Mapping genotype to phenotype for linkage analysis

We model functions that use genetic information as input and trait information as output to understand genetic linkage in complex diseases. Using simulated data from GAW11, we have applied categorical classification methods and neural network analysis. We use sharing at selected markers as input, and the classification of the sib pair (for example, affected-affected or affected-unaffected) as output. In addition, our methods include environmental risk factors as predictors of phenotype. Categorical and neural network methods each led to results consistent with findings from other methods such as the logistic regression method of Rice et al. [this issue]. Post-analysis comparison with the GAW11 answers showed that these methods are capable of detecting correct signals in a single replicate. One advantage of our methods is that they allow analysis of the entire genome at once, so that interactions among multiple trait-influencing loci may be detected. Furthermore, these methods can use a variety of sib pairs rather than affected pairs only.     

Nonparametric linkage and family-based association studies of a simulated complex disorder

Affected sibling pairs are widely used to identify chromosomal regions harboring genetic loci underlying common disease. We explore the utility of nonparametric sibling pair and family-based association methods to search for disease susceptibility loci in simulated pedigree data for a qualitative disease trait. Logistic regression was used to model gene x gene and gene x environment interactions when significant linkage and association were detected. Using these methods, we were able to detect three of the four susceptibility loci underlying the disease trait with multipoint lod scores of 1.0 or greater.     

Genetic analysis of a complex disease in the presence of an environmental risk factor

The role of a gene in a disease may be hidden by the presence of another risk factor such as an environmental factor. In that case, stratifying the data according to this factor strengthens power to detect linkage or association. We followed this strategy on the simulated data provided by GAW11. The transmission/disequilibrium test (TDT) and the maximum likelihood score (MLS) were performed on the first replicate of 100 sib pairs from the population in which the disease risk was significantly influenced by an environmental factor (E1). However, only the TDT was powerful enough to detect one of the four loci involved in the genetic determination of the disease. The MLS showed no evidence for linkage after taking into account the fact that multiple tests were performed. Even when stratifying the sample according to the presence of E1, no additional loci could be detected. Given the simulated models, 100 sib pairs are too low a sample size for a systematic screening of the genome, which in this case was an analysis of 300 markers.     

Haseman and Elston revisited

Haseman and Elston (H-E) [1972] proposed a method to detect quantitative trait loci by linkage to a marker. The squared sib-pair trait difference is regressed on the proportion of marker alleles the pair is estimated to share identical by descent: a significantly negative regression coefficient suggests linkage. It has been shown that a maximum likelihood method that directly models the sib-pair covariance has more power. This increase in power can also be obtained using the H-E regression procedure by changing the dependent variable from the squared difference to the mean-corrected product of the sibs' trait values. Multiple sibs in a sibship can be accommodated by allowing for the correlations between pairs of products in a generalized least squares procedure. Multiple trait loci, including epistatic interactions, involve only multiple linear regression. Multivariate traits can use the method of Amos et al. [1990] to find the linear function of the traits that maximizes the evidence for linkage, which now leads more simply to a test of significance. Multiple markers can be the basis of a multipoint analysis. Results of simulation studies for a continuous trait are presented that investigate Type I error and power. A similar general scheme can be used to study affected sib pairs, testing whether their identity by descent sharing probabilities are greater than would be expected in the absence of linkage, and to study other types of relative pairs.     

Genetic dissection of a complex trait

A number of genetic and statistical tools were applied to various partitions of the simulated data to identify susceptibility loci, relevant environmental factors, and their interaction(s). The distribution of genotypes at D1G24 among affected children in the first population was found to differ significantly from Hardy-Weinberg expectation. Two transmission/disequilibrium tests identified the preferential transmission of allele 1 as the source of the disequilibrium. Simple contingency table analysis revealed a positive association between exposure to environmental factor E1 and disease phenotype. Multipoint linkage analyses on various subsets of the data identified three "signal" regions (in addition to the aforementioned D1G24) localized at D1G9-10, D3G45, and D5G38. The even numbered chromosomes appeared to be devoid of susceptibility loci. Further analyses of subsamples of affected sib pairs, selected according to their disease phenotype and their exposure to E1, clarified some linkage relationships, particularly for D3G45, thereby suggesting the presence of a specific gene x environment interaction. Logistic analysis designed to clarify the relationship between disease phenotype and two risk factors (E1 exposure and the presence of allele 1 at D1G24) in the first population, revealed a significantly negative interaction which, upon learning the details of the generating model, we now attribute to the presence of heterogeneity.     

