Over the past decade many linkage studies have defined chromosomal intervals containing polymorphisms that modulate a variety of traits. Many phenotypes are now associated with enough mapping data that meta-analysis could help refine locations of known QTLs and detect many novel QTLs.Hipp1a and 37% for Hipp9a. We first generate locus-wise permuted P-values for association with the phenotype from multiple maps, which can be done using a permutation method appropriate to each population. These results are then assigned to defined physical positions by interpolation between markers with known physical and genetic positions. We then use Fisher's combination test to combine position-by-position probabilities among experiments. Finally, we calculate genome-wide combined P-values by generating locus-specific P-values for each permuted map for each experiment. These permuted maps are then sampled with replacement and combined. The distribution of best locus-specific P-values for each combined map is the null distribution of genome-wide adjusted P-values.We describe a simple approach to combining QTL mapping results for multiple studies and demonstrate its utility using two hippocampus weight loci. Using data taken from two populations, a recombinant inbred strain set and an advanced intercross population we demonstrate considerable improvements in significance and resolution for both loci. 1-LOD support intervals were improved 51% for Our approach is applicable to a wide variety of segregating and non-segregating mapping populations, facilitates rapid refinement of physical QTL position, is complementary to other QTL fine mapping methods, and provides an appropriate genome-wide criterion of significance for combined mapping results. The majority of traits that show variation based on genetic influences are affected by multiple genes of small effect as well as by environment. When compelling candidates for direct investigation are not available, QTL mapping provides an effective approach to localizing regions of the genome that are likely to mediate genetic variation in the phenotype. Mapping a QTL to an interval of 20–60 Mb has become a relatively routine matter for traits with at least moderate heritability, but narrowing the interval to a small region that includes only a few candidate genes (1–5 Mb at most) is still a highly challenging task.A variety of methods for accomplishing the task of narrowing a QTL interval have been proposed Our method calculates locus-specific P-values using the distribution of alleles at each locus. For large populations of genetically independent animals, the negative log of these locus-specific P-values is very similar to the more typically reported LOD scores, but for smaller populations like recombinant inbred strains, and non-independent populations such as advanced intercross lines, and especially for populations with missing data, they are an important innovation. For these populations, converting to locus-specific P-values is more informative and allows us to apply Fisher's combination test to combination of QTL mapping results.Since each QTL mapping effort originates from an independently generated population, the pattern of alleles inherited in one population is independent of the pattern of alleles inherited in another population. Therefore under the null hypothesis of no linkage, locus-specific P-values for any arbitrary point on the genome are strictly independent between data sets. Given the independence of our data sets, we chose to address the problem of combining multiple testing results by using Fisher's combination test.Since Fisher's combination test operates on P-values, our approach first defines locus-specific P-values in the original and permuted QTL maps, then combines QTL maps on a point-wise basis using Fisher's combination test. We then convert sample permuted QTL maps from each data set to locus-specific P-values, combine them, and order the best genome-wide combined P-values from these samples to define the null distribution of genome-wide adjusted P-values.Previous efforts to meta-analyze different mapping populations have included taking the best P-value for each QTL interval and combining these values using Fisher's combination test Province A more recent paper by Li and colleagues Our simple method also has the advantage of not requiring adjustment for use with crosses that represent different numbers of effective tests across the genome. For instance, the number of independent tests represented by an RI strain set will be greater than the number represented by a standard F2, since the genetic length of the RI genome is four times that of the F2 genome. no locus should be associated with a real genetic effect, this should be the case among loci as well, and the distribution of P-values for each permutation should also be constant and range from 0 to 1. This is the case in a variety of tested permutations  at tested markers. Interpolation of P-values between markers does seem to slightly reduce the number of P-values observed at the very low and high ends of the distribution, however.Under the null hypothesis of no genetic effect at a locus, the distribution of P-values should be constant with a range of 0 to 1 In large data sets with independent observations—most F2 populations, for instance—the distribution of P-values under the null hypothesis of no linkage is approximately the same for each analyzed locus in the genome. The equivalent distribution of P-values by locus under the null hypothesis means that any two positions in the genome are equally likely to be the best P-value in the genome in a given permutation of an original data set. This assumption does not always hold in small data sets such as RI populations and populations with non-independent observations such as AILs.  For consfEven when using Sen and Churchill's imputation Hipp1a was originally reported as significant in the BXD strain set Hipp1a the 1-LOD support interval  is 34 Mb in the BXD strains, 17.5 Mb for the AIL, and the composite map is slightly better at 16.5 Mb, an average 51% improvement over the individual maps. For Hipp9a the interval was 24.5 Mb for the BXDs, 21.5 Mb for the AILs, and only 14.5 Mb for the composite map–an average improvement of 37% over the individual mapping efforts.As an example of the composite mapping method, we mapped bilateral hippocampus weight in two populations, each of which has already been individually reported We have developed and implemented a simple method for combining QTL mapping results from multiple QTL experiments. The ready availability of dense marker maps and physical positions as well as genetic positions for markers facilitates incorporation of positional information. This method can therefore be used not only to report combined probability of the existence of a QTL locus more accurately than simply combining the best P-values for multiple mapping approaches We have demonstrated that notable improvements in genome-wide significance and QTL confidence interval are possible using our method by using the example of two hippocampus weight loci. With only two mapping populations for this phenotype, we saw improvements of 37% to 51%, in 1-LOD confidence intervals. The extensible nature of the method means that any number of available mapping populations can be added to further improve the results.combined = 0.0001, which is very likely significant genome-wide. Results from small mapping populations generated using the same parental strains can therefore profitably be combined using this method. Combining suggestive results (P = 0.001) with small additional results (P = 0.01) also generates much improved composite results. (Pcombined = 0.00012)In addition, combining loci that are barely significant or narrowly miss the criteria for significance in multiple populations can clearly lead to strong observations of new loci or improved confidence in previously known loci. For instance, combining mapping results at a locus significant at a point-wise P = 0.05 for seven mapping populations or P = 0.01 for three mapping populations results in a PWhile we have concentrated on multiple crosses using the same progenitor strains, it would be simple to extend this method to include crosses in other strains or, for that matter, other phenotypes measured in independent crosses. The implicit assumption in these situations is that measurement of an equivalent trait is occurring despite the cross or phenotype difference. In the case of multiple strains, this means the allele difference causing the QTL occurs in the same gene between the strains crossed in each population. Populations such as the BXD, BXA/AXB, CXB, and BXH RI strain sets, when the common allele (B6) may differ from the other strains, could fall in this category. In the case of multiple phenotypes  the assumption is that the phenotypes are measuring the effect of the same polymorphism between progenitor strains for the cross.Genetic positions are necessary for generating QTL maps using methods such as interval mapping Assigning a P-value to a physical position requires interpolation of physical positions for markers  with unknown physical positions. It also requires interpolation between these markers and the regular, set physical positions that are ultimately reported. For dense marker maps such as those typical of RI strains, the assumption that intermediate physical position can be linearly interpolated from genetic positions and flanking physical positions is reasonable. Some caution may be appropriate, however, when interpolating physical positions for widely spaced markers.2 time with respect to number of permutations. When converting LODs to P-values, however, under the null hypothesis of no linkage, approximately half the genome will be associated with LOD = 0  which should equate to P≅0.72 Since locus-specific P-values are not required in the case of sufficiently large RI sets, intercrosses (F2), and backcrosses (N2), the process of explicitly computing QTL maps for each data set and performing the permutation described could be approximated by deriving P-values for each position in some more generic manner, for example from the LOD score, and combining these values as described to generate composite QTL maps and genome-wide thresholds. This is particularly useful when a simple cross with highly significant loci is being considered since the software used to sort P-values (OutParser.py) runs in approximately NWhen the distribution of permuted P-values across the genome is uniform, combination of multiple P-values for each locus should result in a uniform combined P-value distribution across the genome. We verified this empirically using a simple simulation, sampling and combining multiple