This paper summarizes the contributions from the Population-Based Association group at the Genetic Analysis Workshop 19. It provides an overview of the new statistical approaches tried out by group members in order to take best advantage of population-based sequence data.Although contributions were highly heterogeneous regarding the applied quality control criteria and the number of investigated variants, several technical issues were identified, leading to practical recommendations. Preliminary analyses revealed that Hurdle-negative binomial regression is a promising approach to investigate the distribution of allele counts instead of called genotypes from sequence data. Convergence problems, however, limited the use of this approach, creating a technical challenge shared by environment-stratified models used to investigate rare variant-environment interactions, as well as by rare variant haplotype analyses using well-established public software. Estimates of relatedness and population structure strongly depended on the allele frequency of selected variants for inference. Another practical recommendation was that dissenting probability values from standard and small-sample tests of a particular hypothesis may reflect a lack of validity of large-sample approximations. Novel statistical approaches that integrate evolutionary information showed some advantage to detect weak genetic signals, and Bayesian adjustment for confounding was able to efficiently estimate causal genetic effects. Haplotype association methods may constitute a valuable complement of collapsing approaches for sequence data. This paper reports on the experience of members of the Population-Based Association group with several novel, promising approaches to preprocessing and analyzing sequence data, and to following up identified association signals. BMC Proceedings and BMC Genetics.Every 2 years, participants of the Genetic Analysis Workshop (GAW) explore a common data set using novel approaches and summarize their findings in a short paper. Contributions to the GAW19, held August 24–27, 2014, in Vienna, Austria, were split up by workshop organizers into 9 thematic groups. The present article summarizes the methods and results from the Population-Based Association group, aiming at providing a motivating, intuitive overview of the new approaches tried out by group members. Technical details and descriptions of individual contributions can be found in the publications Members of the Population-Based Association group worked in pairs in the weeks preceding the GAW. Each participant contacted the other pair member, read the preliminary version of his/her individual contribution, and discussed findings and results with him/her. On the first day of the workshop, group members briefly presented the contributions of the other pair member. Engaged discussions and intensive team work during 4 group meetings and a poster session led to a consensus summary of the group contributions, which was presented to all GAW participants in a plenary session.After submission and peer review, 9 individual papers from the Population-Based Association group were accepted for publication in the GAW19 proceedings , and homogenizing ). To examine the ability of principal component analysis to capture ancestry, principal components were estimated relying on a genetic relationship matrix that was calculated based on 4 subsets of whole genome sequence variants: rare (MAF <0.01 or MAF <0.05) and common (MAF >0.01 or MAF >0.05). Table The analysis of association between binary phenotypes and single rare variants is challenging because conventional logistic regression approaches often violate the large-sample assumption for test statistics, resulting in poor type I error control and low statistical power. In particular, standard score tests can be extremely anticonservative under the null. Shin et al. explored alternative tests for low-frequency and rare variants, including 2 sparse-data approaches to single-variant tests, and collapsing tests for sets of variants. The first explored sparse-data approach was the Firth-type likelihood ratio test based on the penalized log-likelihood functioni(β) is the Fisher information matrix. The second sparse-data approach was a modified score test which incorporates small-sample variance and/or kurtosis to obtain the null distribution. The investigated variant-collapsing tests included a MAF-weighted burden test, a nonburden sequence kernel association test (SKAT), and a unified approach that optimally combines SKAT and the burden test (SKAT-O). Investigated variant-collapsing tests were applied to sets of rare variants alone, rare and low-frequency variants, and all variants within defined subregions built according to physical proximity. Table where Thompson and Fardo compared mapping methods that account for the evolutionary relatedness among individuals (tree-based) with standard methods that ignore evolutionary relationships (non–tree-based association mapping methods). Each genetic variant has an evolutionary history that can be represented by a phylogenetic tree  transformations of the second phenotype. The fifth phenotype was the null trait Q1 provided by workshop organizers.In next-generation sequence data, the proportion of rare variants is substantially larger than the proportion of common variants typically measured in array-based genome-wide association studies. Rare variants present a challenge because often there are too few of the rare alleles for traditional statistical tests, and the increased variant density results in multicollinearity, making it difficult to identify independent associations. Schwantes-An et al. investigated the effect of the MAF, chromosomal position, significance threshold, and departure from normality of the investigated phenotype on the type I error rate. Five quantitative phenotypes were simulated under the null hypothesis. The first phenotype followed a standard normal distribution, the second followed a gamma distribution. The third and fourth phenotypes were the logFernández-Rhodes et al. compared type I error rates and statistical power for 2 gene–environment interaction methods. The first method (“interaction model”) uses a gene–environment interaction term to measure the change in outcome when both the genetic marker and environmental factor are present, compared to the presence of the genetic marker alone. The second method tests for effect-size differences between strata under distinct environmental exposures . The 2 methods can be applied to test gene–environment interactions with 1° of freedom (df), as well as to test both main genetic and gene–environment interaction effects with 2 df tests. They were compared relying on genotype-medication interactions simulated by the GAW19 organizers. Gene–environment interaction analyses were adjusted for age, sex, population structure, and family relatedness.Estimation of causal effects of genetic variants on disease may help to bridge the gap between assessment of association and function, allowing at the same time an improved localization of disease variants. The causal effect of genetic variants on clinical phenotypes may be confounded by demographic and clinical characteristics, and also by other genetic variants as a result of linkage disequilibrium. Wang et al. explored the estimation of the average causal effect of genetic variants on clinical phenotypes using the Bayesian adjustment for confounding method. This method has been proposed to estimate average causal effects in the presence of many confounders, assuming all of them have been measured.MAP4). Table Bayesian adjustment for confounding utilizes a Bayesian model averaging approach and estimates causal effects by a posterior weighted average of average causal effect estimates from a battery of models with different sets of covariates. In contrast to standard Bayesian model averaging, Bayesian adjustment for confounding incorporates the strength of associations between covariates in the