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AB - The performance of some weakly parametric linkage tests in common use was compared on 200 replicates of oligogenic inheritance from Genetic Analysis Workshop 10. Each random sample for the quantitative trait was dichotomized at different thresholds and also selected through 2 affected sibs, generating 8 combinations of sample and variable. The variance component program SOLAR performed best with a continuous trait, even in selected samples, when the population mean was used. The sib-pair program SIBPAL2 was best in most other cases when the phenotype product, population mean, and empirical estimates of pair correlations were used. The BETA program that introduced phenotype products was slightly more powerful than maximum likelihood scores under the null hypothesis and approached but did not exceed SIBPAL2 under its optimal conditions. Type I errors generally exceeded expectations from a χ2 test, but were conservative with respect to bounds on lods. All methods can be improved by use of the population mean, empirical correlations, logistic representation for affection status, and correct lods for samples that favour the null hypothesis. It remains uncertain whether all information can be extracted by weakly parametric methods and whether correction for ascertainment bias demands a strongly parametric model. Performance on a standard set of simulated data is indispensable for recognising optimal methods.

N2 - The performance of some weakly parametric linkage tests in common use was compared on 200 replicates of oligogenic inheritance from Genetic Analysis Workshop 10. Each random sample for the quantitative trait was dichotomized at different thresholds and also selected through 2 affected sibs, generating 8 combinations of sample and variable. The variance component program SOLAR performed best with a continuous trait, even in selected samples, when the population mean was used. The sib-pair program SIBPAL2 was best in most other cases when the phenotype product, population mean, and empirical estimates of pair correlations were used. The BETA program that introduced phenotype products was slightly more powerful than maximum likelihood scores under the null hypothesis and approached but did not exceed SIBPAL2 under its optimal conditions. Type I errors generally exceeded expectations from a χ2 test, but were conservative with respect to bounds on lods. All methods can be improved by use of the population mean, empirical correlations, logistic representation for affection status, and correct lods for samples that favour the null hypothesis. It remains uncertain whether all information can be extracted by weakly parametric methods and whether correction for ascertainment bias demands a strongly parametric model. Performance on a standard set of simulated data is indispensable for recognising optimal methods.

Traditional nonparametric “multipoint” statistical procedures have been developed for assigning allele-sharing values at a locus of interest to pairs of relatives for linkage studies. These procedures attempt to accommodate a lack of informativity, nongenotyped loci, missing data, and related issues concerning the genetic markers used in a linkage study. However, such procedures often cannot overcome these phenomena in compelling ways and, as a result, assign relevant relative pairs allele-sharing values that are “expected” for those pairs. The practice of assigning expected allele-sharing values to relative pairs in the face of a lack of explicit allele-transmission information can bias traditional nonparametric linkage test statistics toward the null hypothesis of no locus effect. This bias is due to the use of expected values, rather than to a lack of information about actual allele sharing at relevant marker loci. The bias will vary from study to study on the basis of the DNA markers, sample size, relative-pair types, and pedigree structures used, but it can be extremely pronounced and could contribute to a lack of consistent success in the application of traditional nonparametric linkage analyses to complex human traits and diseases. There are several potential ways to overcome this problem, but their foundations deserve greater research. We expose many of the issues concerning allele sharing with data from a large affected-sibling-pair study investigating the genetic basis of autism.

For backcross matings, we obtainThe null hypothesis is that there is no distortion of segregation due tolinkage between the trait locus and the marker locus.

