We compare and contrast the performance of SIMPLE, a Monte Carlo based software, with that of several other methods for linkage and haplotype analyses, focusing on the simulated data from the New York City population. First, a whole-genome scan study based on the microsatellite markers was performed using GENEHUNTER. Because GENEHUNTER had to drop individuals for many of the pedigrees, we performed a follow-up study focusing on several regions of interest using SIMPLE, which can handle all pedigrees in their entirety. Second, 3 haplotyping programs, including that in SIMPLE, were used to reconstruct haplotypic configurations in pedigrees. SIMPLE emerges clearly as a preferred tool, as it can handle large pedigrees and produces haplotypic configurations without double recombinant haplotypes. For this study, we had knowledge of the simulating models at the time we performed the analysis. SIMPLE is a software package based on a Monte Carlo sequential imputation method. In particular, the S-pairs statistic has been implemented and well tested [Whole-genome scan (WGS) with microsatellite markers is currently one of the frequently used strategies in preliminary linkage analysis. For complex traits such as Kofendrerd Personality Disorder (KPD), nonparametric linkage (NPL) methods based on allele sharing statistics are popular approaches, as the underlying genetic models are complex and hard to estimate. In particular, the S-pairs statistic implemented in GENEHUNTER (GH)  is frequl tested .In post-genome research, as high-throughput data become increasingly available at a relatively low cost, greater attention has been given to haplotype analysis, including estimation of population haplotype frequencies and reconstruction of haplotypic configurations (HCs) in pedigrees. Haplotypes reconstructed for individuals in pedigrees can be used for association studies. They can also point to (genotyping) errors if multiple (double or more) recombinations occur in a small chromosomal segment. In the current study, we focus on comparing 2 types of methods for reconstructing haplotypes for pedigrees. One is rule/combinatorial-based; we use the PEDPHASE program  with theSince New York City is the only population among the 4 in the simulated data consisting of extended pedigrees, we focused on that population. The phenotype of interest is the affection status for KPD. We performed the linkage analysis using the microsatellite markers. For the haplotype analysis, we focused on the region of interest on chromosome 3 (at the end of the chromosome) identified from our linkage analysis. Specifically, we used the last 8 3-cM-density single-nucleotide polymorphism (SNPs) on chromosome 3.SIMPLE ,5 is a MFor haplotype analysis, the imputed ordered genotypes and the associated importance sampling weights are used to form consistent estimates of the probabilities of HCs. Thus, this likelihood-based method can examine the whole distribution of HC, and can offer multiple HCs for further consideration, such as for usage in an association study. The class of chi-square recombination models, which has been demonstrated to fit human data adequately , is alsoWe also used the software package GENEHUNTER  for NPL PEDPHASE  is a sofThe WGS analysis using the microsatellite markers on all 4 populations and a number of replicates identified 4 regions  with high NPL scores from GH, although the results from New York City is the least significant. Therefore, we performed a follow-up analysis focusing on these 4 regions (based on 8 microsatellite markers in each of the regions) using the first replicate from the New York City population to see whether SIMPLE can provide any improvement, since it can use information from all individuals. Note that for this replicate, GH had to drop some individuals in 34 of the 50 pedigrees in the dataset. The results in Figure Eight SNPs on chromosome 3, C03R0274-C03R0281, from the first New York City replicate were used in the haplotype analysis. Except for pedigrees 34 and 36, the best HCs in the other pedigrees inferred from SIMPLE (with both m0 and m4), GH, and PEDPHASE all have only single recombinations. Furthermore, the numbers of recombinations in the inferred HCs from SIMPLE match those from PEDPHASE as well as those from GH for the pedigrees that can be analyzed as a whole. The numbers of individuals dropped by GH in the other pedigrees are shown in Table For pedigree 36, under PEDPHASE, GH, and SIMPLE m0, the HCs inferred all have a total of 7 recombinations, each including a double recombinant haplotype  in individual 3. These results are shown in Figure Since GH cannot analyze pedigree 34 as a whole, we focus on the results from SIMPLE and PEDPHASE only. For SIMPLE, both m parameters lead to a HC with 7 single recombinations, although the 2 HCs differ in several individuals in the first and second generations. On the other hand, although the HC inferred by PEDPHASE also has a total of 7 recombinations, it includes a double recombinant haplotype  in individual 10, as opposed to 2 single recombinations, one on each chromosome, under SIMPLE. This shows that using MRHC as a criterion can be problematic because it may lead to a configuration with multiple recombinations within a small segment of the chromosome, a situation often regarded as potential error.Although substantial power gains over GH can be obtained using SIMPLE, the differences between the SIMPLE and GH scores are small for the first replicate from the New York City population. The most likely explanation is that because there are only a couple of affected individuals among those dropped, the amount of information lost using GH is negligible.Reconstructing HCs on pedigrees by minimizing the total number of recombinations (PEDPHASE) or maximizing the probability of the configuration (SIMPLE and GH) are 2 competing objectives. Through the analyses of the 50 New York City pedigrees, it is clear that observing the latter objective can lead to results that are comparable or better than those based on achieving the former objective (as it is currently implemented in PEDPHASE). More importantly, the ability to account for interference is a valuable asset that cannot be discounted. As we have seen here, if interference is known to exist but is being ignored, the HCs inferred  can be misleading, which may diminish the usefulness of these haplotypes in genetic studies as they may be regarded as errors.On a different note, different HCs caused by the different formations of a founder's haplotype pair, but with similar recombination features for the rest of the individuals in the pedigree, as we see in pedigree 34, can emerge as competing configurations. Under the linkage equilibrium assumption, made by both SIMPLE and GH, these configurations may be equally probable. For markers that are closely linked, especially for SNPs within a gene, the assumption of linkage equilibrium is almost certainly to be violated. One way of eliminating the linkage equilibrium assumption in SIMPLE is to make use of population haplotype frequencies. To this end, we have investigated the performances of several programs, including SNPEM and PHASE, with a purchased package of SNPs located at the end of chromosome 3. We found that the results from all programs show strong linkage disequilibrium in the region, indicating that the linkage equilibrium assumption needs to be lifted before SIMPLE can be applied to correctly infer haplotypes based on these SNP data. However, the estimated population haplotype frequencies from different programs are inconsistent, signaling the need for further investigations before these estimated population frequencies can be incorporated into SIMPLE.GH: GENEHUNTERHCs: Haplotypic configurationsHMM: Hidden Markov modelKPD: Kofendrerd Personality DisorderMRHC: Minimum recombinant haplotypic configurationNPL: Nonparametric linkageSNP: Single-nucleotide polymorphismWGS: Whole-genome scanSL designed the study and wrote the manuscript. All authors contributed to the analyses performed, read and approved the final manuscript.


Heritable electrocardiographic (ECG) and heart rate variability (HRV) measures, reflecting pacemaking, conduction, repolarization and autonomic function in the heart have been associated with risks for cardiac arrhythmias. Whereas several rare monogenic conditions with extreme phenotypes have been noted, few common genetic factors contributing to interindividual variability in ECG and HRV measures have been identified. We report the results of a community-based genomewide association study of six ECG and HRV intermediate traits.Genotyping using Affymetrix 100K GeneChip was conducted on 1345 related Framingham Heart Study Original and Offspring cohort participants. We analyzed 1175 Original and Offspring participants with ECG data  and 548 Offspring participants with HRV data , in relation to 70,987 SNPs with minor allele frequency ≥ 0.10, call rate ≥ 80%, Hardy-Weinberg p-value ≥ 0.001. We used generalized estimating equations to test association of SNP alleles with multivariable-adjusted residuals for QT, RR, and PR intervals, the ratio of low frequency to high frequency power (LF/HFP), total power (TP) and the standard deviation of normal RR intervals (SDNN).-3 were found for 117 (QT), 105 (RR), 111 (PR), 102 (LF/HF), 121 (TP), and 102 (SDNN) SNPs. Several common variants in NOS1AP  were associated with adjusted QT residuals, consistent with our previously reported finding for NOS1AP in an unrelated sample of FHS Offspring and other cohorts. All results are publicly available at NCBI's dbGaP at http://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?id=phs000007.Associations at p < 10bona fide QT-associated SNPs among the top 117 results for QT duration supports the importance of efforts to validate top results from the reported scans. Finding genetic variants associated with ECG and HRV quantitative traits may identify novel genes and pathways implicated in arrhythmogenesis and allow for improved recognition of individuals at high risk for arrhythmias in the general population.In the community-based Framingham Heart Study none of the ECG and HRV results individually attained genomewide significance. However, the presence of  Quantitative non-invasive measures of cardiac electrical activity recorded in electrocardiographic (ECG) and heart rate variability (HRV) studies are widely available in community-based samples and have been found to be predictive of cardiovascular events including sudden cardiac death -7. AggrePrior studies, including our own, have reported the heritability of common indices of myocardial repolarization and HRV measures. The heritability of electrocardiographic QT interval duration, a measure of myocardial repolarization, has been reported to be approximately 35%, indicating that 35% of the variability in adjusted QT interval duration is attributable to heritable factors -11. ElecThe heritability of ECG and HRV traits suggests there is a significant genetic component to the determination of these measures of myocardial repolarization, sinus node function, atrioventricular conduction, and autonomic function. Rare variants in ion channel genes have been implicated in rare Mendelian Long QT Syndromes. Historically, efforts to identify genetic determinants of common, complex traits have