Combining Multiple Phenotypic Traits Optimally for Detecting Linkage with Sib‐Pair Observations

A number of investigators have proposed regression methods for testing linkage between a phenotypic trait and a genetic marker with sib‐pair observations. Xu et al. [Am J Hum Genet 67:1025–8, 2000] studied a unified method for testing linkage, which tends to be more powerful than existing procedures. Often there are multiple traits, which are linked to a common set of genetic markers. In this paper, we present a simple generalization of the unified test to combine information from multiple traits optimally. We use the simulated Genetic Analysis Workshop 12 data to illustrate this methodology and show the advantage of using the combined tests over the single‐trait tests. For the four quantitative traits (Q1,...,Q4) studied, our linkage results suggest that major loci affecting Q1 and Q2 localize at or near markers D02G172, D19G032, and D09G122, while loci affecting Q3 and Q4 localize at or near markers D09G122 and D17G051. © 2001 Wiley‐Liss, Inc.     

Linkage analysis of a common oligogenic disease using selected sib pairs

Sib pairs drawn from the simulated common oligogenic disease families were selected for extreme quantitative trait scores and analyzed using interval mapping and multipoint methods. Linkage analyses of 112 selected sib pairs, in which one or more members had trait values exceeding the disease threshold, were compared with analyses of the total unselected sib-pair sample (771 pairs). Selected sample regression models yielded comparable significance levels to those obtained from the unselected sample at most loci on the six simulated chromosomes, demonstrating the efficiency of selected sib-pair analysis for quantitative characters. Two of the three disease QTLs were detected in both selected and unselected samples. Interval mapping and multipoint analyses yielded location estimates close to the simulated positions of the QTLs. The combined strategy of using interval mapping and multipoint methods with selected sib pairs appears to provide improved accuracy and sensitivity over more traditional sib-pair methods for detecting quantitative trait loci. © 1995 Wiley-Liss, Inc.     

A brute force dichotomization approach to quantitative trait linkage analysis

The effect of dichotomizing a continuous phenotype in linkage analysis of a simulated oligogenic trait is explored. We conclude that dichotomization does not in itself preclude the detection of loci which account for as little as 16% of the genetic variance of the disease. The effects of inclusion of known covariates and quantitative trait linkage analysis are also discussed. © 1995 Wiley-Liss, Inc.     

Covariates in linkage analysis

We apply a novel technique to detect significant covariates in linkage analysis using a logistic regression approach. An overall test of linkage is first performed to determine whether there is significant perturbation from the expected 50% sharing under the hypothesis of no linkage; if the overall test is significant, the importance of the individual covariate is assessed. In addition, association analyses were performed. These methods were applied to simulated data from multiple populations, and detected correct marker linkages and associations. No population heterogeneity was detected. These methods have the advantages of using all sib pairs and of providing a formal test for heterogeneity across populations.     

Score test for detecting linkage to complex traits in selected samples

We present a unified approach to selection and linkage analysis of selected samples, for both quantitative and dichotomous complex traits. It is based on the score test for the variance attributable to the trait locus and applies to general pedigrees. The method is equivalent to regressing excess IBD sharing on a function of the traits. It is shown that when population parameters for the trait are known, such inversion does not entail any loss of information. For dichotomous traits, pairs of pedigree members of different phenotypic nature (e.g., affected sib pairs and discordant sib pairs) can easily be combined as well as populations with different trait prevalences.     

Genome screening using extremely discordant and extremely concordant sib pairs

We applied extreme sib-pair methods in two ways to the GAW10 Problem 2A data sets to detect susceptible quantitative trait loci using extremely discordant sib pairs only, and combining them with the available extremely concordant sib pairs as suggested by the authors elsewhere. Ten successive original replicates were combined into one sampling pool so as to get the necessary number of extreme sib pairs. A total of 100 replicates were used to produce 10 such data sets for both initial detection and confirmations. Strong signals were found with markers D5G15 for Q1, D8G27-28 for Q4, and D9G7-9 for Q5. © 1997 Wiley-Liss, Inc.     

