Quantitative trait loci analysis assumes that the trait is normally distributed. In reality, this is often not observed and one strategy is to transform the trait. However, it is not clear how much normality is required and which transformation works best in association studies.We performed simulations on four types of common quantitative traits to evaluate the effects of normalization using the logarithm, Box-Cox, and rank-based transformations. The impact of sample size and genetic effects on normalization is also investigated. Our results show that rank-based transformation gives generally the best and consistent performance in identifying the causal polymorphism and ranking it highly in association tests, with a slight increase in false positive rate.For small sample size or genetic effects, the improvement in sensitivity for rank transformation outweighs the slight increase in false positive rate. However, for large sample size and genetic effects, normalization may not be necessary since the increase in sensitivity is relatively modest. Genome-wide association (GWA) studies have been used to identify over 200 potential causal loci in complex diseases such as metabolic/cardiovascular disorder, autoimmune disorder, and cancer -6. The aIn most cases, quantitative traits are not normally distributed and one strategy is to perform parametric transformation to approximate normality. In cases where the traits are left-skewed, the appropriate transformation may not be so straight-forward. Transformation is crucial for meta-analyses, where two or more populations are combined to improve statistical power. Preferably, the traits are transformed similarly to enable comparison of genetic effects. This may prove challenging when the traits from different populations are not similarly distributed and cannot be transformed in the same manner. Literature search in this area shows evaluation of normalization methods in pedigree studies -11, lookIn the absence of comprehensive study on various transformation methods for association studies, it is difficult to decide which transformation to apply. How much normality will suffice for the underlying assumption of association tests? In the context of sample size and genetic effects, what are the effects of these methods? Although it is generally accepted that deviation from normality can reduce the power of the study, the effects of different normalization methods are not clearly understood.In this paper, we report the effects of these normalization methods in basic quantitative association tests on simulated data. Our objective was to quantify the effects of normalization in GWA studies. Since a large sample is needed to detect small effects, we also evaluated the effects of normalization on varying sample sizes and genetics effects. For simplicity, we limit our study on additive models. We also approached the evaluation by emulating GWA studies, measuring performance of the normalization based on the sensitivity of discovering causal single nucleotide polymorphism (SNP) and its respective ranking in association tests after Bonferroni corrections.To assess the effects of normalization, genotype data was generated from a disease model with one causal SNP allele using HAPSIMU . For eacA GWA study is an expensive venture which requires careful design and quality control. One such consideration is normalization. Our simulation indicated that in studies where the effects and sample size were large; transformation had little effect. Performance issues arise when the genetic effect was less than moderate and sample size was not large. In this case, the type of normalization became a serious consideration with impacts on results.rank-based/sensitivityuntransformed) varied from 2.43 to 5.67 (1000 samples), 1.83 to 3.50 (2000 samples), 1.2 to 1.63 (4000 samples), 1.23 to 1.46 (8000 samples) for PV = 0.01. For PV = 0.2, the improvement factor ranged from 1.04 to 1.11 (1000 samples), 1.02 to 1.11 (2000 samples), 1.07 to 1.17 (4000 samples), and 1.03 to 1.06 (8000 samples). The improvement factor tended towards 1 for PV = 0.2, indicating that for larger genetic effects, transformation was not so critical . This trend was also observed in the case of larger sample size regardless of the distribution of original traits.The results showed that larger PV (more genetic effects) and samples size generally gave higher sensitivity and smaller displacement with a slight increase in false positive rate. When PV varied from 0.01 to 0.2, untransformed normal distribution showed sensitivity of 4.27% to 50.86% (PV = 0.01), 13.27% to 64.96% (PV = 0.02), and 71.79% to 97.44% (PV = 0.2) for 1000 to 8000 samples  and 5.03 (PV = 0.2). With rank-based transformation, the displacement improved: 18.97 (PV = 0.01), 16.38 (PV = 0.02), and 4.78 (PV = 0.2).False positive rate is a concern in GWA studies. In our study, the false positive rate increased with PV and sample size. The simulation showed that rank-based transformation incurred a slightly higher false positive compared with the other methods. We recognize that the false positive rate computed here was subjective, depending on the 99 non-causal SNPs in simulated data. Nevertheless, it gave an indication of false positives amongst the different settings in simulations; i.e. traits distribution, sample size, and genetic effects. Does this mean that rank transformation has no benefits? For small sample size and genetic effects, the increase of sensitivity outweighs the slight increase in false positive rate. For large sample size and genetic effects, this is not true so caution is needed on transformation. We propose no transformation in this scenario.th percentile of the distribution and the BB's distribution towards 67th percentile. The consistent variance of 1 in each genotype meant less overlap between the distributions, accentuating the discriminating additive signals in association test. This also explained why false positive increased correspondingly since the same effects would be applicable on non-causal SNPs.Despite the concerns of rank-based transformation being too 'perfect', results showed that it improved the sensitivity and ranking, both important in deciding genes or loci of interest for fine-mapping. One of the reasons sensitivity improved was due to the effects transformation had on the distribution of each genotype. The transformation attempted to keep the distribution of each genotype within its respective tertile (3 genotypes) while maintaining a variance of 1 Figure . In the It was noted in Figure In the simulations, Box-Cox sometimes achieved a normal distribution Figure  though nIn our literature review, the traits were usually generated as non-normally distributed trait and not well defined traits such as those in our study  where we could assess the effects of transformation on different distributions. This arises from the difficulty of generating quantitative traits to meet these distributions using genotype, especially using real genotype data. In Peng et al (2007), the normal trait was transformed to meet certain skewness and kurtosis for their evaluation. We adopted the same idea in our simulation by transforming the trait after genotype has been generated. This approach has the advantage of allowing us to use existing genotype data  to study effects of different trait distributions.The four quantitative traits investigated here are common distributions described by several statistical empirical distributions. Simulations were done on common factors affecting results of GWA study, such as normalization, sample size, and genetic effects. The simulation showed that rank-based transformation gave the best performance in terms of sensitivity and displacement regardless of the distribution of the trait. This is however accompanied by a slight increase in false positive rate. The positive effect of rank-based transformation decreased with increasing sample size and genetic effects. For large sample size and genetic effects, normalization is not recommended.log [-[xi-min(x)]] where xi is the quantitative trait for sample i), and rank-based transformation [The normalization methods investigated were: logarithm, Box-Cox, inverse-logarithm  and frequency (f) of the disease susceptibility allele. It utilizes informative marker loci from the ENCODE regions genotyped in CEPH and YRI. A normally distributed trait is generated for each of the genotypes . To avoid confounding factors such as polygenic effects and population admixture, one causal SNP was generated out of 100 SNPs in a homogenous population of YRI for our simulations. We noted that 100 SNPs is not representative of GWAS data, neither is one causal SNP the realistic scenario. However, given that most complex diseases are polygenic model involving probably thousands of causal SNPs, the scenario of 1 causal out of 100 SNPs can be reasonably extrapolated to a GWAS dataset of few thousands causal SNPs; a reasonable representation of a polygenic, additive disease model. The settings for HAPSIMU are shown in Figure Quantitative traits generated by HAPSIMU are normally distributed with mean and standard deviation determined by PV and f. To investigate various trait distributions such as left- and right- skew as well as bimodal, traits were log and beta transformed. Four traits were obtained after HAPSIMU , and each of these traits was transformed using logarithm, inverse-logarithm, Box-Cox, and rank-based, i.e. total of 20 traits. Quantitative traits were tested using the common GWAS software Plink  which im-4. Significant causal SNPs were considered true positives while significant non-causal SNPs were false positives. Sensitivity or True Positive Rate (TPR) was computed for the 120 datasets using TP/(TP+FN)*100 where TP, FN were true positive and false negative respectively from the confusion table tabulated from 120 datasets. False Positive Rate (FPR) or Type I error was computed as FP/(FP+TN)*100 where FP and TN were false positive and true negative from the confusion table. Since there was only one causal SNP, false negative was either 1 or 0 for each simulation, so sensitivity was synonymous with power.Criteria for performance assessment were based on (1) displacement ranking of causal SNP out of the 100 SNPs, where expected rank was 1 (i.e. displacement is 0), and (2) Bonferroni corrected p-value for significant association was <5 × 10LG and VBY conceived the study and participated in its design and coordination. LG wrote the Matlab code, performed the analyses and drafted the manuscript. All authors read, edited, and approved the final manuscript.Supplementary Tables. Table S1: Performance of simulations with PV = 0.02  for 4 sample sizes and 4 quantitative traits  transformed using logarithm (log), inverse-logarithm (ilog), Box-Cox, and rank-based. Table S2: Performance of simulations with PV = 0.2 (large effects) for 4 sample sizes and 4 quantitative traits  transformed using logarithm (log), inverse-logarithm (ilog), Box-Cox, and rank-based.Click here for file