been focused on linkage or association of a small number of such biologic candidate genes with limited success and conflicting results.INSIG2 and obesity . We After filtering all autosomal SNPs on call rate ≥ 80%, minor allele frequency ≥ 0.10 and Hardy-Weinberg p-value ≥ 0.001, we observed a distribution of the 70,987 p-values that approximated a null distribution. The proportions of p < 0.0001 or p < 0.001 averaged across all six ECG and HRV phenotypes were 0.00018 and 0.0016, respectively Table . The prohttp://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?id=phs000007. From the primary GEE analyses, the strongest associations for the QT, RR and PR phenotypes were for SNPs rs10507380 (p = 8.4 × 10-6), rs2179896 (p = 1.7 × 10-5), and rs882300 (p = 3.2 × 10-7), respectively (Table -6), rs9315385 (p = 7.7 × 10-6), and rs2966762 (p = 2.0 × 10-5), respectively (Table -3 were found for 117 (QT), 105 (RR), 111 (PR), 102 (LFHFP), 121 (TP), and 102 SNPs (SDNN).Results can be found at NOS1AP gene with adjusted QT interval variation in 3 independent cohorts, including an unrelated set of Framingham Heart Study participants (on the Unrelated Plates), as part of a three-stage genome-wide association study [NOS1AP, all partially correlated with rs10494366: rs6683968 , rs945713  and rs1932933 . For illustrative purposes, we further considered a two-staged design in which one genotyped all SNPs associated with the QT phenotype with p < 0.001 (n = 117) found in the Related Plate set 100K analysis in an additional approximately 1500 independent Framingham offspring cohort participants on the unrelated plate set . In such a design the p-value for SNP rs10494366 of 0.0009 would rise to a combined p-value of 8.9 × 10-6 on joint analysis of the two samples.We have previously reported the association of a common variant rs10494366 (MAF 38%) in the on study . In the We observed suggestive evidence of linkage to the following phenotypes with LOD scores exceeding 2.2: LOD 2.50 on chromosome 3 (8.72 Mb) for QT interval, which has previously been reported for a largely overlapping sample using microsatellite markers ; 2.52 onNOS1AP had p < 0.05 for association with QT interval duration  in 9 genes implicated in congenital Long QT Syndromes or QT interval duration, only SNPs in -7 required for Bonferroni correction for six traits and 70,987 SNPs. The failure to achieve a genome-wide p-value threshold reflects the massive penalty incurred by testing so many hypotheses and the limited power to achieve such a p-value given the modest effects of common variants that contribute to complex traits. However, the presence among the test results with nominal p < 0.001 for association with QT interval duration of common variants at the NOS1AP locus, a recently identified and multiply replicated myocardial repolarization gene [We confirmed the heritability of electrocardiographic RR interval (inverse heart rate) and PR interval and reproduced our previously demonstrated findings that QT interval and HRV traits are heritable in our community-based European ancestry sample ,16. We hion gene , supportStrengths of our study include the moderate-sized, well-characterized community-based sample, without ascertainment on phenotype, and the precision of the ECG and HRV measurements as supported by their substantial heritability. Some limitations pertain. Our study had limited power to detect modest genetic effects in a single stage. The Affymetrix 100K GeneChip, a first generation genotyping array, has patchy coverage of common genetic variation, leaving many regions untested. Our sample is almost exclusively of European ancestry, potentially limiting extension to other populations with different linkage disequilibrium patterns or environmental exposures.Staged GWAS designs in which a modest number of results from GWAS in the first stage are tested in a second independent sample and the combined statistical evidence considered, are powerful and efficient approaches to identify common variants associated with complex traits ,30. SuchECG = electrocardiogram; FBAT = family-based association test; GEE = generalized estimating equations; GWAS = genome wide association study; HRV = heart rate variability; LF/HF = ratio of low frequency to high frequency power; LOD = log-likelihood ratio; SNP = single nucleotide polymorphism; TP = total powerThe authors declare that they have no competing interests.Drs. Larson and Newton-Cheh had full access to all of the data in the study and take responsibility for the integrity of the data and the accuracy of the data analysis.Study concept and design: Newton-Cheh, Levy, O'Donnell, Larson; Acquisition of data: Levy, O'Donnell, Newton-Cheh; Analysis and interpretation of data: Newton-Cheh, Larson, O'Donnell, Levy, Guo; Drafting of the manuscript: Newton-Cheh; Critical revision of the manuscript for important intellectual content: Larson, Levy, O'Donnell, Wang; Statistical expertise: Guo, Larson; Administrative, technical, or material support: Levy, O'Donnell; Study supervision: Newton-Cheh, Larson, Levy, O'Donnell.


H19, and we genotyped three of these SNPs in families from the contemporary ALSPAC UK birth cohort  in order to explore associations with size at birth and cord blood IGF-II levels.Common genetic variation at genes that are imprinted and exclusively maternally expressed could explain the apparent maternal-specific inheritance of low birthweight reported in large family pedigrees. We identified ten single nucleotide polymorphisms (SNPs) in H19 2992C>T SNP genotypes showed associations with offspring birthweight (P = 0.03 to P = 0.003) and mother's genotype was also associated with cord blood IGF-II levels (P = 0.0003 to P = 0.0001). The offspring genotype association with birthweight was independent of mother's genotype (P = 0.01 to P = 0.007). However, mother's untransmitted H19 2992T allele was also associated with larger birthweight (P = 0.04) and higher cord blood IGF-II levels (P = 0.002), suggesting a direct effect of mother's genotype on placental IGF-II expression and fetal growth. The association between mother's untransmitted allele and cord blood IGF-II levels was more apparent in offspring of first pregnancies than subsequent pregnancies (P-interaction = 0.03). Study of the independent Cambridge birth cohort with available DNA in mothers (N = 646) provided additional support for mother's H19 2992 genotype associations with birthweight (P = 0.04) and with mother's glucose levels (P = 0.01) in first pregnancies.Both offspring's and mother's H19 2992T allele, in the mother or offspring or both, may confer reduced fetal growth restraint, as indicated by associations with larger offspring birth size, higher cord blood IGF-II levels, and lower compensatory early postnatal catch-up weight gain, that are more evident among mother's smaller first-born infants.The common  Parent-of-origin effects were sought using quantitative and qualitative methods, allowing for possible confounding by the effects of non-transmission of mother's alleles [Associations between offspring or mother's genotype and size at birth were determined by ANOVA. Multivariate analysis  was used to identify independent effects of mother's and offspring genotypes. Associations with  alleles ,37.ALSPAC – Avon Longitudinal Study of Parents and ChildrenIGF – insulin-like growth factorPrimip – primiparousSNP – single nucleotide polymorphismCP performed genotyping and drafted the manuscript. KO contributed to the study design, and co-ordination, performed statistical analyses and drafted the manuscript. BB performed SNP identification, and contributed to the study design. DW performed Cambridge cohort recruitment, DNA preparation and genotyping. HC performed statistical analyses. SR supervised preparation of ALSPAC DNA samples and validation of genotyping results. MR participated in the design and co-ordination of the ALSPAC study, and supervised DNA management. WR participated in the conception and design of the study. JT supervised SNP identification, genotyping and data analyses. DD was responsible for the study conception, and contributed to the study coordination, analyses and drafting the manuscript. All authors read and approved the final manuscript.H19 2992/1737/3238 genotypes .Birthweight SD score  by combination of Click here for fileH19 indicating exons, SNPs published on dbSNP and also published SNPs identified by the Juvenile Diabetes Research Foundation/Wellcome Trust Diabetes and Inflammation Laboratory (DIL) T1Dbase . H19 2992 is indicated by the labels rs217727 and DIL1049.Schematic map of Click here for file


Arabidopsis thaliana accessions, and that established methods for controlling for population structure are generally insufficient. Here, we use the same sample together with a number of flowering-related phenotypes and data-perturbation simulations to evaluate a wider range of methods for controlling for population structure. We find that, in terms of reducing the false-positive rate while maintaining statistical power, a recently introduced mixed-model approach that takes genome-wide differences in relatedness into account via estimated pairwise kinship coefficients generally performs best. By combining the association results with results from linkage mapping in F2 crosses, we identify one previously known true positive and several promising new associations, but also demonstrate the existence of both false positives and false negatives. Our results illustrate the potential of genome-wide association scans as a tool for dissecting the genetics of natural variation, while at the same time highlighting the pitfalls. The importance of study design is clear; our study is severely under-powered both in terms of sample size and marker density. Our results also provide a striking demonstration of confounding by population structure. While statistical methods can be used to ameliorate this problem, they cannot always be effective and are certainly not a substitute for independent evidence, such as that obtained via crosses or transgenic experiments. Ultimately, association mapping is a powerful tool for identifying a list of candidates that is short enough to permit further genetic study.A potentially serious disadvantage of association mapping is the fact that marker-trait associations may arise from confounding population structure as well as from linkage to causative polymorphisms. Using genome-wide marker data, we have previously demonstrated that the problem can be severe in a global sample of 95  Arabidopsis thaliana, and that established statistical methods for controlling for population structure are insufficient. Here, we evaluate a broader range of methods. We find that a recently introduced mixed-model approach generally performs best. By combining the association results with results from linkage mapping in F2 crosses, we identify one previously known true positive and several promising new associations, but also demonstrate the existence of both false positives and false negatives. Our results illustrate the potential of genome-wide association scans as a tool for dissecting the genetics of natural variation, while at the same time highlighting the pitfalls.There is currently tremendous interest in using association mapping to find the genes responsible for natural variation, particularly