We propose a novel multifactor dimensionality reduction method for epistasis detection in small or extended pedigrees, FAM-MDR. It combines features of the Genome-wide Rapid Association using Mixed Model And Regression approach (GRAMMAR) with Model-Based MDR (MB-MDR). We focus on continuous traits, although the method is general and can be used for outcomes of any type, including binary and censored traits. When comparing FAM-MDR with Pedigree-based Generalized MDR (PGMDR), which is a generalization of Multifactor Dimensionality Reduction (MDR) to continuous traits and related individuals, FAM-MDR was found to outperform PGMDR in terms of power, in most of the considered simulated scenarios. Additional simulations revealed that PGMDR does not appropriately deal with multiple testing and consequently gives rise to overly optimistic results. FAM-MDR adequately deals with multiple testing in epistasis screens and is in contrast rather conservative, by construction. Furthermore, simulations show that correcting for lower order (main) effects is of utmost importance when claiming epistasis. As Type 2 Diabetes Mellitus (T2DM) is a complex phenotype likely influenced by gene-gene interactions, we applied FAM-MDR to examine data on glucose area-under-the-curve (GAUC), an endophenotype of T2DM for which multiple independent genetic associations have been observed, in the Amish Family Diabetes Study (AFDS). This application reveals that FAM-MDR makes more efficient use of the available data than PGMDR and can deal with multi-generational pedigrees more easily. In conclusion, we have validated FAM-MDR and compared it to PGMDR, the current state-of-the-art MDR method for family data, using both simulations and a practical dataset. FAM-MDR is found to outperform PGMDR in that it handles the multiple testing issue more correctly, has increased power, and efficiently uses all available information. The International HapMap Project The role of genetic interactions in explaining phenotypic variability has been described in several publications One of the potential reasons for the small number of large-scale genetic interaction studies performed in humans so far is that although genetic interactions identified from model organisms provide insight into biological processes, these biological processes often lack sufficient overlap with other types of gene/protein associations with traits of interest http://www.healthsystem.virginia.edu/internet/addiction-genomics.One non-parametric approach developed for epistasis analysis is Multifactor Dimensionality Reduction The need for new statistical methods to overcome some of the remaining statistical hurdles in epistasis detection, has led to the development of FAM-MDR. The method combines features of the GRAMMAR approach In the www.statgen.be. The approach consists of two parts.FAM-MDR is an acronym for FAMily Multifactor Dimensionality Reduction and is an adaptation to related individuals of the Model-Based Multifactor Dimensionality Reduction method http://cran.r-project.org/web/packages/GenABEL/index.html. The relationship matrix Part I: In order to deal with familial correlations between observations, data are first analyzed using a polygenic modelThe residualsPart II: Once the data have been prepared in Part I, FAM-MDR proceeds with investigating the association between the newly defined trait R method . It is jKey steps involved in a FAM-MDR Part II analysis are summarized graphically in http://www.recercat.net/handle/2072/5001.In MB-MDR step 1, for a selection of a pair of SNPs, each genotype cell is tested against the eight others for association with the trait. The cells that are found to be significantly associated with the outcome, at a liberal threshold of 0.1, are then called high risk  to a (two-locus) measured genotype (MG) model Finally, a note on how FAM-MDR handles missing data. For missing genotypes, FAM-MDR uses the available cases (AC) paradigm. In other words, if a particular pair is considered, only individuals with complete data for this pair are included in the analysis, while individuals with missing data for one or two SNPs involved are not considered. Individuals with missing trait values are used in FAM-MDR Part I only when they are useful for deriving the relationship matrix, but never for the polygenic calculations themselves. Indeed, if the number of markers is small, the theoretical relationship matrix is used and the complete pedigree is needed for calculating this in a correct way. When the number of markers is large, FAM-MDR relies on the genomic kinship matrix and there is no need to keep individuals with missing trait values in the analysis. Note that since we are not using the individuals with missing trait values for the polygenic calculations, we essentially are performing a complete case (CC) analysis. Also, when correcting for main effects/covariates - since we only use those individuals with complete data on the main effects/covariates that are regressed out in Part I, we are again following the CC paradigm. In Part II, FAM-MDR obviously does not use missing new trait values, whether these are due to missing trait values or missing main effects/covariates adjusted for. Missing new trait values are also not included in the permutation procedure. It is good to recall that both AC and CC are valid under a missing completely at random (MCAR) missingness process We simulated data consisting of 250 nuclear families, with the number of children drawn from a multinomial distribution with probabilities 1/4 to have one child (hence a trio), 1/2 to have two children, and 1/4 to have three children. On average, this gave rise to 1000 individuals. We assumed that no data were missing. In other words, complete information on genotypes at all loci and complete information on phenotypes were available.To generate genotypes for these individuals, we first generated ten diallelic markers: Assuming the presence of additive polygenes and a residual environmental effect, phenotypes were simulated according to the (two-locus) MG modelFirst, we notice that the population two-locus model variance The total phenotypic variance, which is given bySecond, the fixed mean part in (3) needs to be determined. For this, we consider two two-locus models, M27 and M170, of Li and Reich To enhance the interpretation of future simulation results, it is instructive to more closely look into the decomposition of the two-locus model variances for Models M27 and M170 into main effects and epistatic variance . We obseThe two different genetic two-locus models (M27 and M170), three possible minor allele frequencies Under the general null hypothesis of no association with the trait , in particular, Because we are primarily interested in detecting epistasis effects above and beyond main effects, when these main effects are present, we also generated a different type of null data, under the null hypothesis of no epistasis, but main effects. Hence, To reduce the computational burden of our extensive simulation study, we adopted a sequential approach Only to enhance an honest comparison of simulations results with PGMDR, we also introduced a liberal version of FAM-MDR, referred to as FAM-MDR*. In contrast to PGMDR Finally, we analyzed all simulated datasets with both FAM-MDR and FAM-MDR*. We applied PGMDR to all simulation settings with non-zero epistasis, and to 200 (out of 400) generated data sets for each of the simulations settings under the general null hypothesis of no association. Every analysis is carried out once with and without main effects correction. The former involves adjusting for SNP1 and SNP2 by assuming a co-dominant mode of inheritance. The analysis with correction for main effects leads to the detection of two-locus effects beyond co-dominant main effects. The analysis without correction for main effects leads to the detection of a two-locus model but without giving a clue about whether this model is genuinely indicative for epistasis or for main effects, or for both. In PGMDR analyses, and when correcting for SNP1 and SNP2 main effects, we created two dummy variables for each of the causal SNPs and submitted them as covariates to the PGMDR software.ADIPOR1, ADIPOR2), adiponectin , calsequestrin 1 (CASQ1), and hepatocyte nuclear factor 4A (HNF4A), in 1427 individuals from a single large multi-generational pedigree subdivided into 243 independent families for analysis and 25 SNPs. In previous analyses in the AFDS rs1884614 in HNF4Ars2275703 and rs617698 in CASQ1rs1029629 in ADIPOR2http://www.biostat.harvard.edu/~fbat/default.html), we used the check.marker function of R package GenABEL on these 725 non-diabetics with GAUC measurement available. We put extr.call and extr.perid.call equal to 0.25, so that markers and individuals with call rates below 0.25 are removed prior to main analysis. For the main analysis we put callrate and perid.call to 0.9 so we discard iteratively markers and individuals with call rates below 0.9. We discarded four SNPs, rs6666089 and rs1342387 in ADIPOR1, and rs617599 and rs1186694 in CASQ1, due to low callrates. All markers had minor allele frequencies above 1%. We also discarded 105 individuals due to low callrates, by putting their GAUC measurement to missing. All analyses are based on the remaining 21 markers and 620 individuals.The Amish Family Diabetes Study In order to derive the correct relationships between the 620 individuals of interest, FAM-MDR also makes use of the remaining 807 individuals without GAUC measurement available and – in order to recognize relationships between offspring – of additional parental information . Hence, “information” of 2231 individuals was exploited by FAM-MDR. The 620 individuals of interest correspond to 136 independent families. Of these, 75 consisted of unrelated single individuals with no genotyped first-degree relatives, 33 were nuclear families , and 28 were multi-generational families. However, these 28 families included 471 or 76% of the 620 individuals.Because the present PGMDR implementation cannot deal with large multi-generational (non-nuclear) pedigrees, and only for reasons of comparison between PGMDR and FAM-MDR, we split multi-generational pedigrees into nuclear families. In the resulting set of nuclear pedigrees, 344 individuals were represented twice, most often as offspring in one pedigree and parents in another. The net result of the splitting process was a set of 584 non-independent nuclear families, comprising 2575 ( = 2231+344) individuals. Of the 620 individuals with GAUC measurement available, 161 were represented twice, resulting in a total of 781 individuals of interest to us, in 363 non-independent families. Of these families, 255 were part of the 28 extended pedigrees, while the remaining 108 were mutually independent. There is clearly a need to account for the lack of independence between these nuclear families. Unfortunately, the PGMDR software is unable to do so. Solely for reasons of comparison, FAM-MDR was applied to the split-pedigree data, as well as to the original multi-generational family data.rs1884614 in HNF4A, rs2275703 and rs617698 in CASQ1, and rs1029629 in ADIPOR2. They were regressed out in FAM-MDR Part I, or entered as covariates in PGMDR, using co-dominant coding. P-values were based on 1000 permutations for both PGMDR and