observations from uniform distributions over 1000 permutations. Since in the ideal case each combined permuted QTL map will have a P-value distribution equivalent to a simple permuted QTL map, existing analytical While any number of independent results can be combined using our method, it is problematic to include mapping results from the same reference population even when phenotyping was entirely independent. For instance, directly combining more than one QTL map from the same RI or congenic population is problematic. Instead it might be practical to combine the data gathered on the population as appropriate and generate a single QTL map from the combined data. This map could then be combined with any other independent mapping experiments using our method.This method can be extended to incorporate data from a variety of data sources, including congenic and consomic data. For a polygenic trait, a test of whether a modifying locus from the introgressed parent is present in a given congenic segment addresses only the association of that region and does not contain information about the rest of the genome.One simple approximate solution is to assume that the LOD = 0 for the remainder of the genome and apply Province's method (2001) to convert to P ≅ 0.72. This is a highly conservative assumption as our actual expectation is that there will be linkage in other parts of the genome as well for a complex trait. Fortunately, Fisher's combination test does not penalize too heavily for failure to observe association. P values for permutations could also be simulated by assigning a P-value, evenly distributed between 0 and 1, to each point outside the congenic interval. In situations where multiple congenics exist, combining the congenic interval results as a single data source might also be a reasonable approach.http://www.nervenet.org/papers/CombineQTL.html or archived at www.genenetwork.org.If meta-analysis of QTLs is limited to simple combination of maximum significance values for a QTL interval, the common practice of reporting QTL significance in terms of this maximum and of providing a figure representing the QTL interval is sufficient. For position specific analyses with joint determination of genome-wide significance thresholds, however, it is important to have access to the original data as well as the specific parameters used to perform the data analysis. Unfortunately, particularly in the older QTL literature, public access to the primary data was seldom a requirement of publication. The authors would strongly advocate that journals require public access to such data both to facilitate transparency and reproduction of results and to facilitate more sophisticated meta-analyses. All data used in generating the results for this paper is available at This method is a simple, easily extensible means of combining QTL mapping results from a wide variety of mapping efforts, and complements other fine mapping methods. The major advantages of this method are its simplicity, incorporation of physical position data and locus-specific P-values, and empirically estimated genome-wide P-value thresholds.The first step in generating a composite QTL map is to assign P-values to regular physical positions on the genome. This is done using permuted QTL maps processed to determine locus-specific P-values as described below. The details of the permutation required to generate the permuted maps are assumed to have been worked out before data is combined.We use locus-specific P-values because in certain data sources such as advanced intercrosses and small RI sets, the correspondence between the likelihood typically reported in mapping output  is the observed LOD at locus j in permutation replicate i. The locus-specific P-value for locus j is P(j) = proportion{ Lperm∃Lobs(j)}. This is the proportion of the permutation replicates that have a LOD score greater than or equal to the observed LOD score at locus j.Once all of the permuted maps are generated, we assign locus-specific p-values to regularly spaced physical positions on each chromosome for the original data. In order to derive locus-specific P-values from raw LOD scores we let be the observed LOD at locus j. For each permutation, LP-values at regular intervals were based on the known physical and genetic positions of markers and their P-values as computed above. First we linearly interpolated missing physical positions using flanking genetic positions for the nearest markers with complete information  After we obtained a complete set of physical positions, we linearly interpolated P values at regular intervals on a grid of physical positions, allowing values from the final marker to the end of the chromosome to equal those at the final marker.For sparsely genotyped data sets it is more accurate to linearly interpolate using LOD scores based on an interval map and derive locus-specific P-values from the interpolated LOD scores, though this method is slower than the one described above. As genotype density increases the order of these steps has less effect. We tested the effect of this difference for our BXD RI data at 300 markers and the average percent difference in P-value between methods was only 12%. For all model data sets except our F2 data set, which is sparsely genotyped, we therefore calculated locus-specific P-values first. We provide an implementation for both methods.For calculating the LOD score equivalent to a locus-specific P = 0.05 (referred to as 95% LOD) in For composite mapping of hippocampus weight QTLs shown in combined(j).At the end of the process outlined above, each data source will be represented by a set of locus-specific P-values associated with regular and defined physical positions. For each of these positions, j, there will be k associated P-values, one from each data source. Since by Fisher's combination test −2 Σ ln P for all k data sources at locus j follows a chi-squared distribution with 2k degrees of freedom in the case of the null hypothesis, (no association between phenotype and genotype) we can easily associate each position with a composite locus-wise P-value, Pcombined(j), but it is also important to have a genome-wide threshold for error control at a specified genome-wide P-value. Genome-wide LOD score thresholds for QTL experiments are typically generated by permuting genotype or phenotype, re-running the mapping phase of the experiment for a large number of permutations The combined map gives us a locus-specific combined P-value for any given locus, Pfixed, for which locus-specific P-values are currently being calculated. We will term the LOD score for ifixed at locus j L and will designate the permuted LOD scores for all permutations except ifixed as Lperm. This process is an excellent approximation of the locus-specific P-value that would result from generating a set of permutations of each ifixed, assuming that Lperm  has a distribution equivalent to Lperm, which should be true for large i.The approach here is similar except that we are first converting LOD scores to P-values for each permutation i. This is done as described above except that observed LOD score at locus j, is the value of the LOD score for a particular permutation in i, designated iperm, combined(j), for each corresponding locus between sampled permuted maps as described above using Fisher's combination test.In other words, for each permutation in i, the locus-specific P-value at j isperm, ombined(j) value from each combined map. This permutation is repeated to create an ordered list of best P-values, Pbest. For a given Pcombined(j) value in the original data set, the genome-wide adjusted P-value, Padjusted, for the combined data isth percentile value for Pbest (genome-wide adjusted P = 0.05).We then record the minimum Phttp://www.nervenet.org/papers/CombineQTL.html. For the customized analyses above, we wrote scripts using Python 2.4 as well as simple R scripts to automate use of R/qtl. Further integration with R/qtl as well as other QTL mapping programs should be relatively straightforward, providing that automation of the mapping functionality itself is achievable as it is with R/qtl. Permutations generated for advanced intercross lines were created using a custom python script designed for the purpose, the operation of which is described elsewhere SimplePerm.py, is included.All software described is available at OutParser.py, and OutParserLI.py to parse the mapping output files from R/qtl and to generate a map of locus-specific P-values at regular, user defined intervals on a physical scale. These versions differ only in that OutParser.py calculates locus-specific P-values at markers then interpolates to regular positions, while OutParserLI.py  reverses the order of these steps. OutParserLI.py is somewhat slower but preferable for sparsely genotyped data sets. These scripts require a data file, markerphyspos.txt in the example files, which contains genetic positions for each marker  in the R/qtl output file as well as physical positions for as many markers as possible. Because the locus-specific P-values will often be used in combination with a similar set of values, defined at the same intervals, in another population (see description of CombineMaps.py below), the P values at the ends of each chromosome must be handled carefully.  The assumption we have made is to repeat the most proximal actual marker value to the most proximal end of a given chromosome and likewise to repeat the most distal value to the distal end. Further, each chromosome is defined as 200 Mb in length  to ensure that values from each new data set can be easily accommodated and to eliminate the need for a separate file specifying length of each chromosome. This is also a convenient convention for plotting composite maps as the “unused” regions can be easily masked and graphs from multiple data sources, which may differ slightly in chromosome length and markers, can easily be lined up and overlaid.We wrote a set of two Python scripts, CombineMaps.py combines QTL maps of locus-specific P-values from different data sources. In order to generate combined maps of original data the program simply applies Fisher's combination test to the locus-specific P-values at equivalent physical positions for each defined position in the genome. The program also implements the method described above for finding genome-wide adjusted P-values. It does this by sampling with replacement from the set of permuted QTL maps for each data source. These maps are combined as described above and the best combined locus-specific P-value is recorded. This list of best P-values can be sorted (easily done in Excel or in Unix using “sort –n filename>sortedfilename”) to allow genome-wide interpretation of locus-specific P-values.


