Multiple diseases in carrier probability estimation: Accounting for surviving all cancers other than breast and ovary in BRCAPRO

Mendelian models can predict who carries an inherited deleterious mutation of known disease genes based on family history. For example, the BRCAPRO model is commonly used to identify families who carry mutations of BRCA1 and BRCA2, based on familial breast and ovarian cancers. These models incorporate the age of diagnosis of diseases in relatives and current age or age of death. We develop a rigorous foundation for handling multiple diseases with censoring. We prove that any disease unrelated to mutations can be excluded from the model, unless it is sufficiently common and dependent on a mutation-related disease time. Furthermore, if a family member has a disease with higher probability density among mutation carriers, but the model does not account for it, then the carrier probability is deflated. However, even if a family only has diseases the model accounts for, if the model excludes a mutation-related disease, then the carrier probability will be inflated. In light of these results, we extend BRCAPRO to account for surviving all non-breast/ovary cancers as a single outcome. The extension also enables BRCAPRO to extract more useful information from male relatives. Using 1500 families from the Cancer Genetics Network, accounting for surviving other cancers improves BRCAPRO's concordance index from 0.758 to 0.762 (p=0.046), improves its positive predictive value from 35 to 39 per cent (p<10^-6) without impacting its negative predictive value, and improves its overall calibration, although calibration slightly worsens for those with carrier probability <10 per cent.