for human disease. In association mapping, researchers seek to identify regions of the genome where individuals who are phenotypically similar  are also unusually closely related. A potentially serious problem is that spurious correlations may arise if the population is structured so that members of a subgroup tend to be much more closely related. We have previously demonstrated that this problem can be severe in  Arabidopsis thaliana [As sequencing and genotyping costs continue to decrease, association mapping  is emerging as a powerful, general tool for identifying alleles and loci responsible for natural variation. Although its application to human disease has received most attention , associathaliana  to cattlthaliana . Indeed,A potentially serious obstacle to association mapping is confounding by population structure. It is well known that population structure may cause spurious correlations, leading to an elevated false-positive rate . WhetherA. thaliana accessions for which genome-wide polymorphism data are available [In an earlier paper, we demonstrated that confounding can be severe in a structured sample of 95 vailable . We alsovailable  and “strvailable , were novailable  and the vailable . We firsWe find that versions of the approach of Yu et al. generally perform best, but a comparison with the results of linkage mapping indicates that some confounding still remains, and, furthermore, that correcting for population structure also introduces false negatives. Nonetheless, the false-positive rate is reduced to levels that make it possibly to use our sample for association mapping, and although our scans have low power due to insufficient marker density and small sample size, we identify a number of plausible associations.FLC [FRI [Mean flowering time for each accession was measured under a variety of experimental conditions, at the University of Southern California (USC) and at the John Innes Centre (JIC). In addition, we measured expression levels of two key flowering time genes: the floral repressor FLC ,20 and iFLC [FRI . The pheFLC [FRI . DependiThe phenotypes were generally strongly correlated across accessions . As expep-values from association scans across all loci for all our phenotypes. The black curves correspond to naive tests of association without correction for population structure. Irrespective of phenotype, the distribution was strongly skewed towards significance, in agreement with our previous observations [And inflated it is. rvations .Pritchard et al.  introducQ matrix) as a fixed effect in the model, as in structured association [Yu et al.  recentlyociation ,14,16.We applied the approach of Yu et al.  to analyQ matrix) and as a random effect (using the K matrix of pairwise kinship coefficients) [Q matrix should be required in addition to the kinship effect. Nonetheless, we found that it is  . While iWe suspected that this might be an artifact of how kinship was estimated. The formula used by Yu et al.  is basedQ matrix and our new kinship estimate as cofactors  be reduced almost as well by using kinship alone. It turns out that the best results were obtained not by considering the fraction of shared SNP alleles, but by considering the fraction of shared fragment haplotypes , presumably because these capture the underlying structure better. As illustrated in tors see . The resQ matrix is that the STRUCTURE algorithm is computationally intensive, and may be impractical on large datasets. With this in mind, Price et al. [Q matrix. We tried this approach as well, and found that although it performed better than using Q alone, it did not perform as well as our modified kinship matrix, nor the approaches that combine kinship estimates with Q. Finally, we tried a mixed-model approach that combined the PCA assignments (the P matrix) with kinship estimates. This approach performed similarly to mixed-models using Q, suggesting that it may be possible to replace the computationally intensive STRUCTURE algorithm with a simple PCA in the mixed-model approach.One reason for investigating methods that do not require the use of the e et al.  suggestep-value for the simulated quantitative trait nucleotide (QTN) was in the 5th percentile (estimated from the genome-wide SNPs).The relative power of the various approaches was compared using data-perturbation simulations. Large numbers of perturbed datasets were generated by assigning a phenotypic effect (expressed as a deviation from the population mean) to randomly chosen SNPs (one per simulated dataset). These datasets were then analyzed using the various approaches, and, for each approach, we recorded the fraction of perturbed datasets for which the While these results might seem to indicate that it is possible to reduce the false-positive rate without paying a price in terms of an increased false-negative rate , this is by no means the case. All the methods used here attempt to reduce confounding by identifying and eliminating genotype–phenotype associations that are in effect genome-wide because they reflect underlying population structure, leaving only those associations that cannot be accounted for by this structure. However, not all the associations thus eliminated will be false; indeed, in a genome-wide scan some of them will almost certainly be true . To givep-value distributions that looked reasonable, we proceeded to analyze the results of our genome-wide scan using the methods that produced reasonably flat p-value distributions. For these analyses, we decided to focus on treating our sequence data as short haplotypes, partly because we expect power to be higher when the information inherent in linkage disequilibrium between SNPs is utilized [Since several of the methods discussed above produced utilized , partly FRI explained between 14% and 24% of the variation for flowering time in the absence of a vernalization treatment , and partly on demonstrable limitations of the study. Our study is clearly underpowered in two different ways . First, reatment . Expectescreened . PuttingThe second reason for skepticism is that the associations observed strongly suggest residual confounding. We have previously noted that many of the strongest associations seem to be due to allele sharing among very late-flowering accessions from Finland and northern Sweden ,27. ThesFRI, and possibly also other loci), the top of Chromosome 5 (with FLC as a strong candidate for at least part of the effect), and the bottom of Chromosome 1 (certainly involving multiple QTL). There was no evidence of any QTL on Chromosomes 2 or 3. Nominally significant associations, in contrast, although far from uniformly distributed, were found across the genome, indicating that most are likely to be spurious even after confounding has been reduced statistically. Note that this argument relies on the linkage mapping experiments having sufficient power; however, it seems unlikely that a QTL would be detectable as an association in a heterogeneous sample of 96 accessions and not be detectable in an F2 cross using twice the sample size.The third and strongest reason for skepticism is direct comparison with linkage mapping results . Figure Given that confounding remains, it was clear that the best we could hope to accomplish was compiling a list of plausible associations worthy of further study. How this should be done is a highly subjective matter. We decided to use consistency across association methods as our main criterion. Specifically, we only consider loci significant at the 0.1% level across all five methods in FRI, the one locus known a priori to be involved in flowering time variation, generally shows the pattern of association we would expect it to show. Particularly noteworthy was the incredibly strong association with FRI expression levels, almost completely due to the cis-regulatory mutation present in Ler and 12 other accessions. Allelic variation at FRI was also associated with variation in FLC expression, in agreement with what is known about the function of these genes [FRI aside, two out six of the significant associations occurred in our candidate genes. Since 18 out of 889 marker loci were located in candidate genes, this is sixteen times more than would be expected by chance. Third, one of the four associations not in a gene identified a priori as a candidate, was in a gene identified a posteriori as a good candidate for being involved in variation for the phenotype with which it was associated . FinCRY2 and FLC, respectively. They claimed to have controlled for population structure by using 79 AFLP markers to identify an “unstratified” population in which to test for associations. This claim was directly contradicted by the observation that the significant associations reported in these papers showed clear geographic patterns, however, and a simple analysis of the distribution of p-values across the AFLP markers reveals a skew similar to the ones we have discussed in this paper  and VERN  for SD, SD/LD (V), and FLC. CRY2 showed no sign of being associated with any phenotype. Clearly, none of these polymorphisms would have been picked up in a genome-wide scan.We decided to investigate these published polymorphisms in our sample, where the genome-wide data would make it possible to evaluate the significance of any associations. Using the various mixed-model approaches, FRI genotype and latitude as terms to the model  often had a dramatic effect on the results. For example, CRY2 was associated  with LDV, SDV, and JIC8W, but became associated with 11 out of 16 phenotypes if FRI genotype was added to the model. The significance of a particular term was often strongly dependent on which other terms were included in the model  often identified what appeared to be highly significant associations. Furthermore, adding he model –S4. ThisQ matrix , the P mP matrix , or selep-values are of course affected by confounding population structure as discussed earlier in this paper, and we therefore attempted to assess their significance by comparing them to the genome-wide distribution of p-values, obtained by testing either all SNPs or short haplotypes in our data using the same model. While this might appear to be a robust procedure guaranteed to yield valid p-values, it is in fact anti-conservative because the candidate polymorphisms were ascertained to be informative about local haplotype structure. For example, the SNPs used to “tag” the three CRY2 “haplogroups” [The nominal ogroups”  are not CRY2 showed no significant associations when compared to the genome-wide distribution of haplotype tests. There were more significant associations than could be expected when genome-wide SNPs were used as a control, but there are several reasons to be skeptical of these: first, the CRY2 polymorphism is in fact a haplotype polymorphism with three alleles, and should thus be compared to the haplotype distribution; second, most of the associations disappear if a CRY2 by FRI interaction term is added to the model; and third, at least one of the associations is directly contradicted by our linkage mapping results (different CRY2 haplotypes segregate in the Col-0 × Ull2–5 cross shown in CRY2 despite an association for JIC8W).Considering the number of phenotypes tested, FLC polymorphism identified by Caicedo et al. [FLC polymorphism was only segregating in one