FAM-MDR, hence no stopping rules were used. The significance level was set at Analyses were carried out with and without correction for the main effects of Without main effects correction, FAM-MDR on the original data uses all 620 individuals with GAUC value available. When correcting for main effects, missing genotype information contributes to an increased missingness rate for the new trait values. Here only 572 or 92% of the 620 individuals have non-missing new trait values. On the split-pedigree data, 781 individuals are available for FAM-MDR without main effects correction, and 726 for FAM-MDR with main effects correction. Note that this is in fact an artificial increase in sample size of 26% and 27% respectively. In contrast to FAM-MDR, PGMDR works with the transmitted genotype information. Of the 620 individuals with a GAUC value available, the 75 unrelated individuals (singletons) obviously did not have parental information available, giving rise to 545 individuals eligible for PGMDR analysis. Furthermore, whenever genotypes for any SNP are completely missing for a family, PGMDR simply discards the whole family from the entire epistasis screening. As a result, PGMDR uses only 537 individuals in an analysis without correction for main effects, and 501 individuals in an analysis with main effects correction, amounting to reductions of 13% and 12% compared to the corresponding FAM-MDR analyses. Consequently, PGMDR does not use all information available.As a quality check on the simulated data, we first assessed the values of the Hardy Weinberg and Linkage Disequilibrium correlation coefficients We first considered simulation results under the general null hypothesis of no association . Empirical type I error rates were defined as the number of times the selected best 2-locus model was assessed significant, divided by the number of simulations. From Second, we considered the simulated null data under the null hypothesis of no epistasis, in the presence of main effects. If under this null a two-locus model is identified , then a type I error has been made with regard to the null hypothesis of no interaction, and the significant result may be largely driven by main effects. Type I error rates for a variety of scenarios are given in t models . Note thThird, we considered simulated data under the alternative hypothesis of epistasis (possibly in the presence of main effects). For every simulation setting, empirical power was defined as the number of times the correct pair odel M27  and Modeodel M27 , but theOur simulation data does not show a systematic trend with increasing total heritability  effects . There ars1884614 in HNF4A, rs2275703 and rs617698 in CASQ1 and rs1029629 in ADIPOR2. Without correction for main effects, FAM-MDR on the cut-pedigree data finds a significant two-locus model involving rs2275703 in CASQ1 and rs1501299 in APM1. When performing a main effects correction, the same best interaction model is identified. However, the interaction is significant only at the 10% significance level, suggesting that the two-locus model is to some extent driven by the main effect of rs2275703. PGMDR without main effects correction does not lead to a significant interaction. With correction for main effects, PGMDR reports a different near-significant two-locus model involving rs2275703 in CASQ1 and rs1028583 in HNF4A. FAM-MDR on the original data, with or without correction for main effects, does not yield any significant two-locus models. Possible explanations for these contradicting results are reviewed in the The objectives of this paper were to introduce a new family-based and flexible epistasis detection analysis method, FAM-MDR, which is based on multifactor dimensionality reduction of multi-locus genotypes, and to compare it to the current state-of-the art MDR methodology for families, PGMDR. Although principles of the initial MDR approach are adopted in FAM-MDR, there are some clear differences. These include an alternative way to identify risk categories associated with multi-locus genotypes, the flexibility to use any outcome type, the possibility to correct for lower order effects, covariates or confounding factors, the possibility to assess significance of multiple higher-order interaction models. Since model selection is not based on evaluating prediction accuracy but on testing associations, FAM-MDR does not involve computationally intensive cross-validation steps.FAM-MDR consists of two parts. In part I, residuals are derived from a polygenic model, removing additive polygenic effects and possibly important lower-order effects or confounding factors. These residuals are subsequently considered as new traits for the second part of FAM-MDR. In Part II, the familial correlation-free residuals are submitted to the MB-MDR algorithm and either the best model (considered in this manuscript), or multiple epistasis models are checked for their significance. In contrary to first implementations of the MB-MDR algorithm, no simulation-based null distributions are derived to assess significance, but a permutation-based strategy is adopted. Under the assumption of familial correlation-free traits in FAM-MDR Part II, permutation-based p-values for the best model can easily be derived by randomly permuting the traits. This is in contrast to PGMDR's implementation of a permutation strategy in that for PGDMR families are considered as the permutation units.The method of removing familial-correlation structure is not new. The GRAMMAR approach of Aulchenko et al. The Current implementation of FAM-MDR is not scalable to GWAS. An efficient C++ implementation and a code version for parallel analyses are on their way. First simulations indicate that these enhancements will make GWAS feasible. For now, when large-scale genomic screenings are performed with thousands of markers, since FAM-MDR Part I is preparatory for subsequent association analysis, FAM-MDR can include a pre-selection step of good candidates of markers for epistasis analysis. These candidates may be selected on the basis of information theoretic measures Also, a Part III can be added to a FAM-MDR analysis to interpret the identified epistasis models. This is an important step of the analysis and may or may not involve deriving good estimates of the significant effects. Special care needs to be taken when carrying out this step, in order not to be the victim of the so-called “winner's curse” Currently, MB-MDR and FAM-MDR are based on Wald statistics, whereas GMDR and PGMDR make use of score statistics. First, the score test is computationally more advantageous because it only needs parameter estimates under the null whereas the Wald test needs parameter estimates under the alternative and the likelihood ratio test needs both. Second, even though the three tests are asymptotically equivalent, the score test is the most powerful of the three when the true parameter is close to the null value. In line with the first release of an MB-MDR R package for unrelated individuals, Wald statistics were implemented in the first version of the FAM-MDR software. In the future, score statistics as well as robust non-parametric statistics will be offered as additional options in FAM-MDR. One of the major results that our simulation study highlights is that PGMDR is too liberal in identifying epistasis models. This is due to the inadequate correction for multiple testing, implemented in the PGDMR software to date ; Panel CA third important result is the influence of correcting for lower-order effects when searching for significant epistatic interactions. As was also pointed out by Calle et al. The current FAM-MDR implementation is only valid under the assumption of no population structure, and our simulations assume a homogeneous population. By using both between- and within-family association – in contrast to PGMDR that uses only within-family association – FAM-MDR gains power but this comes at the price of sacrificing the built-in protection against spurious results if population structure is present. A possible solution to this problem lies in the use of Genomic Control Regarding missing genotypes, PGMDR discards families entirely when data on one SNP are missing. Without minimizing the need to also improve FAM-MDR's handling of missing data (whether at the genotype or phenotype level), not being able to account for the full complexity of a pedigree is certainly a drawback of PGMDR. We believe that methods that can accommodate mixed study designs will become more and more important due to the increasing practice of combining data from different groups in consortia collaborations. FAM-MDR flexibly deals with both unrelated and related individuals in the same analysis whereas PGMDR excludes unrelated individuals, hereby reducing the power of the association analysis.rs1884614 in HNF4A, rs2275703 and rs617698 in CASQ1, and rs1029629 in ADIPOR2, no evidence for a significant interaction (or two-locus model) was found  FAM-MDR correction for main effects of as found . Weak inCAPN10 , then NIDDM1) and 15 ) in contributiing to T2DM susceptibility ADRB3) and Uncoupling protein 1 (UCP1) genes observed in weak DIO2) and ADRB3 polymorphisms showed a synergistic effect on an increased BMI, suggesting an interaction between these two common gene variants Improving the ability to detect gene-gene interactions in family studies of complex disease may prove critical in identifying the underlying sources of observed heritability. While it is apparent that type 2 diabetes mellitus (T2DM) is polygenic, the genetic sources of the observed heritability have yet to be completely identified In conclusion, FAM-MDR – unlike PGMDR – is able to handle complex and large pedigrees with additional unrelated individuals. In fact, FAM-MDR analysis on split pedigree data should not be trusted because it might lead to overly optimistic results. On the other hand, as pedigree size increases, the inherent conservative nature of FAM-MDR could become more pronounced. Finally, PGMDR results – and in fact also GMDR results – are too liberal as no correction for multiple testing is carried out.Figure S1Probability-probability plots for FAM-MDR analyses under the null hypotheses of no association and no epistasis. The situation considered is p = 0.5 and h2 = 0.3. Analyses are performed both with and without correction for main effects. Results are based on 100 replicates. Panels A and B show results for data generated under the null of no association, whereas panels C and D consider data generated under the null hypothesis of no epistasis, for model M27 and with g2 = 0.1. Panels A and C show results for analysis with correction for main effects, panels B and D without.(0.50 MB TIF)Click here for additional data file.Figure S2Additional power results for model M27, based on 100 replicates. Panels A and B show results for h2 = 0.5 and h2 = 0.8 respectively. Abbreviations: Corr. = with main effects correction, No Corr. = without main effects correction.(1.54 MB TIF)Click here for additional data file.Figure S3Additional power results for model M170, based on 100 replicates. Panels A and B show results for h2 = 0.5 and h2 = 0.8 respectively. Abbreviations: Corr. = with main effects correction, No Corr. = without main effects correction.(1.53 MB TIF)Click here for additional data file.