model and the exposure into the prior. It has been shown that the method tends to give large posterior weights to models that have been fully adjusted for confounding, thus resulting in unbiased causal effect estimates  and the three collapsing methods  methods when causal variants are not genotyped, and when multiple variants act in (Panel A), the histogram of median counts revealed that most variants had a median count of zero (Panel B). González Silos et al. found 105 variants with a median count exactly equal to 254 (Panel B). The origin of this peak was investigated but, unfortunately, it could not be unveiled and information on downsampling was not available. Panel C represents a histogram of alternative allele counts for the variant in position Ch3:16249998, which presented a median (mean) count of 254 (40.03). This variant showed a MAF of 0.168 . Panel D compares the distributions of the ratio “alternative allele count/number of reads” and called genotypes.Figure The investigated regression models with the best control of type I error rates were zero-inflated and Hurdle-negative binomial regression for the relationship between alternative allele counts and adjusted diastolic blood pressure, and standard and robust linear regression for the relationship between the ratio “alternative allele count/number of reads” as response variable and adjusted diastolic blood pressure as explanatory variable. The simultaneous consideration of ability to discriminate variants with small associated probability values, occurrence of convergence problems, and robustness of probability values against departing blood pressure observations indicated that Hurdle-negative binomial regression constitutes a promising approach.Regarding the selection of variants for kinship estimation, markers that were not ancestry informative resulted in the most accurate estimates. The homogenizing selection strategy with the maximum likelihood and PC-Relate estimators assigned correct relationships for more than 90 % of pairs of first- and second-degree relatives and unrelated subjects. All methods assigned relationships incorrectly for 20 % of third- and fourth-degree relative pairs. European and Native American ancestries were best captured by principal component analysis based on common variants, with similar results for variants with a MAF >0.01 or >0.05. The ability to capture African ancestry was poorer, and resulted as maximized when principal components relied on variants with a MAF <0.05. Clearly allele frequency plays an important role in estimates of relatedness and population structure, and should be carefully considered in such analyses.MAP4 gene, the sparse-data methods generally improved the control of type I errors. Statistical power was sufficient to detect low-frequency and common variants, but remained low for the rare variants. The occurrence of conflicting p values from standard and small-sample tests of the same hypothesis can indicate that large-sample approximations are invalid. Although previous studies have found variant-collapsing tests to have higher power than single-variant tests for rare variants, simulation results for MAP4 showed low power for variant-collapsing tests when they only included rare variants. The statistical power increased when low-frequency variants were included. Because the power of variant-collapsing tests depends on the number, frequency, and effect sizes of associated and neutral variants, identification of better grouping and weighting strategies may translate into an improved power to detect regions that only contain rare variants.Concerning the alternative tests for low-frequency and rare variants investigated by Shin et al., the penalized logistic likelihood ratio test and the small-sample modified score test were both better choices than standard single-variant tests. In tests of association between a simulated binary hypertension phenotype and variants in the With reference to the consideration of evolutionary relationships, the type I error rate of tree-based mapping methods appeared to be well controlled, whereas non–tree-based association mapping showed inflated type I error rate for all 5 investigated genes. Regarding detection, both methods performed well when analyzing genes with large-effect variants, and both methods showed small power in the analysis of genes with low-penetrance variants. Regarding localization of true causal loci, both methods showed similar mapping abilities for genes with large effects. In the case of small-effect variants, tree-based outperformed non–tree-based association mapping, which may point to an advantage of using evolutionary information to detect weak genetic signals.MAP4 with SBP and diastolic blood pressure (DBP).Under the Bayesian variable selection approach to detect associations with both rare and common genetic variants, marginal posterior probabilities were quite robust against the MAFs used to define variant rarity (from 0.05 to 5 %), and they clearly surpassed empirical probabilities based on permuted phenotypes for several positions, pointing to associations between rare and common variants in In agreement with Fig. Regarding the behavior of rare variants interacting with environmental factors, type I error rates did not surpass the expected nominal 5 % significance threshold for either of the 2 investigated gene–environment interaction methods (“interaction model” and “med-diff” approach to test effect size differences between strata) for variants with at least a MAF of 1 %. The statistical power was higher for the “med-diff” approach for variants with a MAF <1 %, but it was higher for the “interaction model” when a variant with a MAF >5 % was evaluated. Nonconvergence was a limitation of the “med-diff” approach.Finally, in respect of the follow up of association signals, mean squared errors were smaller for estimates based on Bayesian adjustment for confounding than for full-model–based estimates of the average causal effect in the investigated scenarios. The reduced variation of estimated average causal effects was a result of the simultaneous consideration of an exposure model and an outcome model in the Bayesian adjustment for confounding, suggesting that this method is able to efficiently estimate the causal effect of genetic variants.Rare-variant haplotype analyses revealed that “hapassoc” often showed convergence problems and, when it converged, association results were similar to that of “haplo.glm.” The haplotypes found to be associated depended on the method. The ranking of methods by the total number of significant haplotypes found on the 2 genes was LBL < haplo.score < haplo.glm. However after permutation of the case–control status to mimic the null scenario, the ratio of associated haplotypes to the total number of haplotypes was also lower for LBL than for “haplo.score” and “haplo.glm,” indicating a controlled false-positive rate for LBL compared to “haplo.score” and “haplo.glm.” SKAT and its variants did not identify statistically significant association signals. Based on these results, haplotype association methods seem to be useful and complementary to collapsing approaches for sequence data.With their results, members of the Population-Based Association group identified several current methodological gaps regarding both the preparation and the statistical analysis of sequence data. Sequence data is noisy, and the investigation of the distribution of allele counts instead of relying on called genotypes could offer some advantage. The selection of genetic variants was found to play a major role in the assessment of population structure and cryptic relatedness. Most statistical methods with good properties for common variants were found inappropriate for rare ones. Methodological gaps were also identified in the follow up of association signals. Novel methods are needed to investigate rare haplotypes and interactions between the environment and rare variants found in sequence data, as well as for causal effect estimation.