CETP) gene remained significant even after correcting for multiple testing in both the univariate (p < 5 × 10-7) and multivariate (p < 5 × 10-9) association analysis. Three genes met significance for multiple traits after correction for multiple testing in the univariate analysis, while five genes remained significant in the multivariate association. We conclude that while both univariate and multivariate family-based association analysis can identify genes of interest, our multivariate approach is less affected by multiple testing correction and yields more significant results.Metabolic syndrome, by definition, is the manifestation of multiple, correlated metabolic impairments. It is known to have both strong environmental and genetic contributions. However, isolating genetic variants predisposing to such a complex trait has limitations. Using pedigree data, when available, may well lead to increased ability to detect variants associated with such complex traits. The ability to incorporate multiple correlated traits into a joint analysis may also allow increased detection of associated genes. Therefore, to demonstrate the utility of both univariate and multivariate family-based association analysis and to identify possible genetic variants associated with metabolic syndrome, we performed a scan of the Affymetrix 50 k Human Gene Panel data using 1) each of the traits comprising metabolic syndrome: triglycerides, high-density lipoprotein, systolic blood pressure, diastolic blood pressure, blood glucose, and body mass index, and 2) a composite trait including all of the above, jointly. Two single-nucleotide polymorphisms within the cholesterol ester transfer protein ( Although various organizations have used different criteria to define metabolic syndrome (MetSyn), it is generally agreed that MetSyn consists of a combination of impaired glucose metabolism, insulin resistance, hypertension, obesity, and dyslipidemia that increases the risk of poor cardiovascular outcomes . ResearcHere we aim to establish the relationship between biomarker data for the components of MetSyn based on the World Health Organization (WHO) definition and single-nucleotide polymorphisms (SNPs) within the 50 k SNP candidate gene panel of the offspring cohort of the Framingham Heart Study (FHS), using full-pedigree information. We will compare the results of our family-based association analyses of MetSyn as a multivariate phenotype to results that consider each component of MetSyn as a univariate trait while accounting for the familial clustering of data in both analysis methods.Before and during this study, all authors signed and complied with the Data Use Agreement for the Framingham Heart Study data and the Case Western Reserve University IRB. Due to large amounts of missing data for the variables of interest in the FHS original cohort, only phenotype data for individuals from the offspring cohort were included in the analyses.However, the family structure from all cohorts was utilized in the analyses. Analyses were restricted to measurements reported from the seventh visit of the offspring cohort because more variability in the quantitative traits was expected in the older study participants. Our study was restricted to non-smokers to remove confounding by smoking status. We further trimmed our data set to reduce computational complexity by removing four pedigrees with more than 200 members each, resulting in 770 individuals and 1052 sibling pairs within 334 pedigrees.Because the data set given did not include fasting insulin levels or waist circumference, we used the WHO 1999 definition of MetSyn to choose the variables to include in our multivariate trait, including: triglycerides (TG), high-density lipoprotein (HDL), systolic blood pressure (SBP), diastolic blood pressure (DBP), blood glucose (BG), and body mass index (BMI) as defined by weight in kilograms divided by height in meters squared .Preliminary modeling identified age, sex, and the interaction of age by sex as covariates to adjust for before the association analysis. To account for the blood pressure lowering effects of medication, a constant of 10 was added to SBP and a constant of five was added to DBP for those individuals who reported using anti-hypertensive medication . Due to Because MetSyn has been extensively studied and many candidate genes named, we chose to analyze the 50 k candidate gene SNP panel. Prior to association analysis, mendelian inconsistencies were identified in the data using MARKERINFO (S.A.G.E. v5.4.2) and the genotypes of all individuals in a family with an inconsistency were set to missing for each given marker.We used the following regression model as implemented in ASSOC, a program in the S.A.G.E. software suite:i, with trait y1, cji is any one of n individual specific covariates, ηi is a random effect comprising, in our study, the sibling and individual specific errors, zi is a genotype indicator for the allele A at a diallelic locus with alleles A and B,where for any individual yj and δ are median unbiased on the original scale of measurement. We simultaneously estimate the effect of allele A, covariates, and the residual variance components. The likelihood is maximized numerically over all parameters, and standard errors determined. p-Values for the regression coefficients and the variance components, based on the likelihood ratio and Wald test, were calculated. Any SNPs for which these two tests did not agree were removed from the results reported.and the regression coefficients yk, for the kth family. After adjusting for individual covariates, the expected value of ykykT is the variance-covariance matrix of the traits for family k, defined as:Multivariate association analysis of quantitative traits was conducted using the S.A.G.E. program RELPAL, which implements the multivariate Haseman-Elston regression technique as a two-stage association and linkage analysis ,13. BecaP is the additive polygenic variance covariance matrix, Φ represents the matrix of kinship coefficients, E is the environmental variance covariance matrix, and I is an identity matrix incorporating random error for each individual. The two-stage approach proposed by Wang and Elston incorporates both identity-by-decent (IBD) sharing and a matrix due to the additive effect of a quantitative trait locus (QTL). However, limiting the analysis to stage 1 of RELPAL by ignoring the linkage component provides a virtually identical multivariate extension to ASSOC ). We report results significant at this threshold as well as one order of magnitude less significant and 0.001. Similarly, for the multivariate analyses, we report results significant at p < 5 × 10-6]), p < 5 × 10-5 and 0.001. Note that because the multivariate approach considers all traits simultaneously, we use a less stringent threshold.Because the purpose of our paper is to compare these methods, we chose to report results from both analyses for possible thresholds rather than only those for a specific threshold. For the univariate analysis, we began by assuming the SNPs within a given gene had a linkage disequilibrium (LD) measure of TCP11L1 gene, which codes for a T-complex protein, met the criteria of p < 8 × 10-6 for more than one of the univariate traits of interest. Relaxing the criteria for significance by an order of magnitude resulted in two additional significant SNPs: one in the GRID1 (glutamate receptor) gene, expressed in the central nervous system, and one in the STAC (src homology 3 and cysteine-rich domain) gene, involved in neural-specific signal transduction .Only one SNP, located in the p < 5 × 10-6 through multivariate analysis (Table CETP) on chromosome 16 (p < 1 × 10-10), which has been associated in multiple studies with HDL. Interestingly, while the univariate analysis of HDL was also highly significant (p = 7 × 10-7), no other univariate traits met even a loose definition of association at these SNPs. This suggests that the additional significance attained in the multivariate analysis is due to a cumulative effect of multiple traits when analyzed in concert. If we relax our criteria for significance to 5 × 10-5, a SNP within the peripheral myelin protein gene (PMP22), which is expressed in the peripheral nervous system, emerges as significant , but found to have a marked gain in significance when incorporating all components of MetSyn into the analysis. This may be due to pleiotropy but with effects modest enough for other traits that are not detectable in a univariate analysis. It may also be due to the fact that incorporating the other components of MetSyn into the analysis yields a trait that is more reflective of the biological phenomenon affected by this gene than the simple clinical measure HDL. Other results also suggest that while univariate analysis may indeed be effective in isolating genetic effects for complex traits like MetSyn, incorporating other components of such a syndrome can allow a prespecified threshold of significance to be met even if accounting only for the performance of fewer tests. Other examples of possible pleiotropy are shown in our analysis, but are not as compelling, both because the gain in significance is not as striking and the genes themselves are not such striking candidates. One such example is LOC65358, a locus of unknown function with a multivariate p-value of 0.0004 and univariate p-values for BG and DBP of 0.002 and 0.01, respectively. We do note, however, one instance in which the univariate result was more significant than the multivariate: C9orf93. This is an open reading frame on chromosome 9 and the univariate analysis of SBP and DBP in this region yielded p-values of 0.0001 and 0.00001, respectively, but the multivariate analysis yielded a p-value of 0.009. Certainly, after considering the increased number of univariate tests done, the difference in the level of significance is not marked. However, this does illustrate one case in which a gene may not be pleiotropic across the components of MetSyn or offer a more biologically relevant trait.As mentioned above, the most striking result found in these analyses was at The purpose of this study was to illustrate, in the context of family-based association analysis, the benefit of simultaneously considering the highly correlated traits that comprise MetSyn. We demonstrate that for multiple genes, one of which is known to be associated with cholesterol homeostasis, significance can be greatly increased when the other components of MetSyn are simultaneously considered. In this we find the benefits of multivariate analysis, because it can serve as a mechanism by which to control for multiple comparisons, better define a trait of interest, and aid in the detection of pleiotropic effects.BG: Blood glucose; BMI: Body mass index; CETP: Cholesterol ester transfer protein; DBP: Diastolic blood pressure; FHS: Framingham Heart Study; HDL: High-density lipoprotein; IBD: Identity by decent; LD: Linkage disequilibrium; MetSyn: Metabolic syndrome; QTL: Quantitative trait locus; SBP: Systolic blood pressure; SNPs: Single-nucleotide polymorphisms; TG: Triglycerides; WHO: World Health Organization.The authors declare that they have no competing interests.ARB and RJG performed the multivariate analyses and drafted the manuscript. EKL helped draft the manuscript. DJB and YES prepared the data for S.A.G.E. analysis and developed the programming scheme. LSP performed the univariate analyses. CLG-M conceived of and designed the study and helped draft the manuscript. All authors read and approved the final manuscript.