The authors discuss a new study that investigated the developmental overnutrition hypothesis in a large cohort of British pregnant mothers. Childhood obesity has become a serious public health problem worldwide. The United States Centers for Disease Control and Prevention estimates that one in three children and adolescents are currently overweight/obese . The advThe obesity epidemic not only represents a public health crisis in our current generation, but may also have lasting adverse consequences on the health of future generations. The developmental overnutrition hypothesis proposes that within the pregnant womb of an overweight/obese mother, the developing fetus is exposed to higher in utero levels of glucose and free fatty acids. Such exposure may permanently disrupt or dysregulate appetite control and hormones and impair energy metabolism, thereby increasing offspring adiposity and risk of obesity . This thHowever, until now, testing such a hypothesis has been exceptionally difficult, as parents exert obvious strong genetic and psychosocial influences on offspring health besides the in utero environment during fetal development. Therefore, although overnutrition of the developing fetus in utero may be one potential explanation of the correlation between maternal and offspring adiposity, the correlation may also be due to shared genetic and social factors. However, cutting-edge methods in genetic epidemiology developed in recent years now allow testing of the hypothesis and of the causal nature of other associations in observational research.PLoS Medicine:This Perspective discusses the following new study published in FTO as an instrumental variable. PLoS Med 5(3): e33. doi:10.1371/journal.pmed.0050033Lawlor DA, Timpson NJ, Harbord RM, Leary S, Ness A, et al. (2008) Exploring the developmental overnutrition hypothesis using parental–offspring associations and FTO gene as an instrumental variable for maternal adiposity, Debbie Lawlor and colleagues found that greater maternal BMI during offspring development does not appear to have a marked effect on offspring fat mass at age 9–11.Using parental–offspring associations and the PLoS Medicine, Debbie Lawlor and colleagues investigated the developmental overnutrition hypothesis in a large cohort of British pregnant mothers, analyzing 4,091 sets of mother–father–offspring trios [FTO gene [In this issue of ng trios . In theiFTO gene , as an “In transferring genes from parents to offspring, genetic alleles are assigned through a random process at the time of gamete formation (Mendel's Second Law). The randomly assorted alleles are analogous to randomly allocated treatments in randomized controlled trials. Based on this principle, MR analysis uses genetic variants with known functions as markers of long-term exposure to estimate unconfounded exposure–outcome associations in observational studies . The anaFTO gene and its established relation to adiposity [In this study, the authors capitalize upon the diposity  to eluciThe study has considerable strength as a prospective study based on a well-established cohort, with anthropomorphic information from a large number of parental–offspring trios. In addition, objective data on adiposity in offspring were available from dual energy x-ray absorptiometry scans. Although the application of MR analysis in the study has certain advantages in estimating causal associations compared to conventional observational analyses, there are potential limitations  that desPLoS Medicine by the same group indicated that distant genes and genes on different chromosomes are uncorrelated between each other, indicating that genes are mostly free of confounding by other genes [The phenomenon of linkage disequilibrium (LD), where one allele is actually a correlated marker for another allele on the same chromosome , is one classical concern. However, LD between neighboring genetic variants can still be acceptable, as many variants are considered markers of a haplotype block characterizing a consecutive region of a gene, thereby representing the net functional effect of a set of alleles. The MR assumption is violated only if the chosen gene is in LD with another gene that has independent effects on the outcome . Anotherer genes .FTO gene is valid as an instrument of MR if the maternal FTO gene's effects on offspring obesity are mediated through the in utero environment, as marked by maternal adiposity). However, the assumption is violated if the FTO gene possesses pleiotropic effects (other biologic effects) on outcome independent of its effects on maternal adiposity. In such instances, the analysis may not yield the true effect of fetal overnutrition, unless one analytically adjusts for and blocks all alternative causal pathways.Another assumption of MR analysis requires that any proposed effect of the gene on outcome should be mediated through its intermediate (i.e., the FTO or not, with the association being drastically altered from positive to null after adjusting for offspring FTO. Conceptually, it is necessary to adjust for the offspring FTO gene to separate the influence of genetic inheritance of the maternal FTO gene from the effect of maternal adiposity during pregnancy. However, as the offspring FTO is a causal pathway intermediate between the maternal FTO and offspring adiposity, the conventional approach of adjustment through stratification may induce bias in estimating the exposure–outcome association [Finally, this study indeed represents a novel application of the MR analysis to transgenerational causal inferences. However, results were strongly dependent on whether analyses were adjusted for offspring ociation . This meOverall, with the unique and large prospective cohort of over 4,000 parental–offspring trios and the integration of genetic data via MR analysis for causal inference, this study presents an important contribution to testing the fetal origin of obesity hypothesis. Not only does this provocative study warrant replication in a different population, but future research should also aim to investigate the fetal origin hypothesis using other direct intermediate measures of in utero “overnutrition,” such as gestational levels of maternal hyperglycemia and free fatty acids. Moreover, it would also be highly informative to investigate the hypothesis via MR using other established or soon-to-be discovered genes responsible for obesity, diabetes, and/or other metabolic disorders. Recent advances in genome-wide association studies have made it possible to identify reproducible genes for these conditions. Larger sample sizes and more robust estimates of the genotype–intermediate phenotype and genotype–outcome associations in future studies would also help provide more precise MR estimates for causal inference.While Lawlor and colleagues' new study does not support the developmental overnutrition hypothesis, the wide confidence intervals do not provide a clear refutation of the hypothesis either. The fetal origin theory still remains supported by a body of plausible biological mechanisms and substantial empirical data. Indeed, an epidemic mechanism whereby obesity may “accelerate through successive generations independent of further genetic or environmental factors”  in a pro


Random forests (RF) is one of a broad class of machine learning methods that are able to deal with large-scale data without model specification, which makes it an attractive method for genome-wide association studies (GWAS). The performance of RF and other association methods in the presence of interactions was evaluated using the simulated data from Genetic Analysis Workshop 16 Problem 3, with knowledge of the major causative markers, risk factors, and their interactions in the simulated traits. There was good power to detect the environmental risk factors using RF, trend tests, or regression analyses but the power to detect the effects of the causal markers was poor for all methods. The causal marker that had an interactive effect with smoking did show moderate evidence of association in the RF and regression analyses, suggesting that RF may perform well at detecting such interactions in larger, more highly powered datasets. Random forests (RF)  is one oIn many genetic association studies, a common approach is to follow up the most significant results from a GWAS by genotyping independent samples for a smaller number of SNPs  using customized arrays [To address this issue, the Genetic Analysis Workshop 16 (GAW16) Problem 3 simulated data set was used to evaluate performance of RF and several other association methods. Given knowledge of the major causative SNPs and risk factors for these simulated traits , we compThe Framingham Heart Study SHARe dataset for GAW16 Problem 2 formed the basis of the simulated data pedigree structures: 6,476 individuals with both phenotype and genotype data in 942 pedigrees across three generations plus 188 unrelated individuals. The genotypes for all Problem three replicates were fixed to those that were actually observed for the Framingham Heart Study SHARe participants. Phenotypes were simulated for all genotyped individuals at three time points, 10 years apart. Total cholesterol (CHOL) was defined as the sum of the simulated phenotypes triglyceride, high-density lipoprotein (HDL), and low-density lipoprotein (LDL). The traits were simulated such that over time, one develops cranial adipose cumulation (CAC). People with high levels of CAC were at higher risk for myocardial infarction (MI). Smoking also increased the risk of MI in these simulated data. The MI trait was simulated so that the age-adjusted incidence of MI was higher for men than for women. The MI and CAC traits, along with the strongest causative risk factors on the etiologic pathway used in the simulation, are detailed in Kraja et al. [p < 0.01) were excluded, leaving 31,538 SNPs for the analyses. Markers showing mendelian inconsistencies were coded as unknown in the parent(s).In the 50 k-SNP panel , quality control measures were performed in the following order: 1) individuals with genotype calls for <95% of the SNPs were removed; 2) all genotypes with a confidence score  <0.9Phenotype observations from the first two replicates in the simulated data were combined for case and control selection (three phenotype time-points per replicate) using both the family data and the unrelated individuals (singletons) as described below. Because the number of unrelated cases with an MI in any one replicate was small, these two replicates were combined to increase the power to detect variables that contribute to risk of the simulated disease by increasing the number of cases. Subjects were classified as a "case" if they had at least one MI and as a "control" if they were free from any MI over all six time-points. Families were classified as "case-families" if they contained at least one case and "control-families" if they had no cases. Among the genotyped persons, 563 unrelated cases  and 553 unrelated controls  were selected. These included all singletons in addition to the youngest case from each case family and the oldest control from each control family. Environmental risk factors  and CAC were taken from the visit that corresponded to the earliest MI for cases and the final visit in the first replicate for controls. Where a case had an MI in both replicates at the same time point, phenotypes from the first replicate were selected. These 1,116 persons were used in all analyses described here.Imputation of missing genotypes (1% of genotypes) was performed using the RfImpute function implemented in randomForest package 4.5 in R 2.7.1. RF analyses were run 100 times, randomly sampling 31,000 SNPs in each run with 1000 trees per forest. Each RF model included covariates of age in years, sex, CHOL, and smoking status  as potential predictors. Analyses were performed for MI as a dichotomous trait for RF classification and CAC as a quantitative trait for RF regression. Each of these analyses was performed in two ways, using either 200 or 7 randomly sampled predictors at each node (mtry option in the randomForest package) in each tree.The results over the 100 RFs were summarized by counting the number of times the major causative loci for the CAC and MI traits appeared in the subsets of SNPs identified by each RF as being most predictive based on importance indices generated by randomForest [p-values were obtained using Wald t-tests; for the Cochrane-Armitage test, they were derived from the asymptotic chi-squared distribution (1 df).Case-control (Cochrane-Armitage trend) and quantitative-trait (linear regression) association analyses were performed in PLINK . Multivap = 0.003) showed a nominal significance level (MI below 0.01)  would have been retained for second-stage analysis using the univariate rankings , but not based on the multivariate analysis.For comparison with our RF analyses, standard significance tests for association were performed for MI and CAC, adjusting for covariates using PLINK. Among the SNPs that were simulated to have the strongest genetic effects on MI and CAC, none showed genome-wide significance, and only rs12565497 ). We observed that the causal SNPs and important covariates were more likely to be included in the top predictor lists to pass to second-stage analysis when the ranking was based on the GINI index for classification . RF performed very well in detecting these environmental risk factors that had comparatively large effects on the traits. RF analyses that included these risk factors had lower mean prediction error rates in 100 RFs  than did RF analyses that did not include these covariates .Table As expected, the number of times that causal SNPs were ranked high enough to be selected for second-stage analysis (top lists) across the 100 RFs increased with the number of SNPs included in the top lists. Only rs12565497, which was simulated to interact with smoking to affect risk of MI , had a mThese RF results supported the use of the GINI (MSE) index rather than MDA, a large number of sampled predictors per node , and categorical coding of genotype data when using RF for the first stage of a GWAS. In this fairly small sample, the strategy of picking random samples of the available SNPs for each RF analysis and then averaging results over 100 forests was not very successful in including the major causative SNPs in the top-ranked sets of SNPs so that they would be included in later replication analyses - only one causal SNP occurred in the top list of SNPs frequently. However, the performance of the RF and regression analyses were very similar and the results suggest that RF may perform well at detecting interactions when the sample size is larger and overall power to detect genetic effects is thus larger. Future simulation studies in much larger samples will be required to resolve this question.CAC: Cranial adipose cumulation; CHOL: Cholesterol; GAW: Genetic Analysis Workshop; GINI: Gini index; GWAS: Genome-wide association study; HDL: High-density lipoprotein; LDL: Low-density lipoprotein; MAF: Minor allele frequency; MDA: Mean decrease in accuracy; MI: Myocardial infarction; MSE: Mean squared error; RF: Random forests; SNP: Single-nucleotide polymorphism.The authors declare that they have no competing interests.YK, RW, RAM, HS helped to design the study, perform analyses and draft the manuscript, LW helped design the study and performed analyses, AK, JM, RKL and JEB-W helped design the study and participated in writing the manuscript.