Background: The number of Mendelian randomization analyses including large numbers of genetic variants is rapidly increasing. This is due to the proliferation of genome-wide association studies, and the desire to obtain more precise estimates of causal effects. However, some genetic variants may not be valid instrumental variables, in particular due to them having more than one proximal phenotypic correlate (pleiotropy).Methods: We view Mendelian randomization with multiple instruments as a meta-analysis, and show that bias caused by pleiotropy can be regarded as analogous to small study bias. Causal estimates using each instrument can be displayed visually by a funnel plot to assess potential asymmetry. Egger regression, a tool to detect small study bias in meta-analysis, can be adapted to test for bias from pleiotropy, and the slope coefficient from Egger regression provides an estimate of the causal effect. Under the assumption that the association of each genetic variant with the exposure is independent of the pleiotropic effect of the variant (not via the exposure), Egger’s test gives a valid test of the null causal hypothesis and a consistent causal effect estimate even when all the genetic variants are invalid instrumental variables.Results: We illustrate the use of this approach by re-analysing two published Mendelian randomization studies of the causal effect of height on lung function, and the causal effect of blood pressure on coronary artery disease risk. The conservative nature of this approach is illustrated with these examples.Conclusions: An adaption of Egger regression  can detect some violations of the standard instrumental variable assumptions, and provide an effect estimate which is not subject to these violations. The approach provides a sensitivity analysis for the robustness of the findings from a Mendelian randomization investigation. Key MessagesMendelian randomization analyses using multiple genetic variants can be viewed as a meta-analysis of the causal estimates from each variant.If the genetic variants have pleiotropic effects on the outcome, these causal estimates will be biased.Funnel plots offer a simple way to detect directional pleiotropy; that is, whether causal estimates from weaker variants tend to be skewed in one direction.Under a weaker set of assumptions than typically used in Mendelian randomization, an adaption of Egger regression (MR-Egger) can be used to detect and correct for the bias due to directional pleiotropy.,,,,,Mendelian randomization,,,In this paper, we view Mendelian randomization of a single study with multiple IVs as analogous to a meta-analysis. The overall causal estimate based on all the IVs can be interpreted as a weighted average of the individual IV estimates, just like a meta-analysis of separate study results. We show that bias resulting from pleiotropy is analogous to small study bias in meta-analysis,In this paper, we describe a general statistical model for Mendelian randomization data with multiple potentially invalid instruments. Using the graphical representations of a scatter plot and a funnel plot, we discuss why the standard method of estimation, two-stage least squares (TSLS), may be biased when pleiotropy is present and when Egger regression can provide a consistent estimate of the causal effect. We apply both methods to data available from two published Mendelian randomization studies, and explore their performance further using simulated data. Finally, we emphasize that the method advanced here can strengthen or weaken evidence for a causal effect but, as for any single Mendelian randomization method, is itself subject to assumptions and limitations.N participants. For each participant, indexed by i, we measure J genetic variants  are more skewed towards either high or low values compared with estimates from large studies (stronger variants). The estimated value of the intercept in Egger regression This model performs Egger regression, a special case of the general method of meta-regression.β. This is illustrated by the solid blue line in It has been also asserted that If genetic variants have different minor allele frequencies (MAFs), then a better measure of instrument strength can be constructed, as causal estimates from variants with low minor allele frequencies will have low precision. Provided that the genetic associations with the outcome are all estimated on the same individuals, the MAF-correction factors will be proportional to the standard errors of the gene–outcome associations To demonstrate this approach for the assessment of directional pleiotropy, we consider two illustrative examples of Mendelian randomization using many genetic variants that have been recently published. We use the available data on genetic associations with the exposure and with the outcome to construct a funnel plot and perform a visual inspection for asymmetry, as well as a formal statistical test using MR-Egger regression. We comment on the differences between the IVW causal effect estimate from et al.et al. The causal estimates represent the increase in FVC for a 1 standard deviation increase in height.In a primarily methodological investigation of weak instrument bias, Davies P-value of 0.75. The bias-adjusted causal effect estimate from MR-Egger regression is 0.60 , a slight increase in magnitude and uncertainty compared with the IVW and TSLS estimates. There was also no apparent heterogeneity in the IV estimates from each genetic variant individually, as evidenced by Cochran’s Q test (P = 0.99). In the Web Appendix (available as Supplementary data at IJE online) we show how the IVW and MR-Egger regression methods were implemented on these data with just a single line of computer code (using R and Stata). In summary, there is no evidence that directional pleiotropy is an important factor for these data.et al.et al. on genetic associations with blood pressure in over 200 000 individuals based on combined discovery and follow-up analysis, and data used by Ehret et al. from the CARDIoGRAM consortium on genetic associations with coronary artery disease in up to 22 233 cases and 64 762 controls of European descent (data available online at [www.cardiogramplusc4d.org]).Ehret Supplementary data at IJE online) and equivalent funnel plots are shown in Figure A1 displays scatter plots for SBP and DBP separately . In contrast, the MR-Egger test for the intercept gives a P-value of 0.21 and a causal estimate closer to the null . For DBP, the IVW causal estimate of 0.083 is again far from the null . The MR-Egger test gives a P-value of 0.054 and a negative causal estimate . Additionally, Cochran’s Q test indicated strong evidence of heterogeneity between IV estimates based on the individual variants (P < 0.001 for both SBP and DBP). Given the presence of apparent asymmetry in the funnel