) is adopted. The confidence intervals construction under the parametric or non-parametric hazard functions are similar, so the subscript P or NP are omitted in the following.…”

“…In Gorfine et al (2013), a similar procedure in the a setting of no competing risks was studied by simulation. Results indicate that under a well-specified frailty distribution, the procedure performs very well, with empirical coverage rates very close to the nominal rates.…”

“…Hence, in these cases, the competing risks conditional method based on (6) may underestimate the total number of events in the population. When this is a concern, Gorfine et al’s (2013) technique of calibrating the risk prediction by considering Ŵ as a risk index can be easily adopted to correct the underestimation.…”

“…Using the frailty-based competing risks model and estimation techniques of Gorfine and Hsu (2011), we extend the risk prediction methods of Gorfine et al (2013) to handle competing risks. The current work focuses on competing risk analysis based on the first event to occur, and thus is restricted to the setting where either the probability of multiple events is negligible (e.g., when all the events are rare) or interest is focused on the first event.…”