A gene-model-free method for linkage analysis of a disease-related-trait based on analysis of proband/sibling pairs

In this paper we investigate the power of finding linkage to a disease locus through analysis of the disease-related traits. We propose two family-based gene-model-free linkage statistics. Both involve considering the distribution of the number of alleles identical by descent with the proband and comparing siblings with the disease-related trait to those without the disease-related-trait. The objective is to find linkages to disease-related traits that are pleiotropic for both the disease and the disease-related-traits. The power of these statistics is investigated for Kofendrerd Personality Disorder-related traits a (Joining/founding cults) and trait b (Fear/discomfort with strangers) of the simulated data. The answers were known prior to the execution of the reported analyses. We find that both tests have very high power when applied to the samples created by combining the data of the three cities for which we have nuclear family data.     

Linkage mapping of a complex trait in the New York population of the GAW14 simulated dataset: a multivariate phenotype approach

Multivariate phenotypes underlie complex traits. Thus, instead of using the end-point trait, it may be statistically more powerful to use a multivariate phenotype correlated to the end-point trait for detecting linkage. In this study, we develop a reverse regression method to analyze linkage of Kofendrerd Personality Disorder affection status in the New York population of the Genetic Analysis Workshop 14 (GAW14) simulated dataset. When we used the multivariate phenotype, we obtained significant evidence of linkage near four of the six putative loci in at least 25% of the replicates. On the other hand, the linkage analysis based on Kofendrerd Personality Disorder status as a phenotype produced significant findings only near two of the loci and in a smaller proportion of replicates.     

Genome-wide linkage and association mapping of disease genes with the GAW14 simulated datasets

We combined the results of whole-genome linkage and association analyses to determine which markers were most strongly associated with Kofendrerd Personality Disorder. Using replicate 1 from the Genetic Analysis Workshop 14 Aipotu, Karangar, Danacaa, and New York City simulated populations, we determined that several markers showed significant linkage and association with disease status. We used both SNP and microsatellite markers to determine patterns and chromosomal regions of markers. Three consistently associated markers were C01R0050, C03R0280, and C10R0882. Using generalized linear mixed models, we modelled the effect of the three predefined phenotypic categories on disease status and concluded that the phenotypes defining the "anxiety-related" category best predicted the outcome.     

Identifying genomic regions for fine-mapping using genome scan meta-analysis (GSMA) to identify the minimum regions of maximum significance (MRMS) across populations

In order to detect linkage of the simulated complex disease Kofendrerd Personality Disorder across studies from multiple populations, we performed a genome scan meta-analysis (GSMA). Using the 7-cM microsatellite map, nonparametric multipoint linkage analyses were performed separately on each of the four simulated populations independently to determine p-values. The genome of each population was divided into 20-cM bin regions, and each bin was rank-ordered based on the most significant linkage p-value for that population in that region. The bin ranks were then averaged across all four studies to determine the most significant 20-cM regions over all studies. Statistical significance of the averaged bin ranks was determined from a normal distribution of randomly assigned rank averages. To narrow the region of interest for fine-mapping, the meta-analysis was repeated two additional times, with each of the 20-cM bins offset by 7 cM and 13 cM, respectively, creating regions of overlap with the original method. The 6-7 cM shared regions, where the highest averaged 20-cM bins from each of the three offsets overlap, designated the minimum region of maximum significance (MRMS). Application of the GSMA-MRMS method revealed genome wide significance (p-values refer to the average rank assigned to the bin) at regions including or adjacent to all of the simulated disease loci: chromosome 1 (p < 0.0001 for 160-167 cM, including D1), chromosome 3 (p-value < 0.0000001 for 287-294 cM, including D2), chromosome 5 (p-value < 0.001 for 0-7 cM, including D3), and chromosome 9 (p-value < 0.05 for 7-14 cM, the region adjacent to D4). This GSMA analysis approach demonstrates the power of linkage meta-analysis to detect multiple genes simultaneously for a complex disorder. The MRMS method enhances this powerful tool to focus on more localized regions of linkage.     