The prevalence of MetS was determined using the National Cholesterol Education Program Adult Treatment Panel III diagnostic criteria, modified with a newly developed correction for medication use. The association test between an SNP and MetS was performed with a generalized estimating equations method under the additive genetic model. Multiple-testing corrections were also performed. The prevalence of MetS in the offspring cohort increased from one visit to the next, and reached the highest point by the seventh exam comparable with the prevalence reported for the general US population. The pattern of the MetS prevalence over time also reflected itself in the association tests, in which the highest significances were seen in the fifth and seventh exams. The association tests showed that SNPs within genes PRDM16, CETP, PTHB1, PAPPA, and FBN3, and also some SNPs not in genes were significant or close to significance at the genome-wide thresholds. These findings are important in terms of eventually identifying with the causal loci for MetS.We investigated the association of metabolic syndrome (MetS) with a 500 k and a 50 k single-nucleotide polymorphism (SNP) gene chip in the Framingham Heart Study. We cross-sectionally evaluated the MetS longitudinal trends. Data analyzed were from the Offspring Cohort (four exams: first ( Metabolic syndrome (MetS) is characterized by abdominal obesity, dyslipidemia, elevated blood pressure, insulin resistance, glucose intolerance, and possibly a prothrombotic and proinflammatory state . MetS isn = 2,441), third , fifth , and seventh  exams) of the Offspring Cohort, and a cross-sectional analysis was performed in the first exam  of the Generation 3 Cohort. The prevalence of MetS was identified using the National Cholesterol Education Program (NCEP) modified diagnostic criteria with a newly developed correction for medication use [2; triglyceride (TG) ≥ 150 mg/dl; high-density lipoprotein cholesterol (HDLC) < 40 mg/dl in men and < 50 mg/dl in women; systolic blood pressure (SBP) or diastolic blood pressure (DBP) ≥ 130/85 mm Hg or use of anti-hypertensive medications; and fasting blood glucose (GLUC) ≥ 110 mg/dl or use of anti-diabetic medications with the age of diagnosis with diabetes mellitus ≥ 40 years. The modified NCEP diagnostic criteria were applied to consider the participants medication use. Thus, TG and HDL for the subjects treated with antihyperlipidemics were corrected to new values based on the following formula: TG/(1-15.2/100), HDLC/(1+6.1/100) (mg/dl). The SBP and DBP for subjects using antihypertensives were corrected to new values based on the following formula: SBP+14.8 and DBP+10.5 (mm Hg). These formulas were based on previous research, which represent corrections of a participant's medicated traits based on the mean values of many summarized treatment clinical trials [The FHS data comprised three generations of longitudinal measurements. The first dataset is the "Original Cohort", the second dataset is the "Offspring Cohort" and the third dataset is the "Generation 3 Cohort". We analyzed data from the Offspring Cohort and the Generation 3 Cohort. The data of Original Cohort were excluded due to missing variables related to MetS. Longitudinal analysis for the prevalence of MetS and its components was performed in each of the four exams . The genotype data were recoded based on the additive model. A logistic regression of recoded genotype on MetS, based on the generalized estimating equation statistical model to account for the familial relationships among subjects within a pedigree, was performed using PROC GENMOD of SAS v 9.1.3 applying parallel computing with Platform SAS under Linux OS. In order to address multiple testing correction issues, we applied the simpleM method, which is an effective number of independent tests approach based on principal-component analysis that takes into account linkage disequilibrium (LD) information among SNPs [p-value ≤ 1.78 × 10-7. For the 50 k chip, based on the same method the significance threshold was 1.29 × 10-6. We considered these two chip results separately because they represent independent chips and also our analyses per type of chip were performed independent of each other.The qualitative MetS variable, which took medication use into account, was used to test its association with both the genome-wide scan 500 k SNPs and the additional 50 k gene SNPs, for a total of approximately 550 k SNPs (GeneChipThe mean (range) age of subjects at the first, third, fifth, and seventh exam in the Offspring Cohort was 33.6 (9-60), 46.2 21-72), 53.1 (28-79), and 60.1 (35-85) years, respectively. The mean (range) age of subjects in the Generation 3 Cohort was 40.2 (19-72) years. The prevalence of MetS at the first, third, fifth, and seventh exam in the offspring cohort was 10.9%, 15%, 23.7%, and 23.6%, respectively. The prevalence of MetS at first exam in the Generation 3 Cohort was 14.2%. The prevalence of subjects having four and five components of MetS beyond their threshold increased with the number of exams, while the prevalence of subjects having three components beyond the threshold decreased on the seventh exam  gene, with the MetS. This gene is already studied extensively for its inhibitors, because inhibition of CETP elevates the fraction of plasma cholesterol associated with HDL [PTHB1 gene. This gene is known also as BBS9 gene and recognized as one of the recent Bardet-Biedl syndrome genes. Such gene polymorphisms are hypothesized to contribute to human obesity and diabetes mellitus [The longitudinal trends of MetS prevalence and of the association tests were evaluated by using the cross-sectional phenotypic measurements. The prevalence of MetS in the Offspring Cohort increased from one visit to the next, and reached the highest point by the seventh exam, comparable with reported MetS prevalence of the US population . The prefunction ,11. Anotwith HDL . SNPs rsmellitus .PAPPA) and rs10408896 (FBN3) were highly significant, but at the same time one must be cautious when considering them as candidate genes for MetS, because of the rare minor allele frequency. Despite the rarity of minor allele frequency for the above two SNPs, PAPPA gene, a metalloproteinase, is reported to regulate the human atherosclerotic plaque [FBN3 (Fibrilin 3) is reported to contribute in the polycystic ovary syndrome, which is associated with obesity [p-values close to significance from the same genes mentioned in the Results and Discussion were present in the FHS data. For space reasons we did not report any of them. Finally, we would like to draw readers attention to a number of SNPs located on chromosome 14 , which although not located on genes, still were associated highly with MetS.In the Generation 3 Cohort first exam, the prevalence of MetS was moderate and comparable with those of the first and third exams of the Offspring Cohort. As a result, only a few associations were highly significant. The SNPs rs2418441 (c plaque ; FBN3 (F obesity . SeveralThese findings are important for identifying the role of the genes reported to be associated with MetS. As such, they need to be further investigated in conjunction with the quantitative risk factors of MetS.BMI: Body mass index; DBP: Diastolic blood pressure; FHS: Framingham Heart Study; GLUC: Fasting blood glucose; HDLC: High-density lipoprotein cholesterol; LD: Linkage disequilibrium; MetS: Metabolic syndrome; NCEP: National Cholesterol Education Program; SBP: Systolic blood pressure; SNP: Single-nucleotide polymorphism; TG: Triglyceride.The authors declare that they have no competing interests.Y-MP, ATK, MAP, and DCR conceived of the idea of this analysis. Y-MP and ATK performed the analysis and wrote the manuscript. MAP, DCR, MF, XG, JW, and DM contributed ideas to improve the manuscript. XG performed the thresholds' p-value calculations.


Both RF importance measures captured most of the LR single-locus and pairwise interaction effects, while joint importance measures also corresponded to full LR models containing main and interaction effects. We furthermore showed that RF measures were particularly sensitive to data imputation. The most consistent pairwise effect on rheumatoid arthritis was found between two markers within MAP3K7IP2/SUMO4 on 6q25.1, although LR and RFs assigned different significance levels.Using parametric and nonparametric techniques, our study investigated the presence of single locus and pairwise effects between 20 markers of the Genetic Analysis Workshop 15 (GAW15) North American Rheumatoid Arthritis Consortium (NARAC) candidate gene data set (Problem 2), analyzing 463 independent patients and 855 controls. Specifically, our work examined the correspondence between logistic regression (LR) analysis of single-locus and pairwise interaction effects, and random forest (RF) single and joint importance measures. For this comparison, we selected small but stable RFs (500 trees), which showed strong correlations (Within a hypothetical two-stage design, pairwise LR analysis of all markers with significant RF single importance would have reduced the number of possible combinations in our small data set by 61%, whereas joint importance measures would have been less efficient for marker pair reduction. This suggests that RF single importance measures, which are able to detect a wide range of interaction effects and are computationally very efficient, might be exploited as pre-screening tool for larger association studies. Follow-up analysis, such as by LR, is required since RFs do not indicate high-risk genotype combinations. The analysis of genetic association studies for complex diseases requires the identification of significant single marker and interaction signals among a vast background of noise. In the presence of epistatically interacting loci, exhaustive searches of all possible two-marker combinations using the classic logistic regression (LR) approach have been shown to be more powerful than single-marker analysis in simulations , even whRFs consist of a collection of classification or regression trees grown from a random selection of variables on bootstrapped samples (bagging). The importance of a variable  can be estimated by the increase in misclassification for the left-out (out-of-bag) samples when using a data vector containing the original variable values and a vector with randomly permuted values. It has been shown by simulation studies that RF importance measures are able to simultaneously detect single-locus heterogeneity models and multiplicative interaction models . RF can Our study investigated the extent to which LR single-locus and pairwise interaction effects correspond to RF single- and joint-importance measures on a small data set of 20 markers  rheumatoid arthritis (RA) candidate gene data set). Because RFs analysis cannot handle missing data , we alsor2 ≤ 0.66) from at least 13 RA candidate genes residing within at least 10 different chromosomal locations; with on average one or two markers per gene. Because some cases within this data set originated from the same pedigree, independent individuals were selected at random to give 463  cases and 855 independent controls, all of Caucasian origin. Hardy-Weinberg equilibrium (HWE) was tested in the complete sample and in the controls. One rare single-nucleotide polymorphism (SNP), HugotSNP8ms2 , showed nominally significant deviations from HWE in the controls (p = 0.008) and in the full sample (p = 0.006) due to an overrepresentation of rare homozygotes, which might be the result of chance or genotyping error. This would have greatest effect on genotypic or haplotype analysis, neither of which was carried out within this study. All tests for HWE were non-significant after correction for multiple testing (20 markers).For our study we choose the GAW15 North American Rheumatoid Arthritis Consortium (NARAC) candidate gene data set (Problem 2) consisting of 20 biallelic markers .Marker genotypes were recoded in terms of additive components  and singZ-scores and significance levels. Z-scores can be inferred from AvImp measures through division by their associated standard error (SE), which is determined by the AvImp measure and the number of trees grown [Z-scores and their significance, however, also continue to increase with increasing number of trees, even when the RF reaches stability . We observed high correlations  for RFs with ~500 trees and more, for both single and joint AvImp measures   based onp-values for the median-replaced data set are reported in the text. In addition, nominal p-values for both median-replaced and imputed data are represented within Figure In the following section, the most significant nominal p = 2 × 10-8), and nominally significant effects for rs237025 (p = 0.003) and CT60 (p = 0.038) in both the median-replaced and the imputed data sets , IGR3138ms1-rs2073838 , IGR2096ms1–IGR3138ms1  and rs237025–rs1248696  using both median-replaced and imputed data  and rs237025 (pRF = 4.6 × 10-10) corresponded to LR single marker and interaction effects. IGR3084ms1, IGR3138ms1, rs2073838, rs2243250, rs577001, rs2268277, and in imputed data sets also IGR2096ms1 (5.6 × 10-14 ≤ pRF ≤ 0.014), were involved in pairwise LR interactions  for both cases and controls. RF analysis identified 11 SNPs (12 in imputed data) with significant single importance  and imputed data sets (70%) and represented predominantly markers with significant single-importance measures  with nonparametric (RFs) analysis techniques when investigating the presence of single-locus and pairwise effects between 20 markers of the NARAC candidate gene data set. Both RF single- and joint-importance measures selected most of the markers for which nominally significant allelic or pairwise interaction effects by LR were detected. RF joint variable importance measures also captured most of the nominally significant full LR models, containing both main  and interaction effects . This correspondence between LR and RFs was improved when analysis was performed with imputed instead of median-replaced data sets, which agrees with the results of Bureau et al. , and couMAP3K7IP2, but rs237025 also causes a non-synonymous change (M55V) within the reverse transcribed SUMO4 [SUMO4 and MAP3K7IP2, which might increase susceptibility for RA. The significance of the statistical effect remains to be evaluated. Whereas LR permutation tests did not indicate the presence of any overall significant interaction, model-free RF analyses, which are robust to noisy variables and overfitting [The most consistent pairwise effect was obtained between the 6q25.1 markers rs237025 and rs577001, for which nominally significant interactions were found by LR as well as significant single and joint RF importance measures. rs237025 also showed nominally significant single-locus effects. Both rs237025 and rs577001 reside within the intronic region of ed SUMO4 . AlthougThe number of markers/marker pairs selected by RF measures was considerably larger than the number of pairs with significant LR interactions (6%) or significant LR full models 47–53%). Some of these might be false positives. However, it might also reflect the ability of RFs to detect a wide range of interaction models including multiplicative or heterogeneity effects [7–53%. SoModel-free analysis by RFs requires further investigation in order to identify high-risk allele or genotype combinations, and parametric follow-up analysis by LR represents one of several follow-up options. Choosing a hypothetical two-stage design, pairwise LR analysis of variables with significant RF single importance would have detected 90% of all nominally significant LR interactions in our small data set while analyzing only 39% of all possible marker combinations. LR analysis of all marker pairs with significant joint importance measures would have detected all nominally significant LR interaction effects while analyzing 70% of all possible combinations. This suggests that RF single-importance measures, which are able to detect a wide range of interaction effects  and are Z-score based RF screening will be affected by selection of RFs with inflated numbers of trees, as these RFs show an increased number of significant signals  was sufficient for the analysis of this small data set, but needs to explored for larger studies.Our study found a strong correspondence between RF importance measures and LR interaction effects, which was improved when data imputation was based on genetic data. The most consistent pairwise effect on RA was observed between two markers within The author(s) declare that they have no competing interests.


