The beta 2 electroencephalogram (EEG) phenotype is used as a quantitative measure related to alcoholism, and evidence of linkage and association has previously been reported in the Collaborative Study on the Genetics of Alcoholism data. In this study, associations between the beta 2 EEG phenotype and single nucleotide polymorphisms from whole-genome Illumina and Affymetrix panels were investigated with the regression of offspring on mid-parent method to identify significant genetic effects and to estimate their heritability. Separate regressions on father and mother were performed to identify parent-specific effects. Estimates of the heritability of the beta 2 EEG phenotype were 0.68 ± 0.12 and 0.52 ± 0.07 based on father-offspring and mother-offspring pairs, respectively. Significant associations at the 0.0005 level, some of which were parent-specific, were found on chromosomes 1, 2, 5, 6, 7, 8, 11, 12, 15, 16, 17, 18, and 19 with heritability attributable to each SNP ranging from 0.01 to 8%. A receptor gene cluster in data from the Collaborative Study on the Genetics of Alcoholism (COGA) [A cluster on chromosome 15q11.2-q12 using a qualitative alcoholism phenotype in these same data.The first component of a trilinear singular value decomposition of the beta 2 band electroencephalogram (EEG) waves has been used as an alcoholism-related quantitative trait. Linkage and association were reported between this phenotype and markers in the chromosome 4p12 GABAm (COGA) . Song etThe goals of this study were: 1) to use the regression of offspring on mid-parent (ROMP) ,6 to tesDeparture from Hardy-Weinberg equilibrium was tested in the founders for each SNP using a chi-square test. The average ± standard deviation minor allele frequency in the founders was 0.39 ± 0.09 (range: 0.08–0.5) for the 4,596 Illumina SNPs and 0.27 ± 0.14 (range: 0–0.5) for the 10,810 Affymetrix SNPs. The ROMP method was used to estimate the heritability of the ECB21 phenotype and to test for association with each SNP from the two panels.h2) of a quantitative trait, a test of association between the trait and a locus, along with an estimate of the locus-specific heritability (hL2). The association test is obtained by adding a locus effect (the genotype of the offspring at the locus) in the regression model. The change in the regression coefficient of the mid-parent value when the locus is added to the model is the locus-specific heritability estimate. ROMP is performed in parent-offspring trios and requires phenotype data on the parents and their offspring but genotype data on the offspring only. The X-chromosome markers were not included in these analyses.ROMP is an extension of the traditional regression of offspring on mid-parent that provides, in addition to the estimate of the heritability (ECB21 was first adjusted for age at exam (ERP age), ERP age squared, and sex. This was done in a separate multiple linear regression model including all offspring. The residuals from this regression were then used in the ROMP analysis. The genotype of the offspring at each SNP was entered in the ROMP analysis assuming an additive allelic effect. ROMP was performed using all offspring from each sibship and a randomly selected single offspring to ensure independent parent-offspring trios. A robust estimate of variance that takes into account the correlation between multiple sibs from nuclear families is not available yet for the locus-specific heritability.p-value from the all-sib analysis was lower than 0.0005, and 2) the one-sib analysis also showed a trend toward significance .SNPs with a minor allele frequency smaller than 0.1 and SNPs for which Hardy-Weinberg equilibrium was rejected at the 0.001 significance level were excluded from the analysis. Results from the association tests were considered significant if: 1) the p-Values were obtained from 10,000 permutations of the parent's sex, keeping the other variables fixed, by counting the number of permuted samples for which the father-mother difference in heritability estimates divided by their respective standard errors exceeded the difference observed in the original sample.Separate regressions of offspring on mother (ROOM) and on father (ROOF) were also performed to investigate parent-specific effects. In these regressions, twice the regression coefficient is the heritability estimate. All-sib and one-sib analyses were performed in the same manner as for ROMP, and the same criteria were applied to determine significance. Permutation tests were used to assess the significance of these parent-specific effects. The father-offspring pairs were combined with the mother-offspring pairs, duplicating the offspring's information if the phenotype was available on both parents. A variable indicating the parent's sex was created. SAS Release 8.2  was usedAnalyses were restricted to the 1,074 non-Hispanic White subjects . These subjects belonged to 119 families ranging in size from 4 to 32 subjects for a total of 270 sibships with an average of 3 offspring (range: 2–10). Of the 13 quantitative traits released in the COGA data, we focused on ECB21, for which linkage and association were previously reported. All SNPs in the Affymetrix and Illumina panels were tested individually. Affymetrix and Illumina SNPs were then combined using the physical map  non-Hispanic White subjects of COGA, 79% of the probands and 44% of the family members were male. The average ERP age ± standard deviation was 42.5 ± 12.8 and 32.2 ± 8.0 for male and female probands, respectively, and 37.5 ± 14.6 and 39.7 ± 14.5 for male and female family members, respectively. The average ECB21 was 13.8 ± 4.9 and 13.6 ± 4.9 for male and female probands, respectively, and 13.9 ± 4.8 and 16.4 ± 5.9 for male and female family members, respectively.p-value < 0.001). A total of 236 trios were used in the ROMP analysis. There were many instances with only one phenotyped parent, resulting in 295 father-offspring pairs and 359 mother-offspring pairs for the ROOF and ROOM analyses, respectively. The trait heritability estimate for father-offspring pairs was slightly higher (0.675 ± 0.123) than for mother-offspring pairs (0.518 ± 0.072), but the confidence intervals overlapped .In a multiple linear regression model, sex, ERP age, and ERP age squared were strongly associated to ECB21. Consequently, ECB21 was adjusted for these variables. The heritability of age- and gender-adjusted ECB21 was high (0.450 ± 0.066) and statistically significant  were taken to be significant . Among the significant results, the proportion of the total heritability attributable to the locus ranged from 0.01% to 8%, with 17 and 3 SNPs having locus-specific heritability greater than 1% and 5%, respectively.p-value < 0.05 was considered a trend in the parent-specific analysis) in both father- and mother-offspring analyses. Mother-offspring associations alone were observed for the remaining 11 SNPs. However, permutation tests indicated that the father-mother difference in locus-specific heritability estimates was significant at a 0.001 level for only one of these 11 SNPs (tsc0972067).Twelve SNPs had similar trends . The SNPs for which significant associations were found in this study are not located within or near any of the known candidate genes for alcoholism [Using ROMP, significant associations at the 0.0005 level were detected between the beta 2 EEG phenotype and 23 SNPs on chromosomes 1, 2, 5, 6, 7, 8, 11, 12, 15, 16, 17, 18, and 19. None of these SNPs are located in the areas where evidence for linkage and/or association was previously found in the COGA data. Four SNPs in the panels are located in the GABAG.E. 4.3 ) and no The estimate of locus-specific heritability may provide insight on the importance of each SNP. Three out of the 23 SNPs that showed significant associations had a locus-specific heritability estimate between 5 and 8%. The separate regressions of offspring on father and mother were performed as a screening tool in an attempt to detect any difference in parental effect. One of the 23 SNPs, tsc0972067, showed a significant association only in mother-offspring trios, suggesting some type of maternal effect.COGA: Collaborative Study on the Genetics of AlcoholismEEG: ElectroencephalogramROMP: Regression of offspring on mid-parentROOF: Regressions of offspring on fatherROOM: Regressions of offspring on motherSNP: Single-nucleotide polymorphismAll authors were involved in the conception of the study. M-HR-G and RAM analyzed the data and wrote the draft manuscript. All authors provided comments on the draft manuscript, and read and approved the final manuscript.


