Genotype-Based Association Analysis Using Discordant Pairs: A Penetrance Odds Ratio Approach


Corresponding author: DAVID C. HAMILTON, Mathematics & Statistics, Dalhousie University, 6316 Coburg Road, P.O. Box 15000, Halifax, Nova Scotia, Canada B3H 4R2; Tel: 902 494 3568; Fax: 902 494 6501; E-mail:


Genotypic counts of paired relatives discordant for a complex late-onset disease are often used to test for genetic association. The power of the various statistical test options, when data on covariates are unavailable, has been the focus of recent research. Comparison of the Cochran-Armitage, Bhapkar, and McNemar tests indicates that none is superior to the others in all cases. Using an alternative approach, we found that the theoretical genotypic frequencies of the discordant pairs depend only on the penetrance odds ratios, after conditioning. These odds ratios can be estimated by maximizing a product binomial likelihood and provide insight into the mode of inheritance. We identified cases where exact maximum likelihood (ML) estimates can be explicitly obtained. This approach led us to two tests for association which depend on likelihood ratio (LR) or score statistics. We quantified the power of these tests analytically and examined their performance through simulation. We explored the utility of these tests with an example from the literature—the association between complement factor H (CFH) polymorphisms and age-related macular degeneration. The LR and Score tests serve as simple and effective ways of interpreting paired case-control data sets.