Guess LOD approach: Sufficient conditions for robustness

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Abstract
Analysis of genetic linkage between a disease and a marker locus requires specifying a genetic model describing both the inheritance pattern and the gene frequencies of the marker and trait loci. Misspecification of the genetic model is likely for etiologically complex diseases. In previous work we have shown through analytic studies that misspecifying the genetic model for disease inheritance does not lead to excess false-positive evidence for genetic linkage provided the genetic marker alleles of all pedigree members are known, or can be inferred without bias from the data. Here, under various selection or ascertainment schemes we extend these previous results to situations in which the genetic model for the marker locus may be incorrect. We provide sufficient conditions for the asymptotic unbiased estimation of the recombination fraction under the null hypothesis of no linkage, and also conditions for the limiting distribution of the likelihood ratio test for no linkage to be chi-squared. Through simulation studies we document some situations under which asymptotic bias can result when the genetic model is misspecified. Among those situations under which an excess of false-positive evidence for genetic linkage can be generated, the most common is failure to provide accurate estimates of the marker allele frequencies. We show that in most cases false-positive evidence for genetic linkage is unlikely to result solely from the misspecification of the genetic model for disease or trait inheritance.