Sampling Distributions of Critical Illness Insurance Premium Rates: Breast and Ovarian Cancer

Abstract

Evaluating the risk of disorders in long-term insurance often relies on rates of onset estimated from quite small epidemiological studies. These estimates can carry considerable uncertainty, hence so may functions of them, such as a premium rate. In the case of genetic disorders, where it may be required to demonstrate the reliability of genetic information as a risk factor, such uncertainty may be material. Epidemiological studies publish their results in a variety of forms and it is rarely easy to estimate the sampling distribution of a premium rate without access to the original data. We found a large study of breast and ovarian cancer that cited relative risks of breast and ovarian cancer onset, with confidence intervals, in 10-year age groups. We obtained critical illness premium rates and their sampling distributions by parametric bootstrapping, and investigated the effect of possible patterns of sampling correlations. We found that this study provides ample statistical evidence that known BRCA1 or BRCA2 mutations, or a typical family history of breast or ovarian cancer, are reliable risk factors, but the sampling covariances of the relative risks could be important at some ages and terms. Studies that cite only standard errors of parameter estimates erect a small but awkward barrier between the models they describe, and some important actuarial questions.