We also extend the MVN framework to the problem of estimating the statistical power of an association study with correlated markers and propose an efficient and accurate power estimation method SLIP. SLIP and SLIDE are available at http://slide.cs.ucla.edu.With the development of high-throughput sequencing and genotyping technologies, the number of markers collected in genetic association studies is growing rapidly, increasing the importance of methods for correcting for multiple hypothesis testing. The permutation test is widely considered the gold standard for accurate multiple testing correction, but it is often computationally impractical for these large datasets. Recently, several studies proposed efficient alternative approaches to the permutation test based on the multivariate normal distribution (MVN). However, they cannot accurately correct for multiple testing in genome-wide association studies for two reasons. First, these methods require partitioning of the genome into many disjoint blocks and ignore all correlations between markers from different blocks. Second, the true null distribution of the test statistic often fails to follow the asymptotic distribution at the tails of the distribution. We propose an accurate and efficient method for multiple testing correction in genome-wide association studies—SLIDE. Our method accounts for all correlation within a sliding window and corrects for the departure of the true null distribution of the statistic from the asymptotic distribution. In simulations using the Wellcome Trust Case Control Consortium data, the error rate of SLIDE's corrected  p-values by the number of markers assuming the markers are independent. Since the markers are correlated due to linkage disequilibrium, this approach leads to a conservative estimate of false positives, thus adversely affecting statistical power. The permutation test is considered the gold standard for accurate multiple testing correction, but is often computationally impractical for large association studies. We propose a method that efficiently and accurately corrects for multiple hypotheses in genome-wide association studies by fully accounting for the local correlation structure between markers. Our method also corrects for the departure of the true distribution of test statistics from the asymptotic distribution, which dramatically improves the accuracy, particularly when many rare variants are included in the tests. Our method shows a near identical accuracy to permutation and shows greater computational efficiency than previously suggested methods. We also provide a method to accurately and efficiently estimate the statistical power of genome-wide association studies.In genome-wide association studies, it is important to account for the fact that a large number of genetic variants are tested in order to adequately control for false positives. The simplest way to correct for multiple hypothesis testing is the Bonferroni correction, which multiplies the  Association studies have emerged as a powerful tool for discovering the genetic basis of human diseases pointwise p-value. We would like to know how significant a pointwise p-value needs to be in order to obtain a significant result given that we are observing per-marker threshold can be defined as the threshold for pointwise p-values which controls the probability of one or more false positives corrected p-value can be defined as the probability that, under the null hypothesis, a p-value equal to or smaller than the pointwise p-value will be observed at any marker There are two common versions of the multiple testing correction problem: per-marker threshold estimation and p-value correction. In a typical study which collects While the Bonferroni (or Šidák) correction provides the simplest way to correct for multiple testing by assuming independence between markers, permutation testing is widely considered the gold standard for accurately correcting for multiple testing In this paper, we correct for multiple testing using the framework of the multivariate normal distribution (MVN). For many widely used statistical tests, the statistics over multiple markers asymptotically follow a MVN Sliding-window approach for Locally Inter-correlated markers with asymptotic Distribution Errors corrected), which differs from previous methods in two aspects. First, SLIDE uses a sliding-window approach instead of the block-wise strategy. SLIDE approximates the correlation matrix as a band matrix , which can effectively characterize the overall correlation structure between markers given a sufficiently large bandwidth. Then SLIDE uses a sliding-window Monte-Carlo approach which samples a statistic at each marker by conditioning on the statistics at previous markers within the window, accounting for entire correlation in the band matrix  efficiently estimates a study's power using the MVN framework.The power estimation problem can be solved within the MVN framework because the test statistic under the alternative hypothesis follows a MVN centered at the non-centrality parameters (NCP). The vector of the NCPs turns out to be approximately proportional to the vector of correlation coefficients  will provide an accurate multiple testing correction; this has been shown to be true for small regions such as those tested in candidate gene studies However, we observe that this discrepancy can appear in genome-wide association studies, in spite of the large sample size, because of the extremely small per-marker threshold  caused by the large number of tests. At its extreme tails, the asymptotic distribution is typically thicker than the true distribution.This phenomenon can be illustrated with a single-SNP experiment using the One may argue that this phenomenon is not important because it mostly occurs at rare SNPs (MAF≤5%) where current studies already have low power to detect associations. However, an incorrect approximation of the distributions at some SNPs affects the corrected p-values of all SNPs. This is because the corrected p-value depends on the distributions of the statistics at all of the SNPs, as it is defined as the probability observing significant results at any marker. For example, suppose we approximate 10 independent normal distributions at 10 independent SNPs. Assume that we correctly approximate 9 distributions, but for one distribution we think that the tails are thicker than the true distribution by a factor of 100. For any given pointwise p-value One can avoid this type of error in corrected p-values by using a method not dependent on the asymptotic approximation, such as the permutation test, or by eliminating rare SNPs in the analysis. It may be sensible to remove rare SNPs with a few or tens of minor allele counts, if the power is very low or if the SNPs are error-prone in their calling. However, SLIDE corrects for multiple testing by using a sliding-window approach to approximate the MVN and then scaling the MVN to approximate the true distribution of the statistic. There are two underlying intuitions. First, a sliding window approach takes into account most of the correlations in the data due to the local LD structure. Second, even though the asymptotic MVN shows a departure from the true distribution at the tail, the scaled MVN will closely approximate the true distribution because the covariance between the statistics is identical in both the true distribution and the MVN. Step 1 — SLIDE first approximates the MVN by using a sliding-window Monte-Carlo approach. Given Under the local LD assumption, the statistics at distant markers are uncorrelated. Thus, given a window size Step 2 — We scale the approximated MVN to fit to the true distribution of the statistic .et al.A discussion of association study power depends on many arbitrary assumptions. Though our framework can be extended to other assumptions, in this paper, we adopt those used in De Bakker For complex diseases, assumption (1) can still be applied if each causal SNP marginally contributes to the risk. Assumptions (4) and (5) can lead to an overestimation of power, especially if the markers are chosen using the reference dataset Finally, we assume that the investigator has determined the number of individuals in the study and the significance threshold.We extend the MVN framework to the power estimation problem. Consider a study design which defines markers and plans to collect Single marker — If marker The case/control study can be thought of as a procedure which draws indirect association), the NCP derivation changes. Suppose a SNP If the marker and the causal SNP are distinct  is equivalent to drawing In practice, approximation in Formula (6) usually leads to an accurate power estimate. However, if the relative risk is very large, the Formula (5) can be computed exactly and used as follows. By Formula (4), we can calculate Let Power depends on the per-marker threshold Given Our method SLIP estimates the power of a study design using the MVN framework. First, like SLIDE, SLIP estimates the per-marker threshold in Formula (8) using a sliding window approach. Then SLIP samples causal SNPs, approximates the alternative MVN to estimate the per-causal-SNP power, and averages per-causal-SNP powers over sampled causal SNPs.Since power is typically larger (e.g. 80%) than a p-value (e.g. .01), a small error in the per-marker threshold barely affects the estimate. Thus, the error caused by using the asymptotic approximation is negligible. Also, given a causal SNP, we can assume that nearby markers (e.g. those within ±1 Mb) can capture most of the statistical power due to local LD. Thus, we can set a window size and only use the markers within that window to estimate the alternative MVN, which will be a The computation becomes very efficient if we use approximation (6). Since approximation (6) states that the covariance is the same for the null and alternative MVNs, we can re-use the null MVN constructed for estimating the per-marker threshold, by shifting it by the NCP to get the alternative MVN. If we re-use the random samples this way, the constructed random samples will be not completely random, as they depend on each other. However, we observe that the inaccuracy caused by this dependency is negligible if we generate a large number of samples for the null MVN. If we re-use the samples, then with almost no additional computational cost, SLIP can generate power estimates for multiple relative risks or study sample sizes, since these only change the NCP.Multiple testing correction is generally performed using the collected data and not the reference data. Recall that the difference between the per-marker threshold for multiple testing correction  from the HapMap project web site http://slide.cs.ucla.eduThe URL for methods presented herein is as follows: In order to compare how accurately and efficiently different methods correct multiple testing, we simulate a study using the WTCCC data −4 to 10−7, whose corrected p-values are from .04 to .0004. We will consider the corrected p-values by the permutation test as the gold standard, and call them permutation p-values. We will assume a method is accurate if its corrected p-values are close to the permutation p-values.First, we perform 10 M permutations to correct ten different pointwise p-values from 10p for p for We use SLIDE, DSA, mvtnorm, RAT, and Keffective to correct p-values. DSA and mvtnorm are MVN-based methods using the block-wise strategy. We use a constant block size (window size) of 100 markers for all methods. Since RAT defines the window size in terms of physical distance, we use 600 kb, the average distance of 100 markers in the dataset. We use -X -e2 option for RAT for an exact computation of the importance sampling procedure as suggested by Kimmel and Shamir DSA is conservative with an average error of 19%. This is equivalent to reducing the error by only about two thirds relative to the Bonferroni correction. The reasons for the errors include the block-wise strategy ignoring inter-block correlations, and not correcting for the error caused by using the asymptotic approximation. In addition to these errors, mvtnorm suffers from an anti-conservative bias which grows as the p-value becomes more significant. This is because the p-value in each block is too small for mvtnorm to accurately estimate. Our simulation shows that this anti-conservative bias increases with the number of sampling iterations (data not shown).Keffective is more accurate and faster than DSA and mvtnorm. The average error of Keffective is 10.6%. Note that