Identifying individuals who are at high risk of cancer due to inherited germline mutations is critical for effective implementation of personalized prevention strategies. Most existing models focus on a few specific syndromes; however recent evidence from multi-gene panel testing shows that many syndromes are overlapping, motivating the development of models that incorporate family history on several cancers and predict mutations for a comprehensive panel of genes. We present PanelPRO, a new, open-source R package providing a fast, flexible back-end for multi-gene, multi-cancer risk modeling with pedigree data. It includes a customizable database with default parameter values estimated from published studies and allows users to select any combinations of genes and cancers for their models, including well-established single syndrome BayesMendel models (BRCAPRO and MMRPRO). This leads to more accurate risk predictions and ultimately has a high impact on prevention strategies for cancer and clinical decision making. The package is available for download for research purposes at https://projects.iq.harvard.edu/bayesmendel/panelpro.

(1) Background: The purpose of this study is to compare the performance of four breast cancer risk prediction models by race, molecular subtype, family history of breast cancer, age, and BMI. (2) Methods: Using a cohort of women aged 40–84 without prior history of breast cancer who underwent screening mammography from 2006 to 2015, we generated breast cancer risk estimates using the Breast Cancer Risk Assessment tool (BCRAT), BRCAPRO, Breast Cancer Surveillance Consortium (BCSC) and combined BRCAPRO+BCRAT models. Model calibration and discrimination were compared using observed-to-expected ratios (O/E) and the area under the receiver operator curve (AUC) among patients with at least five years of follow-up. (3) Results: We observed comparable discrimination and calibration across models. There was no significant difference in model performance between Black and White women. Model discrimination was poorer for HER2+ and triple-negative subtypes compared with ER/PR+HER2−. The BRCAPRO+BCRAT model displayed improved calibration and discrimination compared to BRCAPRO among women with a family history of breast cancer. Across models, discriminatory accuracy was greater among obese than non-obese women. When defining high risk as a 5-year risk of 1.67% or greater, models demonstrated discordance in 2.9% to 19.7% of patients. (4) Conclusions: Our results can inform the implementation of risk assessment and risk-based screening among women undergoing screening mammography.

In 1982, Tsallis derived a formula which proposed an exact value of 0.522372078... for the bond percolation threshold of the kagome lattice. We use the substitution method, which is based on stochastic ordering, to compare the probability distribution of connections in the homogeneous bond percolation model on the kagome lattice to those of an exactly-solved inhomogeneous bond percolation model on the martini lattice. The bounds obtained are $0.522394<p_c(\mbox{kagome}) < 0.526750$, where the lower bound shows that the value conjectured by Tsallis is incorrect.

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.