Path analysis and sib-pair linkage

When the distance between linked loci is expressed in terms of the correlation between the identity-by-descent (idb) values of the loci, then a path model may be used to order loci with data on sib-pairs and their parents. The relationship between the recombination fraction and the correlation coefficient is developed and a method for fitting a covariance matrix predicted by a specific ordering of loci to an observed covariance matrix is proposed. © 1993 Wiley-Liss. Inc.     

A novel polylocus method for linkage analysis using the lod-score or affected sib-pair method

A novel approach to combining data from multiple linked loci is proposed that can provide substantial increases in power over normal two-point linkage analysis or sib-pair analysis, with a substantial saving in computing time over traditional multipoint methods. © 1993 Wiley-Liss, Inc.     

Commentary: the affected sib-pair method in the context of an epidemiologic study design.

The purpose of this commentary is to provide a framework for using the well-known sib-pair methodology in the context of epidemiologic study designs. Using examples from the Pittsburgh family studies of insulin-dependent diabetes mellitus, we illustrate that the sib-pair method can be used in family-based epidemiologic studies. In a cohort study, unaffected relatives of probands ascertained from well-defined populations are followed for disease development. Disease risks are then stratified according to the number of alleles at one or more loci (0, 1, 2) that are identical by descent (ibd) with the proband. In the absence of linkage between the marker locus and the disease locus, disease risks are expected to be identical in the three groups. Measures of relative risk can be computed (with share-0 as baseline group). In a case-control study, relatives of probands that become affected (cases) are compared to a sample of relatives of probands that stay unaffected (controls) with respect to the number of alleles ibd with the proband. Measures of odds ratio can be computed (with share-0 as baseline group). In both cohort and case-control approaches, covariates including other genetic markers and environmental exposures can be evaluated in relation to disease risk and also for evidence of interaction with the specific marker of interest using stratified and multivariate analyses. Family-based epidemiologic studies allow investigators to study, in a single design, the role of environmental factors and specific gene loci in the etiology of diseases.     

A general approach to detect gene (G)-environment (E) additive interaction leveraging G-E independence in case-control studies

It is increasingly of interest in statistical genetics to test for the presence of an additive interaction between genetic (G) and environmental (E) risk factors. In case-control studies involving a rare disease, a statistical test of no additive G×E interaction typically entails a test of no relative excess risk due to interaction (RERI). It has been shown that a likelihood ratio test of a null RERI incorporating the G-E independence assumption (RERI-LRT) outperforms the standard approach. The RERI-LRT relies on correct specification of a logistic model for the binary outcome, as a function of G, E, and auxiliary covariates. However, when at least one exposure is not categorical or auxiliary covariates are present, nonparametric estimation may not be feasible, while parametric logistic regression will a priori rule out the null hypothesis of no additive interaction in most practical situations, inflating type I error rate. In this paper, we present a general approach to test for G × E additive interaction exploiting G-E independence. Unlike the RERI-LRT, it allows the regression model for the binary outcome to remain unrestricted, and nonetheless still allows for covariate adjustment in order to ensure the G-E independence assumption or to rule out residual confounding. The methods are illustrated through extensive simulation studies and an ovarian cancer study.     

The power of two-locus affected sib-pair linkage analysis to detect interacting disease loci

It has been shown that two-locus linkage analysis can, for some two-locus disease models, be used to detect effects at disease loci that do not reach significance in a genome scan. However, few examples exist where two-locus linkage has been successfully used to map genes. We study the possible gain in power of affected sib-pair nonparametric two-locus linkage analysis for two-locus models which fulfil the two-locus triangle constraints. Using a new parameterization of the two-locus joint identity-by-descent sharing probabilities we can, for fixed marginal sharing at both of two unlinked disease loci, derive a two-locus distribution such that the power of a two-locus analysis is maximized. In a simulation study we look at two test statistics, the two-locus maximum likelihood score and the correlation between nonparametric linkage scores, and study power as a function of marginal sharing. We show that in a best-case scenario two-locus linkage can have considerable power to detect pairs of interacting loci if there is a moderate increase in allele sharing at one of the two loci, even if there is a very small increase in allele sharing at the other locus. But we also show that the power to detect interacting loci in a two-locus analysis decreases as the marginal sharing at the two loci decreases and for any distribution with a small increase in allele sharing at both loci the power of a two-locus analysis is always low.     

