Estimating successive cancer risks in Lynch Syndrome families using a progressive three-state model

Lynch Syndrome (LS) families harbor mutated mismatch repair genes,which predispose them to specific types of cancer. Because individuals within LS families can experience multiple cancers over their lifetime, we developed a progressive three-state model to estimate the disease risk from a healthy (state 0) to a first cancer (state 1) and then to a second cancer (state 2). Ascertainment correction of the likelihood was made to adjust for complex sampling designs with carrier probabilities for family members with missing genotype information estimated using their family's observed genotype and phenotype information in a one-step expectation-maximization algorithm. A sandwich variance estimator was employed to overcome possible model misspecification. The main objective of this paper is to estimate the disease risk (penetrance) for age at a second cancer after someone has experienced a first cancer that is also associated with a mutated gene. Simulation study results indicate that our approach generally provides unbiased risk estimates and low root mean squared errors across different family study designs, proportions of missing genotypes, and risk heterogeneities. An application to 12 large LS families from Newfoundland demonstrates that the risk for a second cancer was substantial and that the age at a first colorectal cancer significantly impacted the age at any LS subsequent cancer. This study provides new insights for developing more effective management of mutation carriers in LS families by providing more accurate multiple cancer risk estimates.