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.     

Two Approaches for Consolidating Results from Genome Scans of Complex Traits: Selection Methods and Scan Statistics

This work has two purposes: (i) empirically selecting levels of significance that maximize the fraction of markers close to a gene (hit rate) when performing linkage analyses of simulated data and (ii) evaluating the utility of a previously reported scan statistic on the same data. Genotype data were simulated from a trait model of seven susceptibility genes. For purpose (i), five statistics were evaluated on all marker loci in fifty replicates; two‐point lod and heterogeneity lod scores maximized over dominance (mlod, mhlod), a multi‐allelic TDT test, an affected sib‐pair test (ASP), and a model‐free test on all sib‐pairs (ALL_SIBS). Within each replicate the fraction of markers (hit rate) significant at specified levels of significance and also (a) within fifty markers of, or (b) on the same chromosome as a major gene was calculated. For purpose (ii), scan statistics of length 15 were calculated for each chromosome and their empirical significance levels estimated on the basis of 500 replicates generated under no linkage. The scan statistic was applied to the mhlod scores from one replicate (Replicate 5). Empirical p‐values for the scan statistic were determined by computing mhlod scores on 500 replicates of simulated null data. For purpose (i), significance levels between 0.001 and 0.01 had the greatest hit rate for all five methods and both criteria. For criterion (a) at the 0.001 level of significance, both mlod and mhlod displayed the highest hit rates, approximately 0.4 for each. For criterion (b), all methods but ALL_SIBS and ASP had hit rates ranging between 0.4 and 0.5. For purpose (ii), the scan statistic proved equally or more powerful than the single‐locus statistic for two of the seven susceptibility genes while the remaining five genes were not detected. © 2001 Wiley‐Liss, Inc.     

Simultaneous localization of two linked disease susceptibility genes

For diseases with complex genetic etiology, more than one susceptibility gene may exist in a single chromosomal region. Extending the work of Liang et al. ([2001] Hum. Hered. 51:64-78), we developed a method for simultaneous localization of two susceptibility genes in one region. We derived an expression for expected allele sharing of an affected sib pair (ASP) at each point across a chromosomal segment containing two susceptibility genes. Using generalized estimating equations (GEE), we developed an algorithm that uses marker identical-by-descent (IBD) sharing in affected sib pairs to simultaneously estimate the locations of the two genes and the mean IBD sharing in ASPs at these two disease loci. Confidence intervals for gene locations can be constructed based on large sample approximations. Application of the described methods to data from a genome scan for type 1 diabetes (Mein et al. [1998] Nat. Genet. 19:297-300) yielded estimates of two putative disease gene locations on chromosome 6, approximately 20 cM apart. Properties of the estimators, including bias, precision, and confidence interval coverage, were studied by simulation for a range of genetic models. The simulations demonstrated that the proposed method can improve disease gene localization and aid in resolving large peaks when two disease genes are present in one chromosomal region. Joint localization of two disease genes improves with increased excess allele sharing at the disease gene loci, increased distance between the disease genes, and increased number of affected sib pairs in the sample.     

Tests for the presence of two linked disease susceptibility genes

For diseases with complex genetic etiology, more than one susceptibility gene may exist in a single chromosomal region. Under explicit assumptions about the number of disease genes in a region, generalized estimating equations (GEE) can be used to estimate the putative disease gene location(s) and expected identical-by-descent allele sharing in affected sib pairs at these gene(s). Extending the work of Liang et al. developed a method for simultaneous localization of two susceptibility genes in one region using marker identical-by-descent (IBD) sharing in affected sib pairs. Here we propose methods to evaluate the evidence for two versus one disease loci in a region in a quasi-likelihood/GEE framework. We describe tests based on approximate quasi-likelihood ratio and generalized score test statistics. Because of difficulties in determining the asymptotic null distributions of these statistics and the small sample sizes that can be available in genetic studies, we recommend that significance be evaluated empirically. Application of the described methods to data from a genome scan for type 1 diabetes yielded some evidence for two linked disease genes on chromosome 6, approximately 20 cM apart (p value for an approximate quasi-likelihood ratio test=0.049). In simulation studies, we found that both tests performed quite well for a range of scenarios. Power to detect the presence of two linked disease genes increased with the number of affected sib pairs, greater IBD sharing at the two loci, and larger distance between the two loci.     

Power of concordant versus discordant sib pairs at different penetrance levels

Knowing the answers, we used the GAW11 data set to compare the power and efficiency of discordant versus concordant affected sib pairs for qualitative traits at different levels of penetrance. Samples of 200 concordant sib pairs outperformed discordant sib pairs for low penetrance (40%) and 70% penetrance models while at 90% penetrance they performed equally well. Increasing the sample size of discordant sib pairs to twice that of concordant pairs was not enough to reach the power of concordant sib pairs at the 40% and 70% penetrance models. For low penetrance using a combination of concordant and discordant sib pairs resulted in higher power than using discordant sib pairs alone. At 90% penetrance, the power of concordant and discordant sib pairs was similar in the region close to the gene while concordant sib pairs performed better at locations further from the gene.     