Methods to test for association between a disease and a multi-allelic marker applied to a candidate region

We report the analysis results of the Genetic Analysis Workshop 14 simulated microsatellite marker dataset, using replicate 50 from the Danacaa population. We applied several methods for association analysis of multi-allelic markers to case-control data to study the association between Kofendrerd Personality Disorder and multi-allelic markers in a candidate region previously identified by the linkage analysis. Evidence for association was found for marker D03S0127 (p < 0.01). The analyses were done without any prior knowledge of the answers.     

Bivariate linkage analysis of the insulin resistance syndrome phenotypes on chromosome 7q

Metabolic abnormalities of the insulin resistance syndrome (IRS) have been shown to aggregate in families and to exhibit trait-pair correlations, suggesting a common genetic component. A broad region on chromosome 7q has been implicated in several studies to contain loci that cosegregate with IRS-related traits. However, it is not clear whether such loci have any common genetic (pleiotropic) influences on the correlated traits. Also, it is not clear whether the chromosomal regions contain more than one locus influencing the IRS-related phenotypes. In this study we present evidence for linkage of five IRS-related traits [body mass index (BMI), waist circumference (WC), In split proinsulin (LSPI), In triglycerides (LTG), and high-density lipoprotein cholesterol (HDLC)] to a region at 7q11.23. Subsequently, to gain further insight into the genetic component(s) mapping to this region, we explored whether linkage of these traits is due to pleiotropic effects using a bivariate linkage analytical technique, which has been shown to localize susceptibility regions with precision. Four hundred forty individuals from 27 Mexican American families living in Texas were genotyped for 19 highly polymorphic markers on chromosome 7. Multipoint variance component linkage analysis was used to identify genetic location(s) influencing IRS-related traits of obesity (BMI and WC), dyslipidemia (LTG and HDLC), and insulin levels (LSPI); the analysis identified a broad chromosomal region spanning approximately 24 cM. To gain more precision in localization, we used a bivariate linkage approach for each trait pair. These analyses suggest localization of most of these bivariate traits to an approximately 6-cM region near marker D7S653 [7q11.23, 103-109 cM; a maximum bivariate LOD of 4.51 was found for the trait pair HDLC and LSPI (the LODeq score is 3.94)]. We observed evidence of pleiotropic effects in this region on obesity and insulin-related trait pairs.     

Linkage analysis of GAW14 simulated data: comparison of multimarker, multipoint, and conditional approaches

The purposes of this study were 1) to examine the performance of a new multimarker regression approach for model-free linkage analysis in comparison to a conventional multipoint approach, and 2) to determine the whether a conditioning strategy would improve the performance of the conventional multipoint method when applied to data from two interacting loci. Linkage analysis of the Kofendrerd Personality Disorder phenotype to chromosomes 1 and 3 was performed in three populations for all 100 replicates of the Genetic Analysis Workshop 14 simulated data. Three approaches were used: a conventional multipoint analysis using the Zlr statistic as calculated in the program ALLEGRO; a conditioning approach in which the per-family contribution on one chromosome was weighted according to evidence for linkage on the other chromosome; and a novel multimarker regression approach. The multipoint and multimarker approaches were generally successful in localizing known susceptibility loci on chromosomes 1 and 3, and were found to give broadly similar results. No advantage was found with the per-family conditioning approach. The effect on power and type I error of different choices of weighting scheme (to account for different numbers of affected siblings) in the multimarker approach was examined.     

Identifying genetic variation affecting a complex trait in simulated data: a comparison of meta-analysis with pooled data analysis

We explored the power and consistency to detect linkage and association with meta-analysis and pooled data analysis using Genetic Analysis Workshop 14 simulated data. The first 10 replicates from Aipotu population were used. Significant linkage and association was found at all 4 regions containing the major loci for Kofendrerd Personality Disorder (KPD) using both combined analyses although no significant linkage and association was found at all these regions in a single replicate. The linkage results from both analyses are consistent in terms of the significance level of linkage test and the estimate of locus location. After correction for multiple-testing, significant associations were detected for the same 8 single-nucleotide polymorphisms (SNP) in both analyses. There were another 2 SNPs for which significant associations with KPD were found only by pooled data analysis. Our study showed that, under homogeneous condition, the results from meta-analysis and pooled data analysis are similar in both linkage and association studies and the loss of power is limited using meta-analysis. Thus, meta-analysis can provide an overall evaluation of linkage and association when the original raw data is not available for combining.     