Keffective is optimized to provide an efficient approximation for the effective number of tests within ∼10% of error. Thus, Keffective is achieving its goal.Both RAT and SLIDE show accurate estimates with the same average error of 0.8%. Thus, the error rate of SLIDE's corrected p-values is more than 10 times smaller than the error rate of Keffective's corrected p-values, more than 20 times smaller than the the error rate of DSA's corrected p-values, and 80 times smaller than the error rate of the Bonferroni-corrected p-values.We now explore how each source of error in MVN-based methods – the block-wise strategy and the use of the asymptotic approximation without correction – affects the error rate. We remove 1,048 rare SNPs (MAF<.05) and perform multiple testing correction with respect to the remaining 4,515 common SNPs. When considering only common SNPs, the error caused by using the asymptotic approximation will be much smaller See . Figure In many settings, SLIDE is 500 times faster than the permutation test and considerably faster than the other methods. The running time of SLIDE, Keffective, DSA, and mvtnorm is approximately independent of the study sample size, whereas the time of the permutation test is linearly dependent on it. Thus, the efficiency gain of these methods relative to the permutation test will increase as the study size increases. We summarize the accuracy and efficiency of the tested methods in −20) so that the specified number of samples will always be sampled. RAT also has some subtleties involving accuracy and efficiency. If we drop the -X -e2 parameters for an approximated importance sampling, RAT becomes much faster, but the resulting p-values are underestimated by a factor of up to 5 (data not shown). We assumed a corrected p-value of 10−4 to calculate the number of iterations for RAT using the formula presented in Kimmel and Shamir Here we describe a few details of our running time measurements. We used our own C implementation for the permutation test. However, we expect that the measured time will be similar to that for commonly used software such as PLINK Using the same WTCCC chromosome 22 dataset, we perform an additional experiment for the unphased genotype data using the trend test, assuming unbalanced case/controls. We find SLIDE achieves similar accuracy .We generate a simulated dataset using the phased haplotype data of 60 HapMap CEU parental individuals. Specifically, we create a new haplotype by randomly shuffling the 120 chromosomes so that the average length of a haplotype segment is approximately 1 Mb. We mutate (flip) each SNP with probability 10We compare the permutation test, Keffective, and SLIDE. RAT is not efficient for this setting because it is optimized for very significant p-values, much smaller than .05. We expect that the results of DSA or mvtnorm will be similar to or worse than those of Keffective, as in the previous experiment.We perform 10 K permutations for this experiment. We run SLIDE with 10 K samplings and window size 100. We run Keffective with window sizes 100 and 10. The dashed lines denote the interval where an accurate methods' estimate will be found more than 95% of the time. SLIDE estimates the effective number as 1,038,888 (2.8% error), which is within the 95% interval. This small anti-conservative error is only due to the stochastic error and not an inherent bias, since the result becomes highly accurate as 1,068,445 (0.03% error) if we increase the number of samples to 100 K.Keffective estimates the effective number as 1,409,811 (32% error) with window size 10 and as 1,252,986 (17% error) with window size 100. Unlike the previous experiment, for this higher-density marker dataset, Keffective no longer keeps the error within 10%. We do not expect that a larger window size will increase the accuracy of Keffective, because the error does not seem to be due to the missing long range correlations, since SLIDE is accurate with the same window size of 100.The running time is 260 hours for permutation, 10 hours for SLIDE, 10 hours for Keffective with window size 10, and 90 hours for Keffective with window size 100.−5 corresponds to the corrected p-value .05. We correct this pointwise p-value using SLIDE with various window sizes, and see if the corrected p-values are close to .05.Since SLIDE takes into account only correlations within the window size, here we investigate the effect of window size on performance. A reasonable choice for the window size will be the number of markers whose average distance is the average or maximum LD distance in the data. For our experiments, we use the WTCCC T2D case/control chromosome 22 dataset. A large number (10 M) of permutations allows us to find that a pointwise p-value 1.53×10We now examine whether the per-marker threshold estimated from the reference dataset can approximate the true per-marker threshold for a study which may have a different sample correlation structure from the reference dataset. The marker set we use is the SNPs in the Affymetrix 500 K chip over the whole genome.−7 corresponding to the significance threshold .05. Then, we permute the WTCCC data to estimate the false positive rate given this per-marker threshold. We use the WTCCC 1958 British birth cohort control data, which consists of 1,504 individuals. We randomly permute the dataset 100 K times. We estimate the false positive rate, as the proportion of permutations showing significance given the per-marker threshold, to be .0508. Thus, in this experiment, the per-marker threshold estimated from the reference data controls the false positive rate with only 1.6% relative error. This result shows that, even if the reference population and the target population are slightly different , the per-marker threshold estimated from the reference data is a reasonable approximation.First, we apply SLIDE to the HapMap data using window size 100, to obtain the per-marker threshold 2.19×10We compare four different methods for estimating genome-wide power: standard simulation, null/alternative panel construction, best-tag Bonferroni, and SLIP. We assume a multiplicative disease model with a relative risk of 1.2 and a disease prevalence of .01, and a significance threshold of .05. We use the CEU population data in the HapMap as the reference dataset. We use the genome-wide markers in the Affymetrix 500 K chip and assume a uniform distribution of causal SNPs over all common SNPs (MAF≥.05) in the HapMap.We first perform the standard simulation, which we will consider as the gold standard. We construct a number of genome-wide ‘alternative’ panels from the HapMap data by randomly assigning a causal SNP for each panel. We permute each panel 1,000 times to estimate the panel-specific per-marker threshold. The power is estimated as the proportion of panels showing significance given its per-marker threshold. Conneely and Boehnke Another panel construction-based approach is the null/alternative panel construction method. Instead of permuting each of alternative panels, this method constructs another set of ‘null’ panels under the null hypothesis. The null panel gives us a ‘global’ per-marker threshold that can be applied to all alternative panels. Since this method is as accurate as the standard simulation but is more efficient, it is widely used We apply SLIP and re-use the samples for the null MVN for estimating the alternative MVNs. Lastly, we apply the analytical best-tag Bonferroni method For the standard simulation, we use 10 K alternative panels. For the null/alternative panel construction method, we use 10 K alternative panels and 10 k null panels. For SLIP, we use 10 K sampling points. For the best-tag Bonferroni method, we use 10 K samples for causal SNPs. For SLIP, we use a window size of 100 markers. For all other methods, we use a window size of 1 Mb.SLIDE and SLIP provide efficient and accurate multiple testing correction and power estimation in the MVN framework. SLIDE shows a near identical accuracy to the permutation test by using a sliding-window approach to account for local correlations, and by correcting for the error caused by using the asymptotic approximation. SLIDE can be applied to datasets of millions of markers with many rare SNPs, while other MVN-based methods become inaccurate as more rare SNPs are included. To the best of our knowledge, SLIP is the first MVN-based power estimation method.Throughout this paper, we considered the classical multiple testing correction controlling family-wise error rate (FWER) We considered the permutation test as the gold standard for multiple testing correction. The permutation test can be performed in two different ways: at each permutation, we can either assess the maximum statistics among the markers (max-T permutation), or assess the minimum pointwise p-value among the markers by performing another permutation for each marker (min-P permutation) In Text S5 and et al.et al.Recently, a different view of multiple testing correction has been introduced In our experiments, we used a constant block size for the block-wise strategy. In practice, it will be more reasonable to split the region according to the LD blocks. However, this is not always possible because LD blocks are often ambiguous and some blocks can be larger than the maximum block size of the method. For example, if we collect 10 million SNPs, a block size of 1,000 is required to cover 300 kb LD. However, the maximum block size of mvtnorm that allows an accurate estimate is currently 300 Recently, a method called PRESTO We considered the pairwise correlation between SNPs. There can also be so-called higher-order correlations, such as the correlation between a haplotype and a SNP. For example, even though three SNPs are pairwisely independent, the combination of the first two SNPs can be a perfect proxy to the third SNP. However, the multivariate central limit theorem proves that the joint distribution of the test statistics is fully characterized by the matrix of the pairwise correlations. Thus, the effect of the other correlation terms on the joint distribution is asymptotically negligible. Nevertheless, our method is not limited to the SNP test. If our method is applied to the weighted haplotype test In summary, SLIP and SLIDE are two useful methods for genome-wide association studies which provide accurate power estimation at the design step and accurate multiple testing correction at the analysis step. The software is available as a resource for the research community.Figure S1Ratios between the corrected p-values and permutation p-values after rare SNPs are removed. We use the chromosome 22 of the WTCCC Type 2 diabetes cases/controls data. Multiple testing is corrected with respect to the 4,515 common SNPs (MAF≥.05).(0.01 MB PDF)Click here for additional data file.Figure S2Ratios between the corrected p-values and permutation p-values for genotype data. We simulate a unphased genotype dataset using the chromosome 22 data of the WTCCC Type 2 diabetes cases/controls data, assuming a unbalanced study of 2,934 controls and 1,928 cases.(0.01 MB PDF)Click here for additional data file.Figure S32 test for HWE.Inaccurate multiple testing correction caused by the use of an allelic test for unphased genotype data. We generate a simulated unphased genotype data of 120 cases and 120 controls from the HapMap CEU population chromosome 22 data. Then we plot the ratios between the corrected p-values by two different permutations: permutation test using the allelic test statistic, and permutation test using the genotypic test statistic. Quality control is performed by the standard χ(0.01 MB PDF)Click here for additional data file.Text S1Rapid and accurate multiple testing correction and power estimation for millions of correlated markers.(0.14 MB PDF)Click here for additional data file.