of our crosses, Col-0 × Edi-0, the only one for which a strong QTL effect overlapping FLC was not seen , and weakly significant for ±V (LD) and VERN. The latter two were also weakly significant in the mixed-model analyses. Although the PHYC polymorphism was segregating in all our crosses, we never observed a QTL overlapping it. Again, the phenotypes measured in the crosses are very different from the ones that appear to be associated with PHYC. results , PHYC apassume anything about the importance of population structure in a particular study; it is straightforward to determine the distribution of test statistics empirically by calculating them across large numbers of loci. In genome-wide scans, large numbers of loci will by definition always be available, and for candidate locus studies, our results simply illustrate the need for an appropriate genomic control. Any association result not accompanied by a demonstration that the reported significance values are actually meaningful should be treated with suspicion .There is currently great interest in applying association mapping to a wide range of organisms, many of which  and, more importantly, several independent sources of evidence.We took advantage of our genome-wide data to evaluate published claims of association in n et al.  and any o et al.  is at ben et al.  does appn et al.  nor Caicn et al.  employedn et al.  based thp-values without changing the rankings of loci, are not likely to be useful in genome-wide scans where the existence of true positives is not in doubt. Most biologists will simply rank the associations by nominal significance and proceed to test the most significant. Methods that attempt to separate true from spurious associations, like the ones used in this study, are of much greater interest. Our results demonstrate that such methods can be very effective at reducing (not eliminating) confounding. It is clear that this is a hard problem, and more theoretical work is certainly warranted. Comprehensive simulation studies (with known null distributions) would be required to determine how the different methods perform in terms of the false-positive rate. The mixed-model approach [K matrix) should be estimated might be attainable, whereas the utility of estimators of population structure are likely to vary greatly from case to case. The underlying structure in our sample appears to be some form of isolation-by-distance [A number of statistical approaches for reducing confounding by population structure have been proposed. Methods, like “genomic control” , which sapproach ,36 seemsdistance , and botdistance  and PCA distance  appear tFRI stand out more clearly in our study, it also eliminates many of the best candidates for the extreme late-flowering phenotype characteristic of the northern accessions. Because these accessions are so distinct on a genome-wide level, any late-flowering allele shared by all or most of them would (and should) be removed by a statistical method that reduces confounding. There has to be segregation for mapping to work.At the same time, it is important to recognize that there are limits to what can be achieved using statistics. As noted above, any method that effectively removes confounding will also effectively remove true positives that are strongly correlated with population structure. Thus, while reducing confounding makes the common, widely distributed alleles of FLC, a central regulator of flowering, may be an example of this. Allelic variation at FLC has been shown to affect flowering [FLC expression is strongly correlated with flowering time  does not correspond to the association previously reported by Caicedo et al. [Interestingly, lowering ,38, and lowering . FLC expo et al. . As discFRI is an example, and we do indeed find it. Of the new associations we have identified  or short-day (8 h light/16 h dark) conditions, using a randomized design (except with respect to growth chambers). Seeds were sown on soil and stratified for 2–3 d at 4 °C to synchronize germination. At USC, experiments were carried out in Conviron MTPS72 growth chambers programmed to have a gradual transition between light and dark conditions. Plants were grown at a constant temperature of 18 °C. The vernalization treatment was done at 4 °C on 3–4-d-old seedlings, using the same light conditions as for the unvernalized plants. Conditions at JIC were similar, but plants were grown in a custom-built walk-in controlled environment room using a temperature of 23 °C, and vernalization was done at 5 °C under short-day (8h light) conditions in a Sanyo-Gallenkamp CE with cool white fluorescent lamps only. There were thus clear differences in both temperature and light quality between the USC and JIC experiments.Flowering times were measured in days from germination to the first opening of flowers (USC) or to plant height reached at 5 cm (JIC). All measurements were replicated (using six plants at USC and ten plants at JIC). The variance across replicates was trivial compared to the variance across accessions; including it in the analyses did not seem to affect results and we therefore carried out all analyses using the accession means. The experiments were continued until either all individuals had flowered or the rate of new individuals starting to flower was deemed to have reached zero. When an experiment was stopped before all accessions had flowered, the remaining individuals were assigned the stopping date as phenotype (the resulting phenotypic distributions can be seen in FT(t) −bt= ae, where FT(t) is the flowering time after t weeks of vernalization. The decay slope b was then used as the phenotype in association mapping.As indicated in FRI and FLC expression was measured as described in Shindo et al. [o et al. . All phey, is modeled asX contains the genotypes, α is vector of allele effects to be estimated, Q contains the population assignments by STRUCTURE, β is vector of subpopulation effects, I is an identity matrix, u are the random deviates due to genome-wide relatedness, and e are random deviates due to noise. Crucially, the phenotypic covariance matrix is assumed to have the formK is the matrix of kinship coefficients, Our basic analyses, including our implementation of “structured association” and estimation of population structure using STRUCTURE  have beeK used by Yu et al. [K*. The former contains the relative kinship coefficients of Ritland [i and j is defined as ij =K (ij − QmQ)/(1 − mQ), where ijQ is the probability of identity in state for random loci from i and j, and mQ is the average probability of identity by state for loci from random individuals from the sample. With this definition, a negative relative kinship coefficient means that the particular pair of accessions is less related than random individuals. In the analysis, all negative values were set to zero [We also varied how we estimated the kinship coefficients. Results are presented for two different choices: the u et al. , and our Ritland  estimate Ritland  from abo Ritland . In this to zero .K*, which contains kinship coefficients defined simply as the proportion of shared haplotypes (with singletons removed) for each pair of individuals.As an alternative to this approach, we introduced All analyses were done using standard methods as implemented in SAS using PROC MIXED. The significance of the fixed effects was obtained from F-tests with the denominator degrees of freedom obtained using the Satterthwaite method .2 statistic with Spearman's rank correlation.We tested the principal components method using a modified version of EIGENSTRAT . Since oQ matrix produced by STRUCTURE with a P matrix containing the eight top principal components from EIGENSTRAT.Finally, we tried a mixed-model approach where we simply replaced the A simulation scheme similar to that of Yu et al.  was usedCausal SNPs were randomly chosen from SNPs with minor allele frequency in the 20%–40% range. A fixed genetic effect was added to each causal SNP. Fixed effects ranging from 0.2 to 1.4 times the standard deviation of the phenotype were used. The percentage of the total phenotypic variation explained by each causal SNP (which depends on the frequency of the SNP as well as its effect) was calculated using a standard linear regression of phenotype on SNP.Col-0 to six different accessions chosen because of their differential response in our association study. Four of these crosses have previously reported by Shindo et al. [(Col-0 × Knox-18 and Col-0 × RRS-10) are reported for the first time here. For details about the crosses, please see [QTL mapping for flowering time was carried out in six F2 populations generated by crossing o et al. , whereasease see .Analysis was done using composite interval mapping as implemented in QTL Cartographer .Dataset S1(5 KB CSV)Click here for additional data file.Dataset S2(1.0 MB ZIP)Click here for additional data file.Dataset S3(8.0 MB ZIP)Click here for additional data file.Figure S1(10 KB PDF)Click here for additional data file.Figure S2(1.2 MB PDF)Click here for additional data file.Figure S3(86 KB PDF)Click here for additional data file.Figure S4p-values from tests of association between genotype and phenotype. The dashed grey line marks a nominal significance level of 0.1%. The position of the candidate genes are highlighted. Nominally significant associations occur throughout the genome, and often correlated across phenotypes.Peak heights represent negative log (132 KB PDF)Click here for additional data file.Figure S5(131 KB PDF)Click here for additional data file.Figure S6(133 KB PDF)Click here for additional data file.Figure S7(126 KB PDF)Click here for additional data file.Figure S8(131 KB PDF)Click here for additional data file.Figure S9The position of certain candidate genes are highlighted in yellow.Col-0 × Kno-18 (blue curve). The dashed grey line marks a genome-wide permutation significance level of 5%.(A) The QTL LOD scores for the cross p-values from a genome-wide scan using the Q + K model.(B ) Negative log p-values from a genome-wide scan using a naive Kruskal-Wallis approach.(C) Negative log (B and C) The dashed grey line marks a nominal significance level of 0.1%, and the colored stars denote associations that should correspond to QTL in the cross.(64 KB PDF)Click here for additional data file.Figure S10The position of certain candidate genes are highlighted in yellow.Col-0 × RRS-10 (black curve), Col-0 × Var2–6 (red curve), and Col-0 × Ull2–5 (green curve). The dashed grey line marks a genome-wide permutation significance level of 5%.(A) The QTL LOD scores for three crosses: p-values from a genome-wide scan using the Q + K model.(B) Negative log p-values from a genome-wide scan using a naive Kruskal-Wallis approach.(C) Negative log In (B) and (C), the dashed grey line marks a nominal significance level of 0.001, and the colored stars denote associations that should correspond to QTL in the cross displayed using the same color.(71 KB PDF)Click here for additional data file.Figure S11(54 KB PDF)Click here for additional data file.Figure S12(11 KB PDF)Click here for additional data file.Table S1(17 KB PDF)Click here for additional data file.Table S2(25 KB PDF)Click here for additional data file.Table S3(18 KB PDF)Click here for additional data file.Table S4(18 KB PDF)Click here for additional data file.