plots  is far from the null  in a one-sample setting. In this case, we found that the performance of standard one-sample TSLS and the IVW method were indeed highly similar.To further investigate the statistical properties of MR-Egger regression under realistic conditions, we perform a simulation study, generating artificial data with 25 genetic variants used as instrumental variables. We generate data in a two-sample Mendelian randomization setting, in which data on the genetic associations with the exposure and with the outcome are estimated in non-overlapping sets of individuals. Furthermore, we allow ourselves to make use of the summary data estimates only . We are particularly interested in the coverage properties of the estimators with a null causal effect, and the power of estimators with a positive causal effect, as salient findings from Mendelian randomization investigations are not only the magnitude of the causal effect—or indeed whether such can be estimated—but also whether a causal effect is present or absent.,A possible situation corresponding to scenario (d) is that the pleiotropic effects of the genetic variants on the outcome act via a confounder. Specifically, if a genetic variant influences a confounder of the relationship between the exposure and outcome, then this will affect its associations with both the exposure and the outcome, leading to the InSIDE assumption being violated. Funnel plots illustrating data generated under each of these four scenarios for 50 genetic variants are provided in Supplementary data at IJE online). Standard errors and P-values (from t-tests) were taken directly from the regression output. All tests were two-sided and performed at a nominal significance level of 5%.Results from the simulation study are given in β = 0. In scenario (a) (no pleiotropy), both the IVW and MR-Egger regression return unbiased estimates for the causal effect, although mean standard errors from MR-Egger regression are generally twice as large as those from the IVW method. Rejection rates for the causal null hypothesis are controlled at the nominal 5% level for both methods. Additionally, rejection rates for the MR-Egger test are well controlled. The results for scenario (b)  are similar to (a) except that balanced pleiotropy has the effect of increasing the standard errors of the IVW and MR-Egger estimates by approximately 20% on average. Despite all instruments being invalid due to pleiotropy, rejection rates for the MR-Egger test of directional pleiotropy remain at 5%.We first discuss results when there is a null causal effect of β and type I error rates of the causal null hypothesis for the MR-Egger estimator remain around the 5% level. As the sample size increases, the power to detect directional pleiotropy rises modestly from 10% to just under 30%. In scenario (d) , the InSIDE assumption does not hold. The pleiotropy due to a direct effect of variant j on the outcome (N = 1000.In scenario (c)  the standard IVW estimate exhibits a marked bias. As the sample size increases, this bias becomes increasingly severe, and rejection rates for the causal null hypothesis increase from 30% to 80%. By contrast MR-Egger regression yields approximately unbiased estimates for β = 0.05. In scenario (a) both methods exhibit a small amount of bias towards the null in their estimates for β for small sample sizes, with MR-Egger regression slightly more affected. This is in line with bias from weak instruments, which in a two-sample setting acts towards the null.We now examine estimator performance with a positive causal effect of β = 0 in scenario (c), with a fixed sample size of N = 2000 but varying the number of genetic variants. The results are shown in J increases from 3 (very strong) instruments to 150 (weaker) instruments. However, this coincides with a reduction in the estimate’s standard error, so that its type I error rate rises sharply from 12% to 100%. MR-Egger regression returns approximately unbiased estimates for β for all values of J. As J increases the power of the MR-Egger test to detect directional pleiotropy increases from around 5% to 95%. The type I error rate of MR-Egger regression to detect a causal effect is well controlled for J ≤ 50 variants, but for over 100 variants some type I error inflation is apparent. In summary, MR-Egger regression works well with large numbers of genetic variants (in the sense that it has an increased power to detect pleiotropy), as long as the variants are not too weak.In a second simulation we investigate the performance of the IVW method and MR-Egger regression under the causal null Box 1. Summary of assumptions for application of MR-Egger regressionWe take summarized genetic association estimates with the exposure . If the intercept differs from zero (the MR-Egger test), then there is evidence of directional pleiotropy. Under the assumption that the associations of the genetic variants with the exposure are independent of the direct effects of the genetic variants on the outcome (the InSIDE assumption), the slope coefficient from the MR-Egger regression is a consistent estimate of the causal effect. This is a weaker assumption than the assumption that all genetic variants are valid instrumental variables.The InSIDE assumption would be violated if the pleiotropic effects act via a confounder of the exposure—outcome association.Supplementary data at IJE online).R and Stata code to perform the inverse-variance weighted and MR-Egger methods is provided in the Web Appendix  pleiotropy, and a valid test of the causal null hypothesis. Under this assumption, the slope estimate from MR-Egger regression is a consistent estimate of the true causal effect. When there are pleiotropic instruments but the InSIDE assumption is not satisfied, MR-Egger regression does not give a consistent estimate of causal effect, but remains a more robust method of inference compared with standard approaches which rely on the stronger assumption that there is no pleiotropy. This renders it an important sensitivity analysis tool in the Mendelian randomization context. In et al.et al. provide an estimation method based on lasso penalizationet al. require at least half of the genetic variants to be valid IVs. Otherwise, if causal estimates from the two sets of valid and invalid genetic variants tended towards different values, it would not be possible to distinguish which of those values is the causal effect. A similar approach is simply to calculate the causal estimates using each genetic variant individually, rank the estimates in order of magnitude and take the median estimate.et al.k-class estimators, a group that also includes the TSLS, bias-corrected TSLS and limited information maximum likelihood estimators.Several statistical methods have been proposed for consistent estimation of causal effects when the