Impact of the diagnosis definition on linkage detection

Previous genome scan linkage analyses of the disease Kofendrerd Personality Disorder (KPD) with microsatellites led to detect some regions on chromosomes 1, 3, 5, and 9 that were identical for the three populations AI, KA, and DA but with large differences in significance levels. These differences in results may be explained by the different diagnosis definitions depending on the presence/absence of 12 traits that were used in the 3 populations AI, KA, and DA. Heterogeneity of linkage was thus investigated here according to the absence/presence of each of the 12 traits in the 3 populations. For this purpose, two methods, the triangle test statistic and the predivided sample test were applied to search for genetic heterogeneity. Three regions with a strong heterogeneity of linkage were detected: the region on chromosome 1 according to the presence/absence of the traits a and b, the region on chromosome 3 for the trait b, and the region on chromosome 9 for the traits k and l. These 3 regions were the same as those detected by linkage analyses. No novel region was detected by the heterogeneity tests. Concerning chromosome 1, linkage analyses showed a much stronger evidence of linkage for traits a and b and for a combination of these traits than for KPD. Moreover, there was no indication of linkage to any of the other traits used to define the diagnosis of KPD. A genetic factor located on the chromosome 1 may have been detected here which would be involved specifically in traits a and b or in a combination of these traits.     

Genetic effects on obesity assessed by bivariate genome scan: the Mexican-American coronary artery disease study

Objective: To identify the genetic determinants of obesity using univariate and bivariate models in a genome scan. Research Methods and Procedures: We evaluated the genetic and environmental effects and performed a genome‐wide linkage analysis of obesity‐related traits in 478 subjects from 105 Mexican‐American nuclear families ascertained through a proband with documented coronary artery disease. The available obesity traits include BMI, body surface area (BSA), waist‐to‐hip ratio (WHR), and trunk fat mass as percentage of body weight. Heritability estimates and multipoint linkage analysis were performed using a variance components procedure implemented in SOLAR software. Results: The heritability estimates were 0.62 for BMI, 0.73 for BSA, 0.40 for WHR, and 0.38 for trunk fat mass as percentage of body weight. Using a bivariate genetic model, we observed significant genetic correlations between BMI and other obesity‐related traits (all p < 0.01). Evidence for univariate linkage was observed at 252 to approximately 267 cM on chromosome 2 for three obesity‐related traits (except for WHR) and at 163 to approximately 167 cM on chromosome 5 for BMI and BSA, with the maximum logarithm of the odds ratio score of 3.12 (empirical p value, 0.002) for BSA on chromosome 2. Use of the bivariate linkage model yielded an additional peak (logarithm of the odds ratio = 3.25, empirical p value, 0.002) at 25 cM on chromosome 7 for the pair of BMI and BSA. Discussion: The evidence for linkage on chromosomes 2q36‐37 and 5q36 is supported both by univariate and bivariate analysis, and an additional linkage peak at 7p15 was identified by the bivariate model. This suggests that use of the bivariate model provides additional information to identify linkage of genes responsible for obesity‐related traits.     

