Statistical methods for assessing linkage disequilibrium at the HLA-A, B, C loci.

Abstract

SUMMARYA number of standard and new statistics for measuring linkage disequilibrium are introduced applicable to any multilocus system. Included are the usual pairwise gametic disequilibrium function, D, the Lewontin disequilibrium index, DL, a Euclidean disequilibrium distance, DE, a hierarchy of stratified linkage disequilibrium functions (e.g. a pairwise disequilibrium value conditioned on the value of a third locus) and an averaged conditional disequilibrium expression, DW. Various global second order measures of disequilibrium are proposed partly based on contingency table statistics and weighted pairwise disequilibrium quantities. A non‐parametric (stochastic) comparison assessment for global linkage disequilibrium is also developed. These measures are compared and contrasted at the HLA‐A, B, C gene complex for a sample of 2000 haplotypes from a healthy Austrian population.Several results from applying these methods include: (1) Of the various pairwise disequilibrium measures examined, D, DE and DW correlated very closely with each other but differ from DL. (2) The ‘third‐order interaction’ between two loci conditional on an allele (or group of alleles) at a third locus indicated that HLA‐AB maintains the classical disequilibrium pairings only for conditioning on CX (the blank allele at locus C), and they mostly disappear for conditioning on C1 to C5. (3) Subpopulations involving C3 or C4 alleles exhibit the significant new combinations A33B17 and A2B15. (4) The B, C loci have a higher total linkage disequilibrium than A, B and A, C; more than expected by mapping distance relationships. (5) The total linkage disequilibrium was significantly larger for conditioning on CX compared to CX (non‐CX), but smaller for the population conditioned by {C3, C4}.A number of interpretations of the results with respect to heterogeneity classifications of populations are discussed.