A log-linear model for binary pedigree data

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Abstract
A pedigree model for binary data, motivated by log-linear modelling, has been developed to examine evidence for familial aggregation in disease status. From an epidemiological point of view a convenient way to express disease concordance between a pair of relatives is in terms of the odds ratio. For a rare disease this is almost equivalent to the relative risk of one family member being affected given that the other is affected, and in extending this to pedigrees it is assumed that these relative risks are multiplicative. In applying the model to the breast cancer data, pedigrees on a rare disease ascertained through an affected proband, it has been shown that estimation of concordance is dependent critically on knowing the probability that a sampled individual is affected. Therefore known population estimates of prevalence or cumulative risk, and an appropriate ascertainment correction, need to be invoked for the model to give proper estimates of disease concordance. The model is flexible in that measured ancillary risk factors, including genetic marker information, can be incorporated into the analysis. Therefore in future studies this information should be collected on all individuals, not just those affected. Suggested statistics for examining a fitted model are presented.

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