Due to the recent gains in the availability of single-nucleotide polymorphism data, genome-wide association testing has become feasible. It is hoped that this additional data may confirm the presence of disease susceptibility loci, and identify new genetic determinants of disease. However, the problem of multiple comparisons threatens to diminish any potential gains from this newly available data. To circumvent the multiple comparisons issue, we utilize a recently developed screening technique using family-based association testing. This screening methodology allows for the identification of the most promising single-nucleotide polymorphisms for testing without biasing the nominal significance level of our test statistic. We compare the results of our screening technique across univariate and multivariate family-based association tests. From our analyses, we observe that the screening technique, applied to different settings, is fairly consistent in identifying optimal markers for testing. One of the identified markers, TSC0047225, was significantly associated with both the ttth1 (p = 0.004) and ttth1-ttth4 (p = 0.004) phenotype(s). We find that both univariate- and multivariate-based screening techniques are powerful tools for detecting an association. Over the last few years, the field of statistical genetics has been the subject of challenging and exciting evolutions. As a result of human genetic sequencing, not only has data quality improved substantially, but the sheer volume of available data has vastly increased. The success of genome-wide association studies will depend upon whether the increase in numbers of single-nucleotide polymorphisms (SNPs) can be translated into an increase in the overall power to detect genotype × phenotype associations, or whether this potential increase in power will be diluted by the problem of multiple comparisons. In Van Steen et al. , the autIn our analysis, the data was restricted to the genotypes from the Affymetrix SNP panel. This SNP data, along with quantitative trait information for approximately 1,613 subjects, comprised our dataset. The 1,613 subjects come from 143 families, with a mixture of large and small pedigrees. Using chromosome 4 as a template for the genome-wide screening techniques, we investigate the association between the 786 Affymetrix SNPs on chromosome 4, and the four measures corresponding to the "late" time window from the Visual Oddball Experiment, ttth1-ttth4. These four measurements correspond to electrode placements on the midline, central midline, and parietal midline channels, respectively. The phenotypes were transformed to standard normal scores for the analysis.r = 0.11, 0.18, 0.26, 0.25 for measurements 1–4, respectively. The correlation between the four "late" window measurements ranges from 0.54 (ttth1 and ttth3) to 0.91 (ttth3 andttth4). Our goal was to conduct both univariate and multivariate (with related traits) analyses on a chromosome with regions suggestive of linkage, and contrast these methods in the context of genomic screening. Because no candidate chromosomes have been suggested for these jointly modelled phenotypes, we opted to use chromosome 4 as a template due to some replication of linkage findings for EEG [While there appears to be no documented research supporting an association between chromosome 4  and the "late" time window measurements, several studies have proposed a region of linkage for the electroencephalogram (EEG) phenotype on chromosome 4 -7. FurthS = ∑ij TijXij, where Xij denotes a coding of the marker genotype of the jth offspring in family i. The coded trait of the jth offspring in the ith family is defined by Tij. In general, the trait will be mean-centered. The test statistic, a score function, in large samples is defined as: Z = ∑ij Tij(Xij - E(Xij))/Var(S)1/2 ~ N, where E(Xij) is the expected value of the coding function for the offspring genotype, conditional on the parental genotype and parental/offspring phenotypes, which are assumed to follow Mendelian segregation under the null hypothesis. This methodology extends readily to scenarios in which the parental genotypes are not known, using the approach of Rabinowitz and Laird [In the first stage of the analysis, we apply our screening technique in a univariate setting to investigate family-based associations with the far frontal left side channel measurements (ttth1). The family-based association test (FBAT) statistic  comprisend Laird . The FBAnd Laird .p-values need only be adjusted according to the size of the selected subset. This screening process is used in both a univariate and multivariate setting. The process differs only in the model that describes the phenotypes as a function of the genotypes, and thus, how the effect-size estimates are generated  of Lange et al. . The FBAp-values < 0.05) were removed, as an indication of genotyping error. Additionally, in genomic association screens, these raw results can no longer be benchmarked against 0.05. For overall significance, using a Bonferroni correction, a p-value < 0.01 is required, based upon the reporting of the top five results by power estimate. One of the observed markers, TSC0047225, demonstrates significant association, with a p-value of 0.004.Table Of the top five markers with the highest power in the univariate analysis, four  also have been identified using the principal components statistic. The results are shown in Table Table Using our screening techniques, we identified a SNP (TSC004275) that is associated with the ttth1-ttth4 phenotypes. This SNP is located at approximately 133 cM on chromosome 4. Concurrent and subsequent analyses will determine whether this finding is supported via other screening methodologies.p = 0.004). The reason for the similarity in significance levels in the FBAT and FBAT-PC analysis, and the non-significance of the FBAT-GEE result may be due to noise created by a particular phenotypic measurement, or ttth1 maybe primarily responsible for the observed association seen in the univariate analysis. The similarity of the FBAT and FBAT-PC results with regard to the identified SNPs also are surprising, and suggest that the ttth1 phenotype may be driving the association. Those performing future association analyses may want to utilize phenotypes (such as ttth and ECB21 phenotype) that are not as strongly correlated.Overall, the analysis of these data, using both univariate and multivariate analyses, highlights a key point. More credibility maybe given to markers that are identified through multiple screening techniques. TSC0047225 was selected in all three analyses, and was significant in two of the three (r = 0.8) and the heritability is constant across phenotypes. In the FBAT-GEE results, the observed heritabilities (not shown) were very similar (~0.4) across phenotypes, and 3 of the 4 ttth phenotypes are highly correlated. Thus, the data suggest a scenario in which the FBAT-PC statistic is likely to have greater power than FBAT-GEE. However, given the similarity of the univariate FBAT and FBAT-PC results, this hypothesis is less likely. Despite the similarity of the FBAT and FBAT-PC results, analysis of multiple phenotypes can be more powerful than that of single phenotypes when attempting to unravel the genetic structure underlying complex traits.Alternatively, there may be an individual locus with pleiotropic effects, and FBAT-PC may simply have more power than FBAT-GEE to detect an association. Using simulated data, Lange et al.  demonstrA final possibility is that there is no causal locus, and the finding is spurious. Using any method for genome-wide screening, this is always a possibility, especially when the findings are not supported by other studies. However, the paper by Van Steen et al.  demonstrIn this paper, we implemented a novel screening technique in the context of genome-wide association testing, and contrasted the results of this screening methodology across univariate and multivariate settings. Through this analysis, it was suggested both univariate and multivariate testing methodologies are useful in detecting genotype × phenotype associations. Additionally, multivariate methods can be powerful tools in finding associations that may not be detectable in the univariate setting.COGA: Collaborative Study on the Genetics of AlcoholismEEG: ElectroencephalogramFBAT: Family-based association testingGEE: Generalized estimating equationPBAT: Pedigree-based association testingPC: Principle componentsSNP: Single-nucleotide polymorphismAM conducted the association analysis and drafted the manuscript. MBM assisted in drafting the manuscript. JS participated in the study design and analysis. PK participated in the design and coordination of the study. RL assisted with study design. NML helped conceive the study and participated in its coordination. CL helped conceive the study and conducted portions of the association analysis. KVS conceived the study, provided additional association analyses, and aided in drafting the manuscript.


For analyzing longitudinal familial data we adopted a log-linear form to incorporate heterogeneity in genetic variance components over the time, and additionally a serial correlation term in the genetic effects at different levels of ages. Due to the availability of multiple measures on the same individual, we permitted environmental correlations that may change across time.Systolic blood pressure from family members from the first and second cohort was used in the current analysis. Measures of subjects receiving hypertension treatment were set as censored values and they were corrected. An initial check of the variance and covariance functions proposed for analyzing longitudinal familial data, using empirical semi-variogram plots, indicated that the observed trait dispersion pattern follows the assumptions adopted.The corrections for censored phenotypes based on ordinary linear models may be an appropriate simple model to correct the data, ensuring that the original variability in the data was retained. In addition, empirical semi-variogram plots are useful for diagnosis of the (co)variance model adopted. Longitudinal designs in family studies represent additional opportunities to model temporal variation in genetic and environmental factors influencing quantitative traits. For certain phenotypes, like anthropometric measures and blood pressure, more insight into its continuous physiological variation may be provided for adopting phenotype (co)variance components as a function of time, rather than scalar components. In this article the term (co)variance is been used to refer both to variance and covariance components.The classical approach to the genetic analysis of longitudinal traits, under the variance component framework, considers an unstructured covariance matrix  for mode in the familial model, where t represents the age in the application. Under this parameterization, a possible heterogeneity of the genetic variance, in continuous time, is being considered through the parameter γ, which represents an interaction effect between genetic and environmental factors. If there is evidence of change in the genetic variance across time, the parameter γ is significantly different from 0. Additionally, the correlation in genetic effects at different ages  was modeled as ρ g = exp (- λ|t - s|), where λ is assumed different from 0.Using the real longitudinal Framingham Heart Study data, we analyzed the systolic blood pressure as the trait of interest. To pursue the major genes influencing the trait, under the mixed-model longitudinal approach, we employed the genetic variance function To absorb the dependence in the sequential measurements within an individual, environmental correlations were added in the model. Data from family members from the first and second cohort that were re-examined 21 and 5 times, respectively, during the longitudinal phase of the study, were used in the current analysis. The precision of the estimates obtained from these analyses was compared. For subjects receiving hypertension treatment, the recorded systolic blood pressure was considered as censored value, and to accommodate it in the analysis, we proceeded with corrections using a nonparametric algorithm to adjust the censored phenotypes, as considered by Levy et al. [For subjects receiving hypertension treatment, the recorded systolic blood pressure was considered as a right-censored value, since one knows that it is less than what the untreated value would be. To accommodate the censoring process in the analysis we addressed corrections on the censored phenotypes through the nonparametric algorithm used by Levy et al. . SeparatYj(t) denote a measurement on the jth individual at the time t. The cross-sectional familial variance component approach [To define the adopted model, let approach  can be eXjt is a covariates vector  at occasion t for the jth individual, β is a parameters vector associated with the fixed effects, gjt and ejt are uncorrelated random effects due to polygenic and environmental sources of variation, respectively. For relatives i and j, observed at t and s occasions, respectively, we assume:where μ is the overall mean, ij is the kinship coefficient between relatives i and j.where 2φ, where t denotes age. The parameter γ accommodates longitudinal changes in the trait heritability, and represents the interaction effect between the polygene and age. Since polygenic correlations between the expressions of the trait at different ages usually depends on their time range, we adopted a monotone decreasing function ρ=exp(-λ|t-s|), as proposed by Diggle [t,s) is different from 1 suggests that different polygenes influence the trait in different ages. Also, modeling the correlation structure in continuous time admits unbalanced sequences of measurements on the different individuals.Following Aitkin , who cony Diggle  and Huggy Diggle . Stating and σe . As stated before, log-linear variance function and serial correlation structure were assumed. Additionally, such parametric (co)variance functions may be extended for longitudinal familial oligogenic model. In this case, for major genes are attributed random effects, which are associated with familial covariance matrices structured in terms of identity-by-descent matrices.To complete the specification of the model, because multiple measurements are available in the same individuals, we need to adopt parametric functions to the environmental components, To estimate the parameters involved in the specification of the (co)variance components under multivariate normal distribution and involving longitudinal and familial dependence patterns, we used a version of the EM (expectation maximization) algorithm, as described by Iturria and Blangero  and impl against the corresponding lag of times (|t - s|). In this regard, the residuals are obtained from ordinary linear regression adjustment of the phenotype in terms of covariates involved in the study. We used the empirical semi-variogram to provide a valuable, but informal, initial check on the longitudinal (co)variance structure, as used by other authors [The empirical semi-variogram of a sequence of measurements within the same individual is a scatter plot of squared differences of residuals,  authors ,9.During the analysis of the second cohort, we considered longitudinal measurements from 1667 individuals , totaling 7177 observations. A vast majority of individual profiles (81%) contain four or five measurements throughout the study. The results of the adjustments for censored phenotypes receiving hypertension treatment are presented in Figure In this work, we presented a methodology to analyze longitudinal familial data set, considering the adoption of parametric functions for modeling genetic and environmental (co)variance components involved. The approach is applied for trials of systolic blood pressure measurements. Considering that the hypertension treatment generates a right-censored response, we proceeded with corrections on the values observed under treatment. The corrections were based on information from residuals obtained through ordinary linear models, an appropriate simple model useful to estimation in this phase of the analysis. Because the vast majority of the data are untreated measures, such replacement ensures the original variability of the data, which will be modeled in terms of genetic and environmental (co)variance components. An initial check of the proposed parametric (co)variance functions, using empirical semi-variogram plots, indicated that the systolic blood pressure dispersion pattern follows assumptions as heterogeneity of variance and autocorrelation process. Having done these preliminary analyses, we are now involved in the estimation and hypothesis tests related to the genetic parameters of the proposed model.