With the advent of increasingly efficient means to obtain genetic information, a great insurgence of data has resulted, leading to the need for methods for analyzing this data beyond that of traditional parametric statistical approaches. Recently we introduced Grammatical Evolution Neural Network (GENN), a machine-learning approach to detect gene-gene or gene-environment interactions, also known as epistasis, in high dimensional genetic epidemiological data. GENN has been shown to be highly successful in a range of simulated data, but the impact of error common to real data is unknown. In the current study, we examine the power of GENN to detect interesting interactions in the presence of noise due to genotyping error, missing data, phenocopy, and genetic heterogeneity. Additionally, we compare the performance of GENN to that of another computational method – Multifactor Dimensionality Reduction (MDR).GENN is extremely robust to missing data and genotyping error. Phenocopy in a dataset reduces the power of both GENN and MDR. GENN is reasonably robust to genetic heterogeneity and find that in some cases GENN has substantially higher power than MDR to detect functional loci in the presence of genetic heterogeneity.GENN is a promising method to detect gene-gene interaction, even in the presence of common types of error found in real data. The field of human genetics is currently experiencing an explosion of genetic data, as genotyping technology becomes more inexpensive and accessible. This creates an analytical challenge for genetic epidemiologists. This challenge is exaggerated in the case of complex diseases since the phenotype is likely the result of many genetic and environmental factors,2. The lRecently, our group proposed a Grammatical Evolution Neural Network (GENN), a machine-learning approach designed to detect gene-gene interactions in the presence or absence of marginal main effects,6. GENN GENN has been shown to have high power to detect interactions in a range of empirical studies with both real and simulated data,6,8,9. TIn the current study, we assess the robustness of GENN to several common types of noise. Data originally simulated for Ritchie et al 2003 was usedGENN methodology and software have been previously described,6. The sIn the case of missing data the algorithm does not include that observation in the calculation of classification error. Only the particular missing instance is ignored, not all data for an entire individual or entire locus. Configuration parameters used in the current analyses were: 10 demes, migration every 25 generations, population size of 200 per deme, maximum of 200 generations, crossover rate of 0.9, tournament selection, standard two-point crossover, selection and a reproduction rate of 0.1.n genetic and/or environmental factors are selected. These factors and their multi-factor classes are divided in n-dimensional space. Then the ratio of cases to controls is calculated within each multifactor class. Each multifactor cell class is then labelled "high risk" or "low risk" based on the ratio calculated, reducing the n-dimensional space to one dimension with two levels. The collection of these multifactor classes composes the MDR model for a particular combination of factors. For each possible model size  a single MDR model is chosen that has the lowest number of misclassified individuals. In order to evaluate the predictive ability of the model, prediction error is calculated using 10-fold cross-validation. The result is a set of models, one for each model size considered. From these models, a final model is chosen based on minimization of prediction error and maximization of cross validation consistency .The steps of MDR, and details of the MDR analyses presented here have been previously described. BrieflyDatasets were originally generated and described for Ritchie et al, 2003. BrieflyEach model was simulated in the presence and absence of common sources of noise, including: 5% genotyping error (GE), 5% missing data (MS), 50% phenocopy (PC), and 50% genetic heterogeneity (GH). For each model, 100 datasets were generated in the absence of any type of noise, 100 datasets were generated for each type of noise, and 100 datasets were generated for each 2, 3, or 4-way combination of the sources of noise. 96 sets of 100 datasets were generated in total.As previously described, GE was The results of all analyses were first considered under a very strict definition of power. Initially, power was defined as the proportion of times across dataset replicates the method found all functional loci, with no false positives. For the majority of models (those without GH), a two-locus model was simulated, so the correct two loci, with no false positives must be chosen as the best final model under this definition of power. For those models with GH, two different two-locus models that both independently confer disease risk were simulated. Therefore, under this strict power definition, all four functional loci must be included in the final best model, with no false positives.The results of the MDR analyses under this definition of power, as found in are showNo synergistic effect is seen between PC and GE or MS for either method. However, different synergistic effects are seen with other combinations of error in comparing the results of the two methods. The MDR results show a major synergistic effect of PC and GH, as any combination of PC and GH, alone or with other types of error, causes the greatest decrease in power. This is unsurprising, because those datasets with only one single type of error that had the greatest drop in power were PC and GH as mentioned above. One would expect to find similar results when these two types of error are combined. The GENN results, however, do not demonstrate this effect. When PC and GH are present, the power is comparable to GH alone. However, there does seem to be a synergistic effect of GH and MS for GENN that is not seen with MDR under this strict definition of power. This effect is lessened for other definitions of power.It is important to note that for most combinations of error, the power of GENN is generally comparable to that of MDR under this original definition of power. The evolutionary computation approach of GENN does not require an exhaustive exploration of all possible combinations of variables, as MDR does. This is an important advantage in terms of computation time; however, this advantage must not come at the cost of power.Recognizing the extremely stringent nature of the original definition of power, especially for the models with GH, the results were re-examined. While it would be ideal for a method to identify all important signals within a dataset, it is important to know what signals a method is able to detect. To gain a more complete understanding of the performance of GENN on models with GH, several other definitions of power were considered. Again, these results are generally compared to those of MDR.First, the power of each method to detect the primary genetic model  was considered. The MDR and GENN results under this definition of power are shown in Tables Next, the power of each method to detect either underlying genetic model was examined. The MDR and GENN results are shown in Tables Finally, the power of each method to detect only correct loci was examined. Under this definition of power, any combination of the four total functional loci simulated as the best model is considered important. The results are shown in Tables The results of the current study demonstrate that GENN is relatively robust to common types of noise. GENN has excellent power in the presence of GE and/or MS, but is more impacted by PC and GH. Strikingly, when the performance is compared to that of MDR, GENN has higher power to detect only true positive loci. GENN's advantage over MDR in the presence of GH may be due to the search process used (an evolutionary strategy instead of an exhaustive search), and/or specific operators (i.e. Boolean operators) used inThese results are encouraging, but it will be important to assess the performance of GENN to detect even more complex models, particularly involving GH and PC. Theoretical and empirical studies should focus on improving the overall performance, as well as evaluating GENN's relative strengths and weaknesses compared to other computational methods in the field.GENN: Grammatical Evolution Neural Networks; MDR: Multifactor Dimensionality Reduction; GE: Genotyping error; PC: Phenocopy; MS: Missing data; GH: Genetic heterogeneity.The authors declare that they have no competing interests.AAM and MDR contributed to the design of the study. AAM, ACD, and TJF contributed to the data analysis. All four authors contributed to the manuscript.