IV assumptions are not all satisfied. For example, Kang Q statistic.As Mendelian randomization with multiple IVs can be viewed as a meta-analysis of summarized genetic association estimates, methods and diagnostic tools developed for meta-analysis can also be used for Mendelian randomization. This is particularly relevant as summarized genetic association estimates from large consortia are increasingly becoming publicly available (such as those from the CARDIoGRAM consortium used in this paper).,Another problem with the use of many genetic variants is that of weak instruments. With many IVs in a one-sample setting , IV estimates (particularly those from the TSLS method) are biased in the direction of the observational association between the exposure and the outcome.Whereas the InSIDE assumption is plausible in some cases, it will not be valid in all circumstances, particularly if the pleiotropic effects of genetic variants act on confounders of the exposure–outcome association. This is because the confounders will induce a correlation between the direct effects of the variants on the outcome and the genetic associations with the exposure. This would occur, for example, in the case of population stratification. Another important way this could occur is if a genetic variant in truth affects an exposure causally upstream of the one under investigation . However, in simulation scenario (d), where the pleiotropic effects through confounders (violating InSIDE) were 2.5 times larger than the direct pleiotropic effects (satisfying InSIDE), estimates from MR-Egger regression were much less biased and rejection rates of the causal null hypothesis were much closer to the nominal 5% rate than those from conventional IV methods. A related limitation is power—although the MR-Egger regression estimator was more robust, power to detect a causal effect was much reduced.,At present, we have not validated a universally reliable method for determining standard errors of the MR-Egger estimator when the causal effect is non-zero. Possible approaches include bootstrapping in a one-sample setting, or a hierarchical likelihood-based model that accounts for uncertainty in the genetic associations used as data points in the regression model. Other methods for giving valid inferences in the context of a meta-analysis and small-study bias have been discussed in the literature.In this article, we have assumed that genetic variants are uncorrelated. If the variants are correlated, and the correlations between variants are known, they can therefore be used within generalized weighted linear regression instead of weighted linear regression in either the IVW or MR-Egger method, incorporating the correlations into the weighting matrix. Further work is currently being undertaken to explore this method.One further limitation of this approach is the assumption that the same causal effect is identified by multiple IVs. This assumption is not unique to our approach, as it is commonly made in IV analyses with multiple IVs. The presence of ‘treatment effect heterogeneity' is a complicating factor in causal analyses more generally, as it is not clear how to interpret a causal effect estimate if its magnitude depends on the nature of the intervention on the exposure. This is an important avenue for further research.In conclusion, the approaches of this paper should not be interpreted as a pretext for conducting Mendelian randomization analyses with large numbers of genetic variants without prior regard to the validity of the IV assumptions. However, they provide simple graphical and statistical methods that can detect some violations of the IV assumptions, and can therefore can used as a sensitivity analysis for assessing whether the effect estimation in a Mendelian randomization analysis is influenced by directional pleiotropic effects of the genetic variants.Supplementary data are available at IJE online.MRC Methodology Research Fellowship (grant MR/L012286/1). Stephen Burgess is supported by the Wellcome Trust (grant number 100114). George Davey Smith directs the MRC Integrative Epidemiology Unit supported by the MRC and the University of Bristol .Jack Bowden is supported by an


Participants in the family-based analysis group at Genetic Analysis Workshop 19 addressed diverse topics, all of which used the family data. Topics addressed included questions of study design and data quality control (QC), genotype imputation to augment available sequence data, and linkage and/or association analyses. Results show that pedigree-based tests that are sensitive to genotype error may be useful for QC. Imputation quality improved with inclusion of small amounts of pedigree information used to phase the data in evaluation of 5 commonly used approaches for imputation in samples of  unrelated subjects. It improved still further when pedigree-based imputation using larger pedigrees was also added. An important distinction was made between methods that do versus do not make use of Mendelian transmission in pedigrees, because this serves as a key difference between underlying models and assumptions. Methods that model relatedness generally had higher power in association testing than did analyses that carry out testing in the presence of a transmission model, but this may reflect details of implementation and/or ability of more general methods to jointly include data from larger pedigrees. In either case, for single nucleotide polymorphism–set approaches, weights that incorporate information on functional effects may be more useful than those that are based only on allele frequencies. The overall results demonstrate that family data continue to provide important information in the search for trait loci. Family-based designs have been a mainstay of genetic studies for more than a century . AlthougThe recent and growing use of sequence data provides new insights into the underlying genetic architecture of many human diseases. Early evaluation of high-throughput sequence data revealed vast numbers of very rare variants , and larFamily-based designs have advantages over designs based on unrelated subjects in a number of key areas. First, required sample sizes for localization of variants in the genome can be far smaller than those required for designs based on unrelated subjects. Family-based designs are particularly well suited for analysis of rare variants, with the sample size differential between family-based designs and designs for unrelated-subjects for trait–gene localization measured in orders of magnitude , 16. SecParticipants in the family-based analysis group at GAW19 all tackled projects with a substantial, and in most cases, exclusive, focus on family-based designs. The 9 contributions discussed here  which pedigree structures to use, and (2) which subjects to include and/or gather data