A Dynamic Family History model Of Hereditary Nonpolyposis Colorectal Cancer and Critical Illness Insurance

Hereditary nonpolyposis colorectal cancer (HNPCC) is characterised by the familial aggregation of cancer of the colon and rectum (CRC). It may be caused by any of five mutations in DNA mismatch repair (MMR) genes or by non-genetic factors, such as life style. However, it accounts for only about 2% of CRC, which is a very common cancer. Previous actuarial models, of diseases with only genetic causes, assumed that a family history of the disease shows mutations to be present, but this is not true of HNPCC. This is a significant limitation, since the best information available to an underwriter (especially if the use of genetic test results is banned) is likely to be knowledge of a family history of CRC. We present a Markov model of CRC and HNPCC, which includes the presence of a family history of CRC as a state, and estimate its intensities allowing for MMR genotype. Using this we find the MMR mutation probabilities for an insurance applicant with a family history of CRC. Our model greatly simplifies the intensive computational burden of finding such probabilities by integrating over complex models of hidden family structure. We estimate the costs of critical illness insurance given the applicant's genotype or the presence of a family history. We then consider what the cost of adverse selection might be, if insurers are unable to use genetic tests or family history information. We also consider the effect of using alternative definitions of a family history in underwriting.