A genome-wide linkage scan was performed on Replicate 1 of the simulated data for fasting triglyceride levels. The aim of this study was to implement mixed-model methodology to estimate breeding values for each individual for this trait and to assess the merit of these breeding values in linkage analysis. These breeding values utilize all the pedigree information, and the genetic and phenotypic correlations with other measured traits across the two cohorts. A genome-wide linkage scan was run on both the new breeding value traits and the original traits.Using breeding values, a maximum LOD of 7.78 was found on chromosome 5 at a position very close to a gene underlying the triglyceride levels. This effect was not detected using the original trait.The results imply that estimating breeding values may be a suitable method of deriving traits for use in genome-wide scans. The best linear unbiased prediction (BLUP) of the breeding value of an individual for a quantitative trait can be calculated by taking into account the genetic and environmental covariances among all related individuals and across all correlated traits ,2. Data Here we explore the merit of using BLUP to generate breeding values for input into a genome scan. Our motivation is that frequently in human genetic analysis there is a primary trait of interest together with a number of covariates that may also be heritable. To improve the precision of measurement of the primary trait, we wish to remove the effect of any environmental covariation with the other traits, but include the effect of any genetic covariation. This is in essence what the animal model achieves.For purposes of illustration, we have used fasting triglyceride level as our primary trait.We chose to analyze Replicate 1 of the complete simulated data sets without any knowledge of the underlying simulation model or the location of the trait loci.The original number of pedigrees from Replicate 1  was 330 families. These comprised 4690 individuals with an average family size of 14, ranging between 7 and 84 individuals. After creating nuclear families (for the genome scan), 1444 pedigrees comprising 5808 individuals were formed, with a family average size of 4, ranging between 3 and 12 members.The following account is taken from Mrode . SimilarFor a mixed model where all genetic variance is additive, the model isi = Xibi + Ziai + ei, y    (1)yi is a vector of observations on individuals, bi is a vector of fixed effects (sex and cohort in this case), ai is a vector of random additive genetic effects , and ei is a vector of random residual effects. Xi and Zi are incidence matrices relating the observations to the respective fixed and random effects, in all cases, subscript i relates to the ith trait.where a and b are usually estimated simultaneously by solving Henderson's [derson's  mixed moX and Z are as defined in equation (1). G is the additive genetic variance and covariance matrix for individual effects, R is the variance covariance matrix for residual effects, and A is the numerator relationship matrix that indicates the additive genetic relationship between each possible pair of individuals, for example in the absence of inbreeding, 1/2 for full sibs, 1/4 for grandparent-grandchild and 1.0 for an individual with him/herself .where A model for a multivariate analysis for two traits could be written as:The extension of model (3) for more than two traits follows the same pattern. Multivariate models have a corresponding increase in complexity for the MME, for more details see .G and R are unknown, these are also estimated from the MME. Here, all parameters were estimated utilizing the analytical gradient method of REML (restricted maximum likelihood) implemented in VCE [If d in VCE . The metEstimation of breeding values in this manner takes into account the presence and absence of data for all traits on all related individuals within a population. As a result, all individuals in the population have an estimated breeding value for all traits. In the extreme case of an individual with no observations and no relatives, the breeding value for a trait on that individual is the estimate of the population mean for that trait. With complete data on all individuals in a pedigree, estimated breeding values still differ from observed phenotype values: genetic and environmental correlations are used to include data on other traits measured on the same individual to improve precision, and genetic correlations similarly allow the inclusion of data from relatives. In the present context, aside from handling problems of sporadic missing observations, this means that breeding values for traits only measured in Cohort 1 can be estimated for individuals in Cohort 2, and vice versa.To fit limitations of time and software, principal component analyses (PCA) were used to construct new traits from the longitudinal data for each cohort using Genstat . The newAll longitudinal measurements were used from the Cohort 2 data for estimating these new PCA traits. Only a selection of such measurements were used from Cohort 1 to keep missing values in the two cohorts comparable: the implementation of PCA does not permit missing values in the component traits, and Cohort 1 had more missing values because measurements were taken over a much longer period of time. For Cohort 1, the original first measurement for fasting triglycerides was used instead of a PCA trait, as subsequent measurements have many missing values.Although this procedure was applied to all traits with multiple measurements, due to software limitations only seven were taken forward for estimation of breeding values. These seven, three from Cohort 1 and four from Cohort 2, were selected based on the genetic and phenotypic correlations between the traits within each cohort. The aim was to select traits that contributed most in estimating genetic and phenotypic variance components for triglyceride, the primary trait of interest in this analysis. A summary of the chosen traits is in Table Five traits were analyzed separately in the genome-wide scan: triglyceride EBVs from Cohorts 1 and 2 , a simple average triglyceride trait from both cohorts in which every individual with a TG measurement on any occasion had a value (TG12_pooled), first PCA for Cohort 2 (TG2_PCA), and the original first TG measurement for Cohort 1 . These last three traits were included to compare with the EBV traits. Mega2 ,10 was uMerlin-regress  was usedSummaries of the maximum LOD scores from the regression method (using Merlin-regress) for the five genome-scans are in Table The pattern of results from the two cohorts was very similar for the triglyceride traits, therefore, only figures from Cohort 1  are presented here.Figure s3 at 8.46 cM in this data set. It is noticeable that none of the three remaining traits provided evidence of linkage at this location: the maximum LODs on chromosome 5 for these being 0.85, 0.28, and 0.42 for TG1_original, TG2_PCA, and TG12_pooled, respectively.The most notable results are the peak LODs of 7.78 and 6.86 on chromosome 5 at 8.22 cM, for TG1_EBV and TG2_EBV, respectively. These two peaks correspond very closely to the location of the gene Variance component analysis of the breeding values gave LODs of 5.12 and 4.50 for TG1_EBV and TG2_EBV, consistent with the results using Merlin-regress.The derivation of an EBV for a single trait occurs without reference to marker data, and is designed only to improve the precision with which the additive genetic value of that trait is estimated.  We speculate that the improved power we see here is primarily the result of the improved precision with which this additive value is estimated. Other multivariate methods used in linkage analysis can also include genetic and environmental correlations among traits, for example . These mAs can be seen in Table To date, we have only applied this method to a single replicate. The analyses of many more replicates and traits are required before we can use this method with confidence.The estimation of breeding values using BLUP may be a suitable method of deriving traits for use in genome-wide scans. In particular, the method makes effective use of correlated traits and provides a simple framework for coping with missing data.


Insulin resistance, obesity, dyslipidemia, and high blood pressure characterize the metabolic syndrome. In an effort to explore the utility of different multivariate methods of data reduction to better understand the genetic influences on the aggregation of metabolic syndrome phenotypes, we calculated phenotypic, genetic, and genome-wide LOD score correlation matrices using five traits  from the Framingham Heart Study data set prepared for the Genetic Analysis Workshop 13, clinic visits 10 and 1 for the original and offspring cohorts, respectively. We next applied factor analysis to summarize the relationship between these phenotypes.Factors generated from the genetic correlation matrix explained the most variation. Factors extracted using the other matrices followed a different pattern and suggest distinct effects.Given these results, different methods of multivariate data reduction may provide unique clues on the clustering of this complex syndrome. The metabolic syndrome (MS) is a cluster of abnormalities including central obesity, abnormal glucose tolerance, elevated insulin and triglycerides, and depressed HDL-C -3. PreviBecause major genes involved in the etiology of common complex diseases are likely to exert an effect on multiple quantitative traits, statistical techniques that permit the joint analysis of correlated traits, such as factor analysis, may aid in analysis . Using fThe Framingham Heart Study was initiated in 1948 and consisted of 5209 men and women between the ages of 30 and 62 recruited from Framingham, Massachusetts. The subjects returned every 2 years for a detailed medical history, physical examination, and laboratory tests. In 1971, a second-generation group consisting of 5124 of the original participants' adult children and their spouses was enrolled. Longitudinal data were available on SBP, height, weight, CHOL, HDL-C, TG, glucose, hypertensive treatment, hypertensive status, number of cigarettes smoked per day, and grams of alcohol per day. Although glucose was available, we were unable to control for diabetes status, and in the absence of this information the trait was not heritable (data not shown).n = 1648).The following five phenotypes from the Framingham Heart Study were used to define MS: CHOL, HDL-C, TG, SBP, and BMI. We chose to focus on a single time point for all phenotypic variables. In the original cohort, we used clinic visit 10 because this is the first visit for which data on CHOL and HDL-C were collected. In the offspring cohort, we used clinic visit 1, at which all of the phenotypic data were available and had been collected during a similar timeframe. We also reasoned that by selecting these visits (as early as possible with the data of interest), we could maximize the number of participants included in our analyses. Outliers more than four standard deviations from the mean were dropped; only individuals having complete covariate data  were kept Ωa and b take the values of 1 or 2 and ρG and ρE are the additive genetic and environmental correlations between the traits. The genetic correlation estimates the proportion of genes shared in common between the traits. This approach has been implemented in SOLAR version 2.0. The phenotypic correlation (ρP) is given by:where  and  are the heritabilities of the traits. These correlations were assembled into phenotypic and genotypic matrices for factor analysis.where The genetic, phenotypic, and genomic correlation matrices were factor analyzed to summarize the relationships between the five phenotypes in the MS using SAS . OrthogoHeritabilities were determined to be significant for BMI (38.7 ± 3.9), CHOL 41.5 ± 5.6), HDL-C (41.5 ± 5.6), TG (45.6 ± 5.7), and SBP (16.4 ± 3.5). The LOD scores for the genome scans of the traits are shown in Figure .5 ± 5.6,Tables Previously, factor analysis has been used to identify components underlying the MS through the construction of factors from phenotypic values. Because factor loadings from the genetic and phenotypic correlation matrices are distinct, however, reliance on phenotypic correlation alone may fail to disclose underlying genetic relationships.In this study we constructed factors not only from phenotypic correlations, but also from the genetic and genome-wide LOD score correlations. Factors extracted from these correlations exhibited variable structure and suggest distinctive effects. With the exception of the second factor from the genome-wide LOD score correlation matrix, SBP loaded strongly on every factor. In other studies, however, SBP has not loaded strongly with other components of MS ,7. BecauHowever, as the genetic correlations are estimated from a polygenic model with no major gene effects estimated, it is possible that the first factor from the genetic correlation matrix is simply summarizing the polygenic effects between the traits. Similarly, the second factor may summarize the QTL effects; indeed, the second factor of the genetic correlation matrix loads similarly to the genome-wide LOD score correlation matrix that summarizes the correlation of QTLs across the genome.In summary, factors extracted using the phenotypic, genetic, and genome wide LOD score correlation matrices followed different patterns and may suggest distinct effects. Thus, these results imply that different methods of multivariate data reduction provide unique clues on the clustering of this complex syndrome.LM and KN performed statistical analyses and interpreted results. JW assisted in the interpretation of the results. TD calculated the IBDs. JB and AC participated in the design of the study. All authors read and approved the final manuscript.