on. All participants in the family-based group chose a class of study design that capitalizes on the presence of related subjects in the sample, just as members of some other GAW19 groups chose a study design that depends on selection of only unrelated subjects. Beyond choice of a general family-based design, however, when an investigator makes a decision to use a particular analysis method, this also results in a design choice that can affect results of the analysis. For example, the papers that used  1 paper  explicit 1 paper  on trio All projects discussed by the family-based group carried out some QC and data-checking analyses. Such analyses were not major components of most of the papers, but most contributions did include standard procedures such as dropping individuals or variants with excessive missing data, checking for unexpected relatedness, and/or using tests such as those used to detect deviation from Hardy-Weinberg equilibrium as steps in the QC process. One paper went further into the problem of suboptimal quality data: Bhatnagar et al.  addresseTwo papers addressed selection of subjects for sequencing, given finite resources , 32. In Two papers carried out evaluation of multiple genotype imputation approaches , 33. TheMany of the current imputation programs were used by Lent et al.  and SaadAccuracy of imputation was evaluated in 2 ways. Both groups masked part of the directly measured WGS data, and compared imputation results in the masked individuals to their true genotypes. Lent et al.  used a lThe main motivation behind all linkage and association approaches used was to use the available data across a spectrum of relatedness. All contributors to the session recognized the importance of using all the collected data because of the cost of data collection, the rich information often available, and ethical research practices that dictate the importance of collecting human subject data only if it will be used. Contributors also appreciated the diversity of pedigree structures available in genetic studies, with pedigree sizes ranging from unrelated subjects and small trio or nuclear family samples to large, multigenerational pedigrees with many dozens of subjects. To this end, participants generally adopted approaches that allowed variable pedigree structures for analysis.An important factor that differentiated among analysis methods is how the methods deal with correlation among related subjects in the sample. The 2 main approaches either (a) exploited or (b) corrected for the correlation induced by related individuals. In essence, methods that exploit the cause of correlation between related individuals treat it as an advantage to be explicitly used, and are pedigree-based approaches. Methods that correct for the family-based correlation treat it as a problem to be removed, and are more broadly simply family-based approaches. Methods used at GAW19 that exploited within-family correlation typically modeled or otherwise made use of transmission information in pedigrees, as this is the genetic source of such correlation. The corresponding methods seek to extract, explain, or use correlations within family data that are there because of Mendelian transmission. Methods within this framework broadly include all linkage analysis methods, joint linkage and association methods, and methods that test association in the presence of linkage. On the other end of the spectrum, within-family correlation was treated as a problem by methods that treat correlation as a nuisance variable. These methods attempt to adjust for relatedness by “decorrelating” the data, typically with correlation that is modeled through a random effects coefficient in a linear mixed model. These methods typically consist of methods that focus only on association methods.T is typically the sum of scores obtained for the individual analysis units, and V(T) is computed under the null hypothesis. These units may be alleles, as in the TDT, genotypes in trios, as in the PDT, or genotypes in nuclear families, as in FBAT. The tests used included the original TDT, as well as an early similar approach for general pedigrees in the PDT [The transmission-based methods used were diverse with 5 groups using 1 or more such methods  [Other methods used by participants treated correlation from relatedness as something that needed to be adjusted for or removed as part of the analysis through “decorrelating” the data. The general approach adjusted for the effect of relatedness among individuals through a random effects model, with the kinship matrix structuring the covariance among subjects , 35, 41.latives) , GEMMA (latives) , FARVAT latives) , Mendel latives) , and implatives) . Additiolatives) , 35. Eaclatives) .With the current focus on rare variants, approaches that are based on SNP-set approaches have become common, and 3 groups used such approaches  causal variants with reasonable evidence for association, and analysis of a bivariate blood pressure trait had greater power to detect 2 of the underlying simulated variants than did analysis of a univariate trait . SimilarContributions of the groups that explored different weights and SNP-set tests were consistent with a model that not all rare variants are deleterious. Starting with FBAT-RV and allele-frequency-defined weights  as a basAs has been found in previous GAWs, the family-based group at GAW19 found many merits to analysis of family data. For example, results obtained by capturing transmission information in the smallest possible family units, compared to no use of family data, showed that there are some types of analyses that can only be carried out in a family-based sample. Other analyses benefitted from use of family data even in situations where the main analysis might be directed at a sample of unrelated subjects. For example, results obtained showed that compared to no use of family data, by capturing transmission information in the smallest possible parent–child family units, phasing prior to imputation leads to improved genotype imputation with any of the available pedigree-agnostic imputation programs. Finally, the GAW19 sample and generating model was able to provide meaningful statistical results with existing methods, even for traits for which variation in individual genes contributes relatively small amounts to the total phenotypic variance. It is important to note that this family-based sample was ludicrously small by the current standards of GWAS studies, and therefore serves as a reminder of the efficiency of family studies for the study of rare variants.Even though some of the simulated effects were detectable in the sample provided, the results also showed that this was not true for all simulated effects. If we are to explain all or even most of the heritability of important genetic traits, more work will be