The Framingham Heart Study, founded in 1948 to examine the epidemiology of cardiovascular disease in a small town outside of Boston, has become the worldwide standard for cardiovascular epidemiology. It is among the longest running, most comprehensively characterized multi-generational studies in the world. Such seminal findings as the effects of smoking and high cholesterol on heart disease came from the Framingham Heart Study. At the time of publication these were novel cardiovascular disease (CVD) risk factors, now they are the basis of treatment and prevention in the US. Is the Framingham study now on it's way to becoming the gold standard for genetic epidemiology of CVD? Will the novel genetic findings of today become the health care standards of tomorrow? The accompanying articles summarizing the results of genome-wide association studies (GWAS) give the reader a first glimpse into the possibilities. The Framingham Heart Study, founded in 1948 to examine the epidemiology of cardiovascular disease in a small town outside of Boston, has become the worldwide standard for cardiovascular epidemiology . It is aThe strength of the Framingham Study has always been and will always be their extensive, well-characterized, longitudinal phenotypes. In an era of human genetics where speed is of the essence, such phenotypes are hard to come by. The recent explosion of genetic information available and low-cost genotyping technology has allowed for extensive hypothesis-free genome-wide interrogation ,6. GenomNature [Replication will be critical in determining which associations are real as we begin to see the results of multiple GWAS. A paper was recently published in Nature  providinThe data presented in the accompanying papers are not optimal. The reports are based on a preliminary GWAS with a lower SNP density  and a less accurate allele calling algorithm (Dynamic modeling or DM) than is the standard today  typed inFirst, because the GWAS was performed in families, results from linkage and association can be compared. Most human geneticists are abandoning linkage in favor of the latest technology-driven methods. However, linkage can provide valuable information to aid in differentiating between real associations and false positives. It was encouraging to see that two of the inflammatory markers (MCP1 concentration and CRP levels) showed concordant linkage and association peaks . HoweverSecond, because Framingham is a cohort without disease-based ascertainment, a multitude of phenotypes can be investigated. Many of these phenotypes are correlated. This provides the opportunity to investigate pleiotropy and to begin to decipher the genetic architecture of complex diseases such as CVD. The Framingham investigators performed a first pass look at this question. They looked for overlap among the top 500 SNPs associated with phenotypes across three "working groups": glycemic/diabetes phenotypes, lipid phenotypes and obesity phenotypes. Eleven SNPs were found in more than one group, but none of these were found in all three -12. Theset al. [et al. [Third, I think it is important to note that, despite the limitations of these data, the Framingham investigators replicated several well-established candidate gene associations. Among these were SNPs in the TCF7L2 gene and diabetes , SNPs inet al.  and McPh [et al. .The analysis of such a large volume of data and presentation of results is a daunting task. The Framingham investigators have done a commendable job in getting the results out and providing the data for other investigators to use. In the process they have entered the "gold rush" to stake claims on GWAS results . AlthougThe pre-publication history for this paper can be accessed here:


R windows by the statistics based on the first sub-sample, and in the second stage, we claimed significant windows by false-discovery rate correction on the p-values of the statistics based on the second sub-sample. By applying the new approach to the Genetic Analysis Workshop 16 Problem 1 data set, we detected 212 out of 531,601 windows to be responsible for rheumatoid arthritis. Except for chromosomes 4 and 18, each of the other 20 autosomes was found to harbor risk windows. Our results supported the findings of some rheumatoid arthritis susceptibility genes identified in the literature. In addition, we identified several new single-nucleotide polymorphism windows for follow-up studies.In genome-wide association studies, new schemes are needed to incorporate multiple-locus information. In this article, we proposed a two-stage sliding-window approach to detect associations between a disease and multiple genetic polymorphisms. In the proposed approach, we measured the genetic association between a disease and a single-nucleotide polymorphism window by the newly developed likelihood ratio test-principal components statistic, and performed a sliding-window technique to detect disease susceptibility windows. We split the whole sample into two sub-samples, each of which contained a portion of cases and controls. In the first stage, we selected the top  Rheumatoid arthritis (RA) is a common chronic destructive disease of an unknown complex etiology. Both genetic and environmental bases are thought to contribute to this disease. The human leukocyte antigen (HLA) region major histocompatibility complex (MHC) on chromosome 6 6p21.3) is known to be associated with RA. This region is the only one that has been consistently shown to be both linked and associated with RA across all populations. It extends over 3.6 Mb and is divided into three sub-regions . It is a highly dense area containing about 220 genes, many of which are thought to have immunoregulatory functions [.3 is knoT2 test [T2 test and the LD contrast test compare the means and the variance-covariance matrices of genotype scores between cases and controls, respectively. More recently, we proposed a likelihood ratio test-principal component (LRT_PC) to compare the means and the variance-covariance matrices of genotype scores simultaneously [Recently, many approaches, e.g., Hotelling's T2 test  and the T2 test ,5, have aneously . HoweverIn this article, we report a novel genome-wide sliding-window approach to detect genetic association between a trait and SNP regions. This approach integrated the LRT_PC with the concept of sliding window  and the n and m are the numbers of cases and controls, respectively, and the K PCs in cases, controls, and the pooled sample, respectively. Wang et al. [T2 test and the LD contrast test [We recently proposed a LRT_PC approach to test the association between a given SNP window and a disease status . To calcg et al.  showed tast test  in most S, then, all the SNPs can be divided into windows 1 to S, 2 to S + 1, 3 to S + 2, and so on.Because the LRT_PC test may be more powerful than other multi-marker tests, we wanted to use it to analyze the data set of GAW16 Problem 1. However, the LRT_PC can only be applied to a small chromosome region. To apply the LRT_PC to genome-wide association studies, we propose a sliding-window approach . To use p-value of the test. For a genome-wide association study, the number of windows usually is more than 500,000 and the number of permutations usually is no less than 1000 . The computation is not feasible for the sliding-window approach discussed above. Thus, we propose a two-stage approach. In the two-stage approach, we split all individuals into two sub-samples. In the first stage, by assuming that all individuals are genotyped at all SNPs, we use the first sub-sample to select R most promising SNP windows with the largest values of the LRT_PC statistic calculated via the first sub-sample. In the second stage, only the genotypes at SNPs within the R most promising windows are used. In this stage, we use the second sub-sample to assess P values for the R selected windows by permutations and claim significance by the false-discovery rate (FDR) correction in Benjamini and Hochberg [Because we do not know the distribution or asymptotic distribution of the test statistic LRT_PC, we need to use a permutation approach to estimate the Hochberg . For theR, is 1000; the sample size of the first sub-sample is 15% of the total sample (15% cases and 15% controls). In the first stage, the number of PCs used in the LRT_PC test in each window is 5, i.e., we do not perform PC analysis. In the second-stage, the number of PCs used in the LRT_PC test in each window, K, is decided by the fact that the first K PCs can explain 85% of the total variability.To analyze the data set of GAW16 Problem 1 using LRT_PC based two-stage sliding-window approach, we use the following settings: window size is 5; the number of windows selected in the first-stage, To choose the sample size of the first sub-sample, we did a power analysis based on a single-marker test similar to that of Wang et al. . Our resAs pointed by Skol et al. , our prop-values. In total, we discovered 212 significant windows by the FDR correction at a nominal level 0.05, among which 126 windows are on chromosome 6. Many of the 212 windows are overlapped, especially for the windows on chromosome 6. After merging the overlapped windows, there were 68 non-overlapped windows left. Among the 68 windows, 26 of them were on chromosome 6. The 26 windows on chromosome 6 were in a region  in high LD with HLA-DRB1, a factor known to have a strong association with RA. The details of these non-overlapped windows (except those on chromosome 6) are summarized in Table We applied the proposed two-stage sliding-window approach to analyze the RA data set from GAW16 Problem 1. After removing duplicated and contaminated samples, this data set contained genotypes at 531,689 SNPs on chromosomes 1-22 for 868 cases and 1194 controls. The missing genotypes were imputed using the method of Browning and Browning [STAT 4" and thus supported the finding in Remmers et al. [FCRL3 on chromosome 1 [SDK2 on chromosome 17.For validation purposes, we used the SNP Search Engine to find genes which contain or are near to SNPs that were discovered. We found rs2357135 nesting at "2q32", which is near to gene "s et al. . In addiIn this article, we proposed a two-stage sliding-window approach and, in each window, our recently proposed LRT_PC test was applied to test the association between a window and a disease. Then, we applied the method to GAW16 Problem 1 to detect risk windows for RA. Different existing RA association studies discovered diverse susceptibility genes on all chromosomes except for MHC candidate genes on chromosome 6. Our analysis supported the findings of some RA susceptibility genes that have been identified to be associated with RA in the literature.p-values of top R promising windows (R = 1000 was used in this study). For a given R, the number of permutations must be large enough to obtain accurate p-values. Thus, the choice of R partially depends on computational capacity. Further efforts are needed to determine the optimal value of R.It is intractable to formulate the null distribution of the LRT_PC statistic and thus the permutation approach must be applied to evaluate the In this study, we used 5 PCs, i.e., we did not perform PC analysis in LRT_PC test for each window of size 5 in the first stage. We did not perform PC analysis (or use 5 PCs) in the first stage for two reasons. One is that we have to use the same number of PCs in different windows so that the values of the test statistic in different windows are comparable. The other is that in the first stage, we only use the test statistic to rank the SNP windows and the results are similar when using different numbers of PCs (results not shown). Another remaining question regarding the proposed method is how to choose the window size. Most often, researchers use windows of size 3. In the LRT_PC test, we use PC analysis to reduce the dimension, and thus we can use a larger window size .In this article, we proposed a two-stage sliding-window approach to detect the association between SNP windows and a disease status. Application to GAW16 Problem 1 data set illustrated its practical advantages. Our results supported the findings of several genes which were identified to be responsible for RA in the literature. We also discovered several additional SNP windows for follow-up studies.FDR: False-discovery rate; GAW16: Genetic Workshop Analysis 16; HLA: Human leukocyte antigen; LD: Linkage disequilibrium; LRT-PC: Likelihood ratio test-principal component; MHC: Major histocompatibility complex; PC: Principal component; RA: Rheumatoid arthritis; SNP: Single-nucleotide polymorphismThe authors declare that they have no competing interests.XW performed the statistical analysis and wrote the first draft of the manuscript. HQ participated in the study design and helped to draft the manuscript. QS contributed to the design of the study and to the manuscript preparation. All authors read and approved the final manuscript.