Complex diseases are generally caused by intricate interactions of multiple genes and environmental factors. Most available linkage and association methods are developed to identify individual susceptibility genes assuming a simple disease model blind to any possible gene - gene and gene - environmental interactions. We used a set association method that uses single-nucleotide polymorphism markers to locate genetic variation responsible for complex diseases in which multiple genes are involved. Here we extended the set association method from bi-allelic to multiallelic markers. In addition, we studied the type I error rates and power for both approaches using simulations based on the coalescent process. Both bi-allelic set association (BSA) and multiallelic set association (MSA) tests have the correct type I error rates. In addition, BSA and MSA can have more power than individual marker analysis when multiple genes are involved in a complex disease. We applied the MSA approach to the simulated data sets from Genetic Analysis Workshop 13. High cholesterol level was used as the definitive phenotype for a disease. MSA failed to detect markers with significant linkage disequilibrium with genes responsible for cholesterol level. This is due to the wide spacing between the markers and the lack of association between the marker loci and the simulated phenotype. Current beliefs hold that complex diseases are generally caused by multiple genetic variation. However, most available linkage and association methods are based on the assumption that a single genetic variation is primarily responsible for the disease under study. Only a few approaches considered interactions of multiple genes and environmental factors in identifying susceptibility loci for complex diseases -3.Hoh et al.  developeThe organization of the paper is as follows. We first briefly describe BSA and provide an intuitive framework for the extension from BSA to multiallelic set association (MSA) as well as a description of the various simulated data sets. Next, we study the type I error and power of the BSA and MSA using simulated data sets based on coalescence with an underlying disease model. Finally, we present the results from applying MSA to Genetic Analysis Workshop 13 simulated data sets without knowledge of the answers to the longitudinal data generated by Daw et al. .n cases and n controls genotyped at a marker locus with k alleles. A 2 × k contingency table is constructed and a statistic of AA is then computed as follows:For completeness, we briefly describe the BSA method of Hoh et al.  for use ps and qs are the frequency of the allele s for the cases and controls, respectively. The above statistic has an approximate χ2 distribution with k-1 degrees of freedom.where 2 distribution with k(k - 1)/2 degrees of freedom, is then calculated among the cases according to the following statistic:HWD , which aqs and qt are the frequencies of alleles s and t, respectively, while pss and pst are the frequencies of genotypes ss and st, respectively. For BSA, k = 2.where d largest case-based HWD values to 0, thereby removing these problematic loci. d is empirically determined from the number of loci whose control-based HWD statistic is greater than , the β quantile of the standard χ2 distribution with one degree of freedom. However it should also be noted that both AA and HWD values are high if the locus is in strong LD with one of the disease variants.Hoh et al.  suggestem bi-allelic marker loci. Hoh et al. [si = AAi * HWDi, where AAi and HWDi are the AA and HWD statistic for marker locus i, 1 ≤ i ≤ m. The values s1, s2,...,sm are then ordered from the largest to the smallest with s(1) ≥ s(2) ≥ ... ≥ sm), and HWD, pHWD(i), on the basis of χ2 approximation, respectively.BSA cannot be directly applied to multiallelic markers because the χd smallest HWD p-values were removed from MSA analysis along with the corresponding pAA. The remaining p-values for AA and HWD were then multiplied and the products were used as a score denoted as si, that is,Trimming was conducted similar to the method of Hoh et al. . Howeversi = pAA (i) * pHWD (i).s(1) ≤ s(2) ≤ ... ≤ sm), along with hypertension diagnosis and treatment were used to simulate the observed phenotypes. The pedigree structure was generated to be nearly identical to the Framingham Heart Study with varying degrees of heritability of eight longitudinal quantitative traits .The first measured cholesterol level was chosen as the phenotype of interest. The empirical distribution of cholesterol level in a replicate set was approximated from the cholesterol levels of all the individuals. Next, the upper 15% and lower 15% quantiles were then estimated from this observed distribution. We considered an extreme sampling design in which an individual was considered affected if the first measured cholesterol level exceeded the upper limit and unaffected if it was below the lower limit. Cases and controls were randomly selected based on these measured cholesterol levels with no two members from the same family. We required that there were no missing genotypes for the selected individuals.Table  was also determined by the number of replicates with significant results divided by total number of replicate sets. The statistical significance level α was set to 0.05. As shown, the estimated type I error rates were close to the true pre-specified type I error of 5%.The values of type I error rates for individual marker method based on AA were calculated by the number of replicates containing at least one locus with a significant result divided by the total number of replicate sets. Bonferroni correction was used to adjust for multiple comparisons. Type I error rates for BSA with trimming at For the power study of BSA, the parameters δ and λ were set to create two complex disease scenarios. The power of the tests should increase as the penetrance λ increases. The power of both individual marker analysis and BSA increases. When comparing the sixth column with the fifth column  in Table As shown in Table All of the 11 different replicates of the simulated data from GAW13 used for MSA resulted in the failure to reject the null hypothesis of no association as shown in Table p-value less than 0.05. However, it should be noted that even if no markers were associated with cholesterol level, an average of 20 markers should show significant results using type I error of 0.05. The 14 markers most likely represented false positive errors and a Bonferroni correction would correct this inflation. The MSA was applied to the data using AA × HWD with trimming threshold set at . An overall non-significant p-value Poverall = 0.5417 was obtained. For the other 10 replicates, MSA showed no significant association with Poverall ranging from 0.08 to 0.94.The upper 15% quantile was calculated at 210 mg/dl and the lower 15% quantile was estimated to be 155 mg/dl. For replicate 26, we obtained 125 cases and 105 controls. Based on individual marker analysis using AA, 14 out of the 399 genome-wide markers had a In this paper, we developed a new approach for genome-wide association studies with multi-allelic markers based on BSA. There are several advantages for MSA over any individual marker analysis. First, it is more powerful than individual marker analysis, which is consistent with conclusions of BSA in Hoh et al. . Second,MSA was applied to 11 simulated GAW13 data sets and no significant associations were found. The result is expected given that the average marker spacing is approximately 8.5 cM and that there were no associations (between the quantitative trait and marker loci) modeled into the simulation. Following typical disease mapping techniques, once a linkage study is conducted to locate potential susceptibility sites, MSA could then be used to detect associations after more markers are genotyped.


Genetic mechanisms underlying alcoholism are complex. Understanding the etiology of alcohol dependence and its comorbid conditions such as smoking is important because of the significant health concerns. In this report, we describe a method based on classification trees and deterministic forests for association studies to perform a genome-wide joint association analysis of alcoholism and smoking. This approach is used to analyze the single-nucleotide polymorphism data from the Collaborative Study on the Genetics of Alcoholism in the Genetic Analysis Workshop 14. Our analysis reaffirmed the importance of sex difference in alcoholism. Our analysis also identified genes that were reported in other studies of alcoholism and identified new genes or single-nucleotide polymorphisms that can be useful candidates for future studies. Alcoholism is a complex disease that is highly concordant within family clusters. It is a widespread problem; nearly 14 million Americans abuse alcohol or are alcoholic , though Smoking is highly associated with alcohol dependence . GeneticClassification trees and forests are known for their ability to identify complex relationships, especially in large, complex datasets . The avaThe COGA data include 1,614 family members. After removing those individuals with missing genotype data on some markers, there were 1,306 individuals in the Illumina genotype dataset. There are 4,752 SNP markers released by Illumina, 32 of them without a map position. The number of SNPs released in the reformatted data was 4,720. Phenotypes used for this analysis are alcohol dependence based on DSM-III-R and Feighner, coded as ALDX1, and smoking. We combined ALDX1 with smoking to construct a comorbid response. Because ALDX1 has 4 levels , the comorbid response has 8 levels. The covariates include sex, parental phenotypes, and the SNP markers. The inclusion of parental phenotypes in such an association analysis is well documented to control for the residual familial correlations [The tree construction consists of two steps: tree growing and pruning. Tree growing is based on recursive partitioning. The classification tree for ALDX1 as the single outcome is shown in Figure t, which can be the root node, and that the outcome variable has q levels, which is 4 for ALDX1 and 8 for the combination of ALDX1 and smoking. The entropy-based goodness of split is defined asIn Figure tL and tR are left and right daughter nodes of node t resulting from split s, respectively,  is the probability for an individual to be in node tL,  is the probability for an individual in node tL to have response level i. The definitions for  and  are analogous to those of  and . The split based on the sex variable for the root node in Figure i(s) after evaluating all possible splits of the root node using all covariates and all SNPs.where vel ii = , ..., q.After splitting the root node into two daughter nodes, we repeated the procedure to further partition the daughter nodes into the next layer, and as a result, the study sample is divided into smaller, and hopefully more homogeneous, daughter nodes hierarchically or recursively. This recursive partitioning procedure produces an initial tree that usually contains many nodes. Because there are a finite number of ways of splitting any given study sample, the recursive partitioning can run for a while, but always terminates when it exhausts all possible splits. To improve the reliability and interpretability of the information contained in a tree, the initial tree from the recursive partitioning procedure is usually pruned to a smaller size.χ2 testing statistic for a 2 × q contingency table was calculated for each internal node. For example, in Figure χ2 value equals 189.8 for testing the independence of cell counts in the table. After the χ2 values are obtained for all internal nodes, we can follow the suggestion of [χ2 values as well as the χ2 values in the subsequent splits do not exceed the predetermined threshold. This pruning step resulted in the tree in Figure We adopted the bottom-up method described in Zhang and Singer  to deletstion of  by prespThanks to a large number of covariates, we may have multiple splits with similar quality in terms of the goodness of split measure and the predictive precision of the phenotype. Biologically, it is possible that there are multiple pathways to a disease. Thus, it is useful to unravel and make use of all competitive split, and form a forest of competitive trees. Although random forests  provide Following the recommendation in , we consUsing the method described above, we obtained an initial tree with 139 nodes for ALDX1. At the significance level of 0.0001 based on a 2 × 4 contingency table, a tree with 39 nodes is determined. At significance level of 0.00001, a tree with 19 nodes is selected as shown in Figure In this report, we identified 37 SNPs that are associated with alcoholism and smoking. Fifteen of these SNPs are within known genes. Table COGA: Collaborative Study on the Genetics of AlcoholismSNP: Single-nucleotide polymorphism