Genome scan for association and linkage

In this paper, a genome search is performed on the GAW Problem 1 data, in an attempt to determine which, if any, of the marker loci are associated and/or linked with the disease. Since there was no clear indication from the data of the likely mode of inheritance, methods were used which did not require such assumptions to be made. A two-stage procedure was used to test for association. Firstly a standard unmatched case-control test was applied to all the loci. The family-based method of Self et al. [1991] was then applied to those loci which gave a positive result in the first stage. This procedure correctly detected loci 1 and 2, and that disease risk was increased for homozygote carriers of the disease allele at each locus, although a false positive result was also found. The affected sib pair method of Holmans [1993] was also applied to the data, although the sample contained far too few sib-pairs for such an analysis to be effective. This analysis failed to find any of the disease loci. ©1995 Wiley-Liss, Inc.     

Statistical validity of the Haseman-Elston sib-pair test in small samples

Simulation experiments were used to determine the empiric type I error rate of the Haseman-Elston sib-pair test for linkage between a quantitative trait and a marker locus in samples with 60 or fewer sib pairs. The effect of different levels of marker-locus heterozygosity on statistical validity was also considered. The test was performed on the trait and each of five unlinked markers, and evaluated using two different degrees of freedom for the t-distribution. The number of degrees of freedom in the first evaluation was based on the number of sib pairs in each sibship, ∑ s_I(s_I - 1)/2 - 2. In the second evaluation, the number of degrees of freedom was based on the number of sibs minus 1 in each sibship, ∑ (s_i - 1) - 2. Empirically determined type I error rates using C s_I(s_I - 1)/2 - 2 degrees of freedom were slightly liberal. For ∑ (s_i - 1) - 2 degrees of freedom, the estimated empiric p-values were nearly identical to their respective nominal p-values. Decreasing levels of heterozygosity did not increase the empiric type I error rate when the sample size was small. © 1993 Wiley-Liss, Inc.     

A graphical approach for presenting linkage results from a genomic screen

Initially, a sib-pair linkage analysis was performed between the marker loci and six untransformed variables. Results from several variations of this initial analysis were compared using a graphical approach (P-plots) to simplify presentation. When results were compared to the generating model, most of the aspects of the generating model were recovered, although we did not find evidence of the polygenic component shared by Q2 and Q3, or evidence of linkage between MG4 and Q4 at the 0.01 level. © 1995 Wiley-Liss, Inc.     

A genetic analysis of common disease data

Simulated common disease data have been analyzed to identify a model of disease expression that involves the complex interaction of quantitative traits controlled by major genes and an environmental factor. Correlation and multiple regression analyses in conjunction with quantitative sib-pair linkage analyses revealed a portion of the model involved. © 1995 Wiley-Liss, Inc.     

Comparison of sib-pair and variance-components methods for genomic screening

The statistical properties of sib-pair and variance-components linkage methods were compared using the nuclear family data from Problem 2. Overall, the power to detect linkage was not high for either method. The variance-components method had better power for detection of linkage, particularly when covariates were included in the model. Type I error rates were similar to nominal error rates for both methods. © 1997 Wiley-Liss, Inc.     

Extensions to methods of sib-pair linkage analyses.

Sib-pair methods provide simple, robust, easily implemented ways to screen for linkage between a marker locus and a suspected disease susceptibility locus. The basic analysis reflects the idea that, in the presence of linkage, siblings who share more alleles at the marker locus should also tend to be concordant for disease. Available sib-pair methods do not lead directly to estimates of risk associated with nongenetic factors, may not account for a variable age-at-onset, or may require that the age-at-onset distribution be known. In this paper, we propose a method for sib-pair linkage analyses that allows for a variable age-at-onset using a logistic model, easily allows modelling of nongenetic factors, reflects the correlation of sibs within a sibship, and allows for nonzero risk in those without the susceptibility genotype. Based on a limited number of simulations, the method has as good or better power than another recently described method that also allows for a variable age-at-onset.     