The data arising from a longitudinal familial study have a complex correlation structure that cannot be modeled using classical methods for the analysis of familial data at a single time point.To fit the longitudinal systolic blood pressure (SBP) pedigree data arising from the Framingham Heart Study, we proposed to use multilevel modeling. That approach was used to distinguish multiple levels of information with individual repeated measurements (Level 1) being made within individuals (Level 2), and individuals clustered within pedigrees (Level 3). Residuals from the subject-specific and pedigree-specific regression models were summed both for the mean SBP and slope of SBP change over time, in order to define two new outcomes that were then used in a genome-wide linkage analysis.Evidence for linkage for the two outcomes (mean SBP and slope) was found in several chromosomal regions with a maximum LOD score of 3.6 on chromosome 8 and 3.5 on chromosome 17 for the mean SBP, and 2.5 on chromosome 1 for SBP slope. However, the linkage on chromosome 8 was only detected when the sample was restricted to subjects between age 25 and 75 and with at least four exams (Cohort 1) or 3 exams (Cohort 2).Multilevel modeling is a powerful approach to detect genes involved in complex traits when longitudinal data are available. It allows for complex hierarchical data structure to be taken into account and therefore, a better partitioning of random within-individual variation from other sources of variability (genetic or nongenetic). The Framingham Heart Study provides long-term repeated measurements of blood pressure and other phenotypes in two large cohorts of related individuals. Longitudinal studies are efficient designs for the investigation of individual changes over time. In the context of familial studies, such designs might be of particular interest to assess the proportion of the trait variability explained by within-individual variation or other sources of variation. However, the data arising from a longitudinal familial study have a complex correlation structure that cannot be modeled using classical methods for the analysis of familial data at a single time point. In this study, we proposed to use multilevel modeling to fit the complex data structure arising from the Framingham Heart Study. Multilevel modeling, also known as hierarchical regression, generalizes ordinary regression modeling to distinguish multiple levels of information in a model . It mighThe Framingham Heart Study data includes 330 pedigrees originally selected for a genome-scan analysis. The pedigrees consisted of 4692 subjects, of whom 2885 have participated in the Framingham Heart Study. Longitudinal SBP data were analyzed for 25,263 examinations on 2662 individuals. Height, weight, gender, age, and hypertensive treatment information were required but if height was missing, the most recent measurement was imputed. Because there might be important variation in individual SBP measurement among younger and older subjects, we also restricted the sample to individuals aged between 25 and 75 years, as in Levy et al. [Yijk denote the SBP measurement at the ith examination for the jth individual in pedigree k. We then assume that Yijk satisfies the following general multilevel model:Let the random variable i = 1,...,21 for Cohort 1 subjects and i = {11, 15, 17, 19, 21} for Cohort 2 subjects. Ageijk, BMIijk, Treatijk are the age, body mass index and hypertension treatment (1 for subjects treated and 0 for subjects untreated) at the ith exam for the jth individual in pedigree k,  and  are the mean values across all exams for the jth individual, and εijk are the error components that account for the within-individual variability. The εijk are assumed to be normally distributed with mean vector zero and variance-covariance matrix Σ defined by a first-order autoregressive structure. The intercept bjk 0represents the average SBP for an untreated subject of average age and BMI across all of the subject's examinations. The regression coefficient bjk 1is used to model the linear variation of SBP with age. We found that every individual profile could be well approximated by a quadratic function of time, measured by the age at examination. We also tested a cubic effect, but it was not significant when we allowed for the individual's linear time trend to differ in each treatment group (interaction between age and treatment). Random effects were added to reflect the natural heterogeneity in the population. In this model, both the intercept and the linear effect for age were allowed to vary across individuals and the individual-specific regression coefficients (random effects) were defined at the second level:where  and  are the sample means for age and body mass index, Sex and Cohort are two indicator variables, coded 1 for males, 0 for females and 0 for Cohort 1 subjects, 1 for Cohort 2 subjects. The random components ujk 0and ujk 1measure the variation of each individual's mean SBP and slope from their average in pedigree k. The intercept bk 00represents the average SBP in pedigree k for males in Cohort 1 with average age and BMI and the intercept bk 10represents the average slope in pedigree k for males in Cohort 1 with average BMI. To account for the correlation of individuals within a pedigree, these two intercepts were allowed to vary between pedigrees. The random effects at different levels of the model are assumed independent.bk 00= β000 + vk00, k = 1,...,Nvk 00and vk 01measure the variation of each pedigree's mean SBP and mean slope from their average in the whole sample.The random components F-statistic was used to test the significance of the fixed effects with number of degrees of freedom computed using the containment method [ and  with equal weights 0.5, where q and q + 1 are the number of random effects estimated under H0 and H1, respectively.Analyses were conducted in both the unselected and selected samples and with and without adjustment for BMI. Multilevel models were fitted using SAS PROC MIXED . Paramett method . The lik and , which measure the random variation of each individual's SBP mean and slope, respectively, from the sample average after adjustment for the fixed effects. A third outcome was also defined using the residuals from a sample-wide regression in which each individual's mean SBP  was regressed on his mean age (centered), mean BMI (centered), gender and cohort, as in Levy et al.'s paper [We used the estimates of the random effects at the subject and pedigree levels to define two new outcomes that were used in the genome-wide linkage analysis. The two outcomes were defined as 's paper . Estimat's paper .All fixed effects included in the model were highly significant in the subject random slope model Table  except fHeritability estimates were 54.3% (SE = 3.1) and 55.6% (SE = 3.4) for the mean SBP, 31.9% (SE = 3.5) and 28.9% (SE = 3.5) for SBP slope over time in the unselected and selected samples, respectively. The heritability estimates for the subject-specific residuals from the sample-wide regression of the mean SBP were 47.7% (SE = 3.4) and 49.7% (SE = 3.8) in the unselected and selected samples, respectively.Evidence for linkage for the two outcomes (mean SBP and slope) was found in several chromosomal regions with a maximum LOD score of 3.6 on chromosome 8 and 3.5 on chromosome 17 for the mean SBP and 2.5 on chromosome 1 for SBP slope (Table Our study demonstrates the value of multilevel modeling in the search for genetic determinants of complex traits when longitudinal pedigree data are available. For the mean SBP, we were able to replicate the linkage result on chromosome 17 previously reported by Levy et al.  and dete


The phenotype has been evaluated in two independent genome-wide linkage scans with evidence for a major locus on chromosome 15q15, and a second independent locus on chromosome 22qIn the positional and brain-expressed candidate genes KIAA0767 and KIAA1646, we searched for variants in the complete exons and adjacent splice-junctions as well as in parts of the 5'- and 3'-untranslated regions by means of a systematic mutation screening in individuals from chromosome 22q-linked pedigrees.The mutation scan revealed 24 single nucleotide polymorphisms, among them two rare codon variants . However, both were neither found segregating with the disease in the respective pedigree nor found at a significant frequency in a case-control association sample.tel in periodic catatonia, we screened two positional brain-expressed candidate genes for genetic variation. Our study excludes genetic variations in the coding and putative promoter regions of KIAA0767 and KIAA1646 as causative factors for periodic catatonia.Starting from linkage signals at chromosome22q D22S1169, and with a heterogeneity Zmax of 1.57 with an estimated 38% of families linked  consists of 18 exons, spanning ~50 kb on genomic DNA [NT_011523.2]. KIAA0767 is a protein of 578 amino acids (aa) putatively localized in the mitochondrion  consists of 13 exons, spanning ~50 kb on genomic DNA. CERK is a cytoplasmatic and membrane-associated protein of 537 amino acids with a calculated molecular weight of 60 kDa. It is a member of a new class of lipid kinases and acts in the signal transduction cascade of the control of apoptosis catalyzing specifically the phosphorylation of ceramide [Human KIAA1646/CERK [GenBank: ceramide . The comceramide  or in phceramide ,29,30. Iceramide ,31. Althceramide .tel in periodic catatonia, we screened two positional brain-expressed candidate genes for genetic variation . Our study excludes variants at coding and putative promoter regions as causative factors in periodic catatonia, but do not exclude the involvement of other regulatory elements in intronic or extended promoter regions. Although negative, the present study narrowed down the putative susceptibility region, and provides a systematic SNP generation for forthcoming LD studies.Starting from linkage signals at chromosome22qThe author(s) declare that they have no competing interests.BK, MS, CR performed laboratory assays, MG, KME performed the data-analysis and drafted the manuscript, TM, TB participated in the design of the study and its coordination, GS participated in the design of the study, interpretation of the data, and drafting of the manuscript. All authors read and approved the final manuscript.The pre-publication history for this paper can be accessed here:


Two factors impacting robustness of the original transmission disequilibrium test (TDT) are: i) missing parental genotypes and ii) undetected genotype errors. While it is known that independently these factors can inflate false-positive rates for the original TDT, no study has considered either the joint impact of these factors on false-positive rates or the precision score of TDT statistics regarding these factors. By precision score, we mean the absolute difference between disease gene position and the position of markers whose TDT statistic exceeds some threshold.We apply our transmission disequilibrium test allowing for errors (TDTae) and the original TDT to phenotype and modified single-nucleotide polymorphism genotype simulation data from Genetic Analysis Workshop. We modify genotype data by randomly introducing genotype errors and removing a percentage of parental genotype data. We compute empirical distributions of each statistic's precision score for a chromosome harboring a simulated disease locus. We also consider inflation in type I error by studying markers on a chromosome harboring no disease locus.The TDTae shows median precision scores of approximately 13 cM, 2 cM, 0 cM, and 0 cM at the 5%, 1%, 0.1%, and 0.01% significance levels, respectively. By contrast, the original TDT shows median precision scores of approximately 23 cM, 21 cM, 15 cM, and 7 cM at the corresponding significance levels, respectively. For null chromosomes, the original TDT falsely rejects the null hypothesis for 28.8%, 14.8%, 5.4%, and 1.7% at the 5%, 1%, 0.1% and 0.01%, significance levels, respectively, while TDTae maintains the correct false-positive rate.Because missing parental genotypes and undetected genotype errors are unknown to the investigator, but are expected to be increasingly prevalent in multilocus datasets, we strongly recommend TDTae methods as a standard procedure, particularly where stricter significance levels are required. One of the most-widely used family-based linkage tests in the presence of association is the original transmission disequilibrium test (TDT) statistic . There a1, R2), population genotype frequencies, and error model parameters under the null hypothesis that the genotypic relative risks are equal to 1 (R1 = R2 = 1) and under the