Boosting alternating decision trees modeling of disease trait information

We applied the alternating decision trees (ADTrees) method to the last 3 replicates from the Aipotu, Danacca, Karangar, and NYC populations in the Problem 2 simulated Genetic Analysis Workshop dataset. Using information from the 12 binary phenotypes and sex as input and Kofendrerd Personality Disorder disease status as the outcome of ADTrees-based classifiers, we obtained a new quantitative trait based on average prediction scores, which was then used for genome-wide quantitative trait linkage (QTL) analysis. ADTrees are machine learning methods that combine boosting and decision trees algorithms to generate smaller and easier-to-interpret classification rules. In this application, we compared four modeling strategies from the combinations of two boosting iterations (log or exponential loss functions) coupled with two choices of tree generation types (a full alternating decision tree or a classic boosting decision tree). These four different strategies were applied to the founders in each population to construct four classifiers, which were then applied to each study participant. To compute average prediction score for each subject with a specific trait profile, such a process was repeated with 10 runs of 10-fold cross validation, and standardized prediction scores obtained from the 10 runs were averaged and used in subsequent expectation-maximization Haseman-Elston QTL analyses (implemented in GENEHUNTER) with the approximate 900 SNPs in Hardy-Weinberg equilibrium provided for each population. Our QTL analyses on the basis of four models (a full alternating decision tree and a classic boosting decision tree paired with either log or exponential loss function) detected evidence for linkage (Z >or= 1.96, p < 0.01) on chromosomes 1, 3, 5, and 9. Moreover, using average iteration and abundance scores for the 12 phenotypes and sex as their relevancy measurements, we found all relevant phenotypes for all four populations except phenotype b for the Karangar population, with suggested subgroup structure consistent with latent traits used in the model. In conclusion, our findings suggest that the ADTrees method may offer a more accurate representation of the disease status that allows for better detection of linkage evidence.     

Modeling the effect of a genetic factor for a complex trait in a simulated population

Genetic Analysis Workshop 14 simulated data have been analyzed with MASC(marker association segregation chi-squares) in which we implemented a bootstrap procedure to provide the variation intervals of parameter estimates. We model here the effect of a genetic factor, S, for Kofendrerd Personality Disorder in the region of the marker C03R0281 for the Aipotu population. The goodness of fit of several genetic models with two alleles for one locus has been tested. The data are not compatible with a direct effect of a single-nucleotide polymorphism (SNP) (SNP 16, 17, 18, 19 of pack 153) in the region. Therefore, we can conclude that the functional polymorphism has not been typed and is in linkage disequilibrium with the four studied SNPs. We obtained very large variation intervals both of the disease allele frequency and the degree of dominance. The uncertainty of the model parameters can be explained first, by the method used, which models marginal effects when the disease is due to complex interactions, second, by the presence of different sub-criteria used for the diagnosis that are not determined by S in the same way, and third, by the fact that the segregation of the disease in the families was not taken into account. However, we could not find any model that could explain the familial segregation of the trait, namely the higher proportion of affected parents than affected sibs.     

Quantitative trait loci influencing low density lipoprotein particle size in African Americans

Genomic regions that influence LDL particle size in African Americans are not known. We performed family-based linkage analyses to identify genomic regions that influence LDL particle size and also exert pleiotropic effects on two closely related lipid traits, high density lipoprotein cholesterol (HDL-C) and triglycerides, in African Americans. Subjects (n = 1,318, 63.0 +/- 9.5 years, 70% women, 79% hypertensive) were ascertained through sibships with two or more individuals diagnosed with essential hypertension before age 60. LDL particle size was measured by polyacrylamide gel electrophoresis, and triglyceride levels were log-transformed to reduce skewness. Genotypes were measured at 366 microsatellite marker loci distributed across the 22 autosomes. Univariate and bivariate linkage analyses were performed using a variance components approach. LDL particle size was highly heritable (h(2) = 0.78) and significantly (P < 0.0001) genetically correlated with HDL-C (rho(G) = 0.32) and log triglycerides (rho(G) = -0.43). Significant evidence of linkage for LDL particle size was present on chromosome 19 [85.3 centimorgan (cM), log of the odds (LOD) = 3.07, P = 0.0001], and suggestive evidence of linkage was present on chromosome 12 (90.8 cM, LOD = 2.02, P = 0.0011). Bivariate linkage analyses revealed tentative evidence for a region with pleiotropic effects on LDL particle size and HDL-C on chromosome 4 (52.9 cM, LOD = 2.06, P = 0.0069). These genomic regions may contain genes that influence interindividual variation in LDL particle size and potentially coronary heart disease susceptibility in African Americans.     

