Practical implementation of frailty models in Mendelian risk prediction

Abstract

There are numerous statistical models used to identify individuals at high risk of cancer due to inherited mutations. Mendelian models predict future risk of cancer by using family history with estimated cancer penetrances (age‐ and sex‐specific risk of cancer given the genotype of the mutations) and mutation prevalences. However, there is often residual risk heterogeneity across families even after accounting for the mutations in the model, due to environmental or unobserved genetic risk factors. We aim to improve Mendelian risk prediction by incorporating a frailty model that contains a family‐specific frailty vector, impacting the cancer hazard function, to account for this heterogeneity. We use a discrete uniform population frailty distribution and implement a marginalized approach that averages each family's risk predictions over the family's frailty distribution. We apply the proposed approach to improve breast cancer prediction in BRCAPRO, a Mendelian model that accounts for inherited mutations in the BRCA1 and BRCA2 genes to predict breast and ovarian cancer. We evaluate the proposed model's performance in simulations and real data from the Cancer Genetics Network and show improvements in model calibration and discrimination. We also discuss alternative approaches for incorporating frailties and their strengths and limitations.

Variation in cancer risk among families with genetic susceptibility

“…For the carrier‐only frailty model, the standard deviation of was 0.097 for carriers and 0.030 for noncarriers. While this does point to a greater heterogeneity across carriers, it also points to the inherent difficulty of estimating variation in risk based on families of relatively small size (Huang et al, 2020). The estimated was 0.681 for carriers and 0.314 for noncarriers, pointing to greater heterogeneity among carriers.…”

“…These biases could be reduced by using an approach that estimates a frailty for each family, such as the maximum likelihood approach proposed in Gorfine et al (2013), and then uses frailty‐adjusted penetrances for the cancer outcome and genotype imputations. On the other hand, estimation of the frailty distribution with realistic sample sizes, family sizes, and multiple cancers can be quite challenging (Huang et al, 2020).…”

“…First, patterns of variations may be more complex than captured by the model, particularly in terms of the dependence between carriers and noncarriers. Second, Huang et al (2020) demonstrated the practical challenges in implementing frailty models in the familial context, including the difficulty of estimating the frailty distribution. Thus, the proposed O / E ratios can be viewed as a simpler and more descriptive approach to quantifying heterogeneity.…”

“…Consider the hazard function for the (discrete) cancer age Here are prespecified baseline hazard functions obtained when the frailty is 0. In our situation, these are derived from the MMRpro penetrances (see Huang et al, 2020 for additional details on the derivation process). The frailty model specifies the hazard functions as This formulation of the frailty model is equivalent to the more common formulation using continuous times (Kalbfleisch & Prentice,…”

“…are prespecified baseline hazard functions obtained when the frailty is 0. In our situation, these are derived from the MMRpro penetrances (see Huang et al, 2020 for additional details on the derivation process). The frailty model specifies the hazard functions as…”