We used Genetic Analysis Workshop 16 Problem 3 Framingham Heart Study simulated data set to compare methods for association analysis of quantitative traits in related individuals. More specifically, we investigated type I error and relative power of three approaches: the measured genotype, the quantitative transmission-disequilibrium test (QTDT), and the quantitative trait linkage-disequilibrium (QTLD) tests. We studied high-density lipoprotein and triglyceride (TG) lipid variables, as measured at Visit 1. Knowing the answers, we selected three true major genes for high-density lipoprotein and/or TG. Empirical distributions of the three association models were derived from the first 100 replicates. In these data, all three models were similar in error rates. Across the three association models, the power was the lowest for the functional SNP with smallest size effects , and for the less heritable trait . Our results showed that measured genotype outperformed the two orthogonal-based association models , even after accounting for population stratification. QTDT had the lowest power rates. This is consistent with the amount of marker and trait data used by each association model. While the effective sample sizes varied little across our tested variants, we observed some large power drops and marked differences in performances of the models. We found that the performances contrasted the most for the tightly linked, but not associated, functional variants. For pedigree-based association analysis, several methods have been developed that utilize information about transmission of alleles, such as the orthogonal test for within-family variation  ,2. The qWe studied the two simulated quantitative traits, high-density lipoprotein (HDL) and triglyceride (TG), measured at Visit 1 in FHS simulated data set. All our analyses were conducted using the first 100 replicates. Within each replicate, we adjusted trait values for sex and age using a linear regression. We used the residual values of HDL and TG as the phenotypes of interest for association testing. We then assessed the distributions of each trait using the 100 replicates. We found that HDL, but not TG , values were normally distributed. The fit to the normal distribution was obtained using a rank-based transformation of TG values (TG_Rob): kurtosis and skewness were equal to -0.02 and 0.003, respectively.p-value ≤ 10-6) hypothesis; (4) zeroing out genotypes of all individuals in a family at any SNP that showed mendelian errors.Genotype data were obtained from the Affymetrix GeneChip Human Mapping 500 k Array. Individual genotype data were filtered based on BRLMM  confidence scores: we used the standard cutoff of 0.5 for call/no-call. Quality control analyses led to 1) exclusion of SNPs with less than 95% call rates, with unknown map position, or with low minor allele frequency (<1%); 2) zeroing out all genotypes at any DNA sample with <95% call rate; 3) exclusion of SNPs not fitting the Hardy-Weinberg equilibrium  of the HDL major genes. TG variability was also explained by two (LPL and CYP2B6) of these genes. Table h2g is the rate of the trait variance explained by each functional SNP, and D' is the standardized Lewontin's disequilibrium coefficient between the functional variant and each SNP being tightly linked to it. The total number of subjects with available phenotype and genotype data ranged from 5,826 to 5,995. Note that two functional SNPs (α2 and δ1) are tightly (~120 kb) linked but not associated (D' = 0.003). For each gene, we used the functional SNP and two "non-associated" SNPs, selected from the set of SNPs tightly linked (<100 kb) and not associated (D' < 0.10) to the functional SNP. Finally, we also investigated association tests using SNPs not linked to any of the functional variants. The 'false' gene was randomly drawn on chromosome 7 .In brief, the simulation models for HDL and TG included the effects of major genes , and polygenic effects (58% for HDL and 38% for TG). Here, we limited our study to three (b'w and b'b). Restricted and unrestricted likelihoods of both the QTDT and QTLD models were maximized as a function of the polygenic component (h2). The MG model is a classical mixed model in which the marker is included as a covariate, and the correlations between relatives are accounted for by h2 [b) is the association parameter. The restricted MG model depends on h2 only (b set to 0). The SNP was coded as the number of rare allele copies across all three methods. The effective sample sizes of these three association tests differ. MG model uses all subjects  with known phenotype and genotype status. From this sample, the two family-based association models discard data on the relatives not fulfilling either one of the two conditions: 1) their two parents are genotyped and at least one of them is heterozygote or 2) they have at least one sibling with a different genotype. The effective sample size of QTDT is further reduced because founders and spouses are not use to estimate the within-component effect.All association analyses were performed using the qtld command of SOLAR 4.0.7 . The resor by h2 . The regEvidence for population stratification (denoted here as STRAT) is assessed through the likelihood ratio of the restricted  to the unrestricted (bw and bb are estimated freely) model. All three association tests, as well as the STRAT test, are assumed to follow a chi-square distribution with one degree of freedom.p-value ≤ 5%. The three association tests were evaluated under varying conditions regarding i) inclusion or exclusion of the dietary effect (covariate "diet" affects TG levels and is correlated among family members) and in the association model, ii) trait distribution, i.e., untransformed vs. transformed trait values. Indeed, these association models assume that trait values are normally distributed, and departures from normality can inflate their type I error or reduce their power.We performed single-SNP association analyses. For each trait and each SNP, we computed the three association tests (and STRAT test) in each replicate, and derived the mean and standard deviation of each chi-square statistic over 100 replicates. We also derived mean and standard deviations of the association parameters (regression coefficients). Power and error rates were defined as the proportion of replicates with a chi-square value exceeding a given nominal threshold value. MG and QTLD analyses were also performed accounting for population stratification (denoted as MG_S and QTLD_S tests): MG and QTLD chi-square values were both set to zero in the replicates having a STRAT p-value of 5%, of QTDT, QTLD, and MG tests when the studied SNP is not associated to the trait. The three association tests were roughly similar in empirical estimates, whether or not the studied SNP is linked to a major gene. In general, error rates were lower or close to the nominal values, except for QTDT with two SNPs. As expected, accounting for population stratification decreased the mean chi-square statistics of both QTLD and MG models. Interestingly, in these data, departure from normality did not yield inflated error rates, except with QTDT for TG and rs4244457. Error rates remained unchanged when diet was included into the model (results not shown).Table Table p = 5%) to detect direct association for HDL and two (α4 and δ1) of the three functional variants. At a lower tabulated threshold (p = 0.1%), the power remained good using the MG model only. For TG, good power was obtained with the MG model with one functional SNP (δ1) and using transformed TG values.In conclusion, our results showed that MG outperformed the two orthogonal-based association models , even after accounting for population stratification. QTDT had the lowest power rates. Similar conclusions were reached by two previous simulation studies ,6. It isFHS: Framingham Heart Study; HDL: High-density lipoprotein; QTLD: Quantitative trait linkage disequilibrium; QTDT: Quantitative transmission-disequilibrium test; MG: Measured genotype; SNP: Single-nucleotide polymorphism; STRAT: Population stratification; TG: Triglyceride.The authors declare that they have no competing interests.ASP carried out the statistical genetic analyses and drafted the manuscript. ZV contributed in the statistical analysis and helped to draft the manuscript. MM conceived the study, coordinated it, and contributed to the draft the manuscript. All authors read and approved the final manuscript.


