Linkage analysis in the presence of errors III:: Marker loci and their map as nuisance parameters

In linkage and linkage disequilibrium (LD) analysis of complex multifactorial phenotypes, various types of errors can greatly reduce the chance of successful gene localization. The power of such studies-even in the absence of errors-is quite low, and, accordingly, their robustness to errors can be poor, especially in multipoint analysis. For this reason, it is important to deal with the ramifications of errors up front, as part of the analytical strategy. In this study, errors in the characterization of marker-locus parameters-including allele frequencies, haplotype frequencies (i.e., LD between marker loci), recombination fractions, and locus order-are dealt with through the use of profile likelihoods maximized over such nuisance parameters. It is shown that the common practice of assuming fixed, erroneous values for such parameters can reduce the power and/or increase the probability of obtaining false positive results in a study. The effects of errors in assumed parameter values are generally more severe when a larger number of less informative marker loci, like the highly-touted single nucleotide polymorphisms (SNPs), are analyzed jointly than when fewer but more informative marker loci, such as microsatellites, are used. Rather than fixing inaccurate values for these parameters a priori, we propose to treat them as nuisance parameters through the use of profile likelihoods. It is demonstrated that the power of linkage and/or LD analysis call be increased through application of this technique in situations where parameter values cannot be specified with a high degree of certainty.