alternative hypothesis that at least one of the genotypic relative risks is not equal to 1 (R1 ≠ 1 or R2 ≠ 1).It has been shown -4 that bThe genotype relative risks for a di-allelic locus with wild-type allele + and disease allele d are defined as:1 = Pr(affected|+d)/ Pr(affected|++)R2 = Pr(affected|dd)/ Pr(affected|++).R2 = R12), the TDTae statistic reduces to the original TDT statistic [It should be noted that when a multiplicative mode of inheritance is assumed,  Workshop. We defined as affected those individuals who were affected  and for whom phenotype E is present .We considered only the three subpopulations consisting of nuclear families. That is, we excluded the New York pedigrees from our analyses, because our TDTae method required significantly more computational time to perform analysis of even one replicate of the New York data. We had knowledge of the true model at the time of the analysis.All replicates were modified by randomly removing 10% of the parental genotypes and also introducing errors to the remaining genotypes using the Sobel-Papp-Lange (SPL) error model [We performed both type I error and precision score analyses by computing the original TDT and the TDTae statistics. The basic unit considered for the analysis within the nuclear families was a trio with two genotyped parents and at least one affected child. For the original TDT , those tp-values less than 0.05 (5%), 0.01 (1%), 0.001 (0.1%), and 0.0001 (0.01%).After computing both statistics for all markers in each of the 100 replicates for either the type I error or precision score study, we selected the subset of markers over all the replicates with p-values less than 0.05, 0.01, 0.001, or 0.0001, respectively.We modified the simulated dataset of 95 single-nucleotide polymorphisms (SNPs) markers from chromosome 7, which does not harbor any disease locus, as specified above (Genotype data modification) to compute the empirical type I error rate in the presence of the aforementioned factors. We defined the empirical type I error rate for each statistic (TDT or TDTae) at a given threshold  as the proportion of SNPs from the total of 9,500 markers over all 100 replicates that showed For the precision score study we considered the SNP trait locus at the end of chromosome 3 and 49 SNPs to one side of it  from the trait locus to a marker that showed a significant We computed the distribution of the precision score for all significance levels with each statistic by considering various percentiles .p-values were less than the value x/100. The values reported in parentheses are the lower and upper end points of the 95% confidence intervals computed using the method implemented in the BINOM program .Table Table It is important to note that this inflation is for data with relatively small genotype error rates. We suspect that there is a compounding effect of the type I error inflation for the original TDT when a dataset contains both genotype errors and missing parental genotypes.Based on the median results for each distribution (Table The results of our analysis on the simulated data suggest that when the alternative hypothesis is true, the TDTae statistic may be a more precise indicator of the trait location than the original TDT statistic in the presence of missing parental data and genotyping errors.Regarding the empirical type I error rate, we have shown that the TDTae statistic is able to maintain proper type I error rate in the presence of errors for these simulated datasets. The original TDT statistic shows a highly inflated false-positive rate when there are missing parental genotypes and random genotyping errors in the dataset. The results of our simulations suggest that the inflation in type I error increases as the significance level becomes more stringent..These results have significant consequences for TDT analyses with large numbers of markers, for example studies using microarray technologies . Many ofWe strongly recommend that researchers apply TDTae methods when missing parental genotypes or undetected genotype errors are present and when the number of markers is large. We reason that when more markers are tested, more stringent significance levels are required to correct for multiple testing issues. However, the false-positive rate increases disproportionately for original TDT methods as the significance level becomes more stringent, while our work here suggests that the TDTae maintains proper type I error rates in the presence of missing parental genotype data and genotype errors, even for more stringent significance levels.GAW14: Genetic Analysis Workshop 14SLP: Sobel-Papp-LangSNP: Single-nucleotide polymorphismTDT: Transmission disequilibriumTDTae: Transmission disequilibrium test allowing for errorsSB performed all statistical analyses and wrote the majority of the manuscript. CH developed the computer programs to introduce the errors and remove parental genotype data. MAL developed the ideas for the precision study and wrote a portion of the Results section. DG proposed the research for the GAW14 dataset, supervised all the research, and reviewed all versions of the manuscript for scientific content and grammar.


Utilizing a linkage resource for association analysis requires consideration both of the marker data used and correlations among relatives in pedigrees. We previously developed a method for association testing in pedigrees. We applied our method to 50 replicates of microsatellite data surrounding five genes involved in high-density lipoprotein (HDL) in the Genetic Analysis Workshop 13 (GAW13) simulated data and examined association with HDL as well as linkage disequilibrium (LD) between markers.Although no association was intentionally simulated, we found significant evidence of weak LD between microsatellite markers (flanking/~5 cM from the genes), in some but not all replicates. This level of LD compared well to that observed in the real GAW13 Framingham data. Only one region had sufficient replicates to assess power, and this was low (12.5–20.8%). More power was attained using all individuals and accounting for relationships, compared with one independent individual/pedigree, although this was not significant due to small sample sizes. Not accounting for relatedness inflated statistical significance (p < 0.0001).A correction for dependence is necessary in association studies to avoid an inflation of significance probabilities. Our results further illustrate that use of microsatellite marker data is not an effective approach for association testing. Association and linkage disequilibrium analyses are tools that are often used to fine-map and refine promising linkage findings. These tools are particularly effective because they increase power to detect genes with small effects . Many peThere is great potential for the utilization of pedigree resources for association analyses. Our group and others have developed methodologies to enable association analyses to be performed in extended pedigrees ,3. If muFor each simulation, our program uses a gene-drop to generate null genotype configurations for a given set of individuals in pedigrees. The gene-drop requires the assignment of genotypes to the pedigree founders, based on allele frequencies estimated from the study population. This is followed by the use of Mendelian inheritance probabilities to determine the genotypes of all descendants. The resulting genotype configuration on each pedigree represents a possible configuration under the null hypothesis of no association between allele and disease. Using the simulated genotypes for individuals for whom real data are available and the true phenotype data, the statistic of interest is calculated . The resulting statistic is from the null distribution because it was derived from data under the null hypothesis of no association. This procedure is repeated many times, creating an empirical null distribution. The real genotype data for the same individuals and real phenotype data are then used to calculate the observed statistic. This observed statistic is then compared with the empirical distribution to determine significance. The method can be applied to pedigrees of any structure and size and to any statistic of interest.Association analyses are based on either testing the true disease-causing variant itself, or alleles at a marker in linkage disequilibrium with the true variant. Since linkage disequilibrium (LD) generally extends over very short distances  and sinThe Genetic Analysis Workshop 13 (GAW13) simulated data were modeled on the real GAW13 Framingham Heart Study data, as a genomic search with average resolution of approximately 9.5 cM, and hence no LD, or association, was intentionally simulated. To investigate the value, if any, of using linkage microsatellite marker data for association studies, we chose to analyze the simulated high-density lipoprotein (HDL) phenotype (dichotomized to the two extreme quartiles: high versus low quartile) and microsatellite markers either flanking or within approximately 5 cM of the true location of five genes involved in determination of baseline simulated HDL, as indicated in the 'answers'.Here we report the results of our empirical simulation method using a chi-squared association analysis for genotype data in the GAW13 simulated data. Although no association was intentionally included in the GAW13 simulated data, we report the underlying linkage disequilibrium (LD) between microsatellite markers and the ability of our empirical association method to detect power and false-positive signals. As a comparison we also report the LD in the Framingham data for the same location as one of the simulated baseline HDL genes.The first 50 replicates of the simulated GAW13 data with missing genotype and phenotype values were utilized in this study. There were 330 families, ranging in size from 7 to 84 members, in each of the 50 replicates studied.Eleven baseline genes  contribute to the HDL phenotype. We chose to study five of these genes , selected to represent a spectrum of percent contribution to the HDL trait , BMI (using mean height and weight across the study period), smoking (ever/never), alcohol (ever/never), and fasting glucose (ever/never > 126 mg/dl).GAW13_HDL(PED)). Second, we used our own linear regression equation to adjust HDL (LR_HDL) using the above listed covariates, where for each replicate we performed a linear regression with these covariates as independent variables to determine the regression coefficients. Third, we performed an 'independent' (IND) analysis by selecting only the first individual from each family with data and also using the GAW13 'answers' (GAW13_HDL(IND)).We considered the analysis of the HDL data in three different ways. First, we adjusted the maximum HDL value using the generating equation as provided in the 'answers'  and for the haplotype frequencies under H0 (no association) were used to calculate the raw disequilibrium, from which D', the proportion of maximum possible disequilibrium, was determined. Significance was determined by the EH program.The estimating haplotype (EH) program  was usedTo compare results of the simulated data to the GAW13 Framingham data, D' for the three most common alleles at the first four markers on chromosome 4, corresponding to the exact position of the four markers surrounding gene b22 in the simulated data set, were analyzed.It should be noted that the simulated data were generated to contain linkage to baseline HDL genes, but not LD or association with particular gene variants in the candidate genes. However, linkage and association differ only in the fact that the former is a phenomenon of loci and the latter of alleles at loci. In replicates where LD exists across markers, the simulated linkage creates a scenario equivalent to allelic heterogeneity for association. While certainly not ideal, allelic heterogeneity is a reasonable model for real data in which multiple common variants within a gene may increase disease susceptibility.GAW13_HDL(PED) with an analysis where we ignored genealogy and included all individuals (ALL) with data in the pedigrees without any correction for relatedness. A paired t-test for the average of the -ln(p) across markers over the 50 replicates was used to compare the results.In all analyses we compared the highest and lowest quartiles of the HDL phenotype of interest. We used the chi-squared statistic for independence considering both dominant and recessive models as our statistic of interest. For each analysis 10,000 simulations were generated to create the empirical null distribution. To illustrate the necessity to correct for relatedness, we compared the results from p < 0.01) for each of the three analysis types, indicating