In the analysis of complex traits such as fasting plasma glucose levels, researchers often adjust the trait for some important covariates before assessing gene susceptibility, and may at times encounter confounding among the covariates and the susceptible genes. Previously, the tree-based method has been employed to accommodate the heterogeneity in complex traits. In this study, we performed a genome-wide screen on fasting glucose levels in the offspring generation of the Framingham Heart Study provided by the Genetic Analysis Workshop 13. We defined one quantitative trait and converted it to a dichotomous trait based on a predetermined cut-off value, and performed association analyses using regression and classification trees for the two traits, respectively. A marker was interpreted as positive if at least one of its alleles exhibited association in both analyses. Our purpose was to identify candidate genes susceptible to fasting glucose levels in the presence of other covariates. The covariates entered in the analysis including sex, body mass index, and lipids  of the subjects, and those of their parents.Four out of seven positive regions in chromosomes 1, 2, 6, 11, 16, 18, and 19 from our analyses harbored or were very close to previously reported diabetes related genes or potential candidate genes.This screen method that employed tree-based association showed promise for identifying candidate loci in the presence of covariates in genome scans for complex traits. Problem 1 of Genetic Analysis Workshop 13 (GAW13) provided the data from the Framingham Heart Study. We focused on the offspring cohort due to the missing rate of the data in the parental cohort.Because the history of medical intervention, including the adjustment of lifestyle and the use of anti-diabetic medications were not available, we chose the highest fasting plasma glucose levels across the course of follow-up as the targeted quantitative trait to indicate the potential risk for abnormal glucose disposal. As suggested by the American Diabetes Association, the impaired fasting glucose  appears as a risk factor for type 2 diabetes mellitus (T2DM) [Our purpose was to identify candidate genes related to the fasting glucose levels in the presence of covariates. We found a few interesting markers that are closely linked with some potential candidate genes biologically relevant to glucose metabolism.For the phenotype measurements, the corresponding covariates were created using their cross-sectional means. The covariates entered in the analysis included sex, body mass index, and lipids  for each subjects. To control for potential familial correlations, the cross-sectional means of the maternal and paternal phenotype measurements were also included as covariates.For the genotypic data, an allele was chosen to enter the analyses if its allele frequency is at least 10%. Alleles with frequencies less than 10% but from the same marker are categorized as an incognito allele. The allelic covariates were created using the technique proposed by Zhang and Bonney .j in the subtree τ until the unconditional misclassification rate  is attained, where c(j|i) is the cost that a class j is classified as a class i and IP is the entropy impurity function. In general, choice of the cost depends on the severity of the misclassification. In this study, equal cost was chosen for both misclassifications because it frequently gives most satisfactory analyses [1|0) = c(0|1). The optimal tree in RT is similar to that in CT with a different impurity function , i.e., the within-node variance in the tree τ. More details of CT, RT, and corresponding splitting criteria are described elsewhere [The classification tree (CT) and regression tree (RT) methods are both built on the recursive partition technique; they can be used to partition a study population into homogeneous disjointed subgroups. The optimal tree is created by both growing and pruning procedures. The maximal tree is built by splitting each node into two child nodes until the purity of the terminal node is achieved. In splitting, the best choice of the child node is derived while the minimum of the entropy impurity function is reached. In pruning, it is processed for each binary class analyses , i.e., clsewhere -5.Tree-based association analysis was implemented by using genotype measurements such as allelic covariates and related phenotype measurements to construct binary trees. An allele shows association with the trait if its corresponding covariate is included in the optimal tree.To illustrate the tree construction, a portion of an optimal tree created by CT is presented in Figure In this study, we conducted a genome-wide screen to identify the candidate gene in the presence of a set of specified covariates. We performed RT- and CT-based association analyses on the quantitative and dichotomy traits, respectively. A marker was interpreted as positive if at least one of its alleles showed association in both association analyses. The allelic covariates from the same chromosome were entered in the analyses simultaneously. The genome-wide screen consisted of 22 such processes for the autosomes. The computer programs QUEST  and RT  were use. For candidate gene search, we used Online Medelian Inheritance in Man at National Center for Biotechnology Information  or euGene .The map position was defined using Ensemble Genome Server at Sanger Institute Table In this study, the intent of our screen method was to identify candidate markers rather than to pinpoint susceptibility alleles, although it can be applied to detect the allelic or non-allelic heterogeneity. The cut-off value used in CT in this analysis was chosen for a biological reason. However, the analysis was sensitive to the choice of cut-offs when the subjects were largely clustered around the cut-off point (>110 mg/dl). Only three regions on 1p, 16q, and 18p were consistently positive at neighboring cut-offs from 100 to 120.Although covariates such as BMI and HBP, which are associated with fasting glucose level, were included in our analyses, the cut-off of these covariates in our final 22 optimal trees were not the same. Further studies are needed to inspect the impact of different cut-off and associated alleles.From a different point of view, our method used the RT analysis on the quantitative trait to validate the results from CT such that the positive markers showed association in both analyses. Notably, four out of the seven candidate regions harbored previously reported genes that are related to glucose metabolism or diabetes mellitus. In conclusion, our screen method shows promise for searching candidate loci in genome scans for complex traits.


A variety of Haseman-Elston type regression procedures were used to perform a genome scan across five chromosomes, using replicates 1–5 of the Genetic Analysis Workshop 13 simulated data. The traits of interest were variables corresponding to 'baseline' and 'slope' effects derived from the fasting glucose phenotypes. Performance in terms of detecting the locations of known trait loci was poor for all methods, even when all five replicates were combined to produce a large data set (9230 sib pairs). All methods performed well, however, when applied to new simulated data in which the true genetic effects were allowed to explain a greater proportion of the overall variance.p is modelled as a linear function of the sib-pair trait difference squared, sibs are assumed to share 0, 1, or 2 alleles IBD with probability (1 - p)2, 2p(1 - p), p2 and an appropriate likelihood is calculated [Haseman-Elston sib-pair regression procedures were used to perform genetic linkage analysis on chromosomes 1, 2, 3, 9, and 21 in replicates 1–5 of the Genetic Analysis Workshop (GAW13) simulated data. All of these chromosomes, except chromosome 2, were known from the 'answers' to contain trait loci that contributed in some way to fasting glucose. This subset of chromosomes analyzed did not contain all loci involved in fasting glucose levels, but did include 8 out of the 12 loci influencing baseline effects  and two out of the four loci influencing slope effects s4 and s6). Independent families were selected for analysis by choosing the largest nuclear family from each pedigree. Multipoint identity-by-descent (IBD) sharing probabilities for each sib pair within a family were calculated from the complete genotype data using the program GENEHUNTER. Trait values were calculated from the complete phenotype data for each sib as described below. Four different regression procedures were used to examine the relationship between the trait values and IBD sharing: the original Haseman-Elston method [. Indepenlculated  as opposThe trait measures α and γ used in the regression procedures were derived by fitting the modelyit = αi+ βT xit + γi (ait - 20)     (1)yit is the fasting glucose value for person i at examination time t, xit is a vector of covariates for person i at examination time t (here chosen as log(weight), log(height), gender, and the interactions gender*log(weight) and gender*log(height)), and ait is the age of person i at examination time t. This model assumes that fasting glucose is determined by a baseline value αi specific to each person at age 20, effects due to covariates (corresponding to the vector of coefficients β) that do not vary with time or age, and a person-specific slope effect γi that allows fasting glucose to increase or decrease linearly with age. Note that this model does not correspond to the model that was actually used to generate the data, which in fact takes the more complicated formusing the statistical software package STATA , where yAlthough this more complicated model (2) could, in principle, be fitted, in real life one would be unlikely to propose such a model without prior knowledge of the 'answers' or some other belief concerning the underlying biological process. We therefore choose to fit model (1) as opposed to (2), since this reflects the model that would be more likely to be assumed and hence the procedure that would be more likely to be followed in practice.Initially the analyses were performed for each replicate separately, but this did not succeed in localizing any of the known genetic effects to their correct locations. The five replicates were therefore pooled and analyzed together to see if the larger ensuing sample size (9230 sib pairs) would help in the detection of the trait loci. Figure i at time t was determined asThese disappointing results could be due to the relatively small proportion of the overall variance that is accounted for by each trait locus, and/or to the fact that our phenotype measures α and γ are very poor measures of the true baseline and slope effects due to the difference between the generating model (equation (2)) and that assumed (equation (1)) when deriving α and γ. To assess the performance of our procedure in a situation where the true generating model does in fact take the form of equation (1), we used the GAW13 simulated data provided as the basis of a new simulation. We simulated data in which the genetic contribution to baseline phenotype was determined solely by genotype at marker locus 2 on chromosome 21: if an individual had any copies of alleles 1–3 at this locus, the mean baseline phenotype was set to 5, otherwise it was set to 3. Similarly, the genetic contribution to slope phenotype was determined solely by genotype at marker locus 5 on chromosome 21: any copies of alleles 1–3 at this locus caused the slope value to have mean 0.002, otherwise mean 0.001. The final simulated glucose phenotype for individual 1 + weight/150 + (slope + ε2)(age - 20) + ε3,glucose = baseline + εi and t, ε1, ε2 and ε3, were sampled from normal distributions with mean 0 and standard deviations 0.4, 0.0001, and 0.0003, respectively. These data were analysed in the same way as the original data, and the results using replicate 1 only (1899 sib pairs) are shown in rows 1 and 2 of Figure where at each The success here could be due to the fact that the effects we simulated were relatively extreme, or to the fact that the generating model (equation (1)) corresponded to that assumed in the analysis. We therefore repeated the simulation using identical baseline and slope effects, but with the final glucose phenotype generating model altered to1, ε2, and ε3 as described previously. The results are shown in rows 3 and 4 of Figure ) with ε) with ε1


We studied a trend test for genetic association between disease and the number of risk alleles using case-control data. When the data are sampled from families, this trend test can be adjusted to take into account the correlations among family members in complex pedigrees. However, the test depends on the scores based on the underlying genetic model and thus it may have substantial loss of power when the model is misspecified. Since the mode of inheritance will be unknown for complex diseases, we have developed two robust trend tests for case-control studies using family data. These robust tests have relatively good power for a class of possible genetic models. The trend tests and robust trend tests were applied to a dataset of Genetic Analysis Workshop 14 from the Collaborative Study on the Genetics of Alcoholism. Testing for linkage disequilibrium or association provides a useful alternative to testing linkage for complex traits with relatively small genetic effects . Among tRecently, there has been an increasing interest in statistical methods that evaluate association between genetic markers and disease status using family-based data ,8. This In this paper we study the two robust trend tests, the maximum test (MAX) and maximin efficiency robust test (MERT), in case-control design applied to family data. These two robust tests account for the correlated individuals and do not rely on the assumption of any particular genetic model. The performance of the robust trend tests and the extended CA trend test is compared by a simulation study. These tests are illustrated using a Genetic Analysis Workshop 14 dataset from the Collaborative Study on the Genetics of Alcoholism (COGA).N and M, where N is a normal allele and M is an allele with high risk. Denote genotypes as g0 = NN, g1 = NM, and g2 = MM. Let the genotype frequencies for cases and controls to be pj and qj, j = 0, 1, 2, respectively, and . Hence, the null hypothesis of no association is to test pj = qj for each j.Consider data for a case-control study of genetic association as in Table Zx = U(x)/(Var[U(x)])1/2, where , and x = ' is a set of increasing scores (weights) assigned to the three genotypes  a priori based on the underlying genetic model. Note that ' can be reparameterized as ' with 0 ≤ x ≤ 1. If cases and controls are from independent random samples, the counts  and  in Table mul and mul, respectively. Under the null hypothesis, it can be shown that , and Zx asymptotically follows a standard normal distribution N.Given the data, the CA trend test for association  between H0 is rejected in favor of the alternative that M is the high risk allele associated with disease when Zx >zα1-, where zα 1-is the upper 100(1 - α)th percentile of N. When it is not certain which allele is high-risk, H0 is rejected when |Zx| > zα/21-.The null hypothesis yi = ' be the genotype indicator vector for the ith case, where yij = 1 for the ith case with genotype gj and ijy= 0 otherwise, i = 1, ..., R. Similarly, we use zj for controls. Then r = ' = , and s = ' = . Furthermore, yi and zj follow the multinomial distributions mul and mul, respectively. Let φ = R/n. The test statistic U(x) can also be written as U(x) = x'[(l - φ) r - φs]. Then,However, since for case-control studies drawn from family data, cases and controls within the same family may be biologically related, Slager and Schaid  proposedwhere the variances and covariances can be calculated based on the multinomial distributions and IBD-sharing probabilities for pairs of the related individuals ,cases and controls may be related. Note that for the special case in which cases and controls are independent random samples, the tests have been studied by Friedlin et al. , where X is a m × (K - 1) matrix with the jth column, xj, as a score vector for the m genotypes corresponding to the jth allele, and Var(U)= X'∑X can be obtained similarly as in the previous section to adjust for correlations among family members. To test the association with this marker, Slager and Schaid [U'[Var(U)]-1 U as it asymptotically follows a chi-squared distribution with (K - 1) degrees of freedom.The above trend tests ol study . For a mm = KK + /2 possibd Schaid  proposedjth allele, the jth element of U is Uj = x'j[(1-φ)r-φs], and we have  = Var(jU) = x'j∑xj and . Then the trend test for each allele, Zj = Uj/σj, j = 1,..., (K - 1), and the correlation for any two tests can be obtained. Hence, for the family of trend tests, MERT and MAX can be used to test for association with a multi-allelic marker.Here, we can apply MERT and MAX as alternatives to this chi-squared test. Corresponding to the To illustrate the robustness of the statistics, MERT, and MAX, and to compare their performance with individual trend tests for given models, we simulated the case-control datasets and computed the empirical powers for all the tests under three genetic models: the recessive, additive and dominant models.K = 0.1 and the allele frequency p = 0.3 with 20,000 replications. To facilitate the calculation, each case-control dataset included 160 cases generated as 80 sib-pairs drawn from 80 different families, and 160 controls as unrelated random samples. It can be shown that the probabilities of 0, 1, 2, alleles shared IBD are 1/4, 1/2, and 1/4 for the sib-pairs when parents' genotype information was unknown. Assuming these IBD probabilities, the variance of the trend test was adjusted for the correlations among related cases. Let the genotype relative risks RR1 = f1/f0 and RR2 = f2/f0, where f0, f1, and f2 are penetrances for genotypes g0, g1, and g2. Thus, equivalently, the null hypothesis H0 can be written as RR1 = RR2 = 1. The alternative hypothesis can be specified by varying RR1 and RR2.The simulations were based on the assumptions that the disease prevalence RR1 and RR2 were chosen so that a particular trend test had about 80% power for each given model. When the true underlying model was recessive inheritance and the corresponding optimal test Zx = 0)  (and Zx = 1)   marker information. The preliminary genome scan by linkage analysis using the microsatellite data suggested that x = 0, 1/2, and 1. The tests showed significant association under both the recessive and additive model assumption (Zx = 0)  , but it failed to show any significant result assuming a dominant model (Zx = 1) . Note that after adjusting for the correlations among family members, standard errors were larger, resulting in smaller test statistics Zx and thus larger p-values compared to the tests without adjusting for the correlations  for the underlying genetic models. The trend tests Zx with 0 ≤ x ≤ 1 correspond to different models, where the statistics Zx above the horizontal dotted line are significant. Due to the uncertainty about the mode of inheritance, different conclusions could be reached and using any single trend test may result in significant loss of power when the model is misspecified. Therefore, we also applied the two robust tests to these data. Given the tests for the recessive, additive, and dominant models, the pair-wise correlations were calculated as Corr(Zx = 0) = 0.334, Corr(Zx = 0) = 0.818, and Corr(Zx = 1/2) (= 0.813. Then we obtained ZMERT = (2.89 + 0.40)/{2(1 + 0.334)}1/2 = 2.01 with p-value = 0.044. By simulations with 1,000,000 replications, the empirical p-value for ZMAX = 2.89 was p = 0.009. In this example, because the correlation between the test statistics under the recessive and dominant models is small, MAX appears to be more powerful than MERT to detect associations between disease status and a marker. Both robust trend tests showed significant association between this SNP marker and alcoholism.Figure In this paper, we applied the trend tests of genetic association to case-control studies drawn from the COGA families. Although the significant results under the recessive, additive, and dominant models were similar for this example, the tests ignoring the correlations among family members would have yielded large false-positive rates and moreover, unadjusted tests would not be valid.We have also studied two robust trend tests, MERT and MAX, for case-control studies with family data. When the genetic model is unknown, these robust tests based on a family of possible genetic models tend to be more conservative against model misspecification. Although we have focused on the examples and models for genetic association, these results hold generally for trend tests of association with correlated cases or controls when the exposure variables have some natural ordering.CA: Cochran-ArmitageCOGA: Collaborative Study on the Genetics of AlcoholismIBD: Identical by descentMAX: Maximum testMERT: Maximin efficiency robust testSNP: Single-nucleotide polymorphismXT involved in the design of the study and statistical analysis, and drafted the manuscript. JJ, GZ, and JPL participated in its design and performed the statistical analysis. All authors read and approved the final manuscript.