Genome-wide association studies (GWAS) aim to identify genetic variants  across the entire human genome that are associated with phenotypic traits such as disease status and drug response. Highly accurate and reproducible genotype calling are paramount since errors introduced by calling algorithms can lead to inflation of false associations between genotype and phenotype. Most genotype calling algorithms currently used for GWAS are based on multiple arrays. Because hundreds of gigabytes (GB) of raw data are generated from a GWAS, the samples are typically partitioned into batches containing subsets of the entire dataset for genotype calling. High call rates and accuracies have been achieved. However, the effects of batch size  and of batch composition  on call rate and accuracy as well as the propagation of the effects into significantly associated SNPs identified have not been investigated. In this paper, we analyzed both the batch size and batch composition for effects on the genotype calling algorithm BRLMM using raw data of 270 HapMap samples analyzed with the Affymetrix Human Mapping 500 K array set.Using data from 270 HapMap samples interrogated with the Affymetrix Human Mapping 500 K array set, three different batch sizes and three different batch compositions were used for genotyping using the BRLMM algorithm. Comparative analysis of the calling results and the corresponding lists of significant SNPs identified through association analysis revealed that both batch size and composition affected genotype calling results and significantly associated SNPs. Batch size and batch composition effects were more severe on samples and SNPs with lower call rates than ones with higher call rates, and on heterozygous genotype calls compared to homozygous genotype calls.Batch size and composition affect the genotype calling results in GWAS using BRLMM. The larger the differences in batch sizes, the larger the effect. The more homogenous the samples in the batches, the more consistent the genotype calls. The inconsistency propagates to the lists of significantly associated SNPs identified in downstream association analysis. Thus, uniform and large batch sizes should be used to make genotype calls for GWAS. In addition, samples of high homogeneity should be placed into the same batch. Nsp I restriction enzyme and ~262,000 SNPs are interrogated. The second chip uses Sty I – cleaved genomic DNA and ~238,000 SNPs are analyzed. Genotypes from Affymetrix GeneChip Human Mapping 500 K array set data are usually determined by the calling algorithm BRLMM [Genome-wide association studies (GWAS) aim to identify genetic variants of single nucleotide polymorphisms (SNPs) across the entire human genome that are associated with phenotypic traits, such as disease status and drug response. The International HapMap project determined genotypes of over 3.1 million common SNPs in human populations and computationally assembled them into a genome-wide map of SNP-tagged haplotypes . Concurrhm BRLMM  embeddedhm BRLMM , GEL [34hm BRLMM , SNiPer-hm BRLMM , MAMS [3hm BRLMM , and CHIhm BRLMM  are alsolinear model that employs Mahalanobis distance for classification [The MPAM algorithm was developed for analysis of raw data  from the first generation of Affymetrix Mapping 10 K array and is based on clustering of chips for each SNP by modified partitioning around medoids . MPAM wafication . RLMM acHigh call rate and accuracy of genotype calling are important and essential issues for success of GWAS, since errors introduced in the genotypes by calling algorithms can inflate false associations and may lose true associations between genotype and phenotype. Each of the algorithms was reported to have a high successful call rate and accuracy, or more precisely, high concordance with genotypes determined by the International HapMap Consortium on the HapMap samples. With the exception of DM and GEL, the algorithms require data from multiple chips  to make genotype calls. A GWAS usually involves analyses of thousands of samples that generate thousands of raw data files . The raw data file for one sample (two CEL files for Affymetrix Mapping 500 K array set: one from Nsp-digested genomic DNA and one from Sty-digested DNA) is about 130 MB in size. Computer memory (RAM) limits make it unfeasible to analyze all CEL files in a GWAS in one single batch on a single computer. The samples are, therefore, divided into many batches for genotype calling. Affymetrix suggests 40 to 96 CEL files for a batch for the BRLMM method. To date, the effects on genotype calls caused  by changing the number and specific combinations of CEL files in batches and propagation of the effects to the downstream association analysis have not been investigated.Since BRLMM is recommended by Affymetrix, we analyzed the effect of batch size and composition on the ability of the BRLMM algorithm to consistently call the 270 samples from the International HapMap project.Methods) for call rate and concordance. The overall call rates, defined as the proportion of successful calls to the total number of calls  for BS1, BS2, and BS3 were 99.48%, 99.50%, and 99.49%, respectively. However, overall call rates are not informative enough to assess the distribution of missed calls on the chip. Batch size effect on genotype calling rates are best compared using one-against-one comparisons of distributions of call rates on individual samples and SNPs. These distributions were calculated from data of samples and SNPs generated from the calling results of the experiments with three batch sizes .Batch size effect was assessed by comparing the genotypes called from BS1, BS2, and BS3 (see Methods) were 0.0304, 0.0416, and 0.0257 for comparisons shown in Figure -6, 0.0296, and 0.0116, respectively, indicating that call rates on samples between calling batch sizes are statistically different.The comparison of call rates of samples using MA-like plots is shown in Figure -16, indicating that the difference of call rates on SNPs between calling batch sizes are statistically significant.The comparisons of the call rates for individual SNPs are depicted by MA-like plots in Figure Comparing call rates in experiments with different batch sizes can only assess the batch size effect on missing calls. Since three genotypes  are possible for a genotype call, we determined the effect of batch size on the ability to consistently call the genotype. To evaluate the batch size effect on successful calls, concordance of successful genotype calls between experiments with different batch sizes was analyzed Table . Batch sMethods) were 99.48%, 99.43%, and 99.41%, respectively. The genetic homogeneity of the batches in BC1 (samples from 1 population group) is higher than that of BC2 (samples from 2 population groups) which, in turn, is higher than that of BC3 (samples from 3 population groups). The batch sizes were the same for all of the three experiments. Thus, higher call rates were obtained when genotype calling was conducted with samples of higher genetic homogeneity. The effect of batch homogeneity was relatively minor by this measure. Because the distribution of missing calls on samples and SNPs was more informative for assessing batch effect in our first experiments (BS studies), we examined the distribution of call rates in the BC experiments.The overall call rate based on all CEL files of the 270 HapMap samples for BC1, BC2, and BC3 , (1 – 0.33 = 0.67), and (0.5 – 0.33 = 0.17). The p-values for all comparisons are 2.2 × 10-16. Therefore, the call rates on samples between calling batch compositions are statistically different.The comparisons of call rates on samples are depicted by MA-like plots Figure . Figure GH differences between the compared experiments: 0.5, 0.67, and 0.17. The p-values for all comparisons are 2.2 × 10-16, confirming that the call rates on SNPs between calling batch compositions are statistically different.The comparisons of call rates on SNPs for BC1 versus BC2, BC1 versus BC3, and BC2 versus BC3 are shown in Figure GH differences of the compared experiments, that is, 0.5, 0.67, and 0.17 for BC1 versus BC2, BC1 versus BC3, and BC2 versus BC3, respectively.To evaluate batch composition effect on successful genotype calls, concordance of successful genotype calls between experiments with different batch compositions was analyzed Table . Batch cThe quality of the raw data is important for comparative analyses and interpretation. The QC scores of the 270 Nsp CEL files and of the 270 Sty chip CEL files of the 270 HapMap samples were calculated using DM .The objective of a GWAS is to identify the genetic markers associated with a specific phenotypic trait. It is critical to assess whether and how the batch effect propagates to the significant SNPs identified in the downstream association analysis. Three case-control based association analyses were conducted for each of the calling results with different batch sizes and compositions to assess the propagation of batch effect in genotype calling to the significantly associated SNPs  was set as "case" while the other two groups were set as "control". Association analyses were conducted to identify SNPs that can differentiate the "case" group from the "control" group. Different lists of SNPs significantly associated with a same population group, identified using the genotype calling results with different batch sizes and compositions, were compared using Venn diagram.The comparisons of the significantly associated SNPs obtained from calling results with different batch sizes are given in Figure It is clear that the batch size effect on genotype calling propagated into the downstream association analyses. Moreover, it was observed that the larger the differences between two batch sizes, the fewer the significantly associated SNPs shared by the two batch sizes. For example, there were 471, 370, and 217 significantly associated SNPs shared only by BS2 and BS3, by BS1 and BS2, and by BS1 and BS3 for the association analyses with European as "case", respectively, that are negatively related to the corresponding differences of batch sizes: 15, 45, and 60. Same trends were observed for the association analyses with African as "case" and with Asian as "case".Figure 2 test) using the genotype calling results from different batch compositions. Therefore, the batch composition effect on genotype calling propagated to the significantly associated SNPs. Moreover, it was observed that the larger the difference of genetic homogeneity between two batch compositions, the fewer the significantly associated SNPs shared by the two batch compositions. For example, there were 555, 512, and 229 significantly associated SNPs shared only by BC2 and BC3, by BC1 and BC2, and by BC1 and BC3, respectively, for the association analyses with European as "case". The numbers are negatively related to the corresponding differences of genetic homogeneity in the batch compositions: 0.17, 0.5, and 0.67. Same trends were observed for the association analyses with