We observed results consistent with previously reported associations between rs599839, on chromosome 1p13, and LDL. We note that the association is significant with LDL intercept but not slope. Markers on chromosome 17q25 were associated with TG slope, and a single-nucleotide polymorphism on chromosome 7p11 was associated with SBP intercept. Growth curve models can be used to gain more insight on the relationships between SNPs and traits than traditional association analysis when longitudinal data has been collected. The power to detect association with changes over time may be limited if the subjects are not followed over a long enough time period.Multivariate linear growth curves were used to model high-density lipoprotein (HDL), low-density lipoprotein (LDL), triglycerides (TG), and systolic blood pressure (SBP) measured during four exams from 1659 independent individuals from the Framingham Heart Study. The slopes and intercepts from each of two phenotype models were tested for association with 348,053 autosomal single-nucleotide polymorphisms from the Affymetrix Gene Chip 500 k set. Three regions were associated with LDL intercept, TG slope, and SBP intercept ( Cardiovascular disease (CVD) is the leading cause of death in the United States and is a significant cause of disability. Worldwide, heart disease is on the rise, and is predicted to become the leading cause of death and disability by 2020 .In order to identify common risk factors leading to CVD, several large-scale epidemiological studies have been undertaken. Most notable is the Framingham Heart Study (FHS), a prospective study which was started over 50 years ago and is still ongoing. It was designed to follow the development of CVD over time in a large group of participants who had not yet developed symptoms of CVD. The original participants underwent extensive medical testing approximately every 2 years, and more recently recruited individuals have also been followed regularly. Through the data arising from the FHS, several major risk factors for CVD have been identified, including hypertension, high blood cholesterol, smoking, obesity, and diabetes. In addition, results from the study have demonstrated significant effects of demographic factors such as age and sex.The longitudinal design of the FHS allows for the study of how certain traits change over time. The analysis of time-dependent data can range from simple plots to complex survival or multilevel modelling. In this paper, we use a latent growth curve (LGC) model to examine the change over time in levels of systolic blood pressure (SBP), high-density lipoprotein (HDL), low-density lipoprotein (LDL), and triglycerides (TG), as well as to explore the relationship between these four traits, which are known to affect the risk of developing CVD. Association analysis was performed to identify genetic factors that are associated with mean baseline values of each trait, as well as the changes over time, using subjects from the FHS.Details about sample recruitment can be found in Cupples et al.  and SplaBecause individuals from the Original Cohort fasted before only one of the four exams, the lipid profiles obtained from these individuals were not ideal for longitudinal analyses. We therefore restricted our analysis to members of the Offspring Cohort, who fasted before all four exams. We selected independent members of the Offspring Cohort as follows. Starting with the original 1538 families, the Generation 3 cohort was removed, which split the pedigrees into 3379 independent sub-pedigrees. Individuals belonging to the Offspring Cohort who had phenotype and genotype data were considered for inclusion in the analysis. We selected independent individuals from this set. In sub-pedigrees in which multiple sets of individuals could be chosen, we randomly selected a set that gave the largest number of independent individuals (as determined by the kinship coefficient). This resulted in 1488 individuals. An additional 171 samples without family data were added, for a total of 1659 independent individuals.A linear LGC model was fit to longitudinal measurements of SBP, HDL, LDL, and TG. One of the strengths of LGC modeling is that it allows the study of multiple outcomes over time in a multivariate framework, which is particularly useful in investigating the change in phenotype values and assessing cross-phenotype relationships . Two modp-value from an exact test for Hardy-Weinberg equilibrium [-6 (4945 markers). Thus, the final marker set consisted of 348,053 single-nucleotide polymorphisms (SNPs).Genotyping was conducted using the Affymetrix GeneChip Human Mapping 500 k Array Set, using the 250 k Sty and 250 k Nsp platforms. Only autosomal markers were considered for analysis. The original set of markers consisted of 487,014 autosomal markers with known chromosomal assignments and physical positions. We removed 32,594 (6.7%) markers where the call rate was <95%, based on all 6848 genotyped individuals. Markers were also removed if the minor allele frequency was <5%  or the Individual-specific intercepts and slopes were obtained from the growth curve models, for each of the phenotypes SBP, HDL, LDL, and TG. These phenotypic summaries were examined for association with each marker separately using linear regression, as implemented in the program PLINK v1.04 , assuminThe sample was composed of 1659 independent subjects who were examined at four different time points. Details about the raw variables and covariates are described in Table p < 1.44 × 10-7 (Table p = 3.04 × 10-10 in the model where BMI was time-varying). The minor G allele was associated with a reduction in LDL intercept values. This marker is approximately 250 kb upstream of PSRC1, which encodes a proline-rich protein. This marker was recently shown to be associated with LDL measured at a single examination in a meta-analysis [p = 0.14), indicating that it may not play a role in the change of LDL levels over time, at least in the age range of individuals studied here. This SNP also showed the most significant association with LDL intercept in the model in which BMI was time-invariant (p = 2.62 × 10-9).We tested 348,053 markers for association with the intercepts and slopes of HDL, LDL, TG, and SBP. A total of six markers in three regions were associated in at least one of the two models, using a Bonferroni cutoff of analysis , and wasanalysis . In thesp = 3.89 × 10-8 and 2.98 × 10-9 for BMI time-invariant and BMI time-varying models, respectively). Three other markers in the same region also show association, although at lower levels of significance. All four markers are in nearly complete linkage disequilibrium  in this data. TG intercept was not associated with these markers .SNP rs6501683 on 17q25 was associated with TG slope (p = 6.88 × 10-8) in the model in which BMI was treated as a time-invariant covariate. In the model in which BMI was treated as a time-varying covariate, the p-value for this SNP falls just above the significance cutoff used here (p = 1.45 × 10-7). This region is peri-centromeric, and is not near any known genes. The observed association was only with the intercept .On chromosome 7p11, rs11976165 was associated with SBP intercept . Because only a small proportion of individuals reported taking trait-altering medication, particularly in Exams 1, 3, and 5, we did not expect the choice of medication adjustment method to have a strong effect on the overall results.Because the distribution of TG was non-normal, we used robust maximum-likelihood estimation , as implWe did not explicitly model time, as measured by age at exam, in the growth model. This implicitly assumes that the exams were evenly spaced, an assumption which seems reasonable, on average, between Exams 3, 5, and 7, but not between Exams 1 and 3. The model could be improved by including a more appropriate measure of time.h2 = 0.52, 0.59, and 0.48 for HDL, LDL, and TG, respectively) [h2 = 0.28) [h2 = 0.23) in the FHS data [The estimates of the slopes tended to be small for all traits, with the exception of TG. Thus, in this sample, the trait values tended to remain stable over time, and perhaps it is not surprising that significant association with a slope trait was only observed with TG. The heritability of the intercepts and slopes from this study cannot be calculated because independent samples were used. However, other analyses of the FHS data showed that the heritability of lipid levels taken at a single exam is moderate (ctively) , while t = 0.28) . StudiesFHS data .The longitudinal nature of the FHS data was exploited using LGC models, which allowed the study of multiple phenotypes simultaneously. Consequently, the effect of each phenotype on each other was accounted for, through pairwise correlations, in the model. An association between a marker and a particular trait, therefore, can be interpreted as an association with the trait, after the effects of the covariates and the remaining three traits have been accounted for. We used phenotypic summaries from these models to search for SNPs associated with the mean value or change over time of lipid and blood pressure phenotypes across the genome. Because long-term averages of lipid phenotypes have been shown to be heritable , this stBMI: Body mass index; CVD: Cardiovascular disease; FHS: Framingham Heart Study; HDL: High-density lipoprotein; LDL: Low-density lipoprotein; LGC: Latent growth curve; SBP: Systolic blood pressure; SNP: Single-nucleotide polymorphism; TG: Triglyceride.The authors declare that they have no competing interests.NMR participated in the design of the study, performed the association analysis, and drafted the manuscript. JSH participated in the design of the study, performed the growth curve modeling, and helped to draft the manuscript. ADP participated in the biological interpretation of the data and analysis results. JB participated in the design of the study. All authors read and approved the final manuscript.