While genome-wide linkage studies have been successful in mapping variants underlying rare monogenic disorders, genome-wide association studies may be more appropriate for detecting common variants of modest effects that underlie common disorders. To this end, we were interested in determining whether genetic variants associated with a phenotype differed depending on whether they were within or outside of regions linked to the phenotype. In particular, we compared allele frequencies and effect sizes between associated single-nucleotide polymorphisms within and outside of linkage regions using the Genetic Analysis Workshop 15 Problem 1. We did not find any statistically significant differences between these two sets. However, our power calculations show that these results may be inconclusive. Linkage analyses have proven effective for the identification of many traits that display a simple Mendelian inheritance pattern. However, these studies have been less successful in deciphering complex traits, potentially due to differing distributions of allele frequencies and effect sizes underlying these diseases across different populations. The common-disease common-variant (CDCV) hypothesis posits that common traits are most likely due to common variants with small to modest effects on disease that may have escaped stringent selection pressure. Hence, linkage analysis can provide greater power to capture a rare variant with a large effect, whereas association studies may have greater power to detect common variants with small effects .It remains unclear, however, whether associated variants will differ depending on whether they are within or outside of regions exhibiting linkage to the phenotype of interest. To investigate this, we compared the distributions of allele frequencies and effect sizes between associated and linked single-nucleotide polymorphisms (SNPs) using data from the Genetic Analysis Workshop 15 (GAW15) Problem 1 and publicly available information from the HapMap project. In particular, we conducted genome-wide linkage and association analyses on a large number of quantitative gene expression phenotypes. Then we evaluated the allele frequencies and estimated effect sizes of SNPs that are linked and/or associated with expression levels.2-transformed expression values and 2882 SNP genotypes for 14 Centre d'Etude du Polymorphisme Humain Utah (CEPH) families consisting of 194 individuals [For genome-wide linkage analyses, we obtained data from the GAW 15 Problem 1 data set, which included 3554 logFor the genome-wide association analyses, we obtained genotype data based on Build 35 of the human genome from the HapMap Project website . 3,719,82-transformed expression phenotypes used for linkage analyses were also used for our association analyses. These were obtained for 57 unrelated founders of the 14 CEPH families from the NCBI Gene Expression Omnibus website [The same 3554 logLinkage was evaluated across a 1-cM interval grid for 3550 phenotypes (SOLAR failed to converge for four phenotypes). In light of the large number of phenotypes evaluated, we adjusted a standard LOD > 3.3 cutpoint for "significance"  for the p < 1.3 × 10-11), which corresponds to a Bonferroni correction across the large number of comparisons. Of course, this correction is likely to be conservative because some of the SNPs – as well as the phenotypes – are correlated. A SNP was deemed "associated" if it surpassed the threshold for any phenotype. Here we detected a total of 227 associated SNPs.Association was tested between 526,935 SNPs and the 3550 phenotypes. We initially specified a two-tailed significance threshold of Z = 6.66 , reflecting a scenario in which only one phenotype was tested, as shown in the bottom four rows of Table As shown in Table Using our most conservative significance criteria we would expect 0.05 false-positive associations. With the more liberal criteria, we expect 178  false-positive results. We observe 227 and 1200 associations, respectively, indicating that the majority of the observed associations (99.99% and 85.17%) are likely to be true associations. While choosing an even more liberal significance criteria could provide addition power to detect true associations, false-positive associations would become a greater proportion of the results. This would obscure any potential differences in allele frequencies and effect size as the false-positive results should reflect the underlying distribution of allele frequencies and effect sizes.-11. The more liberal threshold (α = 4.74 × 10-8) provides modest gains in power. In contrast, if expression data were available for all 210 unrelated individuals from HapMap, power of 0.8 or greater would exist for detecting more modest effects (>2.0) and also for larger effects with low allele frequencies.To investigate the statistical power available using this small sample of 57 independent subjects, we calculated power for a variety of allele frequencies and effect sizes and both significance criteria. Table Based on the CDCV hypothesis, we expected to see distinct differences in the distributions of allele frequencies and effect sizes between associated SNPs inside and outside regions of linkage. Our observation that allele frequencies did not differ between markers inside and outside linkage peaks was initially intriguing considering the CDCV hypothesis. However, because our data set included expression phenotypes of normal individuals, we should have an overrepresentation of common variants.To confirm whether effect size played an important role for marker alleles inside versus outside linkage regions, we compared the regression coefficients β between the two distributions as an estimate of effect size. Although the use of β as a measurement of effect size might be questionable for linear regression, we minimized the variability in the ranges of values among all the traits through the use of log-transformed values. Our analysis showed that there were slight differences in the median effect size between the associated and linked versus associated-only bins, although these differences were not statistically significant.An interesting phenomenon is the abundance of rare variants in the set of SNPs that were associated, which clearly deviates from the average MAF of 22% in the Illumina SNP panel, even though rare variants have low power  with small effects (<1.5) would require more than 1500 subjects.In summary, there are at least two possible explanations for our observations. First, that the lack of difference between SNPs inside and outside linkage regions, is a real phenomenon. This would suggest that association effects are the same regardless of whether one is within or outside of a linkage region . Another more compelling explanation is that with the GAW15 Problem 1 and publicly available data there was simply insufficient power to detect a difference between the distributions of either allele frequencies or effect sizes due to the small number of individuals available for association analyses.The author(s) declare that they have no competing interests.