INSIG2 gene, rs7566605, was recently found to be associated with obesity as measured by body mass index (BMI) by Herbert and colleagues. The association between increased BMI and homozygosity for the minor allele was first observed in data from a genome-wide association scan of 86,604 SNPs in 923 related individuals from the Framingham Heart Study offspring cohort. The association was reproduced in four additional cohorts, but was not seen in a fifth cohort. To further assess the general reproducibility of this association, we genotyped rs7566605 in nine large cohorts from eight populations across multiple ethnicities . We tested this variant for association with BMI in each sample under a recessive model using family-based, population-based, and case-control designs. We observed a significant (p < 0.05) association in five cohorts but saw no association in three other cohorts. There was variability in the strength of association evidence across examination cycles in longitudinal data from unrelated individuals in the Framingham Heart Study Offspring cohort. A combined analysis revealed significant independent validation of this association in both unrelated (p = 0.046) and family-based (p = 0.004) samples. The estimated risk conferred by this allele is small, and could easily be masked by small sample size, population stratification, or other confounders. These validation studies suggest that the original association is less likely to be spurious, but the failure to observe an association in every data set suggests that the effect of SNP rs7566605 on BMI may be heterogeneous across population samples.A SNP upstream of the  INSIG2. We present our attempts to further evaluate this potential association with obesity in additional populations. We find evidence of increased risk of obesity for people carrying two copies of the minor allele in five out of nine cohorts tested, using both family- and population-based testing. We indicate possible reasons for the varied results, with the hope of encouraging a combined analysis across study cohorts to more precisely define the effect of this INSIG2 gene variant.Obesity is an epidemic in the United States of America and developing world, portending an epidemic of related diseases such as diabetes and heart disease. While diet and lifestyle contribute to obesity, half of the population variation in body mass index, a common measure of obesity, is determined by inherited factors. Many studies have reported that common sequence variants in genes are associated with an increased risk for obesity, yet most of these are not reproducible in other study cohorts, suggesting that some are false. Recently, Herbert et al. reported a slightly increased risk of obesity for people carrying two copies of the minor allele at a common variant near  Body mass index (BMI) is a heritable measure of obesity that is routinely obtained in large cohorts, is correlated with other measures of obesity, and predicts morbidity and mortality from obesity-related diseases –4. Thus,Recently, Herbert and colleagues, including several of the authors of this study, reported a novel association between homozygosity for the minor allele of a single nucleotide polymorphism (SNP), rs7566605, and increased BMI . The SNP2). In the NHS cohort alone, the 95% confidence interval (CI) for the odds ratio (OR) for obesity was 0.58–1.13. Subsequently, two further groups reported no evidence of association in large cohorts, and a third found association only for people on the overweight end of their population  was not applicable to the children that made up a substantial part of each cohort.) The family-based portion of the Scandinavian cohort was composed of adults, but the incidence of obesity was only 13% (n = 66), limiting the power of a dichotomous analysis. Because BMI changes rapidly during childhood, we compared the results for the pediatric cohorts using three different measured outcomes: BMI, BMI adjusted for age and gender, and BMI-for-age percentile ; the p values for the corresponding FBAT statistics were essentially identical in each cohort (unpublished data).Finally, we tested SNP rs7566605 for association with increased BMI in three family-based samples, using PBAT . Two of p values of the family-based studies using Fisher's method provided evidence of replication  so this cohort was excluded from the combined analyses. Mantel-Haenszel two-tailed p values ranged from 0.011 using FHS exam 3 to 0.054 using FHS exam 6 (2) associated with the C/C homozygous genotype ranged from 1.13 to 1.18, somewhat lower than the effect size estimated by the original report /[n(G0)/m(G0)], where n and m denote genotype counts in obese and non-obese individuals, respectively. The genotyping procedure has been previously described ) project and continued since 1996 within the German Kooperative Gesundheitsforschung in the Region Augsburg (KORA) platform. The third survey, KORA S3, which was the study used in our analysis, was conducted in 1994–1995. Subjects  were recruited via registry according to the same protocol as the fourth survey (KORA S4) performed in 1999–2001, which was part of the initial replication samples in Herbert et al. The KORA surveys were described previously ,26. GenoDNA samples were obtained from 1,515 unrelated people from the offspring generation of the FHS . We consDNA samples were obtained from 874 unrelated people, self-described as African-Americans, from the same cohort as was described in the original association report . Genotyp2; mean BMI 36.02 ± 5.38 kg/m2) and 391 were lean controls . Genotyping completion rate was >99.8% with no discordances among replicate genotypes. Of the 415 families with genotypic data, 408 had complete phenotypic data and were included in the analysis.Nuclear families (415) of children with asthma in the Central Valley of Costa-Rica, a relative genetic isolate of predominantly Spanish and Amerindian ancestry ,33. ChilThe Childhood Asthma Management Program (CAMP) is a multicentered North American clinical trial designed to investigate the long-term effects of inhaled antiinflammatory medications in children with mild to moderate asthma . ChildreThe unrelated sample consisted of individuals from the Botnia Study chosen as control subjects from two cohorts to study diabetes. The first group were controls from a Scandinavian sample of 471 case-control pairs individually matched for gender, age, BMI, and geographic region in Sweden and Finland. The second group were from a Swedish sample of 514 case-control pairs who were individually matched for gender, age and BMI. Subjects were characterized as unaffected for diabetes by glucose tolerance testing as previously described . The famp value > 0.01). Tests for association of rs7566605 with obesity were performed for the five population-based cohorts under a recessive model, classifying non-obese people as BMI < 30 kg/m2 and obese as BMI ≥ 30 kg/m2. Significance was assessed using a χ2 test with one degree of freedom and two-tailed p values were reported. The Mantel-Haenszel method was used for the combined analysis, and testing for heterogeneity was performed using the Breslow-Day test, as described previously [The genotype data in each population was tested for deviation from Hardy-Weinberg and found to be consistent  for each exam individually, and also for the mean of all available Z scores across the six exams. For the KORA S3, Maywood, and Scandinavian cohort analyses we used standard linear regression with log transformed BMI and adjusted for age and gender. The linear regression analysis in the Maywood cohort excluded 270 people, who had been selected as the most obese person in their family, to avoid possible bias. The Iceland analysis was done with log transformed BMI as a continuous trait under a recessive model, adjusting for age and sex in the multiple regression (sex + age + sex × age).For the four samples that had population-based components, an association analysis was performed using BMI as a continuous trait, adjusting for age and gender. A second analysis of the FHS cohort was done to make use of longitudinal data collected across six exams, approximately 4 y apart spanning 26 years from 1971–1997. For each exam, Z score under a recessive model. For the Costa Rica and CAMP populations, tests were also done for the outcome BMI adjusted for age and gender, and BMI-for-age percentile . Because these studies were similarly sized, a combined analysis was performed using Fisher's method for combining p values, in which twice the negative sum of the natural log of k one-tailed p values is distributed as a χ2 distribution with 2k degrees of freedom [p value for an effect in the opposite direction is first corrected by subtracting the p value from one; as all the effects in our studies were in the same direction, this correction was not necessary.Association testing of rs7566605 in the family-based cohorts was performed using the FBAT-approach as implemented in PBAT ,38, with freedom . In thisTable S1(66 KB DOC)Click here for additional data file.http://www.ncbi.nlm.nih.gov) accession numbers for the gene and gene product discussed in this paper are INSIG2 (NM_016133) and INSIG2 (NP_057217).The National Center for Biotechnology Information (NCBI) (


Genetic interaction networks were derived from quantitative phenotype data by analyzing agar-invasion phenotypes of mutant yeast strains, which showed specific modes of genetic interaction with specific biological processes. We have generalized the derivation of genetic-interaction networks from quantitative phenotype data. Familiar and unfamiliar modes of genetic interaction were identified and defined. A network was derived from agar-invasion phenotypes of mutant yeast. Mutations showed specific modes of genetic interaction with specific biological processes. Mutations formed cliques of significant mutual information in their large-scale patterns of genetic interaction. These local and global interaction patterns reflect the effects of gene perturbations on biological processes and pathways. Phenotypes are determined by complex interactions among gene variants and environmental factors. In biomedicine, these interacting elements take various forms: inherited and somatic human gene variants and polymorphisms, epigenetic effects on gene activity, environmental agents, and drug therapies including drug combinations. The success of predictive, preventive, and personalized medicine will require not only the ability to determine the genotypes of patients and to classify patients on the basis of molecular fingerprints of tissues. It will require an understanding of how genetic perturbations interact to affect clinical outcome. Recent advances afford the capability to perturb genes and collect phenotype data on a genomic scale -7. To exA, with a single genetic perturbation; a perturbed genotype, B, with a perturbation of a different gene; and a doubly perturbed genotype, AB. Gene perturbations may be of any form . Also, two perturbations can interact in different ways for different phenotypes or under different environmental conditions.A genetic interaction is the interaction of two genetic perturbations in the determination of a phenotype. Genetic interaction is observed in the relation among the phenotypes of four genotypes: a reference genotype, the 'wild type'; a perturbed genotype, X, as ΦX, then we can write a phenotype inequality representing a specific example of epistatic genetic interaction, for example, ΦA < ΦWT < ΦB = ΦAB. Likewise, a synthetic interaction occurs when two single mutants have a wild-type phenotype and the double mutant shows a deviant phenotype, for example, ΦWT = ΦA = ΦB < ΦAB. Synthetic interactions reveal mechanisms of genetic 'buffering'  were assigned a phenotype inequality relation. This was done by first defining the error-bounded interval Ig =  for each genotype. All pairs of genotypes were assigned an equality, Φg1 = Φg2 if interval Ig1 overlapped with Ig2. Transitivity of equalities  was applied to yield disjoint groups of phenotype equalities. Inequalities, greater than (>) or less than (<) were assigned for the relations between equality groups. The resulting inequalities were assigned to genetic-interaction modes and asymmetries as described below. The results of all tests of genetic interaction were rendered as a graph as illustrated in Figure The following steps were carried out using PhenotypeGenetics software. Phenotypes and errors of genotypes A and B, or reversing the effect of both alleles (for example reversing the effect of the A mutant gene with ΦWT< ΦA gives ΦA < ΦWT). Additional data file 1 lists each of the 75 phenotype inequalities and their assigned genetic-interaction mode and asymmetries. Figure The 75 possible phenotype inequalities were assigned to modes of genetic interaction based on computable criteria. For each mode, we list the criterion for the inclusion of a phenotype inequality. In these criteria, 'background' refers to a genotype with its complement of wild-type and mutant genes, into which other genetic perturbations are added, and 'effect' refers to a change in a phenotype, either an increase or a decrease, upon a single genetic perturbation of a background. In the examples below, additional cases may be generated by operations such as exchanging A has no effect in the WT and B backgrounds , or B has no effect in the A and WT backgrounds, or both hold true .A and B have different effects (in terms of direction or magnitude) on the wild-type background and the double mutant has the same phenotype as either A or B  .A has an effect only in the B background, or the B mutant has an effect only in the A background .A has an effect on WT, but that effect is abolished by adding the suppressor B, which itself shows no single-mutant effect ; or, the corresponding holds under exchange of A and B .WT <ΦA= ΦB<ΦAB, ΦB < ΦWT = ΦAB < ΦA, ΦWT < ΦA < ΦB < ΦAB, ΦB < ΦWT < ΦAB < ΦA, and all additional inequalities obtained by interchanging A and B, or reversing the effect of both A and B .Single-mutant effects combine to give a double-mutant effect as per ΦA and B have no effect on the WT background, but the AB combination has an effect .A, B, and the AB combination all have the same effect on the WT background .B shows opposing effects in the WT and A backgrounds ; or, A shows opposing effects in the WT and B backgrounds, but not both .A and B show opposing effects in the WT background and the background with the other mutant gene .Both P-values were assigned relative to a cumulative hypergeometric distribution. The result was a computer-generated list of biological statements