Many psychiatric conditions and traits are associated with significant heritability. Genetic risk for psychiatric conditions encompass rare variants, identified due to major effect, as well as common variants, the latter analyzed by association analyses. We review guidelines for common variant association analyses, undertaking after assessing evidence of heritability. We highlight the importance of: suitably large sample sizes; an experimental design that controls for ancestry; careful data cleaning; correction for multiple testing; small P values for positive findings; assessment of effect size for positive findings; and, inclusion of an independent replication sample. We also note the importance of a critical discussion of any prior findings, biological follow-up where possible, and a means of accessing the raw data. Extensive evidence suggests that many psychiatric conditions have a substantial genetic component. A long-standing perspective in the field of psychiatric genetics is that a significant proportion of risk arises from common variants, including single nucleotide polymorphisms (SNPs) . GenomeNature Genetics, recognizing the difficulties in replicating candidate gene association findings in complex conditions or phenotypes, published an editorial [Ten years ago, ditorial  that pro"Ideally, they should have large sample sizes, small P values, report associations that make biological sense and alleles that affect the gene product in a physiologically meaningful way. In addition, they should contain an initial study as well as an independent replication, the association should be observed both in family based and population-based studies, and the odds ratio and/or attributable risk should be high" (pp. 1-2).Nature Genetics editorial, i.e., that genetic association studies have mostly (but not entirely) failed to replicate. Third, for many conditions, samples are available through international repositories. And, fourth, we have greater understanding of sources of error in association studies, as well as how to best address them.While these remain excellent guidelines, advances over the course of the past decade are such that these guidelines need to be revisited. First and foremost, genotyping has become much more efficient, widespread, and less expensive. For this reason genome-wide association studies are more common. On the other hand, most laboratories with access to clinical samples can now carry out smaller (candidate gene) association studies. Second, empirical data have dramatically re-enforced the fundamental concerns that precipitated the http://www.nimhgenetics.org/, AGRE http://www.agre.org and Simons Foundation http://sfari.org/ websites. The empirical data showing just how extensive the problems are warrant brief review, as do some of the evolving methods to address them.The widespread availability of less expensive genotyping and the access to international DNA repositories do not need further elaboration here, and in relation to autism we would direct the reader to the NIMH APOE in Alzheimer disease, INS in type I diabetes, CCR5 in HIV infection, PRNP in Creutfeldt-Jakob disease, CTLA4 in Graves' disease, and F5 in deep vein thrombosis.In 2002, Hirschhorn et al.  surveyedDRD3  and 1.07 for HTR2A . Most recent analyses of these (and other) candidate genes in schizophrenia by meta-analysis find less support, if any, for association [In a follow-up analysis, 301 studies covering 25 different associations were studied in greater detail . Pooled ociation ,7. In anhttp://www.genome.gov/gwastudies/)[http://wren.bcf.ku.edu/ and http://gene.sfari.org/).These effect sizes are consistent with both those derived from studies in model organisms  and those now arising from genome-wide studies . Going iGiven this failure to replicate, we feel it would be useful to elaborate on the recommendations made a decade ago, as follows:"large sample sizes" - In light of the modest effect sizes anticipated in any study in psychiatric genetics, power becomes a serious concern. Investigators now recognize that a genome-wide study requires sample sizes on the order of several thousand cases and controls or trios to ensure detection of some common variants of modest effect, unless the circumstances are exceptional. Candidate gene studies are not much different, even if the significance level for P-value used for the test is larger. For example, even for effects on the high side of the allelic odds ratio , sample sizes of 500 or more cases and controls or trios would be required to have good power to reject the null hypothesis - even if one of the genotyped and tested variants is a risk variant. When the true odds ratio approaches 1.1, the required sample size is roughly an order of magnitude larger. Note, moreover, that these kinds of power calculations ignore the prior probability that any selected gene contains a risk variant. This probability is likely to be small, given the limited scope of the study and the findings regarding replication described earlier. Large sample sizes are warranted even in the case of a replication study where the first study gives a higher estimated effect size, as it is likely that the estimated effect size from the primary study represents an overestimate (sometimes referred to as "winner curse")."small P values" - While small P values remain important , a focus on P values alone is inadequate. A consideration of effect size is always required (see below), and identical P values in different studies "can have different implications for the plausibility of a true association depending on the factors that affect the power of the test, such as the minor allele frequency (MAF) of the SNP and the size of the study" [e study" . An undeData cleaning needs to be both rigorous and reported. In addition to removing markers with low minor allele frequency, markers and samples with higher failure rates need to be removed, as do markers that fail Hardy-Weinberg testing or cluster poorly. Data should be analyzed for cryptic duplicates and Mendelian and sex inconsistencies. Finally, some sense of genotype error rates should be presented. Note that there is no "perfect" approach to data cleaning, and it is difficult to determine a priori the impact of poor quality data. It might have little noteworthy effect in a single data set, yet the effect could be compounded when numerous data sets are combined, such as by meta-analysis. Making raw data available for scrutiny and meta-analysis, increasingly the norm in genome-wide studies and in studies making use of public DNA repositories, is therefore encouraged.Correction for multiple testing. While the standard in genome-wide studies, candidate gene studies often fail to provide correction for multiple testing. Reporting a nominal P value that is likely the result of chance is not accepted in science as a whole and should not be a part of psychiatric genetic research. With the advent of DNA repositories it is becoming much harder to provide sample-wide correction, but certainly experiment-wide correction is to be expected. With software programs like PLINK and UNPHASED now available for permutation testing [ testing ,11, runn"report associations that make biological sense and alleles that affect the gene product in a physiologically meaningful way" - This remains an ideal but has a different interpretation in genome-wide studies. In genome-wide studies the hypothesis-independent approach can lead to novel findings that do not make sense in the current conceptualization of a condition or phenotype, even if true. And for psychiatric conditions it is possible to develop an ad hoc story based only on the fact that a gene is expressed in the brain. So, the criterion of biological plausibility is a bonus but not necessarily a requirement. Follow-up analyses (or an a priori focus) on functional alleles can help to making biological sense of the association data. That is, if a genetic finding gives rise to a physiologically well-specified hypothesis that can be tested beyond a genetic design, this constitutes stronger converging evidence."they should contain an initial study as well as an independent replication" - Including replications in the same report is the sine qua non for a meaningful conclusion. With the advent of DNA repositories it has become harder to conceive of a study of a common categorical trait that cannot avail itself to a replication sample. The emphasis here is on the word 'independent', since a within-sample replication may not be sufficient .In addition, if there are other studies of the same locus in the literature, careful analysis of sample overlap needs to be described to ensure the principle of independence. Furthermore, the extent to which the study being presented replicates the prior findings should be discussed, and should address whether the same marker (or a marker in linkage disequilibrium) is showing the same effect in the same direction."the association should be observed both in family based and population-based studies" - The requirement for a family-based cohort arose from the potential for false-positive findings due to population stratification. With the advent of methods that adjust for ancestry, it is more relevant to expect the design to control for ancestry by either a family-based design or sufficient number of markers to estimate and adjust for ancestry. In general, case-control studies should include matching based on ancestry using standard approaches [proaches -14; and "the odds ratio and/or attributable risk should be high" - This criterion warrants some elaboration. Empirical data indicate that for many conditions and phenotypes, high odds ratios and high attributable risk is the exception, not the norm. It is for this reason that the field of psychiatric genetics has moved to ever-increasing sample sizes. It is more appropriate to expect that, for a suitably-powered study, some measure of effect size be provided. The replication sample gives an opportunity to estimate effect size, which is likely - due to winner's curse - to be much more accurate than such an estimate from the discovery sample.Many psychiatric conditions are associated with significant heritability , and man• Evidence of heritability for the condition or trait• Suitably large sample sizes, in the context of expected effect sizes and power• Standardized, careful data cleaning, described in detail• Correction for multiple testing• Inclusion of an independent replication sample• Experimental design that controls for ancestry by either a family-based design or by the inclusion of a sufficient number of markers to estimate and adjust for ancestry• Small P values for positive findings• Presentation of metrics of effect size for positive findings• A critical discussion of any prior findings• Biological follow-up • A means of accessing the raw dataMolecular Autism.JDB and SBC are Editors-in-Chief of


A procedure to measure connectedness among herds was applied to a beef cattle population bred by natural service. It consists of two steps: (a) computing coefficients of determination (CDs) of comparisons among herds; and (b) building sets of connected herds.The CDs of comparisons among herds were calculated using a sampling-based method that estimates empirical variances of true and predicted breeding values from a simulated n-sample. Once the CD matrix was estimated, a clustering method that can handle a large number of comparisons was applied to build compact clusters of connected herds of the Bruna dels Pirineus beef cattle. Since in this breed, natural service is predominant and there are almost no links with reference sires, to estimate CDs, an animal model was used taking into consideration all pedigree information and, especially, the connections with dams. A sensitivity analysis was performed to contrast single-trait sire and animal model evaluations with different heritabilities, multiple-trait animal model evaluations with different degrees of genetic correlations and models with maternal effects.Using a sire model, the percentage of connected herds was very low even for highly heritable traits whereas with an animal model, most of the herds of the breed were well connected and high CD values were obtained among them, especially for highly heritable traits (the mean of average CD per herd was 0.535 for a simulated heritability of 0.40). For the lowly heritable traits, the average CD increased from 0.310 in the single-trait evaluation to 0.319 and 0.354 in the multi-trait evaluation with moderate and high genetic correlations, respectively. In models with maternal effects, the average CD per herd for the direct effects was similar to that from single-trait evaluations. For the maternal effects, the average CD per herd increased if the maternal effects had a high genetic correlation with the direct