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

Abstract

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 can be increased through application of this technique in situations where parameter values cannot be specified with a high degree of certainty.

Figure 1

Example pedigree demonstrating the importance of marker-locus allele frequencies in linkage analysis. Assuming a rare dominant disease with no phenocopies, the maximum LOD score in this pedigree is 0 when the frequency of marker-locus allele 1 is set to its correct value of .5. If the frequency of the 1 allele were set erroneously to .0001, the maximum LOD score in this pedigree would be inflated to 1.8. In multipoint analysis, the marker-marker LD correlations also play a role (see text for details).

Figure 2

False-positive LOD-score distribution as a function of the number of marker loci with incorrect allele-frequency estimates analyzed jointly. In the simulation, the disease locus is unlinked to diallelic marker(s) having true allele frequencies of .2 and .8. Shown are the results using the profile-likelihood approach (Z_p) and when equal allele frequencies of .5 were falsely assumed for each of the 1 (Z₁), 2 (Z₂), 3 (Z₃), or 4 (Z₄) marker loci analyzed jointly. While the LOD-score distribution of the profile likelihood approach fits the predicted 0.5χ² distribution well, the false positive tendency clearly increases as the number of marker loci with fixed and erroneous assumed marker-locus allele frequencies considered jointly increases. The results are based on 100 simulated replicates of 350 affected sib-pairs with ungenotyped parents.