Association tests using unaffected-sibling versus pseudo-sibling controls

We used family-matched case-control data to screen the genome for markers associated with disease in the simulated data set. Two different types of controls were considered: (1) unaffected siblings and (2) 'pseudo siblings,' a comparison sample created using the parental alleles. The scans were conducted on the first replicate of each study population. Overall, the two methods identified 14 marker loci associated with disease at the 0.001 significance level. Marker D1G24 (locus D) was the only true disease locus found by both approaches. No associations were found at any of the markers flanking the unobserved disease susceptibility loci (A, B, or C). We subsequently pooled the 25 replicates from a single population. This large sample still did not yield any associations at the flanking markers. We tested for association at locus D using a pseudo-sib approach restricted to alleles shared identical by descent between affected sib pairs. The power was 44% (11/25 replicates) at a significance level of 0.001.     

Assessing the Effect of Sampling Strategies on the Power of Linkage Analysis to Identify Pathway‐Specific Loci Underlying a Complex Disease

Using the simulated general population data sets, we first examined the effect of sampling strategies on the power of identifying linkage by selecting samples with (A) two affected sibs in a nuclear family and (B) one affected sib and one sib with an intermediate trait value in the upper quantiles. Second, we evaluated the improvement in power when analyzing correlated traits simultaneously. Under each selection criteria, 100 replicates of 300 nuclear families were sampled and analyzed with two‐point linkage analysis for ten markers (1 cM apart) from each of the candidate regions. Different genes were identified under different sampling strategies. When a gene has a pleitropic effect, it is more powerful to analyze correlated traits simultaneously, either by using a linear combination or the larger value of standardized traits, than to analyze each trait separately. © 2001 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.     

The Use of Sequential Designs in Genome Scans for Asthma Susceptibility Loci With Affected Sib Pairs

We use optimized group sequential study designs to analyze data from two genome scans (German and CSGA) for asthma susceptibility loci with affected sib pairs from Genetic Analysis Workshop (GAW) 12. Results are compared with those from a fixed sample design and the sequential probability ratio test (SPRT). The SPRT does not reach significance at any position. Using the fixed sample design, evidence for linkage is found on chromosomes 6 and 9 in the German and on chromosome 1 in the CSGA scan. The group sequential designs identify the same regions on chromosomes 1 and 6 with a reduced sample size. © 2001 Wiley‐Liss, Inc.     

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.     

Two-stage global search designs for linkage analysis using pairs of affected relatives

We investigate the two-stage procedure proposed by Elston [(1992) Proceedings of the XVIth International Biometric Conference, Hamilton, New Zealand, December 7–11, 1992, pp 39–51, and (1994) “Genetic Approaches to Mental Disorders.” Washington, DC: American Psychiatric Press, pp 3–21] for performing a global search of the genome to locate disease genes by linkage analysis using affected relative pairs. The optimal design depends on the type of pairs studied, the effect of the disease locus, the relative costs of recruiting affected persons and typing markers, how informative the markers are, and the amount of genetic heterogeneity. It is specified by the initial number of markers to use, the number of affected relative pairs to study, the initial significance level α^* to use at the first stage, and the number of flanking markers to use at the second stage around markers significant at the first stage. Asymptotically, the optimal design does not depend separately on either the desired final significance level or power, but rather on a function of the two. Both as the effect of the disease locus increases and as the relative cost of recruiting a subject increases, the optimal number of initial markers increases and the optimal number of pairs decreases. The expected cost of the study decreases as the effect of the disease locus increases, but increases as the relative cost of recruiting a subject increases. The optimal initial number of markers decreases but the number of pairs increases when there is genetic heterogeneity present; conversely, the optimal initial number of markers increases when markers are less than fully informative. Compared to a one-stage procedure, a two-stage procedure typically halves the cost of a study. © 1996 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.     

Association and Linkage for Age at Onset of a Common Oligogenic Disease Using Genetic Variance Component Models

The aims of our analysis were: (1) to investigate association of single nucleotide polymorphisms (SNPs) and other covariates with age at onset in the simulated Genetic Analysis Workshop (GAW) 12 general population data, and (2) to use the polygenic random effects estimated during model fitting (sigma squared A random effects) as input to a Haseman‐Elston linkage analysis. The association analyses used genetic variance component models in a generalized linear mixed models framework and were fitted using Gibbs sampling. This method successfully detected the only three sequenced genes that were also major genes. The single‐point linkage analysis used all markers provided. Regions of linkage were found close to all four of the sites of major genes that explained a non‐trivial component of the variance of age at onset. In all four cases the linkage peak fell within 5 cM of the true location. In three cases the peak significance was p < 0.01. © 2001 Wiley‐Liss, Inc.     