Effects of marker information on sib-pair linkage analysis of a rare disease

Model-free sib-pair linkage analysis was used to screen the GAW9 - Problem 1 data set for evidence of linkage of a rare disease to any of 360 highly polymorphic marker loci. Negative regressions nominally significant at the α = 0.05 level were obtained for 44 markers; however all of these proved to be Type I errors. None of the four disease loci were detected by sib-pair linkage, which was not surprising, given the particular model and sampling scheme used to generate these data. Neither deleting parental marker genotypic information nor misspecifying marker allele frequency estimates substantially increased the Type I error rate. A two-stage testing procedure using a 10 or 20 cM map and a liberal first stage significance level gave the same overall results as a one-stage 2 cM map but required only about 42% or 22% as many markers, respectively. ©1995 Wiley-Liss, Inc.     

Genetic epidemiologic analysis of quantitative phenotypes using gibbs sampling

We analyzed two quantitative traits (Q1 and Q2) provided in the ‘Common Disease’ data set with the aim of detecting both genetic and environmental determinants. We used linear regression for screening measured variables, maximum likelihood segregation and linkage analyses for detecting and localizing unmeasured genes, and Gibbs sampling for joint segregation and linkage analyses with estimation of gene-environment interaction and polygenic effects. For both Q1 and Q2, we successfully detected the unmeasured codominant major gene (MG) that was tightly linked to candidate gene C2. We also detected all of the measured variables used in generating Q1 (age, Q3, candidate gene C5) and Q2 (EF). Although our final models differed slightly from the true data generation models, our multifaceted analytic approach was successful in characterizing the determinants of Q1 and Q2. © 1995 Wiley-Liss, Inc.     

A comparison of sib-pair linkage tests for disease susceptibility loci

An analytical study is conducted of the properties of statistical tests to detect linkage between a disease locus and a very polymorphic marker locus when data on sib pairs are available. In most instances the most powerful test is the test based on the mean number of marker alleles shared identical by descent by the two members of a sib pair, and the most efficient sampling strategy is almost always to sample only pairs with both sibs affected. We show it is valid to use the information from all possible sib pairs as though they came from separate families when data on sibships of size three or larger are available, though more power may be obtained if different weights are given to the different sibship sizes.     

The effect of selective sampling on mapping quantitative trait loci

Sib pairs were selectively sampled for extreme concordance or discordance for the quantitative trait Q1, a simulated phenotype (GAW10). Two selective sampling criteria were used (SC1 and SC2), and results for these were compared to linkage analyses using all pairs (ALL). In total 773 sib pairs were available, which reduced to an average of 59.7 pairs under SC1, and 134.1 pairs under SC2. Whole genome screens were performed on 10 different data replicates for each selection criterion (ALL, SC1, and SC2). Fine screens were then performed over regions which indicated at least suggestive linkage, and these regions were also fine screened in an independent data replicate in an attempt to repeat any areas found. The results for the coarse genome screens were similar under each of the criteria, although in general lower maxima and slightly more erratic lods were found under the stricter selection methods. The correct region on chromosome 5 (responsible for approximately 22% of the variance of Q1) was detected (p < 0.0001) in 6/10 of the data replicates using ALL, and 4/10 using SC1 and SC2. The second quantitative trait locus (QTL) on chromosome 8 (only 0.5% of the variance of Q1) was detected in only a single data replicate using SC1. False positive rates were similar for each criterion, whereas power decreased using selective sampling compared to ALL, although this was probably due to an insufficient initial sample size. © 1997 Wiley-Liss, Inc.     

Screening for linkage and association in nuclear families

We applied linkage analysis with a sib-pair method, which also takes into account information on unaffected siblings, and family-based methods of association analysis to determine the disease affecting loci in Problem 1. Whereas the first two disease loci were correctly identified by association analysis, the sib-pair linkage method failed to detect the disease loci 3 and 4. We therefore determined the data structure and sample size necessary for demonstrating linkage to these loci. ©1995 Wiley-Liss, Inc.     