African as "case" and with Asian as "case".The Venn diagrams demonstrated that for a same "case-control" setting different lists of significantly associated SNPs were identified by the same statistical test  and 5422 (Sty), 4356 (Nsp) and 4358 (Sty), and 3612 (Nsp) and 3618 (Sty) for calling batches in BS1, BS2, and BS3, respectively. The difference of batch sizes is related to the difference of numbers of non-monomorphism SNPs used to estimate the prior distribution which is, in turn, related to the difference of genotype calling results. The average number of non-monomorphism SNPs used to estimate the prior distribution are 5468 (Nsp) and 5422 (Sty), 6399 (Nsp) and 6308 (Sty), and 6788 (Nsp) and 6688 (Sty) for calling batches in BC1, BC2, and BC3, respectively. Differences in genetic homogeneity of samples are related to differences in the numbers of non-monomorphism SNPs used to estimate the prior which, in turn, is related to the difference of genotype calling results.As demonstrated above, both batch size and batch composition affect genotype calling results of GWAS using the BRLMM algorithm. The larger the difference of batch sizes, the larger the effect. When the samples in the calling batches are more homogenous, more concordant genotypes are called. Batch effect propagates to the downstream association analysis and makes the significantly associated SNPs identified inconsistent. Therefore, we suggest from our studies that the same or larger batch sizes should be used to make genotype calls for GWAS and homogenous samples should be put into the same batches.. The CEL file format was described on Affymetrix's developer pages . The file name indicated the population code (CEU/YRI/CHB+JPT), the sample identifier , followed by the Affymetrix array type (based on restriction enzyme name: Nsp or Sty). Three population groups composed the data sets and each group contained 90 samples: CEU had 90 samples from Utah residents with ancestry from northern and western Europe (termed as European in this paper); CHB+JPT had 45 samples from Han Chinese in Beijing, China, and 45 samples from Japanese in Tokyo, Japan (termed as Asian in this paper); YRI had 90 samples from Yoruba in Ibadan, Nigeria (termed as African in this paper).The raw data (CEL files) from the Affymetrix GeneChip Human Mapping 500 K array set of the 270 HapMap samples were downloaded from the International HapMap project website The quality of the raw data from the Affymetrix Human Mapping 500 K array set was assessed using DM  before g® arrays. These programs are available on the Affymetrix website . APT programs are intended for "power users" who prefer programs that can be utilized in scripting environments and are sophisticated enough to handle the complexity of extra features and functionality. The function of apt-probeset-genotype in APT is an application for making genotype calls using SNP Arrays . BRLMM is one of the genotype calling algorithms implemented in this function, and enables many parameters to be changed by a user. For the studies reported here, all the parameters, except as noted in the narrative were set to the default values recommended by Affymetrix. The chip description files (cdf) for both Nsp and Sty chips of the Mapping 500 K array set, as well as files for defining SNPs on chromosome X, were also used before genotype calling. They were downloaded from Affymetrix website. Nsp and Sty CEL files were genotype-called separately.All experiments of genotype calling by BRLMM reported in this paper were conducted using apt-probeset-genotype of Affymetrix Power Tools 1.8.5. Affymetrix Power Tools (APT) contains a set of cross-platform command line programs that implement algorithms for analyzing and working with Affymetrix GeneChipThree experiments were designed and conducted in order to assess the effect of batch size. In the first experiment (BS1), the 270 HapMap samples were divided into three batches based on their population groups: 90 Europeans, 90 Asians, and 90 Africans. The genotypes were called separately by BRLMM using the default parameter setting suggested by Affymetrix . Genotype calling results on Nsp files and on Sty files of the three batches in this experiment were then merged for comparison with results of other experiments with different batch sizes. The second experiment (BS2) used a batch size of 45 samples. Genotypes were called from the CEL files from 90 European samples in two batches, each with 45 CEL files using BRLMM with the same parameter settings as in the first experiment. The procedure was repeated for the Asian and African samples. In the third experiment (BS3), the batch size was 30 samples from each population groups.The selection of samples (CEL files) to place in each batch can also be anticipated to alter genotyping call rates. The term batch composition effect is used here to denote the selected arrays within batches. BRLMM was used with default parameter settings and the CEL files of 270 HapMap samples to test batch composition effects. In the first experiment (BC1), the 270 samples were placed in three batches. One batch contained 90 samples from the same population group, Europeans, Asians, or Africans. In the second experiment (BC2), the 90 samples in each of the three population groups were evenly divided into two subgroups with each subgroup having 45 unique samples. Genotype calling was then conducted in three batches with composition of: (i) subgroup 1 of Europeans + subgroup 1 of Asians, (ii) subgroup 2 of Europeans + subgroup 1 of Africans, and (iii) subgroup 2 of Africans + subgroup 2 of Asians. In the third experiment (BC3), the 90 samples in each of the three population groups were evenly divided into three subgroups with each subgroup having 30 unique samples. Genotype calling was then conducted in three batches with composition of: (i) subgroup 1 of Europeans + subgroup 1 of Asians + subgroup 1 of Africans, (ii) subgroup 2 of Europeans + subgroup 2 of Asians + subgroup 2 of Africans, and (iii) subgroup 3 of Europeans + subgroup 3 of Asians + subgroup 3 of Africans. In each of the three experiments, genotype calling results of the three batches were merged together before conducting the comparisons.In each of the experiments reported here, the genotype calling results by BRLMM from different calling batches were first merged using a set of in-house programs written in C++. When merging the calling results, genotypes of SNPs in Nsp and Sty chips of the same samples were merged followed by assembling together all genotypes of all of the 270 HapMap samples. Thereafter, overall call rates for each of the experiments, call rates of individual samples and SNPs in each of the experiments, and concordant calls between experiments were calculated and exported as tab-delimited text files using the in-house programs written in C++. Comparison of calling results was done using the R package.Paired two samples t-test in R package (t.test) was used to statistically test the alternative hypothesis that call rates on samples or SNPs between two calling experiments are different.To quantify batch effect, average absolute differences in call rates were calculated for the comparisons using formula (1).where 2 statistics test for associations between the SNPs and the case-control settings.In order to study the propagation of batch effect to the significantly associated SNPs, all genotype calling results of the raw data of 270 HapMap samples using BRLMM with different batch sizes and compositions were analyzed using Chi2 test for Hardy-Weinberg equilibrium was calculated for all SNPs at first and then the p-values were adjusted for multiple tests using Benjamini and Hochberg false discovery rate (FDR) [Prior to association analysis, quality control (QC) of the calling results was conducted to remove markers and samples with low quality. For each of the calling results, call rate of 90% was used to remove SNPs and samples. Minor allele frequency was used to filter SNPs and its cut-off was set to 0.01. Departure from Hardy-Weinberg equilibrium (HWE) was check for all SNPs. The p-value of Chite (FDR) . FDR of To mimic "case-control" in GWAS, for each of the genotype calling results, each of the three population groups  was assigned as "case" while the other two as "control" to form a data set for association analysis for identifying the SNPs significantly associated with the "case" population group.2 statistics test was applied on the contingency table to calculate a p-value for measuring the statistical significance of the association between the testing SNP and the corresponding case-control setting. After raw p-values for all SNPs in a data set were calculated, Bonferroni correction was applied to adjust the raw p-values. Lastly, a criterion of Bonferroni-corrected p-value less than 0.01 was used to identify the significantly associated SNPs.In the association analyses, a 2 × 3 contingency table was generated for each SNP and a case-control setting. Then ChiThe authors declare that they have no competing interests.HH coordinated the project, designed the experiments, conducted the genotype calling and association analysis, compared the calling results using R package, and wrote the manuscript. ZS wrote all of the in-house C++ programs, and involved discussions on the experiments and analysis of the calling results. WG calculated all of the call rates and concordant calls and involved discussions on the experiments and analysis of the calling results. LS, RP, JK, JCF, and WT involved discussions on designing the experiments and analysis and assisted the writing manuscript. HF, JX, JC, and TH involved discussions on experimental design and data analysis. All authors read and approved the manuscript.


