Using Lod Scores to Detect Sex Differences in Male-Female Recombination Fractions

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Abstract
Human recombination fraction (RF) can differ between males and females, but investigators do not always know which disease genes are located in genomic areas of large RF sex differences. Knowledge of RF sex differences contributes to our understanding of basic biology and can increase the power of a linkage study, improve gene localization, and provide clues to possible imprinting. One way to detect these differences is to use lod scores. In this study we focused on detecting RF sex differences and answered the following questions, in both phase-known and phase-unknown matings: (1) How large a sample size is needed to detect a RF sex difference? (2) What are ‘optimal’ proportions of paternally vs. maternally informative matings? (3) Does ascertaining nonoptimal proportions of paternally or maternally informative matings lead to ascertainment bias? Our results were as follows: (1) We calculated expected lod scores (ELODs) under two different conditions: ‘unconstrained,’ allowing sex-specific RF parameters (Θ♀, Θ♂); and ‘constrained,’ requiring Θ♀ = Θ♂. We then examined the ΔELOD (≡ difference between maximized constrained and unconstrained ELODs) and calculated minimum sample sizes required to achieve statistically significant ΔELODs. For large RF sex differences, samples as small as 10 to 20 fully informative matings can achieve statistical significance. We give general sample size guidelines for detecting RF differences in informative phase-known and phase-unknown matings. (2) We defined p as the proportion of paternally informative matings in the dataset; and the optimal proportion pcirc; as that value of p that maximizes ΔELOD. We determined that, surprisingly, pcirc; does not necessarily equal ½, although it does fall between approximately 0.4 and 0.6 in most situations. (3) We showed that if p in a sample deviates from its optimal value, no bias is introduced (asymptotically) to the maximum likelihood estimates of Θ♀ and Θ♂, even though ELOD is reduced (see point 2). This fact is important because often investigators cannot control the proportions of paternally and maternally informative families. In conclusion, it is possible to reliably detect sex differences in recombination fraction.