Performance comparison of two-point linkage methods using microsatellite markers flanking known disease locations

The Genetic Analysis Workshop 14 simulated data presents an interesting, challenging, and plausible example of a complex disease interaction in a dataset. This paper summarizes the ease of detection for each of the simulated Kofendrerd Personality Disorder (KPD) genes across all of the replicates for five standard linkage statistics. Using the KPD affection status, we have analyzed the microsatellite markers flanking each of the disease genes, plus an additional 2 markers that were not linked to any of the disease loci. All markers were analyzed using the following two-point linkage methods: 1) a MMLS, which is a standard admixture LOD score maximized over theta, alpha, and mode of inheritance, 2) a MLS calculated by GENEHUNTER, 3) the Kong and Cox LOD score as computed by MERLIN, 4) a MOD score (standard heterogeneity LOD maximized over theta, alpha, and a grid of genetic model parameters), and 5) the PPL, a Bayesian statistic that directly measures the strength of evidence for linkage to a marker. All of the major loci (D1-D4) were detectable with varying probabilities in the different populations. However, the modifier genes (D5 and D6) were difficult to detect, with similar distributions under the null and alternative across populations and statistics. The pooling of the four datasets in each replicate (n = 350 pedigrees) greatly improved the chance of detecting the major genes using all five methods, but failed to increase the chance to detect D5 and D6.     

Investigation of altering single-nucleotide polymorphism density on the power to detect trait loci and frequency of false positive in nonparametric linkage analyses of qualitative traits

Genome-wide linkage analysis using microsatellite markers has been successful in the identification of numerous Mendelian and complex disease loci. The recent availability of high-density single-nucleotide polymorphism (SNP) maps provides a potentially more powerful option. Using the simulated and Collaborative Study on the Genetics of Alcoholism (COGA) datasets from the Genetics Analysis Workshop 14 (GAW14), we examined how altering the density of SNP marker sets impacted the overall information content, the power to detect trait loci, and the number of false positive results. For the simulated data we used SNP maps with density of 0.3 cM, 1 cM, 2 cM, and 3 cM. For the COGA data we combined the marker sets from Illumina and Affymetrix to create a map with average density of 0.25 cM and then, using a sub-sample of these markers, created maps with density of 0.3 cM, 0.6 cM, 1 cM, 2 cM, and 3 cM. For each marker set, multipoint linkage analysis using MERLIN was performed for both dominant and recessive traits derived from marker loci. Our results showed that information content increased with increased map density. For the homogeneous, completely penetrant traits we created, there was only a modest difference in ability to detect trait loci. Additionally, as map density increased there was only a slight increase in the number of false positive results when there was linkage disequilibrium (LD) between markers. The presence of LD between markers may have led to an increased number of false positive regions but no clear relationship between regions of high LD and locations of false positive linkage signals was observed.     

Smoothing of the bivariate LOD score for non-normal quantitative traits

Variance component analysis provides an efficient method for performing linkage analysis for quantitative traits. However, type I error of variance components-based likelihood ratio testing may be affected when phenotypic data are non-normally distributed (especially with high values of kurtosis). This results in inflated LOD scores when the normality assumption does not hold. Even though different solutions have been proposed to deal with this problem with univariate phenotypes, little work has been done in the multivariate case. We present an empirical approach to adjust the inflated LOD scores obtained from a bivariate phenotype that violates the assumption of normality. Using the Collaborative Study on the Genetics of Alcoholism data available for the Genetic Analysis Workshop 14, we show how bivariate linkage analysis with leptokurtotic traits gives an inflated type I error. We perform a novel correction that achieves acceptable levels of type I error.     

Joint Multipoint Linkage Analysis of Multivariate Qualitative and Quantitative Traits. I. Likelihood Formulation and Simulation Results

We describe a variance-components method for multipoint linkage analysis that allows joint consideration of a discrete trait and a correlated continuous biological marker (e.g., a disease precursor or associated risk factor) in pedigrees of arbitrary size and complexity. The continuous trait is assumed to be multivariate normally distributed within pedigrees, and the discrete trait is modeled by a threshold process acting on an underlying multivariate normal liability distribution. The liability is allowed to be correlated with the quantitative trait, and the liability and quantitative phenotype may each include covariate effects. Bivariate discrete-continuous observations will be common, but the method easily accommodates qualitative and quantitative phenotypes that are themselves multivariate. Formal likelihood-based tests are described for coincident linkage (i.e., linkage of the traits to distinct quantitative-trait loci [QTLs] that happen to be linked) and pleiotropy (i.e., the same QTL influences both discrete-trait status and the correlated continuous phenotype). The properties of the method are demonstrated by use of simulated data from Genetic Analysis Workshop 10. In a companion paper, the method is applied to data from the Collaborative Study on the Genetics of Alcoholism, in a bivariate linkage analysis of alcoholism diagnoses and P300 amplitude of event-related brain potentials.     