needed to design more efficient studies and to develop methods that can extract more information from a limited number of samples. There were suggestions for approaches that might contribute to these goals, including more careful choice of subjects for sample inclusion based on phenotype information and relative position of subjects to be sequenced within a pedigree. As has been found over and over again, more is not always better: a small clean sample with a strong signal can have more power than a larger dirty sample, given finite resources.It is encouraging that there continue to be gains in the quality of genotype imputation, since such imputation provides information for very little cost. It is also notable that some of these gains are the consequence of adding information that can still only be obtained from pedigree data, even for the goal of genotype imputation in unrelated subjects. Not surprisingly, the advantages of incorporating pedigree information were particularly notable for rare variants. In addition to improvements in pedigree-agnostic imputation, results at this workshop and elsewhere  demonstrIt is clear that there are many trait analysis methods that can be used for family data. The evaluation of the group even found new uses for older tests, such as use of the TDT as a potential additional QC filter for use in pedigrees with sequence data. Sensitivity of the TDT to genotype error is well known, but this has not before been used as a feature rather than something that needs correction . DemonstOne additional challenge for the future is the choice of weights for SNP-set approaches. Results from this workshop showed that a good choice of weights can make a difference, but there was no further discussion of strategies for determining the number of variants or size of a region to be evaluated jointly. Workshop presenters also showed that some allowance for functional impact seemed to work better than simply applying an allele-frequency weight, but there are still many options for determining detailed weights. Presumably ability to generalize these results to real data will depend on the quality of our information regarding functional impact. However, given the vast number of rare variants in the genome, it is not surprising that allele-frequency, alone is an insufficient filter.BMC Genetics Volume 17 Supplement 2, 2016: Genetic Analysis Workshop 19: Sequence, Blood Pressure and Expression Data. Summary articles. The full contents of the supplement are available online at www.biomedcentral.com/bmcgenet/supplements/17/S2. Publication of the proceedings of Genetic Analysis Workshop 19 was supported by National Institutes of Health grant R01 GM031575.This article has been published as part of


Multiple hypothesis testing is a major issue in genome-wide association studies (GWAS), which often analyze millions of markers. The permutation test is considered to be the gold standard in multiple testing correction as it accurately takes into account the correlation structure of the genome. Recently, the linear mixed model (LMM) has become the standard practice in GWAS, addressing issues of population structure and insufficient power. However, none of the current multiple testing approaches are applicable to LMM.We were able to estimate per-marker thresholds as accurately as the gold standard approach in real and simulated datasets, while reducing the time required from months to hours. We applied our approach to mouse, yeast, and human datasets to demonstrate the accuracy and efficiency of our approach.We provide an efficient and accurate multiple testing correction approach for linear mixed models. We further provide an intuition about the relationships between per-marker threshold, genetic relatedness, and heritability, based on our observations in real data.The online version of this article (doi:10.1186/s13059-016-0903-6) contains supplementary material, which is available to authorized users. Genome-wide association studies (GWAS) have discovered many variants implicated in complex traits in studies of both humans –8 and mop value threshold for significance, referred to as the per-marker threshold, must be adjusted to control the overall false positive rate. The Bonferroni correction [One of the major challenges in GWAS is multiple hypothesis testing. Because each GWAS involves computing up to millions of statistical tests, the rrection  assumes rrection , which rrrection . The perrrection , which srrection –24.Recently, the linear mixed model (LMM) –31 has bHowever, the current approaches for multiple hypothesis testing correction cannot be applied to LMM. Even the gold standard, the permutation test, is not applicable to LMM, because the underlying idea is that each permutation represents a sample from the null distribution. This is not the case in LMM, because the phenotypes have a covariance structure induced by the complex patterns of relatedness among the individuals. Unfortunately, to date no available approach can correct for multiple testing in LMM, because almost all known multiple testing correction approaches are based on the permutation test and aim only to increase the efficiency of the permutation test –24, 41. In this paper, we first set up the gold standard approach for multiple testing correction in LMM. Our approach is a bootstrapping resampling approach that is the equivalent of the permutation test for LMM. Specifically, our parametric bootstrapping approach samples randomized null phenotypes from the distribution fitted by LMM. This approach straightforwardly accounts for the effect of between-individual genetic relatedness on phenotypes. However, like the permutation test, this approach is computationally expensive due to the large number of resamplings, and is therefore only suitable for small datasets.To address this issue, we developed a new approach called multiple testing in transformed space (MultiTrans), which can efficiently correct for multiple testing for LMM. To approximate the results of parametric bootstrapping efficiently, we employ a strategy that directly samples statistics instead of sampling phenotypes. Both sampling phenotypes in bootstrapping and sampling of statistics in our new approach involve sampling from a multivariate normal distribution (MVN). However, the sampling of statistics is much more efficient because the time complexity of the sampling procedure is independent of the number of individuals. To obtain the covariance matrix of the MVN for statistics, previous strategies –24 that α. Let us assume the following linear model: In multiple testing correction, our goal is to find the per-marker threshold that gives an overall false positive rate of n is the number of individuals, μ is the mean of the phenotypic values, 1n is a vector of n ones, Y is a vector of length n with the