Familial recurrence risk with varying amount of family history

The familial recurrence risk is the probability a person will have disease, given a reported family history. When family histories are obtained as simple counts of disease among family members, as often obtained in cancer registries or surveys, we propose methods to estimate recurrence risks based on truncated binomial distributions. By this approach, we are able to obtain unbiased estimates of risk for a person with at least k-affected relatives, where k can be specified to determine how risk varies with k. We also derive robust variances of the recurrence risk estimate, to account for correlations within families, such as those induced by shared genes or shared environment, without explicitly modeling the factors that cause familial correlations. Furthermore, we illustrate how mixture models can be used to account for a sample composed of low- and high-risk families. Using simulations, we illustrate the properties of the proposed methods. Application of our methods to a family history survey of prostate cancer shows that the recurrence risk for prostate cancer increased from 16%, when there was at least one affected relative, to 52%, when there was at least five affected relatives.