Impact of adjustments for intermediate phenotypes on the power to detect linkage

Since the manifestation of a complex disease is likely to be influenced through multiple genetic and/or environmental pathways, it may be advantageous to adjust for these multiple factors in a genetic analysis of a complex quantitative trait. Sib- pair linkage analysis was performed on the simulated complex quantitative trait Q1 after adjustment for age, sex, and the environmental factor (i.e., minimally adjusted) and all combinations of the four intermediate phenotypes Q2, Q3, Q4, and Q5 (n = 15) for all 200 replications of the nuclear families data set. From the minimally adjusted Q1, the power to detect suggestive linkage to any of the three loci affecting Q1 was 0.585 with a false positive rate of 0.0025. Adjusting Q1 for Q3 increased the power to detect suggestive linkage to 0.860 with a similar false positive rate. Additional adjustments for Q2, Q4, and Q5 yielded no substantial improvements in power nor changes in the false positive rate. The power to detect significant linkage was also substantially improved after adjustment of Q1 for Q3 with no change in the false positive rate. The adjustment of a complex trait for other factors in the causal pathway reduces the phenotype variability and enhances the ability to detect linkage. © 1997 Wiley-Liss, Inc.     

Testing the utility of mod scores and sib-pair analysis to detect presence of disease susceptibility loci

Linkage analyses and association studies were employed to detect disease susceptibility loci leading to elevated Q1 levels in Problem 2B. Phenotypes were defined to be the dichotomous affection status, the quantitative value for Q1, and Q1 adjusted for covariates. The method of mod-scores (for the dichotomous phenotype) and the Haseman-Elston sib-pair test on the dichotomous and quantitative phenotypes were used to screen for linkage of disease susceptibilitygenes to 367 markers. These analyses were performed on a sample ascertained from the first 60 replicates. The mod-score method detected linkage to MG1, MG2, and MG3 with scores of 1.5,5.0, and 1.6 respectively. Sib-pair analysis using quantitative phenotypes signaled linkage only to the area surrounding MG1; the dichotomous phenotype detected linkage only to MG2. Association studies used ANOVA on all founders in the first 60 replicates and ASSOC on the ascertained families and on a subset of families from the 60 replicates but only confirmed an association to MG1. In conclusion, the mod-score method may be a useful tool for genomic screens. © 1997 Wiley-Liss, Inc.     

Effects of genotype-by-sex interaction on quantitative trait linkage analysis

Genotype-by-sex (G × S) interaction refers to the interaction of autosomal genes with male or female physiological “environments.” G × S interaction has been demonstrated in quantitative genetic analyses of a variety of traits including serum lipid concentrations and anthropometrics, and the importance of considering sex-specific major gene effects in segregation analyses also has been demonstrated. The goal of this study was to examine the effects of G × S interaction on the power to detect linkage. Trait Q3 in GAW10 Problem 2 was analyzed because it was modeled to have G × S interaction at the major gene locus MG3. All 200 nuclear family and 200 extended pedigree replicates were first screened for the presence of G × S interaction in Q3 using a quantitative genetic method. More than half of both the nuclear family and extended pedigree replicates evidenced significant G × S interaction. Variance components linkage analysis was then performed using all markers on GAW10 chromosome 4 in all 200 nuclear family and 200 extended pedigree replicates. A peak lod score of 1.92 at the correct chromosomal location was obtained using the extended pedigree data and incorporating G × S interaction effects. Not incorporating G × S interaction lowered the peak lod score from the analyses of the extended pedigrees to 1.53. Incorporation of G × S interaction effects also increased the power to detect linkage in the nuclear family replicates, although the nuclear families had considerably less power than the extended pedigrees to detect linkage, whether or not G × S interaction was modeled. Incorporation of G × S interaction effects can increase the power to detect linkage, even when the G × S interaction effects are modest. © 1997 Wiley-Liss, Inc.