An Analysis of Correlated Multivariate Binary Data: Application to Familial Cancers of the Ovary and Breast

Abstract

SUMMARY The association between ovarian and breast cancer, both within and between family members, is examined using pooled data from five case-control studies. The occurrences of these diseases in sisters and mothers are analysed using a quadratic exponential model, which is an extension of the model of Zhao and Prentice for correlated univariate data. An advantage of this model is that the associations between pairs of diseases and pairs of relatives, which are of primary importance, are related to simple functions of its parameters. Also, the model applies to non-randomly sampled data, such as the case-control data, because it completely specifies the joint distribution of responses. A major weakness is that it is not immediately applicable to studies of families of different sizes. None-the-less, we find it to be useful under certain conditions, such as rare diseases. Our analysis of the data suggests that the risk of ovarian cancer is highly dependent on maternal history.