Parametric and Nonparametric Linkage Analysis

Abstract

Parametric or model‐based linkage analysis assumes that models describing both the trait and genetic marker loci are known without error, although sensitivity analysis approaches allow one to account for uncertainty in the trait model. Nonparametric, model‐free or weakly parametric linkage methods make fewer assumptions about the trait model. Family‐based linkage analysis in general is most powerful to detect genetic variants that have large effects on risk of a disease or variation of a quantitative trait. These variants tend to be rare in the population for any disease which is likely to have undergone negative selection over evolutionary time. Linkage studies are more powerful than genome‐wide association studies (GWAS) to detect genes with rare, high penetrance risk variants, whereas GWAS are more powerful to detect common risk variants which tend to have small individual effects on risk. Thus, both linkage and association analysis strategies are useful in the era of whole‐genome sequencing. Both parametric and nonparametric linkage methods are useful for detecting regions of the genome harbouring high penetrance risk variants which are of particular interest for precision medicine. Key Concepts Linkage analysis evaluates the likelihood that a specific allele or haplotype of alleles co‐segregates with a disease or trait in a family or group of families. Linkage analysis searches for evidence of a violation of Mendel's Law of Independent Assortment of alleles at two loci to the offspring. Linkage is due to the fact that long stretches of DNA on a specific chromosome are transmitted together to an offspring. Genetic loci on different chromosomes are not linked and do segregate independently to offspring. Genetic loci on the same chromosome that are close together show some evidence of linkage, but loci that are far apart on the same chromosome may not show evidence of linkage due to the fact that chiasmata occur at the four‐strand stage of meiosis, which results in recombination between the chromatids of the parental pair of chromosomes. Linkage is a measure of the probability of recombination between two loci (such as a risk allele for a disease and a genetic variant somewhere in the genome) given the observed genotypes of the parents and offspring. In parametric linkage, a model is assumed that specifies the mode of inheritance, allele frequency and penetrance of all genotypes for the disease locus (probability of a given value of a quantitative trait) plus the mode of inheritance, allele frequency and probability of observing each laboratory phenotype given genotype for the genotyped marker loci (usually codominant and 100% for modern single‐nucleotide polymorphism and DNA sequencing genotypes). In nonparametric linkage, no specific assumptions are made about the trait model, but the genotyped marker locus model must be fully described as above for parametric linkage. The power of these two approaches depends on many different factors, but both depend on the observation of large numbers of meioses; so, large families with multiple affected individuals (or a wide range of quantitative trait values) in which all individuals have both phenotype and genotype data are most powerful. Linkage analyses are particularly useful for detecting genetic variants with large effects on risk of disease or large effects on the variance of a quantitative trait, which are of particular utility for precision medicine.