P<5×10−8, and 5 with suggestive association (P<5×10−6). The loci included several genes with links to tooth and other organ development . Genes at four of the identified loci are implicated in the development of cancer. A variant within the HOXB gene cluster associated with occlusion defects requiring orthodontic treatment by age 31 years.Tooth development is a highly heritable process which relates to other growth and developmental processes, and which interacts with the development of the entire craniofacial complex. Abnormalities of tooth development are common, with tooth agenesis being the most common developmental anomaly in humans. We performed a genome-wide association study of time to first tooth eruption and number of teeth at one year in 4,564 individuals from the 1966 Northern Finland Birth Cohort (NFBC1966) and 1,518 individuals from the Avon Longitudinal Study of Parents and Children (ALSPAC). We identified 5 loci at  Genome-wide association studies have been used to identify genetic variants conferring susceptibility to diseases, intermediate phenotypes, and physiological traits such as height, hair color, and age at menarche. Here we analyze the NFBC1966 and ALSPAC birth cohorts to investigate the genetic determinants of a key developmental process: primary tooth development. The prospective nature of our studies allows us to exploit accurate measurements of age at first tooth eruption and number of teeth at one year, and also provides the opportunity to assess whether genetic variants affecting these traits are associated with dental problems later in the life course. Of the genes that we find to be associated with primary tooth development, several have established roles in tooth development and growth, and almost half have proposed links with the development of cancer. We find that one of the variants is also associated with occlusion defects requiring orthodontic treatment later in life. Our findings should provide a strong foundation for the study of the genetic architecture of tooth development, which as well as its relevance to medicine and dentistry, may have implications in evolutionary biology since teeth represent important markers of evolution. Heritability of primary tooth emergence is estimated to be over 70% To identify genetic loci regulating primary dentition we performed a general population based genome-wide association (GWA) study of tooth development in infancy among individuals from the 1966 Northern Finland Birth Cohort (NFBC1966) and the Avon Longitudinal Study of Parents and Children (ALSPAC). Specifically, we tested for associations with time to first tooth eruption and number of teeth by one year of age. These phenotypes are relevant to later tooth development because teeth largely acquire their final form at a very early age P<5×10−8). We tested 300,766 SNPs common to both studies (each used the Illumina platform). The analyses were adjusted for sex, gestational age and population structure . ResultsKCNJ2 (inward rectifier potassium channel 2) . KCNJ2 has been implicated in Pierre Robin sequence EDA  gene . EDA was fundamental in forming the first teeth in organisms The strongest association with both phenotypes was for SNP rs8079702, located 15 kb downstream of P<5×10−8) have SNPs located within the genes RAD51L1 (RAD51-like1), IGF2BP1 (insulin-like growth factor 2 mRNA binding protein 1) and MSRB3 (methionine sulfoxide reductase B3). RAD51L1 is involved in DNA repair and a variant in the gene has been found to confer susceptibility to breast cancer IGF2BP1 regulates the growth factor IGF2, and knockouts of the gene in mice suggest a role in organ development MSRB3 to be in the top 100 most expressed genes of 34,000 examined The three remaining loci at genome-wide significance  and number of teeth by one year , after controlling for sex and gestational age. Selecting the SNP with the most extreme signal for either phenotype to represent each locus (“top SNPs”), and analysing them together, the additive effects of these five top SNPs explain 2.9% of the variance of both tooth eruption time and number of teeth in the NFBC1966, and 4.2% and 4.0% of the variance in tooth eruption and number of teeth in ALSPAC. Without a suitable external replication cohort these estimates were derived in the two discovery cohorts and therefore may overestimate the true values due to the “winner's curse”. GWA studies have thus far explained only a small proportion of heritability We also summarized the predictive power of the five top SNPs by defining a ‘delayed tooth eruption’ measure as the number of alleles across the SNPs that delay tooth eruption. P-values between 5×10−6 and 5×10−8 (HOXB1 (homeobox B1) and HOXB2 (homeobox B2). Although previous studies have indicated that tooth development is independent of a Hox patterning program IGF2BP1, but the two SNPs show almost no linkage disequilibrium with each other (r2 = 0.002 in NFBC1966 and r2 = 0.006 in ALSPAC). Furthermore, a test for association of rs6504340 conditional on rs9674544 was significant  gave a significant association, where each G allele . A smaller number of teeth at 1 year also predicted higher risk of orthodontic treatment . However, when number of teeth or time to first tooth were included in the model with dental occlusion as outcome, the associations with the G allele remained , suggesting an independent association between rs6504340 and dental occlusion.Given the influence of tooth development on dental occlusion, we hypothesized that genetic determinants of early tooth eruption may associate with dental occlusion later in life. We tested for associations between the SNP with the most extreme signal for either phenotype at each of the 10 identified loci and defects in occlusion requiring orthodontic treatment by the age of 31 years in the NFBC1966 (data not available in ALSPAC). A total of 611 individuals (13.5%) reported a defect in occlusion that had required orthodontic treatment. Of the 10 SNPs tested, SNP rs6504340 , EDA  and IGF2BP1 (intestines) HOXB gene cluster is an established regulator of development, and the HMGA2 gene has previously been associated with adult height IGF2BP1 and RAD51L1 have been implicated in cancer HOXB2, 2q35, and HMGA2Teeth and several other organs have common growth and developmental pathways during early life HOXB gene cluster and the requirement for orthodontic treatment due to defective occlusion by the age of 31 years. Further GWA studies of developmental processes during infancy may establish whether the genetic determinants of infant development can contribute to the study of chronic diseases, such as cancer, that occur later in life.We provide the first detailed insight into the genetic architecture of primary dentition and our findings could have implications for the study of other developmental and organogenic processes. Exploiting the availability of longitudinal cohort data The data was derived from two genome-wide scans of the geographically defined prospective birth cohorts; the NFBC1966 and ALSPAC. The NFBC1966 followed pregnancies in the two northernmost provinces of Finland with expected delivery dates in 1966. ALSPAC recruited mothers during pregnancy with expected dates of delivery between April 1991 and December 1992 from Bristol and the surrounding area in the South West of England. A total of 4,564 samples were available from the NFBC1966 and 1,518 from ALSPAC. In both cohorts, two separate measures of primary tooth development were collected: i) date of first tooth eruption (in months), and ii) number of teeth (measured at 12 months in NFBC1966 and 15 months in ALSPAC). In the NFBC1966 date of first tooth eruption and number of teeth was gathered by public health professionals during children's monthly visits to child welfare centers . In ALSPAC, parents reported the date of first tooth eruption and number of teeth at 15 months on a questionnaire. In order to ascertain the accuracy of the parental responses, a subsample were examined and validated by a dentist. Information on date of first tooth eruption was available for 4,523 individuals in the NFBC1966 (99% of available GWA samples) and 1396 (92%) in ALSPAC and for number of teeth, 4,326 (95%) in the NFBC1966 and 1,426 (94%) in ALSPAC. All aspects of the study were reviewed and approved by the Ethics Committee of the University of Oulu and the ALSPAC Law and Ethics Committee and by the respective local research committees. Participants (in NFBC1966) and parents (in ALSPAC) gave written informed consent.P<10−4 in NFBC1966, P<5×10−7 in ALSPAC), or if the MAF was <1%. After quality control, 329,091 SNPs in NFBC1966 and 310,611 in ALSPAC were available. We report here the results from the 300,766 genotyped SNPs common to both studies.The Illumina HumanCNV370-Duo DNA Analysis BeadChip was used for genotyping the NFBC1966, and Illumina HumanHap317K BeadChip for ALSPAC. The genotyping and quality control procedures have been described elsewhere P<0.05 Age of first tooth eruption in the NFBC1966 was recorded in months, such that the first tooth could have erupted at any time between the end of previous month and the end of the recorded month. In ALSPAC it was recorded to the nearest month and 3 individuals were recorded as having no teeth after 15 months. To account for the censoring in the two cohorts the outcome was analyzed using parametric survival analysis in the R software package 2.7.1.The Gaussian distribution gave a good fit to the data in both cohorts and was used to model the underlying event time. Number of teeth in the NFBC1966 was recorded at 12 months. In ALSPAC, measurements were taken at around 15 months but there was variability in the exact time of measurement, therefore the ALSPAC analysis was adjusted for age of measurement. Teeth typically erupt in pairs from the upper and lower jaw (75% of children had an even number of teeth in the NFBC1966), making the Poisson distribution inappropriate for modeling the number of teeth. Therefore ordinal logistic regression was used as implemented by the polr function in the R package. Analyses of the X chromosome treated males as homozygous females. The allele frequencies of the identified SNPs on the X chromosome did not differ significantly between the sexes. GWA analyses were adjusted for sex, gestational age and population stratification using principal components (PC). Each analysis was corrected for population stratification separately by including those of the top 10 PCs that were associated with the phenotype at P<5×10−6. Results from the two studies were combined using fixed effects inverse variance meta-analysis http://www.jax.org; NCBI, http://www.ncbi.nlm.nih.gov; R project, www.r-project.org; Uniprot, http://www.uniprot.org.Jackson Laboratory website, Figure S1P<5×10−8).Manhattan plots for the 300,766 SNPs from the genome-wide association meta-analysis for (A) time to first tooth eruption, and (B) number of teeth at 12 months. The (blue) line indicates the genome-wide significance threshold ((0.17 MB PDF)Click here for additional data file.Figure S2P<5×10−8). (A) Locus 17q24 (KCNJ2), (B) Locus Xq13 (EDA), (C) Locus 14q24 (RAD51L1), (D) Locus 17q21.4 (IGF2BP1), and (E) Locus 12q14 (MSRB3). The (blue) line indicates the genome-wide significance threshold (P<5×10−8).Manhattan plots and linkage disequilibrium (LD) diagrams for five identified loci ((0.89 MB PDF)Click here for additional data file.Figure S310P values versus the expectation under the null for (A) time to first tooth eruption and (B) number of teeth at 12 months. The most associated 10,000 SNPs from the meta-analysis are shown.Quantile-quantile plots of observed -log(0.07 MB PDF)Click here for additional data file.Figure S4Additive effect of delayed tooth eruption alleles in identified loci in ALSPAC. Subject classified by the number of delayed tooth eruption alleles. SNPs chosen had the strongest signal for time to first tooth eruption at each locus. Mean time of first tooth eruption is plotted in black. The bars represent the number of individuals for each count of “delayed tooth eruption” alleles. Lines through points are linear regression fits.(0.05 MB PDF)Click here for additional data file.Table S1Summary of the candidate genes located within the top loci.(0.08 MB PDF)Click here for additional data file.


