EXACT INFERENCE FOR FAMILY DISEASE CLUSTERS

Abstract

In many epidemiologic studies the first indication of an environmental or genetic contribution to the risk of disease is the way in which the diseased cases cluster within the same family units. The concept of clustering is contrasted with incidence. We assume that all individuals within the same family are independent, up to their disease status. This assumption is used to provide an exact test of the initial hypothesis of no familial link with the disease, conditional on the number of diseased cases and the sizes of the various family units. Ascertainment bias is described and the appropriate sampling distribution is demonstrated. Two numerical examples with published data illustrate these methods.

Keywords:

• Exact inference
• Multivariate discrete distributions
• Ascertainment sampling
• Sparse categorical data
• Binomial distribution

ACKNOWLEDGMENTS

This research was supported by grant P30-CA16359 awarded to the Yale Comprehensive Cancer Center by the U.S.'National Institutes of Health. We wish to thank Michael Boehnke, Lee Schacter, and'Emile Salloum for helpful discussions. The FORTRAN program for exact tests is available from the corresponding author.