a power estimate for each. Two regions (surrounding b14 and b18) had sufficient replicates without LD (p > 0.5) to assess false-positive findings. For these regions we show the proportion of replicates without LD for which significant associations were found (p < 0.01).We report the number of replicates showing LD at various levels of significance for each gene region. Only one region surrounding gene b22 had sufficient replicates with significant LD to assess power. For this region we also show the percentage of the replicates with significant LD for which a significant association was found (LR_HDL) and classic chi-square analyses (for GAW13_HDL(IND)) were performed using STATA 6.0 . Fisher's exact p-values are reported for the GAW13_HDL(IND) analyses, where appropriate.All regression analyses (for IND) analysis the average sample size per replicate with data was 328.7 individuals and ranged between 324 and 330 individuals. For all other analyses using all individuals with available data, the average sample size per replicate was 1672.6 individuals and ranged between 1627 and 1715. More than 95% of families within the 50 replicates had two or more members per family with data.For the 'independent' (GAW13_HDL(PED) with the uncorrected GAW13_HDL(ALL) showed extreme statistical significance , suggesting that not accounting for correlations among family members substantially underestimates the variance and inflates the significance, as expected.A comparison of the empirical method using p < 0.05) was present in at least one replicate , values of D' ranging from 9.7 to 47.6 were observed. These values compared well to those found for the simulated data (D' = 9.4–31.8).p < 0.01) was found using the various analyses. Power was low for all comparisons and ranged from 12.5–20.8%. Power was higher for analyses that corrected for covariates and that used pedigree data , rather than 'independent' data , although these differences are not statistically significant due to a small sample size (n = 24). However, 20.8 % is significantly different from 0.05 (type I error rate) as assessed by binomial distribution theory with n = 24 (p = 0.006).As the region containing b22 was the only one with significant LD present in sufficient replicates (24/50), we chose to further study power of the association analyses for only this region. Table p > 0.5). Two regions surrounding genes b14 and b18 had sufficient replicates  to assess false-positive findings. Results are shown in Table The number of false-positive results was assessed in gene regions for which sufficient replicates were available and for which LD was not evident . In fact, the frequency of detectable LD in replicates correlated reasonably well with available marker density  of the regions did not exhibit a high frequency of LD over the 50 replicates. Furthermore, as pointed out above, even for the one region with significant LD, power was low. These results could be extrapolated to association analyses in the real GAW13 Framingham data where LD was comparable and where small effect genes are expected. This indicates caution in the interpretation of any positive association findings in those data.Microsatellite markers are not an ideal marker type for association testing. We selected the nearest two to four markers for each gene (each either flanking or within ~5 cM of the gene of interest). However, 5 cM represents a large distance between markers and true gene variants for association testing. Testing single-nucleotide polymorphism (SNP) variants within the gene, which are more likely to be in strong LD with disease-causing variants, would have been a more powerful situation.A limitation of our analysis is that not all alleles were analyzed. Only the three highest frequency alleles for each marker were used to both increase the chance of an allele being observed sufficiently for association testing and to reduce multiple testing problems. This modified allele system is not biased for investigating LD, since alleles were not grouped according to their respective disequilibria. Further, we used the same allele definition for LD estimation and association, thus they are directly relevant to one another. We may, however, have missed positive association findings by not testing all alleles. A further limitation is that these data were not simulated to specifically contain association, and our power will be limited by the situation equivalent to allelic heterogeneity, which has been shown to reduce power in association-based analyses . In addiIn conclusion, our results indicate that the empirical approach makes efficient use of data collected from extended pedigrees. Further, this study illustrates the lack of power available by using linkage microsatellite markers, and strongly cautions against doing so for association testing.


We report tree-based association analysis as applied to the two Framingham cohorts and to the first replication of the simulated data obtained from the Genetic Analysis Workshop 13. For this analysis, familial association is ignored. The two endpoints examined are hypertension status at initial visit and time-to-hypertension, using a censored data approach. Although linkage association has previously been reported with hypertension, we found no association using the tree-based methodology. The Framingham Heart Study is a rich data set filled with information about hypertension status in a population-based cohort observed over an extended period of time. As shown by Levy et al.  and HuntOur analysis focused on the two Framingham cohorts and the first replicate of the simulated cohorts. Cohort 2 was also used for validation of results obtained from the Cohort 1 analyses. Answers were obtained for the simulated data. In the Framingham study partial data were available on 1213 of the original (largely unrelated) Cohort 1 subjects and 1668 of the original  Cohort 2 subjects. However, in Cohort 1 only 32% of the subjects had genetic marker data; in Cohort 2 the number was much higher (78%) though there were still a large number of uninformative subjects. Although the tree models can handle missing data through the use of surrogate variables, we felt that the large number of observations with completely missing genetic data warranted their deletion. In addition, the age ranges of the two cohorts varied, hence we focused the analysis on the 390 Cohort 1 subjects and the 726 Cohort 2 subjects with genetic marker information who were between 30 and 55 years of age at the initial visit. Similar limiting of the simulated data resulted in 346 Cohort 1 subjects and 1060 Cohort 2 subjects. We defined two primary response variables based on the available phenotype data and models were fit separately for each of the two cohorts. We first looked at hypertension status at the baseline visit . Three Framingham Cohort 2 subjects who were being treated for hypertension at the baseline visit but were not diagnosed with hypertension were removed from the analysis. Our second end-point used a censored "time-to-hypertension" approach, in which age was used as the time scale. Subjects entered the risk set at their first visit and exited the risk set when they were lost to follow up (censored) or were diagnosed with hypertension. For those subjects that did not already have hypertension at their first visit, 52% of Framingham Cohort 1 and 29% of the Framingham Cohort 2 went on to develop the disease by age 55. The simulated cohorts each had estimates around 30% at age 55. Subjects who started treatment for hypertension before diagnosis of hypertension were censored at the time of treatment (this occurred in less that 2% of the subjects in each cohort). The 398 genetic markers were used as predictors along with the environmental variables of age, sex, cigarettes per day, body mass index, and alcohol consumption. The markers were expanded so that every allele of every marker created a new allelic variable. For instance, chromosome 1, marker 1, allele 1 (c1m1a1) could have the values 0, 1, or 2 depending on how many copies of the mutation an individual carried. This resulted in the creation of over 4400 predictors., where C is the number of end-point classes (in our case 2), piA is the proportion of those in node A that belong to class i, and f is some impurity function. If node A is pure then I(A) = 0. For the classification end-point "hypertension at visit one" we used the impurity function called the Gini index where f(p) = p(1 - p) and we used the split which maximized the impurity reduction ΔI = p(AParent)I(AParent) - p(ALeft)I(ALeft) - p(ARight)I(ARight). For the censored "time-to-hypertension" end-point we used a splitting criterion which is equivalent to a likelihood ratio test for two Poisson groups: DParent - (DLeft + DRight). The deviance , where ci is the observed event count for observation i, ti is the scaled observation time, and  is the predicted rate of the node. The time variable is modified slightly using exponential scaling to get a straight line curve for log under a parametric exponential model [Construction of trees using recursive partitioning necessitates defining a splitting rule and pruning rule. Splitting rules are used to examine all possible splits of the full group of subjects (root node) and to identify the variable at each level that produces the most homogenous children. For classification endpoints like "hypertension at visit one", impurity is used to determine the best split. Impurity, or the diversity, of a node A can be written as al model . This isal model .For pruning we chose to use a fixed complexity parameter of 5% and the 1-SE rule. The complexity parameter α is a measure of improvement in the tree impurity. Heuristically, the tree building process can be compared to forward step-wise regression, where variables (splits) are made until the F-test of the remaining variables fails to achieve some level of α. An α level of 5% suggests that further splits will add less than 5% to the overall fit of the tree. The 1-SE rule uses cross-validation, which involves randomly partitioning the original samples into 10 fitted sub-samples and computing an average misclassification rate for each sub-tree (corresponding to the different splits). The sub-tree with the smallest average misclassification rate is identified, as are all sub-trees that have an average misclassification rate within one standard error of this smallest rate . The simplest model is picked. Thus, we identified a sub-tree that provides the least complexity and the least misclassification of subjects. All recursive partitioning models were fit using the SPLUS library rpart .Analysis of the Framingham Cohort 1 data examining "hypertension at visit one" as built to the complexity parameter of 5% includes the environmental variables age and body mass index (BMI), and 11 different markers: c10m5a5, c12m17a7, c17m7a7, c19m8a1, c1m32a4, c2m21a3, c2m21a6, c2m2a11, c5m20a1, c6m12a7 and c6m13a7. No variables remain in the model after pruning using the 1-SE rule. Results are similar when only marker data is used or when only a subset of the marker data is used . Analysis of the Framingham Cohort 2 data resulted in similar conclusions, with no variables remaining after pruning with the 1-SE rule.th decimal point.Table As is illustrated in Figure Although the recursive partitioning approach should be ideal for detecting sub-populations of individuals that have hypertension, we were unable to detect any association between the hypertension status and the 398 genetic markers. Similarly, because hypertension is highly age-related the end-point using a censored "time-to-hypertension" approach, where age was used as the time scale, should have been useful for separating out subjects who perhaps had earlier onset of the disease. Neither methodology found any consistent positive results. A large proportion of the subjects did not have genetic marker data and were thus deleted (68% of the Framingham Cohort 1 subjects and 22% of the Cohort 2 subjects) whereas in a familial analysis some of the markers could have been estimated from family members. In the Framingham Cohort 1, those without marker data were on average older, heavier, smoked more, drank more and had, at baseline, more hypertension (41.5% vs. 22.1%). The same patterns were also seen in Cohort 2, though the differences were not as great. Because the missing patterns are significantly related to hypertension status, this probably introduced bias into the study, perhaps making meaningful associations more difficult to find. Another problem could be that hypertension is too common a condition for study using this methodology (the cumulative incidence at age 80 is over 80% (Figure