FTO, MC4R, and TMEM18, we detected two new loci for obesity: one in SDCCAG8  and one between TNKS  and MSRA , the latter finding being limited to children and adolescents as demonstrated in the GENERALIZATION step. The odds ratios for early-onset obesity were estimated at ∼1.10 per risk allele for both loci. Interestingly, the TNKS/MSRA locus has recently been found to be associated with adult waist circumference. In summary, we have completed a meta-analysis of two GWAS which both focus on extremely obese children and adolescents and replicated our findings in a large followed-up data set. We observed that genetic variants in or near FTO, MC4R, TMEM18, SDCCAG8, and TNKS/MSRA were robustly associated with early-onset obesity. We conclude that the currently known major common variants related to obesity overlap to a substantial degree between children and adults.Meta-analyses of population-based genome-wide association studies (GWAS) in adults have recently led to the detection of new genetic loci for obesity. Here we aimed to discover additional obesity loci in extremely obese children and adolescents. We also investigated if these results generalize by estimating the effects of these obesity loci in adults and in population-based samples including both children and adults. We jointly analysed two GWAS of 2,258 individuals and followed-up the best, according to lowest p-values, 44 single nucleotide polymorphisms (SNP) from 21 genomic regions in 3,141 individuals. After this DISCOVERY step, we explored if the findings derived from the extremely obese children and adolescents (10 SNPs from 5 genomic regions) generalized to (i) the population level and (ii) to adults by genotyping another 31,182 individuals (GENERALIZATION step). Apart from previously identified  SDCCAG8 on chromosome 1q43–q44 and between TNKS/MSRA on chromosome 8p23.1). We also re-identified variants in or near FTO, MC4R, and TMEM18 to be associated with extreme obesity. In addition, we assessed the effect of the markers in 31,182 obese, lean, normal weight, and unselected individuals from population-based samples and showed that the variants near FTO, MC4R, TMEM18, and SDCCAG8 were consistently associated with obesity. For variants of TNKS/MSRA, the obesity association was limited to children and adolescents. In summary, we detected two new obesity loci and confirmed that the currently known major common variants related to obesity overlap to a substantial degree between children and adults.Genome-wide association studies (GWAS) have successfully contributed to the detection of genetic variants involved in body-weight regulation. We jointly analysed two GWAS for early-onset extreme obesity in 2,258 individuals of European origin and followed-up the findings in 3,141 individuals. Evidence for association of markers in two new genetic loci was shown ( FTO . In parallel, a combined analysis of 34,416 individuals from Iceland, the Netherlands, North America (European and African descent) and Scandinavia revealed 11 regions of genome-wide significance at ≤1.6×10−7 . Finally, shifting to the analysis of extremely obese subjects, Meyre et al. NPC1 , near MAF (v-maf musculoaponeurotic fibrosarcoma oncogene homolog gene) and PTER (phosphotriesterase related gene), which were followed-up in 14,186 European subjects. Altogether, 16 genetic loci relevant for body weight regulation have been identified by these three GWAS approaches Recent genome-wide association studies (GWAS) conducted in adult population-based samples assessed for body mass index (BMI) or in case-control designs for extreme obesity led to the discovery of genetic loci relevant for body weight regulation. The first genetic loci were detected via variants in intron 1 of the While meta-analytic combinations of multiple GWAS were highly successful in population-based samples, no such approach has up to now been applied to case-control designs for obesity. Here we combined GWAS based on two samples that were specifically ascertained for the analysis of paediatric extreme obesity de novo) genotyped all SNPs with strong evidence for an association to obesity  genotyped 31,182 individuals in the GENERALIZATION step).In particular, our study design was based on two steps to enable hypothesis-free SNP identification and confirmation. In the DISCOVERY step, we screened 2,239,392 genotyped or imputed SNPs and tested 1,596,878 SNPs  for association in a combined French and German sample of 1,138 extremely obese children and adolescents and 1,120 normal- or underweight controls as based on a minor allele frequency above 1%. Next, we  and downstream of MC4R , rs473034 indicates a new genetic locus for early onset extreme obesity located on chromosome 8p23.1 (p = 2.77×10−8) with the closest genes TNKS  and MSRA . In addition to the three genome-wide significant regions, the GWAS data revealed 18 genomic regions of interest which were defined by (i) two-sided p-values of a lead SNPs ≤10−5 and (ii) more than a single SNP within a locus (lead SNP ±500 kb) showing evidence for association as defined via a p-value rank <1,500  genotyped 44 SNPs representing these 21 genomic regions of interest in independent 1,181 obese children and adolescents and 1,960 normal- or underweight controls and in up to 715 nuclear families with at least one extremely obese offspring (−4 (TMEM18), 16q12.2 (FTO), 18q21.32 (3′ of MC4R) as well as two new loci on chromosome 1q43-q44 and on chromosome 8p23.1  whereas the second new locus on chromosome 8p23.1 between the TNKS and MSRA had already showed evidence for an association at the genome-wide level in the initial paediatric extreme obesity GWAS meta-analysis.As part of our DISCOVERY step, we subsequently , 1.35–1.45 (TMEM18) and 1.10–1.19 (SDCCAG8). For the SNPs related to MC4R and the new TNKS/MSRA locus, however, we observed age dependent differences: For MC4R, we confirmed the findings by Loos and co-workers MC4R; p = 9.39×10−3 for the interaction of genotype and group). For TNKS/MSRA, we found an effect in children and adolescents but no effect in adults . These differences in obesity risk effects between children and adolescents as compared to adults, however, were not due to large differences in allele frequencies as based on the population-based samples with a maximum difference of 0.82% for rs11127485 of TMEM18. We then compared (extreme) obesity assessed in case-control designs to the analyses of quantitative BMI data derived from population-based samples in the GENERALIZATION step . The MC4R SNP, however, would have been harder to detect ; detection of the two new loci SDCCAG8 and TNKS/MSRA would have been impossible  and two new loci (SDCCAG8 and TNKS/MSRA) with estimated odds ratios that ranged from ∼1.07 to ∼1.44 in children and adolescents and from ∼1.17 to ∼1.45 in adults with the strongest overall signals related to the FTO locus. Modelling of the joint and epistatic effects revealed that <1% of the BMI (or BMI-SDS when BMI is expressed as standard deviation score) variance can be attributed to the five variants analyzed in or near TNKS/MSRA, SDCCAG8, TMEM18, FTO, and MC4R. For children and adolescents this value did not change upon inclusion of gender, age and age2 as covariates whereas it changed to 11% for the adult sample (KORA S2-S4). Applying the model including the same covariates derived in one population-based data set of adults (KORA S2-S4) to a second population-based data sets of adults  r2 dropped from 11% to ∼2%. Proceeding similarly for epistatic effects, we found no evidence for strong epistatic effects using regression tree analyses , a locus on 11p14.1 near BDNF, and a gene-rich locus on 12q13.13 near BCDIN3D all showed directionally consistent effects of the respective SNPs . Details on all analysed candidate gene SNPs are provided in 2>.9).In addition to our hypothesis-free step-wise design, we investigated our paediatric extreme obesity GWAS meta-analysis data focussing on recently reported GWAS-based candidate markers FTO, MC4R and TMEM18 using a hypothesis-free step-wise design. Leaving the hypothesis-free approach and focussing on known GWAS-based candidate markers, we were able to substantiate another four loci  of the 16 obesity loci previously detected in GWAS FTO, MC4R, TMEM18, NEGR1SEC16B, BDNF and BCDIN3D; NPC1, MAF and PTER was not possible here.We identified two new genomic loci associated with paediatric obesity on chromosomes 1q43–q44 and 8p23.1 by a meta-analysis of two GWAS for early onset extreme obesity with a total 2,258 individuals of European origin. In addition, we confirmed the three known loci 2>.9) which are located in introns 6, 9 and 10 of SDCCAG8. There is no obvious indication for an involvement of SDCCAG8 in body weight regulation. Data on this gene are scarce. It has been shown that SDCCAG8 is located in centrosomes during interphase and mitosis in human and murine cells. N- and C- terminal truncations of the human protein alter this location; a possible role of SDCCAG8  in centrosomal organization has been suggested SDCCAG8 is ubiquitously expressed, amongst other tissues in thymus, small intestine, colon mucosa, liver and brain (http://www.genecards.org/cgi-bin/carddisp.pl?gene=SDCCAG8). Hypothalamus, pituitary and adrenals have been shown to have a particularly high transcript abundance. This pattern indicates a role of SDCCAG8 in this pivotal hormonal axis that is well-known for its impact on body weight regulation CEP170  and AKT3  gene, ∼168 kb upstream of rs12145833) with the latter being the more interesting candidate. The protein encoded by this gene is a member of the AKT family known to regulate cell signalling in response to insulin and growth factors. In particular AS160, an Akt substrate of 160 kDa, and TBC1D1  have been suggested to have complementary roles in regulating vesicle trafficking in response to insulin TBC1D1 being persuasively linked to body weight regulation 2>.9) to any likely functional relevant variant in a region of ±1 Mb around the lead SNP (rs12145833) using Ensembl . TNKS and MSRA are the genes located closest to our association finding. MSRA encodes a repair enzyme for oxidative damage in proteins by enzymatic reduction of methionine sulfoxide. Oxidation of methionine residues in proteins is considered to be an important consequence of oxidative damage to cells MSRA is mainly expressed in kidney followed by liver, brain, and adipose tissue (http://biogps.gnf.org/#goto=genereport&id=4482). The other candidate gene at the chromosome 8p23.1 locus is TNKS which is ubiquitously expressed (http://biogps.gnf.org/#goto=genereport&id=8658). Tankyrase is a Golgi-associated poly-ADP-ribose polymerase, which is involved in the regulation of GLUT4 trafficking in 3T3-L1 adipocytes. Mice lacking Tnks show increased energy expenditure, fatty-acid oxidation, and insulin-stimulated glucose utilization; they are lean even with excessive food intake 2<.01 (D' = .03) according to Ensembl version 56). Thus, further research is needed to elucidate if our finding for TNKS/MSRA detected in paediatric extremes of the quantitative trait BMI and the finding for waist circumference in adults The new chromosome 8p23.1 locus, for which we observed genome-wide significance in our GWAS meta-analysis , , was aFTO, MC4R and TMEM18NEGR1, SEC16B, BDNF and BCDIN3D. Thus, one may speculate, that the genetic architecture in the paediatric extremely obese is in part similar to the BMI findings based mainly on adults from large population-based assessments  was calculated and the extremes were defined using percentile criteria of large population-based samples of the general population http://www.hapmap.org). From this GWAS meta-analysis, we selected 44 SNPs covering 21 loci (de novo) genotyped in 1,181 overweight and obese children and adolescents and 1,960 normal weight or lean children and adolescents and young adults (controls) of European ancestry and up to 715 nuclear families with obese offspring of European ancestry were examined. The SNP selection was based on (i) an unadjusted two-sided p-values ≤10−5 and (ii) more than a single SNP within a locus (lead SNP ±500 kb) showing evidence for association . As BMI-SDS already includes information on gender and age additional sensitivity analyses were performed where these covariates were omitted. Note that the case-control analyses in GENERALIZATION step are not completely independent from the population-based analyses. In particular, controls in GENERALIZATION were individuals from the population-based samples which either had a BMI<25 for adults or a BMI percentile below the median. Due to the similarity to the original design it was nevertheless decided to report both analyses.In both the DISCOVERY and the GENERALIZATION part of the study either log-additive or additive genetic models were applied. Case-control samples were analysed using logistic regression (both with and without gender and age as covariates). The nuclear families were analysed using UNPHASED  of all five loci  and explored joint and epistatic effects . More details on quality control and power considerations are provided in Unless otherwise stated, all reported p-values are nominal, two-sided and not adjusted for multiple testing. To address multiple testing in the paediatric extreme obesity GWAS meta-analysis we applied a Bonferroni-corrected αThe study, including the protocols for subject recruitment and assessment, the informed consent for participants, were reviewed and approved by all local IRB boards.Figure S1DISCOVERY: Quantile-quantile plot of SNPs of the GWAS meta-analysis focussing on extremely obese children and adolescents joint analysis Click here for additional data file.Figure S210 of the two-sided p-value). The plots were generated using SNAP  against the meta-analysis association signal on the y-axis (shown as -loging SNAP .(8.26 MB TIF)Click here for additional data file.Figure S3FTO genotype and then by TMEM18 genotype. Here we observe some weak evidence for a marker by marker interaction as the sub-branching in the FTO genotype branches is not the same for both branches.GENERALIZATION: Regression trees to explore epistatic effects of validated markers in two independent population-based samples of adults Click here for additional data file.Figure S42; see main text and FTO genotype and then by MC4R genotype. However, as shown on the right panel, if age (regression tree based cut-off at 13.19 years) is included only the FTO genotype remains as predictor.GENERALIZATION: Regression trees to explore epistatic effects of validated markers in one population-based sample of children and adolescents Click here for additional data file.Figure S5−5 Click here for additional data file.Figure S6SDCCAG8. All variants of Ensembl  in a region of ± 1Mb around the lead SNP (rs12145833) are displayed. The x-axis displays the chromosomal position of the variant whereas the y-axis indicates LD (r2) of that variant with rs12145833; the different colours code for different variant classes (see legend). The plots were generated using CandiSNPer Click here for additional data file.Table S1DISCOVERY: Description of samples that were jointly analysed in our genome-wide association analysis.(0.05 MB DOC)Click here for additional data file.Table S2DISCOVERY: Genotype data for both GWAS in extreme early onset obesity.(0.04 MB DOC)Click here for additional data file.Table S3DISCOVERY: Evidence from obese children and adolescents  versus controls  and 715 nuclear families with obese offspring. All these samples were not part of the meta-analysis of two GWAS for early onset extreme obesity.(0.20 MB DOC)Click here for additional data file.Table S4DISCOVERY: GWAS-based SNPs of previously reported candidate markers for BMI and/or obesity sorted by chromosome and physical position. The first two columns indicate the name of a previously identified marker and the implied, described candidate genes (in bold those which were confirmed and which are reported in the introduction of the main text). The columns 6–11 summarize the data of three recently published large-scale GWAS , Thorleifsson et al., 2009 (publication “TH”), and Meyre et al., 2009 (publication “ME”)). Note that parts of the data sets in Meyre et al. (2009) overlap with our meta-analyses data set. The table displays the phenotype, obesity risk effect allele, the frequency of the effect allele, the estimated additive effect and the related nominal p-value are derived from publicly available resources. The effect is displayed using the measurement regarded most appropriate for the design of the GWAS. The remaining columns correspond to the respective results observed GWAS meta-analysis.(0.54 MB DOC)Click here for additional data file.Table S5DISCOVERY: SNPs of previously identified ‘classical’ obesity candidate genes. The first column indicates the name of a previously identified candidate gene. The second column indicates SNPs which showed strongest association in Scuteri et al. (2007) for the phenotype, effect allele, frequency, the estimated additive effect and the related nominal p-value in columns 6–9. The remaining columns correspond to the respective results observed in our GWAS meta-analysis .(0.07 MB DOC)Click here for additional data file.Text S1DISCOVERY and GENERALIZATION.(0.27 MB DOC)Click here for additional data file.