The power of linkage analysis of a quantitative disease endophenotype was compared for the following family selection designs: 1) Random samples: randomly chosen nuclear families, 2) "coronary artery calcification (CAC)" samples: selection of each nuclear family through a proband with abnormally high levels of the simulated quantitative endophenotype, CAC, and (3) "MI" samples: selection of each nuclear family through a disease affected proband, in this case a proband who had been simulated to have a myocardial infarction (MI) event.We assessed the power to detect linkage to five loci  that were modeled as determinants of the simulated CAC levels. We did this using a Haseman-Elston regression-based linkage analysis of the adjusted CAC levels that considered each locus separately and then used a multiple regression extension of the Haseman-Elston method in which we considered the allele sharing at two true epistatic loci simultaneously and their interaction as possible factors related to the squared sibpair differences in adjusted CAC.p < 0.0001). We noted however, that the largest average τ3 and τ4 (mean Based on comparison of the mean square root of the LOD scores, there was no one sampling design that resulted in consistently greater power for these five loci. That is, we observed significant locus-by-sampling-design interaction ( It is well established that the selection of probands, or sibpairs, with extreme phenotypes in small nuclear families increases power over random sampling for detection of linkage with quantitative trait loci ,2. SibpaWe are usually interested in a quantitative trait because of its association with some disease. Sometimes the quantitative trait of interest is a clinical measure that more accurately captures the extent of the disease than the disease diagnosis itself, but often the quantitative trait is a risk factor for some complex disease, and hence a disease endophenotype. Thus, one would expect that a linkage analysis of a quantitative trait based on sibpairs in which there is at least one disease-affected individual would be more powerful than an analysis based on randomly selected sibpairs. Sung et al.  refers tIn this paper we compared three methods for sampling nuclear families for linkage analysis of a quantitative endophenotype. The three methods we considered were random selection of nuclear families, selection of nuclear families through probands simulated as having the complex disease, and selection of nuclear families through probands who had high values of the disease-associated quantitative endophenotype.τ1, τ2, τ3, τ4, and τ5), which had genotypes modeled to have direct effects on the simulated CAC values and five SNPs  on chromosome 5. Two pairs of these genes, τ1 with τ2 and τ3 with τ4, were modeled to have epistatic effects on CAC values, whereas τ5 was a major gene with an over-dominant allele for high CAC. In addition to these five genes, three covariates  values) also were modeled to affect CAC values. We considered the M1-M5 SNPs because these SNPs 1) were not involved in the simulation of CAC or any of the CAC related traits ), 2) were in Hardy-Weinberg equilibrium, and 3) had minor allele frequencies greater than 0.1.We analyzed the Problem 3 data provided by the Genetic Analysis Workshop 16. The genotype and pedigree structure of the individuals in the data set were provided by the Framingham Heart Study. However, all phenotypic information was simulated based on the models described in Kraja et al. . The quabVAR; VAR = CHOL, HDL, and AGE) were then used to obtain adjusted CAC values at each of the three time points for each individual. The procedures for adjusting CAC values at time t were conducted by replicate as follows:We first regressed the nonzero CAC values obtained at age less than 60 on age (AGE), CHOL levels, and HDL levels using all of the 6,476 subjects in each of the 200 simulations. The regression coefficients obtained for each given simulation  refers to the value for VAR = CAC, HDL, CHOL, and AGE recorded at visit t. Then we averaged the three CAC adjusted values (CA60t) to get the average adjusted CAC values (CA60), which were the values we used in the linkage analyses through out this paper.Here, the notation CA60) values of no less than 3,240 . Parental genotypes are also obtained for the allele sharing identity-by-decent (IBD) calculation.In each case we only sampled unrelated nuclear families for which there was marker data available on both the parents and the siblings of the probands and for which there was simulated CAC data for every sibling. The families denoted as "Random" were randomly chosen. The disease-ascertained families (MI) were obtained by first selecting the disease affected probands, i.e., individuals simulated as having MI events and then including all their siblings. The quantitative-trait-ascertained families (CAC) were obtained similarly to the disease-ascertained families except the probands were ascertained for having adjusted CAC  sibpairs from an average of 284 families (SD = 9.7) in each of the 50 combined MI samples, on average 698 (SD = 85.0) sibpairs from an average of 362 families (SD = 46.4) in each combined CAC sample, and 688 sibpairs in 360 families in each combined Random sample.In each of the 200 replicates, there were on average about 71.0 unrelated nuclear families (SD = 5.8) with at least one individual having an MI event, and on average about unrelated 90.6 nuclear families (SD = 26.8) with at least one individual having CAC value over 3240. We randomly selected 90 unrelated nuclear families from each simulation so as to have approximately the same number of sibpairs as in the selected samples. We considered each nuclear family with Y = α + βgIg. Here, Y denotes the squared difference in CA60 in each sibpair and Ig denotes the number of alleles shared IBD at the SNP g . The Merlin software was used to extract the IBD values of all of the sibpairs at these ten SNPs.The Haseman-Elston regression-based method  was implCA60 in sibpairs from the same families, we selected (s-1) sibpairs in each family with s offspring by pairing the proband with each remaining offspring. In the randomly chosen nuclear families the probands are defined as the individuals having the smallest subject ID numbers among the offspring in the families.In order to reduce the correlation between squared differences in Y = α + βiIi +βj Ij + βijIi Ij. Here, Y denotes the squared difference in CA60 and Ii and Ij denote the IBD at the SNP i and SNP j respectively . This extension has been proposed in the past to detect several quantitative trait loci and epistasis [We then did multiple regression extension of the Haseman-Elston method, which we refer to in this paper as the multivariable analysis. Specifically, we considered the regression equation pistasis .βi = 0, and under the alternative hypothesis, βi < 0. The usual regression t statistic (estimated coefficient divided by its estimated standard error) was used to test this hypothesis. These t values were converted to LOD scores by setting LOD = t-value < 0 and LOD = 0 if t-value ≥ 0.Under the null hypothesis of no linkage, the regression coefficients equal 0, i.e., The power of the sampling approaches was evaluated by comparing the average The mean We obtained a null distribution of the Z|, where Z has standard normal distribution). The significance level associated with a We also can derive the asymptotic mean value of We applied two-way ANOVA to determine whether sampling methods were a significant factor and whether the effects of sampling method are the same across loci. Upon observing a significant interaction, the averages of the mean square-root-transformed LODs were compared at each locus using the Scheffe test.In Table τ1, τ3, and τ4, 2) higher average τ2, τ5, and the τ1 τ2 interaction, and 3) the highest average τ3 τ4 interaction. Because the genetic variance is determined by the joint distribution of the genotypes as well as the effects of the genotypes, these values apply only to the Random samples.We also included in this table the values of the genetic variance attributable to each locus and each interaction. These were calculated from the information on the population allele frequencies and the mean effects of the genetic components given in the Genetic Analysis Workshop 16 Problem 3 answer . Accordiτ1τ2 epistasis, all of our observed average τ3τ4 epistasis.We have denoted those findings which under the alternative are above (+) or below (-) our calculated 95% prediction intervals for SNPs unrelated to CAC for the given sampling method. The values without any sign are on the 95% prediction interval under the null hypothesis. We noted that, with the exception of the τ1, τ2, τ3, τ4, and τ5 and the τ1τ2, τ3τ4 interactions. The findings upon inclusion of all terms were closer to what we would expect in light of the genetic variance attributable to the individual genotypes. That is, the highest observed mean τ3τ4 interaction , and τ4 .We did not show here the results of another multivariable analysis that included all the main effects of τ3 and locus τ4 on the adjusted CAC. These linkage methodologies all are based on the detection of a relationship between phenotype differences in sibpairs and genotype differences in sibpairs. Thus a sample of only sibpairs with large phenotype differences, i.e., discordant sibpairs, would not be appropriate for these analyses.We chose to focus on regression-based linkage analyses because they would be computationally feasible for a genome-wide analysis. Furthermore, the extensions to multiple regression allows for us to effectively consider situations where there is epistasis. Interestingly, the multiple-regression linkage analysis approach showed fairly good power to detect the complete epistasis between locus τ5 locus, where it is 0.2, and hence random sampling results in a substantial proportion (0.4-0.75) of families with at least one heterozygous parent. This may account for our observation in detecting epistasis that the selected samples (MI and CAC) resulted in greater power than the random samples.We expected that both the selection based on quantitative trait (CAC) and the selection based on disease (MI) would show an increase in power over random sampling. However, no one sampling method was consistently the best or the worst. The purpose of selected sampling is to increase the proportion of families with at least one parent heterozygous for the disease-predisposing allele. The allele frequencies of the disease-predisposing allele are 0.5 for all of these loci except the A very surprising result was our observation of significantly higher than expected average It was reassuring to observe that the analyses based on MI sibpairs had the same or greater power as the analyses based on the CAC sibpairs. If abnormal levels of the quantitative trait in the absence of the disease were not harmful to one's health, it might be difficult to ascertain individuals with abnormal values. However, if the disease is associated with the high values of this trait, then in identifying a sample of individuals with the disease, we would automatically have a large proportion of individuals with the abnormal values.τ5, the SNP with the highest variance between genotypes , was not more powerful than that for the other SNPs, which had much lower variance between genotype. On the other hand, when we did a multivariable regression of squared differences on IBD alleles at each locus and included the interaction terms for the two pairs of epistatic SNPs, the magnitudes of the average τ5, and lower values for values for the τ1, τ3, and τ4. These findings may indicate that there may be some association between the number of alleles IBD at τ5 with the number of alleles IBD at these other CAC-determining SNPs or the need to follow up significant single-SNP linkage findings with multivariable analysis.We were quite surprised that the univariate linkage analyses of AASP: Asymmetrically ascertained sibling pairs; CAC: Coronary artery calcification; CHOL: Cholesterol; HDL: High-density lipoprotein; IBD: Identity-by-decent; MI: Myocardial infarction; SNP: Single-nucleotide polymorphism.The authors declare that they have no competing interests.CH developed the methodology for the study, performed the genetic and statistical analyses, and drafted the manuscript. KL, RSF, S-WC, SHC, and TS performed the data reduction and helped to perform the genetic and statistical analyses. KL and SYS managed the databases and developed a file with the relevant parameters for the analysis. NRM and SJF conceived of the study, participated in its design and coordination, and helped to draft the manuscript. All authors read and approved the final manuscript.


