A General Method for Linkage Disequilibrium Correction for Multipoint Linkage and Association

Azra Kurbasic and Ola Hössjer

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
Lately, many different methods of linkage, association, or joint analysis for family data have been invented and refined. Common to most of those is that they require a map of markers that are in linkage equilibrium. However, at the present day, high-density SNPs maps are both more inexpensive to create and they have lower genotyping error. When marker data is incomplete, the crucial and computationally most demanding moment in the analysis is to calculate the inheritance distribution at a certain position on the chromosome. Recently, different ways of adjusting traditional methods of linkage analysis to denser maps of SNPs in linkage disequilibrium have been proposed. We describe a hidden Markov model which generalizes the Lander-Green algorithm. It combines Markov chain for inheritance vectors with a Markov chain modelling founder haplotypes and in this way takes account for linkage disequilibrium between SNPs. It can be applied to association, linkage, or combined association and linkage analysis, general phenotypes and arbitrary score functions. We also define a joint likelihood for linkage and association that extends an idea of Kong and Cox (1997) for pure linkage analysis.
Key words:
Hidden Markov model, linkage, association, linkage disequilibrium, SNPs