Exploring pleiotropy using principal components

A standard multivariate principal components (PCs) method was utilized to identify clusters of variables that may be controlled by a common gene or genes (pleiotropy). Heritability estimates were obtained and linkage analyses performed on six individual traits (total cholesterol (Chol), high and low density lipoproteins, triglycerides (TG), body mass index (BMI), and systolic blood pressure (SBP)) and on each PC to compare our ability to identify major gene effects. Using the simulated data from Genetic Analysis Workshop 13 (Cohort 1 and 2 data for year 11), the quantitative traits were first adjusted for age, sex, and smoking (cigarettes per day). Adjusted variables were standardized and PCs calculated followed by orthogonal transformation (varimax rotation). Rotated PCs were then subjected to heritability and quantitative multipoint linkage analysis. The first three PCs explained 73% of the total phenotypic variance. Heritability estimates were above 0.60 for all three PCs. We performed linkage analyses on the PCs as well as the individual traits. The majority of pleiotropic and trait-specific genes were not identified. Standard PCs analysis methods did not facilitate the identification of pleiotropic genes affecting the six traits examined in the simulated data set. In addition, genes contributing 20% of the variance in traits with over 0.60 heritability estimates could not be identified in this simulated data set using traditional quantitative trait linkage analyses. Lack of identification of pleiotropic and trait-specific genes in some cases may reflect their low contribution to the traits/PCs examined or more importantly, characteristics of the sample group analyzed, and not simply a failure of the PC approach itself.     

Quantitative founder-effect analysis of French Canadian families identifies specific loci contributing to metabolic phenotypes of hypertension

The Saguenay-Lac St-Jean population of Quebec is relatively isolated and has genealogical records dating to the 17th-century French founders. In 120 extended families with at least one sib pair affected with early-onset hypertension and/or dyslipidemia, we analyzed the genetic determinants of hypertension and related cardiovascular and metabolic conditions. Variance-components linkage analysis revealed 46 loci after 100,000 permutations. The most prominent clusters of overlapping quantitative-trait loci were on chromosomes 1 and 3, a finding supported by principal-components and bivariate analyses. These genetic determinants were further tested by classifying families by use of LOD score density analysis for each measured phenotype at every 5 cM. Our study showed the founder effect over several generations and classes of living individuals. This quantitative genealogical approach supports the notion of the ancestral causality of traits uniquely present and inherited in distinct family classes. With the founder effect, traits determined within population subsets are measurably and quantitatively transmitted through generational lineage, with a precise component contributing to phenotypic variance. These methods should accelerate the uncovering of causal haplotypes in complex diseases such as hypertension and metabolic syndrome.     

Power of maximum HLOD tests to detect linkage to obesity genes

Background

We investigate the power of heterogeneity LOD test to detect linkage when a trait is determined by several major genes using Genetic Analysis Workshop 13 simulated data. We consider three traits, two of which are disease-causing traits: 1) the rate of change in body mass index (BMI); and 2) the maximum BMI; and 3) the disease itself (hypertension). Of interest is the power of "HLOD2", the maximum heterogeneity LOD obtained upon maximizing over the two genetic models.

Results

Using a trait phenotype Obesity Slope, we observe that the power to detect the two markers closest to the two genes (S1, S2) at the 0.05 level using HLOD2 is 13% and 10%. The power of HLOD2 for Max BMI phenotype is 12% and 9%. The corresponding values for the Hypertension phenotype are 8% and 6%.

Conclusion

The power to detect linkage to the slope genes is quite low. But the power using disease-related traits as a phenotype is greater than the power using the disease (hypertension) phenotype.