We examined the properties of growth mixture modeling in finding longitudinal quantitative trait loci in a genome-wide association study. Two software packages are commonly used in these analyses: Mplus and the SAS TRAJ procedure. We analyzed the 200 replicates of the simulated data with these programs using three tests: the likelihood-ratio test statistic, a direct test of genetic model coefficients, and the chi-square test classifying subjects based on the trajectory model's posterior Bayesian probability. The Mplus program was not effective in this application due to its computational demands. The distributions of these tests applied to genes not related to the trait were sensitive to departures from Hardy-Weinberg equilibrium. The likelihood-ratio test statistic was not usable in this application because its distribution was far from the expected asymptotic distributions when applied to markers with no genetic relation to the quantitative trait. The other two tests were satisfactory. Power was still substantial when we used markers near the gene rather than the gene itself. That is, growth mixture modeling may be useful in genome-wide association studies. For markers near the actual gene, there was somewhat greater power for the direct test of the coefficients and lesser power for the posterior Bayesian probability chi-square test. Growth mixture modeling (GMM) is an important tool for analyzing longitudinal data -3. GMM ht-statistics of the trajectory group parameters, the estimated frequency of each trajectory group, the Bayesian posterior probability (BPP) that each subject is a member of each trajectory component and the Bayesian information criterion (BIC) statistic, which is used to assess the number of trajectory components. Mplus also reports these statistics.We use the SAS TRAJ procedure  and the τ1, ..., τ5, ϕ1, ϕ2 and 10 SNPs v1, v2, ..., v10 on human chromosome (HC) 22 that were not in the genetic mechanism determining the simulated CAC and myocardial infarction (MI) events. The genes τ1, ..., τ5 determined the CAC level, and the genes ϕ1, ϕ2 determined MI but not the CAC level [v1, v2, ..., v10 are the basis of the empirical null distribution of our test statistics. The distribution for ϕ1, ϕ2 should be similar to the empirical null distribution. We also report PROC TRAJ results for four SNPs near τ5 and τ2 that had a minor allele frequency (MAF) greater than 0.1 and were in Hardy-Weinberg equilibrium (HWE) to demonstrate the applicability of this procedure for genome-wide association studies (GWAS).For each gene considered, we create the two indicator variables, whether the subject's genotype is the more common homozygote and whether the subject's genotype is the less common homozygote. We study 17 single-nucleotide polymorphisms (SNPs): n = 6,476). We treat the subjects as independent observations.We consider two sets of analyses applied to the 200 replicates. For each of the 17 SNPs, the first uses the longitudinal CAC measures with the two genetic indicator variables used as traits but without any TVCs. The second is the longitudinal CAC with the TVCs cholesterol (CHOL) and high-density lipoprotein (HDL) level and with the two genetic indicator variables as traits. We use a quadratic trend function and set the number of components to two and three. The dataset consists of subjects with genotypes and simulated phenotypes  indicator variables associated with gene i, i ∈ {τ1, ..., τ5, ϕϕ21, , v1, ..., v10}. For example, for the τ5 gene (which has homozygous genotypes AA and GG), there are estimated coefficients for the two homozygous indicators in Groups 2 through c. Group 1 is a reference group with coefficients of trait variables set to 1 identically in the SAS TRAJ procedure. With τ5, we calculate v1, v2, ..., v10. We call this the "direct coefficient test" (DCT) and use level of significance 0.05 with the empirical critical value from the distribution for v1, v2, ...., v10.In an analysis that identifies c trajectory group column contingency table. We classify each subject into the trajectory group that has the largest BPP. A significant value of the chi-square test for independence  indicates association with the gene.Our second procedure is the BPP chi-squared test on the three genotype rows by p < 0.05 based on the distribution of the chi-square test for v1, v2, ...., v10) indicates association with the gene.Our third procedure is the likelihood-ratio test statistic (LRTS). We take the difference of the likelihood function with the two genetic indicator variables and the likelihood function without the two genetic indicator variables. We perform this test without TVC and with TVC. A significant value of the LRTS . The rejection rate for one of the nearby SNPs was 100% for both DCT and BPP, and the rejection rate was greater than 50% for DCT for two nearby SNPs. The rejection rate for the remaining SNP was very low. The rejection rate for BPP was somewhat less than the rejection rate for DCT. Similar results held for τ2 (data not shown).Figure p-value of the DCT or BPP is to use a permutation method.The Mplus software was not effective in analyzing this data due to computational instability and lengthy computing time. Computational instability also affected the SAS TRAJ procedure. For example, about 17% of the replicates did not have a solution when three groups were specified with TVCs. One effect of this instability was that using TVCs did not increase the overall power as expected. The LRTS was not usable, possibly due to the dependence of subjects within pedigree and the non-normality of the distribution of CAC, especially for the first visit. The empirical distribution of the DCT and BPP for genes not associated with CAC values appeared to depend on whether the gene was apparently in HWE. Because violation of HWE is often used as a test for large genotyping error rates , a questn vectors  of CAC values. The fraction of permutations that yield a value of the statistic larger than the one observed is the permutation p-value.Specifically, one can generate a large number of random permutations of the τ5 association and good power (97.5% rejection rate) to detect the τ2 association using either DCT or BPP. The associations with τ1, τ3, and τ4 were not detected with this approach. The rejection rates at a marker near τ5 could be as large as the τ5 rejection rate. The rejection rate for DCT was high for most markers near τ5. The BPP had somewhat lower rejection rates than the DCT. Similar results held for τ2.The analyses based on the SAS TRAJ procedure have power to detect genes associated with longitudinal for CAC QTLs. For CAC, the SAS TRAJ analysis of unadjusted CAC values with two trajectory groups and no TVCs had excellent power (100% rejection rate) to detect the We conclude that the SAS TRAJ procedure is useful in GWAS to identify longitudinal QTLs. In an actual genetic analysis, one should follow Maclean et al. and consider multiple transformations of the data to reduce the chances that skewness of the data would result in an apparent genetic association . ProceduBIC: Bayesian information criterion; BPP: Bayesian posterior probability; CAC: Coronary artery calcification; DCT: Direct coefficient test; GMM: Growth mixture modeling; GWAS: Genome-wide association studies; HC: Human chromosome; HWE: Hardy-Weinberg equilibrium; LRTS: Likelihood-ratio test statistic; MAF: Minor allele frequency; MI: Myocardial infarction; MLE: Maximum likelihood estimate; QTL: Quantitative trait loci; SNP: Single-nucleotide polymorphism; TVC: Time-varying covariate.The authors declare that they have no competing interests.S-WC developed the methodology, carried out the statistical and genetic analyses, organized the group, and drafted the manuscript. SHC, KL, RSF, CH, and TS participated in the data mining and statistical analyses. KL was also in charge of the data distribution and management. KA, DG, WK, RW, NRM, and SJF conceived of statistical theories and possible applications. NRM and SJF also participated in the study design, group coordination, and manuscript drafting. All authors read and approved the final manuscript.