Linkage analysis has been a workhorse for gene discovery in human genetics research for the past 50 years or so (Lander and Schork ^{}; Schork and Chakravarti ^{}). Although there have been spectacular successes in the application of parametric linkage analysis to overtly Mendelian, monogenic traits and diseases (e.g., cystic fibrosis and neurofibromatosis), there has been a noticeable and somewhat discouraging lack of success in the application of nonparametric linkage analyses to more complex traits and diseases, such as hypertension and psychiatric disorders. This is the case despite the fact that nonparametric linkage analysis models have been developed, expanded, and tested for years in complex trait analysis (Weeks and Lange ^{}; Lander and Schork ^{}; Whittemore ^{}; Blangero et al. ^{}; Sengul et al. ^{}). This lack of success has raised many questions, including the suggestion that traditional nonparametric linkage analysis strategies are inherently flawed and should be replaced with other gene-discovery strategies and study designs (Risch and Botstein ^{}; Risch and Merikangas ^{}). However, despite the fact that nonparametric linkage analysis strategies are plagued by certain problems, many of these problems are not only identifiable but potentially correctable. Thus, before abandoning nonparametric linkage-analysis gene-discovery strategies, it makes sense to attempt to identify and correct any problems they might possess, in an effort to determine their ultimate utility.

The non-parametric linkage (NPL) scores estimated in the region harboring the causal allele are evaluated to assess the statistical power for different genetic (allele frequency and risk) and heterogeneity parameters under various sampling schemes (age-cut and sample size).

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For thebackcross for two codominant markers x ,To work out the form that deviations from this null hypothesis willtake, we have to add up the probabilities over the two possible phasesthe heterozygote parent is in, either coupling / orrepulsion /.

Although in the context of longevity studies, parental genotype information is usually missing, the non-parametric linkage analysis suitable for studying genes linked to late-onset diseases could b...

This report investigates the power issue in applying the non-parametric linkage analysis of affected sib-pairs (ASP) [Kruglyak and Lander, 1995: Am J Hum Genet 57:439–454] to localize genes that contribute to human longevity using long-lived sib-pairs.

One problem plaguing traditional nonparametric linkage analysis techniques is rooted in the use and estimation of a quantity of fundamental significance to their foundation: the fraction of alleles that are shared identical by descent (IBD) at a locus of interest between pairs of relatives. This quantity is often tested directly for its significance in, for example, affected sibling pair analyses (as a deviation from an expected null hypothesis value of 0.5), or it is related to some measure of phenotypic similarity for quantitative trait analyses (e.g., squared difference in phenotypic values between the relative pairs for Haseman-Elston regression analysis [Haseman and Elston ^{}] or covariation in relative-pair trait values for variance-components–based analysis [Blangero et al. ^{}]). In this article, we argue that the manner in which measures of allele sharing are computed and assigned to pairs of relatives in traditional nonparametric linkage analyses can be very problematic and can induce biases in associated test statistics toward the null hypothesis of no linkage—a fact that may explain why many applications of nonparametric linkage analysis to complex traits and diseases are controversial or not compelling. These problems stem from the use or assignment of expected allele-sharing values to pairs of relatives when marker information is uninformative (to whatever degree) and/or when interpolating allele-sharing values at loci between distant marker loci. To introduce our discussion, we provide a simple analogy.

Now the connection to allele-sharing–based nonparametric linkage analyses can be made. Consider the simplest case of an affected sibling pair analysis in which one wants to test the hypothesis that there is skewing at a locus toward greater allele sharing among the affected sibling pairs than expected (i.e., expected allele-sharing values are consistent with expected values dictated by Mendel’s laws). If some fraction of the sibling pairs’ genotypes are uninformative at the locus, then assigning them allele-sharing values consistent with expectation will bias the test toward the expected, null hypothesis outcome that there is no skewing toward greater allele sharing, just as in the case of the coin tosses! The problem with using expected allele-sharing values is not unique to affected sibling pair analyses; it carries over to regression and variance-component–analysis techniques for quantitative traits, although the effect of the bias is more subtle.

The problems inherent in the use of the traditional allele-sharing measures that we describe can be overcome, to some degree, through the use of weighting procedures, modified (and more appropriate) mixture models, and/or removing uninformative relative pairs from the analysis. These strategies are considered in more detail in the “Discussion” section. We argue that such strategies should motivate greater theoretical research into nonparametric linkage analysis methods.

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