Search for susceptibility genes, gene x gene interactions, and gene x environment interactions utilizing nonparametric linkage analysis

There may be a different genetic basis for the two forms of the disease simulated in Problem 2 and the complex disease may be affected by environmental factors. Hence, we investigate the effects of two environmental factors. We selected 400 nuclear families from the data generated for Problem 2. Affection status was investigated in several ways. Individuals with severe and mild forms of the disease were both considered affected, individuals with only the severe form were considered affected while those with the mild form were considered unknown, and individuals with only the mild form were considered affected while those with the severe form were considered unknown. We found evidence of linkage between putative disease loci and markers in the D3G042-D3G049 and D5G031-D5G042 regions when we considered severely and mildly affected individuals as affected and also in the region D1G004-D1G013 when mildly affected individuals were considered unknown. We observed interactions between the first environmental factor and D1G043 among healthy sib pairs.     

Comparison of methods incorporating quantitative covariates into affected sib pair linkage analysis

For complex traits, it may be possible to increase the power to detect linkage if one takes advantage of covariate information. Several statistics have been proposed that incorporate quantitative covariate information into affected sib pair (ASP) linkage analysis. However, it is not clear how these statistics perform under different gene-environment (G x E) interactions. We compare representative statistics to each other on simulated data under three biologically-plausible G x E models. We also compared their performance with a model-free method and with quantitative trait locus (QTL) linkage approaches. The statistics considered here are: (1) mixture model; (2) general conditional-logistic model (LODPAL); (3) multinomial logistic regression models (MLRM); (4) extension of the maximum-likelihood-binomial approach (MLB); (5) ordered-subset analysis (OSA); and (6) logistic regression modeling (COVLINK). In all three G x E models, most of these six statistics perform better when using the covariate C1 associated with a G x E interaction effect than when using the environmental risk factor C2 or the random noise covariate C3. Compared with a model-free method without covariates (S(all)), the mixture model performs the best when using C1, with the high-to-low OSA method also performing quite well. Generally, MLB is the least sensitive to covariate choice. However, most of these statistics do not provide better power than S(all). Thus, while inclusion of the "correct" covariate can lead to increased power, careful selection of appropriate covariates is vital for success.     

Discussing gene-gene interaction: warning--translating equations to English may result in jabberwocky

Interest in mapping susceptibility alleles for complex diseases, which do not follow a classic single-gene segregation pattern, has driven interest in methods that account for, or use information from one locus when mapping another. Our discussion group examined methods related to epistasis or gene x gene interaction. The goal of modeling gene x gene interaction varied across groups; some papers tried to detect gene x gene interaction while others tried to exploit it to map genes. Most of the 10 papers summarized here applied newly created or newly modified statistical methods related to gene x gene interaction, while two groups primarily examined computational issues. As is often the case, comparisons are complicated by little overlap in the data used across the papers, and further complicated by the fact that the available data may not have been ideal for some gene x gene interaction methods. However, the main difficulty in comparing and contrasting methods across the papers is the lack of a consistent statistical definition of gene x gene interaction. But despite these issues, two clear trends emerged across the analyses: First, the methods for quantitative trait gene x gene interaction appeared to perform very well, even in families initially ascertained as affected sib pairs; and second, dichotomous trait gene x gene interaction methods failed to produce consistent results. The difficulty of using (primarily) affected sib pair data in a gene x gene interaction analysis is explored.     

Effectiveness of extreme discordant sib pairs to detect oligogenic disease loci

A method for the genomic screening of quantitative traits using extreme discordant sib pairs (EDSPs) has recently been described by Risch and Zhang [1995; 1996]. For many models relevant to common, genetically complex diseases, EDSPs are the most powerful siblings for detecting linkage. Thus, if such siblings can be identified and collected, powerful studies with reasonable genotyping budgets can be conducted. Using a subset of the GAW10 data, we have simulated a genomic screen using EDSPs. From the 4,780 total families in the first 20 replicates of 239 families, there were 100,104,155,107, and 180 EDSP families for Q1, Q2, Q3, Q4, and Q5, respectively. EDSP data were analyzed for each trait using a modified version of MAPMAKER/SIBS capable of handling extreme discordant sib pairs. Four regions, one for Q1, one for Q2, and two for Q4, were able to exceed a threshold for linkage corresponding to a 0.001 pointwise significance level. In three cases, maximum lod score (MLS) peaks occurred within 3.8 cM of a major gene. In the fourth case, the MLS peak occurred 28.4 cM from a major gene. Omission of parents and an alternative definition of EDSP were also investigated. © 1997 Wiley-Liss, Inc.     