This simulation-based report compares the performance of five methods of association analysis in the presence of linkage using extended sibships: the Family-Based Association Test (FBAT), Empirical Variance FBAT (EV-FBAT), Conditional Logistic Regression (CLR), Robust CLR (R-CLR) and Sibship Disequilibrium Test (SDT). The two tests accounting for residual familial correlation (EV-FBAT and R-CLR) and the model-free SDT showed correct test size in all simulated designs, while FBAT and CLR were only valid for small effect sizes. SDT had the lowest power, while CLR had the highest power, generally similar to FBAT and the robust variance analogues. The power of all model-dependent tests dropped when the model was misspecified, although often not substantially. Estimates of genetic effect with CLR and R-CLR were unbiased when the disease locus was analysed but biased when a nearby marker was analysed. This study demonstrates that the genetic effect does not need to be extreme to invalidate tests that ignore familial correlation and confirms that analogous methods using robust variance estimation provide a valid alternative at little cost to power. Overall R-CLR is the best-performing method among these alternatives for the analysis of extended sibship data. This method can be applied to both dichotomous and quantitative phenotypes in a variety of family types regardless of the structure of missing data, and multiple relatives are used while accounting for correlation in allele transmission among them  in the absence of parental data. Because the true genetic model is generally unknown, it may be preferable to use a method that does not make any assumptions about the mode of inheritance. For this reason, we further compare the power of all these model-based tests  under correct and incorrect models with the Sibship Disequilibrium Test SDT, , a modela priori as discordant sibships with missing parents, with the common situation of late onset diseases in mind. A mixture of sibship sizes are considered with variable numbers of affected and unaffected siblings. The family structures simulated are based on those found in a cardiovascular disease candidate-gene study  robustness to model misspecification is assessed by calculating power assuming a dominant and a recessive model with data simulated using an additive model. Also, since there is generally no guarantee that the polymorphism under investigation is the actual disease locus, situations are considered in power estimation where they coincide and are maximally associated (D’ = 1.0) and where they are at a certain  distance from each other and linkage disequilibrium (LD) between them is weaker (D’ = 0.5). As CLR and R-CLR allow estimation of the strength of genetic effect, the bias of this estimate is evaluated when the tested locus is the disease locus and when it is a nearby marker. ne study .2= 0.25). This level of LD at this distance was chosen because an average D’ of 0.50 has been observed at ∼50 kb in 19 randomly selected regions across the human genome , but it hits 99% (97% for SDT) in the strongest model analysed. In designs where GOR = 2.67, valid tests EV-FBAT and R-RCLR appear to remain as powerful as FBAT and CLR, indicating that there is little cost to power from using robust variance even for strong locus effects. However some drop of power would be expected when robust variance is used, and this is more apparent when more stringent significance levels are applied, moving the power away from 100%. As can be seen in vs. robust variance). In all the designs considered, CLR and R-CLR show an unbiased estimate of GOR and good CI coverage as long as the analysed marker is the disease locus  assuming dominant and recessive models. Under the dominant model, all four methods remain equally powerful . Power ithe genetic effect needs to be quite extreme before residual familial correlation due to linkage led to false positive inference’ using CLR. In our study, we found that CLR is not valid (level 0.001) for a GOR of 2.67 which is far less extreme than 20. Our study demonstrates that familial correlation is not only influenced by the strength of the genetic effect, but also, maybe more critically, by the number of affected siblings within a family. Robust variance should therefore be recommended in the analysis of large sibships even when a modest genetic effect is suspected.Family-based association methods were originally designed to test for the presence of linkage or association. While testing this composite null hypothesis can be interesting in some instances, many candidate gene fine-mapping studies aim to search for association in a region where linkage has already been found or where it can be reasonably assumed. Therefore, the methods that can test association in families while accounting for linkage are valuable tools. In this study, we compare the performances of five methods of family-based association analysis: FBAT, EV-FBAT, CLR, R-CLR and SDT. Our study shows that in the case of low genetic risk all five tests have a correct type 1 error rate . HoweverOur study of power confirms the results of All the tests compared under incorrect genetic model specification have shown similar results: with the additive model simulated, a small drop in power when the dominant model is assumed and a sharper power decrease with the recessive model . UnsurprCLR and R-CLR provide precise estimates of the GOR when the marker is the disease locus. However, as expected, when the marker and the disease loci are distinct and are not maximally associated, the estimate of GOR is always biased and the 95% CI coverage can be very poor. The stronger the true genetic effect and the commoner the disease allele frequency, the higher the bias. Our study has some limitations. First, this is not a comprehensive evaluation of all existing family-based association tests. There are now many methods, most of which were optimised for particular data configurations and are not necessarily perfectly comparable. We chose to focus on one general statistical approach (CLR) and one specialised genetic method (FBAT) both of which are very widely used for sibship data. Second, a comprehensive comparison would necessitate a larger spectrum of family structures, sample sizes and disease models , not all of which would be feasible to consider in one study. We chose instead to concentrate on one large mixture of family structures as observed in an actual study of affected and unaffected siblings with cardiovascular disease . AlthougIn conclusion, our simulations show that the genetic effect does not need to be extreme to invalidate tests that use standard variance estimators (CLR and FBAT). For more complex pedigrees EV-FBAT has clear advantages, but, based on power, validity and robustness to model misspecification, R-CLR provides a powerful suitable alternative for the analysis of extended sibships.


In all of these fields, inference can be thwarted by failure to quantify and account for data errors, and kinship inference in particular can benefit from separating errors into two distinct classes: allelic dropout and false alleles. Pedant is MS Windows software for estimating locus-specific maximum likelihood rates of these two classes of error. Estimation is based on comparison of duplicate error-prone genotypes: neither reference genotypes nor pedigree data are required. Other functions include: plotting of error rate estimates and confidence intervals; simulations for performing power analysis and for testing the robustness of error rate estimates to violation of the underlying assumptions; and estimation of expected heterozygosity, which is a required input. The program, documentation and source code are available from  Microsatellite genotype data underpin a wide diversity of genetic studies, in fields including individual identification in forensics, mapping disease genes, kinship inference and population genetics. All but the smallest microsatellite data sets will contain genotyping errors, which can be substantially misleading when undetected. Awareness of the implications of genotyping error has increased greatly in recent years, and there is an emerging consensus that error rates should be estimated and reported, particularly when performing error-sensitive analyses such as parentage analysis or individual identification . AlthougAB being genotyped twice as AA). Secondly, many analyses benefit from breaking down single error rates into two distinct classes of error—allelic dropout and false alleles  counting Mendelian inconsistencies in parent—offspring pairs; (2) comparing error-prone genotypes with high-quality reference samples; and (3) counting mismatches between duplicated genotypes. The first two approaches will generally yield more reliable estimates than the third, but may not be feasible because pedigree data and reference samples will often be unavailable. The third option of re-genotyping a random subset of samples at all loci is widely recommended  and will alleles —which is1 is the probability of an allele dropping out, and ɛ2 is its probability of being mis-typed as another allele , and only two possible fathers (genotypes CD and CC). Neither candidate father matches the offspring, so an error must be invoked, but because we cannot say in which candidate the error is more likely to have occurred, the data are uninformative. However, suppose we can break down the total error probability into ɛ1 = 5% for allelic dropout and ɛ2 = 2% for false alleles. We will then have greater confidence in genotypes AB and CD than in CC, because only CC can have been affected by allelic dropout (assuming only one error per genotype), and attributing AB or CD to error would require us to invoke a less likely class of error. Thus, when separate error rates are known, the data become more informative: the candidate with genotype CC is the more likely father. This principle has been successfully applied to pedigree reconstruction  or a false allele in an underlying AA (giving AB). Instead, Pedant counts different types of matching and mismatching duplicate genotypes  and searches for the pair of error rates that maximises the likelihood of the observed counts  is known. However, as Ho will be biased by allelic dropouts and false alleles, Pedant uses instead expected heterozygosity, He, which will equal Ho only when the study population is in Hardy Weinberg equilibrium (HWE). Deviations from HWE, such as a substantial heterozygote deficit (FIS > 0.1), that cannot be corrected for using prior knowledge will lead to biased estimates  can lead to underestimation of both ɛ1 and ɛ2. Nevertheless, testing of Pedant on real and simulated data suggests that the method is robust to modest deviations from its underlying assumptions , and when these conditions do not apply sample size should be increased to compensate. If average cross-locus error rate estimates are sufficient, all loci can be pooled as a single locus, so with 10 loci perhaps only 25 to 50 duplicate genotypes per locus might be necessary. On the other hand, if locus-specific estimates are required then at least 100 repeats per locus might be required. These figures are very rough guidelines only. Specific scenarios can be explored using Pedant’s simulation function, which allows users to simulate the estimation of error rates from multiple data sets while varying parameters . For each error class the individual estimates and their mean and standard deviation are plotted, allowing rapid visual assessment of estimation accuracy under a variety of parameter combinations. Five hundred simulated data sets can be analysed in about 30 seconds.The second step in using Pedant is to decide how many genotypes to duplicate at each locus. This will depend mainly on the degree of accuracy required by the downstream analysis, but approximate estimates will generally be adequate . The mosHe estimates for each locus. To minimise the effect of sampling error, He should be estimated from the whole data set, not just the subset that has been duplicated. He (and its standard error) can be calculated in Pedant.When the data have been deemed suitable for analysis using Pedant and sample size has been decided, samples should be selected at random and repeat-genotyped blind at all loci. Pedant accepts genotypes in tab-delimited text format, which is easy to create from a spreadsheet. Alternatively, a Pedant input file can be converted from genepop format using an R script included in the download. The input file must contain When the input file has been loaded, Pedant locates the maximum likelihood (ML) estimates, of ɛ1 and ɛ2, which takes about one second per locus, and outputs the estimates together with 95% confidence intervals calculated using the relative log-likelihood function. Estimates and confidence regions can also be plotted for individual loci . Details1 and ɛ2 across markers is available in MasterBayes, an R package for Bayesian pedigree reconstruction , their underlying error models are similar and they would be expected to reach similar estimates. We compared the two programs using two simulated data sets: low error  and high error . The low rates are typical of highly automated genotyping while the higher rates represent smaller, more error-prone studies . Comparison of the mean error estimates across 100 loci (2 = 0.005), with MasterBayes overestimating  and Pedant underestimating . Overall Pedant recovered the population error rates more accurately, although it should be noted that the accuracy of both programs will vary with other parameters such as He and sample size. For the small sample sizes that are likely to be feasible, by far the greatest source of estimation error will be sampling error (as reflected by the width of the interquartile range), which is beyond the control of either method. Given that the two programs produce similar results, the choice of which to use should be guided by more pragmatic considerations. Pedant is simpler to use, in that it has a user-friendly interface  are available from