Pairwise analysis of radiation hybrid mapping data

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Abstract
Two point lod scores are widely used in pedigree analysis as they provide a fast and efficient method of establishing linkage. Groups of markers that lie in close proximity to one another can be formed by admitting any locus that is linked to at least one existing member of the group with lod score greater than some predetermined value. It seems natural to extend this technique to Radiation Hybrid Mapping both for constructing groups of tightly linked loci that may then be analysed using more powerful statistics and as a method of ordering in its own right. A general extension of two point analysis is derived and the problems associated with radiation hybrid data are discussed. In particular, the additional parameters representing the probabilities of different fragments being retained (which have no parallel in classical linkage analysis) lead to a range of estimators of the breakage probability, O, which have equal and maximal likelihood. Ways of circumventing this problem are discussed along with the potential errors they introduce. Importantly the ambiguity in estimation of theta is not carried through to the lod score as this depends only on the maximum value of the likelihood and not on the particular value of theta at which it occurs. Thus even though two point analysis fails to provide robust estimates of either breakage probabilities or the distance between loci, it represents a simple and effective method of constructing linkage groups that may be analysed with more powerful statistical methods. This is particularly important given the large number of microsatellites, ESTs and candidate genes currently being typed on radiation hybrids.