Two-stage global search designs for linkage analysis I: use of the mean statistic for affected sib pairs

Two-stage global search designs for linkage analysis using pairs of affected relatives were shown by Elston et al. [1996] to typically halve the cost of a study compared to a one-stage design. The statistic used for testing linkage in that study was based on the proportion of pairs sharing no marker alleles identical by descent (IBD). However, it has been established that the mean statistic often has the greatest power for full sib pairs [Blackwelder and Elston, 1985; Schaid and Nick, 1990; Knapp et al. 1994]. In this paper, we study optimal two-stage global search designs, in the case of affected full sib pairs, when using the mean test statistic to test for linkage. When dominant genetic variance is present, using the mean statistic is usually more cost efficient than using the proportion of pairs sharing no maker alleles IBD; in the case when there is no dominant genetic variance, the mean statistic leads to a better design, in the sense of being more cost-saving, provided that the relative risk ratio for first-degree relatives is small. The effect of heterogeneity and markers' informativeness is also investigated, the latter using the Linkage Information Content value for sibs.     

Genetic Analysis of Quantitative Traits in Highly Ascertained Samples: Total Serum IgE in Families with Asthma

The objective of this study was to compare the effect of an approximate ascertainment correction using proband phenotypes with heuristic corrections based on sample trait means and on published “standard” population values. Data were from the Collaborative Study on the Genetics of Asthma, which comprises 225 families ascertained through sib pairs affected with asthma. In variance component linkage analysis of IgE no lod scores greater than 3.0 were observed, either with or without several attempted corrections for ascertainment. The ascertained nature of the sample may have compromised the power to detect linkage to a quantitative trait (IgE) associated with the focal phenotype (asthma). © 2001 Wiley‐Liss, Inc.     

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.     

Strategy for mapping minor histocompatibility genes involved in graft-versus-host disease: A novel application of discordant sib pair methodology

We introduce a novel application for linkage analysis: using bone marrow donor-recipient sib pairs to search for genes influential in graft-versus-host disease (GVHD), a major cause of morbidity and mortality following allogeneic bone marrow transplantation. In particular, we show that transplant sib pairs in which the recipient developed severe GVHD can be used to map genes in the same way as traditional discordant (affected/unaffected) sib pairs (DSPs). For a plausible GVHD model, we demonstrate that the transplant/discordant sib pair analog of the “possible triangle test” [Holmans (1993) Am J Hum Genet 52:362–374] has similar power to that of the simpler “restricted test” proposed by Risch [(1990b) Am J Hum Genet 46:229–241; (1992) Am J Hum Genet 51:673–675]. Moreover, we show that the restricted test has superior power in much of the DSP possible triangle and significantly inferior power in only a small region. Thus, we conclude that the restricted test is preferable for localizing genes with transplant/discordant sib pairs. Finally, we examine the effects of heterogeneity on the power to detect GVHD loci and demonstrate the gain in efficiency by dividing the sample into genetically more homogeneous subgroups. Genet. Epidemiol. 15:595–607,1998. © 1998 Wiley-Liss, Inc.     

Detection of major genes underlying several quantitative traits associated with a common disease using different ascertainment schemes

Using the Problem 2A data sets of GAW10, we assessed the power of four ascertainment schemes to localize major genes underlying a disease trait; the schemes were based on disease or quantitative trait status of nuclear families. MAPMAKER/SIBS was used to perform sib-pair analysis for all four data sets using marker data from three chromosomes, 4,5 and 8. Each scheme varied in power to identify major genes underlying the quantitative traits depending on the genetic architecture of the data set. Three different methods, Haseman-Elston quantitative trait locus (QTL) regression analysis, maximum likelihood variance estimation and a non-parametric method, were used to assess the strength of linkage in all four data sets. False positive mappings localizing to the same region of the genome, verifiable across all three methods did not occur. Two major genes, MG1 and MG2, were successfully assigned to chromosomes 5 and 8, respectively, by at least one of the ascertainment schemes. MG1 was localized under two schemes, selection of families with exactly two affected sibs and selection of families with two sibs who had extremely discordant values for Q1. Additional weak evidence of the location of MG1 was also obtained under the other two ascertainment schemes. MG2 could not be detected by analyzing data sets ascertained either by affected sib pairs or by sib pairs with extremely discordant values for Q1. In the data set ascertained by a third strategy, selection of families with sib pairs extremely discordant for Q2, MG2 could be mapped to chromosome 8. A random ascertainment scheme yielded a data set in which we could find weak evidence for MG1 and no evidence for MG2. Thus our ability to detect major genes underlying the QTL depended on several factors which included the ascertainment scheme, the population allelle frequencies, linkage and epistasis. © 1997 Wiley-Liss, Inc.     

A meta-analysis of chromosome 18 linkage data for bipolar illness

We find a meta-data set (715 families, up to 1,124 sib pairs) for bipolar illness to have a strong signal in a 10 cM region around D18S40, and excess paternal sharing on the q arm near marker D18S64. We describe a method for meta-analysis of microsatellite marker data using affected sib-pair (ASP) methodology. Inherent difficulties in such analysis include heterogeneity of allele frequencies and protocol design, measurement errors in genotyping, and map construction. Using identity-by-descent (IBD) allele sharing as the dependent variable, a logistic regression to test for heterogeneity finds only mild heterogeneity, and a limited parent-of-origin effect. © 1997 Wiley-Liss, Inc.     

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.