A more powerful robust sib-pair test of linkage for quantitative traits

A more powerful robust test for linkage is developed from the methodology of Haseman and Elston [Behav Genet 2(1):3-19, 1972]. This new robust test uses weighted least-squares (WLS) methods to detect linkage between a quantitative trait and a polymorphic marker. For comparison, the characteristics of a test for linakge that uses known trait genotypes for the parents are also studied. Sample sizes needed to detect linkage, calculated using asymptotic results, are compared for 1) the usual Haseman-Elston method, 2) the WLS method, and 3) the method that uses parental trait genotype data. The WLS method needs at most twice the number of sib pairs as does the method that uses information on the trait genotypes of the parents. The small sample properties of the Haseman-Elston (H-E) and WLS tests are investigated by simulation. The power calculations for the H-E method are found to be accurate. The power of the WLS method is overestimated when fewer than 300 sib pairs are studied, but the WLS method is nonetheless more powerful than the usual H-E method. In samples of fewer than 300 sib pairs, the WLS test tends to be anticonservative. Treating all sib pairs from sibships of size 3 or 5 as independent does not increase the significance of the tests.     

Robust methods for the detection of genetic linkage for quantitative data from pedigrees

The robust method for detecting linkage developed by Haseman and Elston [The investigation of linkage between a quantitative trait and a marker locus. Behav Genet 2:3-19, 1972] for data from sib pairs is extended to any type of noninbred relative pair. The regression of the squared relative-pair trait difference on the estimated proportion of genes identical by descent (i.b.d.) at a marker locus is shown to depend upon the recombination fraction between the two loci; the regression coefficient is negative if the trait and marker loci are linked. A test for linkage based on data from any informative type of relative pair can thus be obtained by testing that this regression coefficient is less than zero. Formulae for the asymptotic power of such tests for linkage based upon independent relative pairs are developed. Results are also given for the special case in which the proportion of genes shared i.b.d. for relative pairs is known. Finally, a general algorithm is described that will incorporate all available pedigree data to calculate an estimate of the proportion of genes that a relative pair shares i.b.d. at a marker locus.     

Multigenic control of resistance to Sendai virus infection in mice

Experimental infection of mice with Sendai virus (SeV) is frequently used as a model of viral pathogenesis of human respiratory disease. To understand the differences in host response to SeV among mice strains, we carried out genetic mapping studies in DBA/2 (D2) (susceptible) and C57BL/6 (B6) (resistant) mice. F₁, F₂, and N₂ backcrossed mice were generated and examined for their disease resistance and susceptibility. For the determination of virulence, percentage body weight loss and survival time were used as phenotypes. We, then, carried out a genome wide scan on 108 backcrossed mice for linkage with percentage body weight loss as phenotype. A major quantitative trait locus (QTL) showing significant linkage was mapped to the distal portion of Chr 4 (SeV1). In addition, two other QTLs showing suggestive statistical linkage were also detected on Chr 8 and 14. We, further, performed genome scan for interactions with least squares analysis of variance of all pairs of informative makers in backcrossed progenies. We identified a highly significant epistatic interaction between D3Mit182 and D14Mit10, then denoted as SeV2 and SeV3, respectively, and the latter was the same locus showing a suggestive level on Chr 14 in QTL analysis. Considered genotypes of these three loci, we could account for more than 90% of genetic effect on the differential response to SeV infection between B6 and D2 mice. These findings revealed a novel gene interactions controlling SeV resistance in mice and will enable the identification of resistance genes encoded within these loci.     

Covariates in Linkage Analysis Using Sibling and Cousin Pairs

Using simulated data from GAW 12, problem 2, we further develop a novel technique to detect and use significant covariates in linkage analysis. The method, first introduced by Rice et al. [Genet Epidemiol 17(Suppl. 1):S691–5, 19991, uses logistic regression to model perturbation in sharing as a function of covariate levels. The original method allows use of all sib pairs (concordant affected, concordant unaffected, and discordant). Here we extend this method to include cousin pairs in analysis. © 2001 Wiley‐Liss, Inc.     

Segregation and linkage analysis of the complex trait Q1

Segregation and linkage analysis of GAW9 Problem 2 quantitative trait 1 (Q1) was performed. Eight segregation models comprising all possible combinations of the environmental factor (EF), quantitative trait 2 (Q2), and quantitative trait 3 (Q3) as covariates were considered. Seven of the eight segregation models showed strong evidence for a major gene, the other model was marginal. When all genotypes are known, some evidence for linkage (lod > 2) was found to all three of the markers that affect Q1. Furthermore, four of the eight models each showed some linkage (lod > 2) to two of the three markers that affect Q1 with no false positives. Each of these segregation analysis major genes is a hybrid combination of the true multiple loci that affect Q1. © 1995 Wiley-Liss, Inc.