effects, but the percentage of connected herds for maternal effects was very low, less than 12%.The degree of connectedness in a bovine population bred by natural service mating, such as Bruna del Pirineus beef cattle, measured as the CD of comparisons among herds, is high. It is possible to define a pool of animals for which estimated breeding values can be compared after an across-herds genetic evaluation, especially for highly heritable traits. The best linear unbiased prediction (BLUP) of breeding values allows meaningful comparisons between animals, but only when genetic links exist between the different environments (e.g. ). ConnecLaloë  has defiThis method was applied by Fouilloux et al.  to beef Bruna dels Pirineus is a local beef breed selected from the old Brown Swiss (derived from the Canton Schwyz), which is similar to the American Braunvieh. The herds are located in the Pyrenean mountain areas of Catalonia (Spain). Genetic differences among beef herds are likely. Herd sizes are generally small, relative to other livestock species, and artificial insemination (AI), an effective tool for connecting herds of other beef and dairy cattle, is practically nonexistent in this breed. In contrast to other countries, cooperative breeding schemes, designed to create such genetic links , have beThe objective of this study was to measure the connectedness among herds of beef cattle bred by natural service. In particular, the CD of comparisons between Bruna dels Pirineus herds will be computed using a sampling method based on an animal model and clusters of well-connected herds will be formed. This study should permit the determination of the risk of bias when comparing and selecting animals from different herds on estimated breeding values (EBV), and the results obtained can then be used as a reference for other beef cattle breeds, which are almost exclusively bred by natural service.Data of the on-farm beef cattle evaluation for the Bruna dels Pirineus breed were used in this study. The dataset consisted of 28546 records and the total number of animals in the pedigree file was 35546. The genetic evaluation model was an animal model that included sex (2 levels), parity (10 levels), twins (2 levels), herd effect (76 levels), month (12 levels) and year (26 levels) as fixed effects. The connectedness was studied among the 76 herds that had calf performances recorded during the last five years.The method presented by Fouilloux and Laloë  to estim1- Starting from the pedigree of the population, the animals involved in the simulation are sorted from the oldest to the youngest. An animal model, including pedigree with full relationships, was used for the simulation. The same one was used in the EBV prediction model.ui of the animal i is calculated according to the status of its sire (j) and dam (k). If j and k are unknown, ui is generated from ui is calculated by ui = 0.5uj + φi where φi is drawn from ui is calculated by ui = 0.5uk + φi where φi is drawn from ui is calculated by ui = 0.5(uj + uk) + φi where φi is drawn from 2- The direct genetic value yi = hi + ui + ei was simulated using its generated breeding value ui and a residual ei drawn from hi were simulated multiplying a value drawn from U by twice the phenotypic standard deviation. The remaining fixed effects were set to 0.3- Performance of each performance-tested animal y. BLUP was estimated using PEST software, ceasing iteration when the convergence criterion was less than 10-6. This process repeated n times leads to vectors of true (simulated) {uk}k = 1, n and estimated breeding values 4- The vector of BLUP estimated breeding values 5- The CD of contrasts of interest are estimated by computing their empirical variances and covariances (quoted with *) following Fouilloux et al. :withandc'u). For instance, on one hand, the CD of the breeding value of a single animal (i.e. its reliability) is obtained by using a vector c' null except a 1 in the appropriate position corresponding to this breeding value. On the other hand, the CD of contrasts among herds i and j is obtained by using a vector c' null except a mi and mj were respectively the number of animals in herd i and j.Typically, a given contrast can be written as a linear combination of the breeding values , moderate (0.25) and high (0.40) genetic variations. Second, the results of an animal model were compared with results from a sire model. In such a case, the data were simulated using an animal model with pedigree but the genetic evaluation was done using a sire model. Here, two models were evaluated: (i) the sire model does not take into account the pedigree, i.e. the sire effects follow a u =  ~ MVN and the residual values were simulated in Step 3 as e =  ~ MVN. The genetic and residual (co)variance matrices were respectively:Third, the estimation of CD was implemented for multi-trait animal models where the genetic values were simulated in Step 2 as Two different multi-trait scenarios were simulated: (i) a lowly heritable trait (0.10) with a moderate negative genetic correlation (-0.25) and moderately heritable trait (0.40); and (ii) a lowly heritable trait (0.10) with a high negative genetic correlation (-0.50) and highly heritable trait (0.40). First, these two scenarios were simulated with a null residual correlation but, as a null residual correlation was not always realistic, the effect of a non-null residual correlation was checked by simulating residual correlations with the same magnitude of the genetic correlations. The simulated data were analyzed jointly in Step 4, but the CDs were estimated separately for each trait in Step 5.u m] ~ MVN. The genetic and residual (co)variance matrices were, respectively:Fourth, the estimation of CD was implemented for models with maternal effects, where the direct and maternal genetic values were simulated in Step 2 as [yi = hi + ui + mk + ei was simulated using the herd effect hi, its generated direct breeding value ui, the maternal breeding value of its dam mk and a residual ei drawn from Two different scenarios with maternal effects were simulated: (i) a trait with a lowly heritable maternal effect (0.10), moderate negative genetic correlation (-0.25) and moderately heritable direct effect (0.25), and (ii) a trait with lowly heritable maternal effect (0.10), high negative genetic correlation (-0.50) and highly heritable direct effect (0.40). Both scenarios were compared in the case of a null genetic correlation among maternal and direct effects. In Step 3, the performance of each performance-tested animal First, the sampling method to estimate CD (reliabilities) of estimated breeding values was applied to an animal model. The mean reliability of the 28546 animals with data decreased from 0.51 to 0.22 as the heritability decreased from a high (0.40) to a low (0.10) value  and high (-0.50) genetic correlation respectively ; in particular, the reliability of dams for maternal effects was 0.21. This reliability increased if a genetic correlation with the direct effects existed. The increase was equal to 0.04 point if the genetic correlation was high (-0.5) with a highly heritable trait (0.40) Table . HoweverOnce the 76 × 76 matrix of CD of contrasts among herds was estimated, the average CD per herd was calculated as the mean of the 76 CD values of each herd column. Later on, mean, standard deviation, minimum and maximum of the 76 average CD per herd were calculated. The mean of average CDs per herd in the single-trait animal model decreased from 0.53 to 0.31 as the simulated heritabilities decreased from 0.40 to 0.10. The percentage of herds contrasts with CD higher than 0.4 decreased with the heritability from 85.93% to 25.54% , but the average CD for maternal effects were lower than in the single-trait evaluation, i.e. 0.19 vs. 0.31 respectively Table . The perThe clustering procedure was applied to the 76 × 76 matrix of CD of contrasts among herds. In the moderate heritability scenario (0.25), a big cluster was found including 48 herds Figure . Two morThe BLUP of breeding values allows comparisons between animals if the reliability is high enough, but the individual reliability is not a sufficient measure of risk in comparing animals across herds, and does not reflect potential bias in models that exclude genetic groups or increased error associated with fitting genetic groups . A betteThe reliability of comparisons among herds increased using an animal model because more pedigree information was added, especially the connections due to maternal and paternal grandsires. In the Bruna dels Pirineus breed, Tarres et al.  found thConnectedness in genetic evaluations for lowly heritable traits can be improved by performing joint evaluations with more heritable and highly correlated traits, especially if the residual correlation among these traits is nearly null. Our results agree with Schaeffer , in the For traits with direct and maternal effects, the CDs of comparisons among herds were considerably high for direct effects. In the case of maternal effects, they can be better evaluated if a high genetic correlation exists with the direct effects. This favors the evaluation of the maternal effects for birth weight that had a heritability of 0.10 and a high negative genetic correlation (-0.5) to the highly heritable direct effect (0.40) . For weaAs a result of these links, most of the herds of the Bruna dels Pirineus breed were well connected, especially for moderately and highly heritable traits. The herds of this breed were located primarily within the same region: the Pyrenean area of Catalonia (Spain). Because almost all of the matings in this beef population were by natural service, the close proximity of these herds has made bulls' and heifers' exchanges more feasible. Furthermore, because they are a one-purpose breed raised for meat production, Bruna dels Pirineus breeders participating in the YRS have similar breeding objectives, creating the potential for many herds to purchase and to use related individuals. This can explain the fact that many of the herds were well connected. According to the results of the connectedness study and although all performances must be included in the genetic evaluation, only genetic values of animals coming from connected herds should be published at a "racial level," while genetic values of animals coming from disconnected herds should be used only within herds or provided with a warning that comparisons between poorly connected herds may be biased. By using sires from well-connected YRS herds, the disconnected herds should, quickly, become strongly connected with other Bruna dels Pirineus herds in the YRS. New herds entering the YRS can, therefore, become rapidly connected to the entire breed by purchasing sires from herds that are already well connected. Exchange of bulls and purchase of bulls from other herds can increase connectedness effectively and reduce the risk of bias when EBVs of animals from different herds are compared .The own dynamics of a beef cattle population bred by natural service could imply an important exchange of breeding animals between herds (connections) that could explain the high CD of comparisons found among herds. It was worthwhile to use an animal model when performing the sampling method to estimate the CD because adding pedigree information and, especially, considering the connections due to the dams, increased the CD values. Connectedness in genetic evaluations for lowly heritable traits can be improved by performing joint evaluations with more heritable traits with a high genetic correlation. Maternal effects can also be evaluated better if a high genetic correlation with direct effects exists. As a result of these links, most of the Bruna dels Pirineus herds were well connected and the genetic evaluation will allow producers to identify breeding animals that are potentially better than their own, especially for moderately and highly heritable traits. The genetic values of animals coming from connected herds should be published at a "racial level," while genetic values of animals coming from disconnected herds should be used only within herds or provided with a warning that comparisons between poorly connected herds may be biased.BLUP: best linear unbiased prediction; CACO: criterion of admission to the group of connected herds; CD: coefficient of determination; EBV: estimated breeding values; YRS: yield recording scheme.The authors declare that they have no competing interests.JT performed the statistical analysis and drafted the manuscript. MF managed the YRS of the Bruna dels Pirineus breed and revised the manuscript critically for important intellectual content. JP supervised the YRS, promoted the study and revised the manuscript critically for important intellectual content. All authors read and approved the final manuscript for authors.