Original Paper Hum Hered 2004;57:100–108 DOI: 10.1159/000077547 Using Lod Scores to Detect Sex Differences in Male-Female Recombination Fractions B. Feenstra D.A. Greenberg S.E. Hodge Division of Statistical Genetics, Department of Biostatistics, Mailman School of Public Health, Columbia University, and Division of Clinical-Genetic Epidemiology, NY State Psychiatric Institute, New York, N.Y., USA Received: December 4, 2003 Accepted after revision: February 18, 2004 Dr. Susan E. Hodge New York State Psychiatric Institute, Unit 24 1051 Riverside Drive New York, NY 10032 (USA) Tel. +1 212 543 5606, Fax +1 212 568 3534, E-Mail seh2@columbia.edu ABC Fax + 41 61 306 12 34 E-Mail karger@karger.ch www.karger.com © 2004 S. Karger AG, Basel Accessible online at: www.karger.com/hhe Key Words Fully informative gametes W Sib pairs W Unequal recombination fraction W Sample size W Power W Ascertainment bias W Imprinting 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 differ- ences contributes to our understanding of basic biology and can increase the power of a linkage study, improve gene localization, and provide clues to possible imprint- ing. One way to detect these differences is to use lod scores. In this study we focused on detecting RF sex dif- ferences 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 differ- ence? (2) What are ‘optimal’ proportions of paternally vs. maternally informative matings? (3) Does ascertaining nonoptimal proportions of paternally or maternally infor- mative 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 (  = ,   Y ); and ‘con- strained,’ requiring   = =   Y . We then examined the ¢ELOD (o difference between maximized constrained and unconstrained ELODs) and calculated minimum sample sizes required to achieve statistically significant ¢ELODs. For large RF sex differences, samples as small as 10 to 20 fully informative matings can achieve statisti- cal 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 data- set; and the optimal proportion p ˆ as that value of p that maximizes ¢ELOD. We determined that, surprisingly, p ˆ 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 maxi- mum likelihood estimates of   = and   Y , even though ELOD is reduced (see point 2). This fact is important because often investigators cannot control the propor- tions of paternally and maternally informative families. In conclusion, it is possible to reliably detect sex differ- ences in recombination fraction. Copyright © 2004 S. Karger AG, Basel