relating genes, interaction classes, and target annotations, with entries such as 'A loss-of-function mutation of HSL1 is suppressed by mutations of cell wall organization and biogenesis genes (-log10P = 2.52).' These are listed in tabular form in Table To identify statistically significant correlations between a given allele's interaction modes and biological processes, the neighbors of every allele in the network were queried for interaction class and Gene Ontology (GO) Consortium database annotations . Each inP-values for the entire network. For example, if a given mutation interacts with N others, NC of the interactions being of class C and NA of those neighbors carrying annotation A, there is a finite set of outcomes for NCA, the number of neighbor mutations with annotation A connected via interaction C. The possible values of NCA follow a discrete hypergeometric distribution, and summing these distributions over all tests in the network yields a formally randomized distribution of P-values which has been constrained by the topology of the actual network. The distributions, real and theoretical, of -log10P values were then compared by performing a chi-square test between comparable histograms. These tests showed a strong excess for -log10P > 1.8.To calibrate the significance of the results, a parallel calculation was performed for every test in the network in which the fractional probabilities of each possible outcome were added to an overall distribution of X, has an observed discrete probability distribution of interaction classes (defined by mode and direction) with its tested interaction partners, P(x), where x ∈ X, the set of interaction classes of perturbation X, and:We calculated the mutual information  of pairsI, of a pair of perturbations, A and B, is the relative entropy of their joint probability distribution relative to their product probability distribution. Thus:Mutual information, P-values were then calculated as the probability of finding a mutual information score at or above the observed score. Allele pairs with probabilities below the cutoff of P < 0.001 are listed in Additional data file 6, and shown as a graph in Figure Significance of mutual information was tested independently for each allele pair by computing the likelihood of obtaining the observed score in randomly permuted data. To remove bias due to our selection of mutant alleles, randomized data were constrained by keeping the wild type and two single-mutant phenotypes fixed and replacing interaction classes only with classes that are consistent with the observed single-mutant phenotypes. The choice among possible replacement classes was weighted by observed frequency in the entire network. Empirical tests showed randomized mutual information scores to be normally distributed, and multiple randomizations were carried out to determine a mean and standard deviation to characterize the distribution for each tested allele pair. The following data are available with the online version of this paper. Additional data file A table showing 75 genetic-interaction inequalities in nine modes of genetic interaction. As described in Materials and methods, all 75 possible phenotype inequalities were classified into nine modes of genetic interaction. The results are listed here.Click here for fileGene perturbations used in this study. This file lists all genes, mutant alleles, and allele forms Click here for filePhenotype error values in the entire dataset. This plot shows the phenotype error values  plotted against percentile of all genotypes ordered by error magnitude.Click here for fileEntire genetic interaction network derived from yeast invasion-phenotype data. Figure Click here for fileWT, A, B, and AB.Phenotype data for all tested interactions. This file lists all tested genetic interactions as well as the phenotype and error values for all genotypes, Click here for fileMutual information in genetic-interaction patterns. This file lists the mutual information, and significance, among pairs of genes connected by edges in Figure Click here for file


Although we do detect significant residual additive genetic correlations between the two traits, there is no evidence of a residual mitochondrial genetic correlation between them. Evidence for autosomal QTL for these traits is improved when linkage screens are conditioned on significant mitochondrial genetic effects. We conclude that mitochondrial genes may contribute to variation in some latent class psychiatric/behavioral variables associated with alcoholism.We report the results of statistical genetic analyses of data from the Collaborative Study on the Genetics of Alcoholism prepared for the Genetic Analysis Workshop 14 to detect and characterize maternally inherited mitochondrial genetic effects on variation in latent class psychiatric/behavioral variables employed in the diagnosis of alcoholism. Using published extensions to variance decomposition methods for statistical genetic analysis of continuous and discrete traits we: 1) estimated the proportion of the variance in each trait due to the effects of mitochondrial DNA (mtDNA), 2) tested for pleiotropy, both mitochondrial genetic and residual additive genetic, between trait pairs, and 3) evaluated whether the simultaneous estimation of mitochondrial genetic effects on these traits improves our ability to detect and localize quantitative trait loci (QTL) in the nuclear genome. After correction for multiple testing, we find significant ( A number of studies have report associations between mtDNA variation and chronic alcoholism. However, the deletions, insertions, modifications, and other rearrangements described in these studies represent damage done to mtDNA in the liver, white blood cells, and elsewhere as a consequence of oxidative stress associated with chronic ethanol consumption ,2. Only The COGA dataset for the Genetic Analysis Workshop 14 includes 1,614 individuals, 788 females and 826 males, aged 17–91 years (mean = 40.09 ± 15.2 years), in 143 pedigrees of varying size and complexity. Families were recruited into COGA on the basis of a positive diagnosis of alcoholism  and Feighner criteria) for a focal proband and 2 first degree relatives.We analyzed data on the 14 latent class variables assessed in 1,181 to 1,388 of the COGA family members. The majority of these latent class variables were measured by COGA researchers on either a dichotomous  or ordinal scale . These variables include: persistent desire to stop drinking (DESIRE), morning drinking (MORNING), craving for a drink (CRAVING), binge drinking (BINGE), narrowing of drinking repertoire (NARROW), gave up other activities to drink (GAVE UP), experience three or more blackouts (BLACKOUT), experienced withdrawal symptoms (WITHDRAWAL), experience physical health problems as a result of drinking (HEALTH), and experienced emotional/psychological problems as a result of drinking (PSYCHOL). By combining the 2 non-zero categories for the ordinal scale variable, spent so much time drinking there was little time for anything else (SPENT), we converted it to a dichotomous trait. We also analyzed the 2 continuous scale traits: maximum number of drinks in a 24 hour period (MAX DRINK) and the number of cigarette packs per day for one year (CIGPKYRS). In linkage analyses reported here we used genotype data at 315 microsatellite marker loci distributed across the 23 chromosomes in 1,376 individuals.2 = ), and residual environmental standard deviation. We extended this basic approach to discrete traits using a multivariate normal threshold model in which the discrete trait is assumed to be determined by a threshold process acting on an underlying, continuous liability distribution [, and its structuring matrix M. M specifies the mitochondrial relationships in the pedigree that share a maternal line of descent [mij = 1 if individuals i,j are members of the same maternal lineage and mij = 0 otherwise [Pedigree, phenotype, and genotype data were managed using PEDSYS  routinesribution . To deteribution  in which descent ; thus matherwise ,11. AspeWe tested for possible mitochondrial genetic pleiotropy between any pairs of traits for which we detected a significant mitochondrial genetic component using a bivariate extension to the univariate variance components approach. This extension allows for the simultaneous estimation of all parameters estimated in the univariate analyses, plus the estimation of a residual additive genetic correlation, a mitochondrial genetic correlation, and a random environmental correlation between pairs of traits. For bivariate analyses of continuous and discrete trait pairings, we employed the method introduced by Williams et al.  to allowp-value consonant with α = 0.05, we divided 0.05 by 1 + (N - 1)(1 - |ρG|), where N is the number of phenotypes, and |ρG| is the mean of the absolute value of the genetic correlations.We used genetic correlations between all 78 latent trait pairs in a modified Bonferroni correction procedure to control for false-positive detection of mitochondrial genetic components to the variance in these 14 traits. To obtain an adjusted p < 0.009) mitochondrial effect to detect evidence for quantitative trait loci (QTL) in nuclear chromosomal regions . Second, we performed locus-specific linkage analyses at the multipoint peaks providing the best evidence for a QTL for each trait to obtain an estimate of the improvement in the LOD score conditional on the mitochondrial genetic component.We conducted a series of multipoint, whole genome linkage screens for each latent class variable exhibiting a significant , the test statistic was distributed as a 1/2:1/2 mixture of χ2 and a point mass of zero [p-values by means of a method suggested by Feingold et al. [Significance of all parameters was determined by likelihood ratio tests in which the likelihood of a more general model in which all parameters are estimated was compared to a nested restricted model in which some parameter values are constrained. The test statistic, twice the difference in the log likelihoods of the two models, was asymptotically distributed approximately as a χ of zero . To contd et al. p(h2mt = 0) ≤ 0.05) is detected for three traits: DESIRE, CIGPKYRS, and CRAVING but, after correction for multiple testing, only the CIGPKYRS and CRAVING remain significant . The mitochondrial genetic component accounts for 14% and 19% of the residual phenotypic variance and 77% and 65% of the additive genetic variance in these two traits, respectively.Table G = 0.06 ± 0.17, ρE = 0.24 ± 0.07, and ρP = 0.06. When a mitochondrial genetic component was included in the bivariate model for the traits, we detected a significant residual additive genetic correlation (ρG = 1.00 ± 0.11), but the estimated mitochondrial genetic correlation between these two traits (ρM= -0.36 ± 0.34) was not significantly different from zero (p > 0.05). The MLE for the residual additive genetic correlation between these two latent class variables was indicative of complete, or nearly complete, pleiotropy. Given the standard errors around the estimate, 60% to 100% of the residual additive genetic variance in each of these traits was due to the effects of genes that also influence the other trait. The residual correlation due to the shared effects of unmeasured environmental factors  was significantly different from zero .Bivariate genetic analysis of the two traits identified above yielded the following correlation estimates when no mitochondrial genetic component was included in the model: ρOur univariate multipoint linkage screens detected no significant evidence for a QTL influencing these two latent class variables on any of the autosomes. The best evidence for an autosomal QTL for each of these three traits is presented in Table The magnitude of the mitochondrial genetic effect on the phenotypic variance of the two latent class traits is likely small. However, mitochondrial genetic effects do account for a substantive proportion of the additive genetic variance in each trait and this proportion may be of biological, as well as statistical, significance.Possible confounding of mitochondrial genetic and non-mitochondrial maternal effects  is a valid concern; the range of pedigree size and complexity in the COGA families may mitigate this concern. We also believe the following observations provide circumstantial evidence that such confounding has not occurred. 1) Addition of the mitochondrial genetic component results in diminution of the residual additive genetic, rather than the environmental, component of the variance. 2) Re-analyses of these data incorporating the following surrogates for maternal effects as covariates, do not eliminate the mitochondrial genetic effect: maternal age at birth and household effects (unpublished data).Our analyses of these data cannot identify the genes, gene products that may be involved, or the mechanisms by which they operate. However, the lack of a significant mitochondrial genetic correlation between the two traits tentatively suggests that multiple mtDNA variants, either in the same gene or in different genes, are responsible for the mitochondrial effects.Lastly, our analyses offer tentative support for inclusion of significant mitochondrial genetic components in variance components models used in linkage screens. In each case, the LOD scores for non-significant multipoint peaks increased, although not quite to the level of genome-wide significance given the finite marker density of the linkage map and the mean recombination frequency in the COGA pedigrees.We detect evidence of mitochondrial genetic variation in two latent class phenotypes associated with susceptibility to alcoholism in data from the COGA families. To our knowledge, this is the first report of such an effect on any alcoholism-related traits.COGA: Collaborative Study on the Genetics of AlcoholismMLE: Maximum likelihood estimatemtDNA: Mitochondrial DNAQTL: Quantitative trait locusLRL and DAW conducted the analyses and interpreted the results of the univariate statistical genetic analyses and were responsible for writing and editing the final manuscript. JTW, instrumental in the development and implementation of both the mixed continuous-discrete bivariate analyses and the method for detecting the mitochondrial genetic component, provided assistance with analyses and interpretation of results. TDD and LA coordinated preparation of the COGA data for investigators at SFBR. MCM was responsible for funding, supervising, writing and editing the initial manuscript, and conducting and interpreting the bivariate analyses. All authors have read and approved this manuscript.


Z matrix that incorporates the clinical correlation of the phenotypes. Specially, the 12 phenotypes were grouped into 3 clusters: 1) communally shared emotions; 2) behavioral related; and 3) anxiety related. A semi-Bayes HM effect estimate for each phenotype was calculated and compared with those from LRM. We observed that using HM to evaluate the association between SNPs and multiple related phenotypes slightly increased power for detecting the true associations and also led to fewer false-positive results.The genetic study of disease-associated phenotypes has become common because such phenotypes are often easier to measure and in many cases are under greater genetic control than the complex disease itself. Some disease-associated phenotypes are rare, however, making it difficult to evaluate their effects due to small informative sample sizes. In addition, analyzing numerous phenotypes introduces the issue of multiple comparisons. To address these issues, we have developed a hierarchical model (HM) for multiple phenotypes that provides more accurate effect estimates with a lower false-positive rate. We evaluated the validity and power of HM in association studies of multiple phenotypes using randomly selected cases and controls from the simulated data set in the Genetic Analysis Workshop 14. In particular, we first analyzed the association between each of the 12 subclinical phenotypes and single-nucleotide polymorphisms within the known causal loci using a conventional logistic regression model (LRM). Then we added a second-stage model by regressing all of the logistic coefficients of the phenotypes obtained from LRM on a  Complex diseases are most commonly evaluated in association studies as a single phenotype. However, they often comprise numerous phenotypes with varying degrees of interrelatedness. For example, in the study of alcoholism, brain electrophysiological measures  can be evaluated as biological markers for developing alcoholism. Focusing on such disease-associated phenotypes can help improve a study if they are under greater genetic control or easier to measure than the ultimate disease endpoint . Nevertheless, analyzing the effect of genes on numerous phenotypes introduces issues of multiple comparisons, and can lead to imprecise estimates of association if the number of individuals exhibiting a disease-associated phenotype is limited.These issues can be addressed by using a hierarchical model (HM) that compromises between analyses of a single phenotype and numerous disease-associated phenotypes. Specifically, this approach shrinks conventional estimates for phenotypes toward a prior mean distinguished by their biologically interrelated nature. Previous work has shown that HM can improve conventional estimation of the association between disease(s) and exposures -4, fine-n = 5,000) for control selection. In light of the limited number of cases, we selected two controls per case, leading to a total of 1,050 subjects per replicate .We used the simulated dataset from the Genetic Analysis Workshop 14 (GAW14) to sample cases and controls for association analyses. Specially, we randomly selected 1 case per family across 4 populations , which gives a total of 350 cases per replicate. Then 50 controls per replicate were pooled together and used as a "population"  | gT) = μm + gTβm + sex βsex,     (1)logit (Pr (Y1... Ym (m = 12) refer to the phenotypes a - l in the simulated data, and g is the single-nucleotide polymorphism (SNP)-specific coding for each individual. For simplicity's sake, we assumed a dominant model for the minor allele, but not for D6, because its common allele is truly functional. Sex was included in Equation 1 because of its potential role in psychiatric disorders. Our HM attempted to improve the first-stage estimates of the SNP-effects on the phenotypes (βm) by adding the following second-stage linear regression model:where binary traits β = Zπ + U     (2)U ~ Nm . Here, Z is a 12 × 3 matrix containing second-stage covariates defining 3 clusters of the 12 phenotypes: 1) communally shared emotions; 2) behavioral related; and 3) anxiety related. In particular, for each phenotype, the corresponding elements in Z are set equal to 1 if they have been defined as being within one of the clusters, and 0 otherwise. π is a column vector of coefficients corresponding to the effects of the second-stage covariates on the SNP . In this way, Z incorporates into a second stage the clinical correlation of the phenotypes, whereby the estimate of each βm "borrows" information from the other estimates. We fixed τ as 0.354, using a semi-Bayes HM . This value implies a four-fold range of residual odds ratios for the SNP on phenotypes (exp(± 3.92*0.354)) after accounting for the relations defined in Z [where To compare the models, we bought 10 packets of markers, which contained 4 disease loci and 2 modifier genes. Four markers were chosen as the causal surrogates because they either provided the highest power compared with other SNPs in the same region  or had higher power while also being informative for the power comparison ). Together with two modifier genes, which were defined as D5 and D6, a total of 6 SNPs were used for the power comparison. We calculated power as the proportion of replicates in which the tested SNP was statistically significantly associated with a phenotype at an alpha level = 0.05.i and j were simulated randomly, so any statistically significant association with these phenotypes is considered a false positive. For each SNP, the FPR was defined as the proportion of replicates showing association at a significance level of 0.05. We analyzed 190 SNPs and compared the validity of HM and LRM by estimating the proportion of SNPs with FPR of greater than 5%.A total of 190 SNPs were used for the type I error comparisons (excluding 10 microsatellite markers). Phenotype .In order to maintain the validity of maximum likelihood estimates (MLE) from LRM when there were no observations for a given phenotype and genotype combination, four "pseudo" subjects were added in the replicates for the type I error comparisons (190 SNPs) and power comparison only in D6. Specificially, each of these additional subjects represents 1 of the 4 possible combinations of phenotype and genotype. Both conventional LRM and HM analyses were undertaken with SAS software , and the codes for HM are available at a and D3. But the conventional LRM provided slightly higher power for some of the associations too, for example: phenotype a and D1. No power is shown for the random phenotypes i and j.We found that HM has slightly higher power than LRM with mean of 58.8% vs. 56.5% Figure . The lari and j, respectively. In contrast, 61 (32%) and 70 (37%) of the tested SNPs showed FPR greater than 5% when using LRM. Testing the difference in FPR between the HM and LRM approaches for phenotypes i and j gave p-values < 0.001.More striking was the decrease in FPR provided by the HM in comparison with the LRM (to the right of the vertical line in Figure Z matrix. In the present study, we grouped phenotypes into three clusters according to the similarity of their clinical characteristics.We observed that using HM to evaluate the association between SNPs and multiple disease-associated phenotypes led to substantially fewer false positives, while slightly increasing power for detecting the true associations. HM can decrease the false-positive rates because the estimate for each phenotype borrows information from other biologically similar traits, through a second-stage b - h were controlled by D2, D3, and D4, and the markers in those regions provided power of 40–100%. In addition, only the SNP in the D4 region showed an association with the single-gene phenotype l, not the others. Two exceptions here are the association between phenotype a and the SNP in the D2 region, and an association between phenotype k and the SNP in the D3 region, which are not the true causal loci. This may be explained by the allelic association among these genes. For example, D1 and D3 are causally associated with phenotype a, and also associated with D2; therefore any association between D2 and phenotype a may simply reflect the effects of D1 and D3. Regardless, these relations should not affect our comparison of HM and LRM.Note that we based our power calculations on the surrogate markers; nevertheless, the results Figure  ultimateWe did not use the "truth" for the simulations, since in practice this knowledge is not available. However, previous simulation studies based on the true underlying model between disease and exposures  or knownGenetic association studies may attempt to reduce phenotype heterogeneity by evaluating subclinical and measurable traits instead of the primary disease of interest. Such disease-associated phenotypes may be under similar genetic control, although other genes and/or environmental factors contribute to the difference among them. By incorporating this information into a higher-level model, HM helps address problems of multiple comparisons while providing more precise estimates than conventional analyses.FPR: False positive ratesGAW14: Genetic Analysis Workshop 14HM: Hierarchical modelLRM: Logistic regression modelMLE: Maximum likelihood estimatesSNP: Single-nucleotide polymorphismXL designed the study, carried out the statistical analysis, and drafted the manuscript. EJ participated in the design of the study and helped to revise the manuscript. JSW participated in the conception, design, analysis, interpretation, and writing of the manuscript. All authors read and approved the final manuscript.