phenotypic values, Xi is a vector of length n with the genotypic values of the ith marker, βi is the coefficient of the ith marker, and e is a vector of length n sampled from Si and Sj be the test statistics for the ith and jth markers under the linear model, accordingly. Under the assumption of a linear model , and the correlation of the genotypes, rij, as follows: Here, The derivation of this equality is described in detail in section “m be the number of markers and Σ be the m×m covariance matrix between the statistics whose th element is Σi,j=Cov. According to the multivariate central limit theorem [n is large, the vector of statistics  asymptotically follows a MVN with mean 0 and variance Σ. Figure p value falls within this region, the null hypothesis is rejected. Figure xy space. Let u be the pointwise p value that is shown as each point in the MVN. The four corners of the shaded rectangle are (Φ−1(u/2),Φ−1(u/2)), (Φ−1(1−u/2),Φ−1(u/2)), (Φ−1(u/2),Φ−1(1−u/2)) and (Φ−1(1−u/2),Φ−1(1−u/2)), where Φ is the cumulative density function of the standard normal distribution. Let pα be the outside-rectangle probability in Fig. α, the per-marker threshold is approximated by searching for the pointwise p value u whose pα is α. Utilizing the equality in Eq. Σ={rij} under the linear model However, in LMM, the properties in Eq. ith marker under the LMM. LMM has an extra term g compared to the linear model  and the permutation test (b), which demonstrate that parametric bootstrapping can accurately approximate the null distribution for LMM. On the other hand, the permutation test yielded inflated p values, which demonstrates that the distribution generated from the permutation cannot be used to approximate the true null distribution for LMM.To show that the permutation cannot approximate the true null distribution for LMM, whereas parametric bootstrapping can do so accurately, we evaluated  dataset  is known dataset , we used LMM Eq.  using a entclass1pt{minimaAs shown in the previous section, the parametric bootstrapping closely approximates the true null distribution for LMM, and can, thus, be used as the gold standard for multiple testing in LMM. MultiTrans is rooted in the idea of parametric bootstrapping. However, to approximate the results of parametric bootstrapping efficiently, MultiTrans samples statistics directly from MVN with a covariance matrix estimated from transformed genotypes. In this section, we show how accurately MultiTrans approximates the covariance matrix of test statistics using the transformation strategy Eq. , by test5 phenotypes were simulated for four different cases, each with heritability, 0, 0.2, 0.5 and 0.8. K. Figure rij. Black bars represent the differences between the covariance of test statistics and the correlation of genotypes transformed by the square root of x-axis) and the correlation of genotypes (y-axis). Red and black dots represent cases in which we did or did not use genotype transformation, respectively. When heritability is zero  from microbiome data, which does not follow a normal distribution. Additional file Q–Q plot of their test statistics estimated from the phenotypes. It shows that even if the phenotypes do not follow a normal distribution, the statistics approximately follows a normal distribution.Nevertheless, for many tests assuming normality of phenotypes, it is known that even if the phenotypes do not follow a normal distribution, the Multiple testing correction is a very well-studied problem in the context of GWAS , 51, 52,Here, we show that the heritability of a trait affects the significance threshold, as well how to perform multiple testing correction in the context of LMM association studies. Our proposed method, MultiTrans, accurately corrects for multiple hypothesis testing and is also efficient, making it applicable to large GWAS. In addition, we demonstrated the accuracy and efficiency of MultiTrans utilizing mouse, yeast and human datasets.4 permutations are used in GWAS [In this paper, we proposed a parametric bootstrapping resampling approach to set up the gold standard approach for multiple testing in LMM. Parametric bootstrapping is consistent with the assumed model of LMMs. Some previous methods try to generate the null samples under LMM by improving the permutation test. Abney  proposed in GWAS , 53, 54,p values for multiple testing in LMM, we showed that the parametric bootstrapping approach is impractical even for a small study, whereas MultiTrans can dramatically reduce the running time.Instead of sampling phenotypes, MultiTrans samples statistics directly from a MVN whose covariance matrix is estimated from transformed genotypes and it applies a sliding-window Monte Carlo approach to speed up the sampling procedure. Comparing the running time of MultiTrans and parametric bootstrapping, which can accurately correct the Our results show that the heritability changes the covariance of statistics and per-marker thresholds. In addition, we made the novel observation that the per-marker threshold tends to decrease as the heritability increases for the HMDP, yeast and HapMap datasets. We also provided an intuition regarding how genetic relatedness in datasets affects the per-marker threshold. To our knowledge, our study is the first study to explain the relationship between heritability, genetic relatedness and the per-marker threshold.The ideas behind our approach extend multivariate normal approaches for modeling the joint distribution of GWAS statistics to scenarios in which mixed models are utilized to compute the association statistics. In this paper, we demonstrated how this extension can be used to compute the significance threshold for multiple testing correction; however, this framework can be utilized for other applications of MVNs as well. For example, similar extensions can be applied to fine mapping methods , 55, 56,The permutation test gives a simple way to compute the null sampling distribution for a test statistic by repeatedly permuting either genotypes or phenotypes and computing the association statistic for each permutation. The permutation test can be thought of as a resampling approach that samples individuals from a uniform distribution without replacement. The permutation test accurately accounts for the correlation structure of the genome, and therefore, has been used as the gold standard for GWAS. However, it is computationally expensive, and its running time is linearly dependent on the number of individuals.Several previous studies proposed alternative approaches to permutation because the permutation test is computationally expensive especially when the number of individuals is large. The idea underlying these approaches is sampling of test statistics directly from MVN, taking advantage of the fact that the statistics over multiple markers asymptotically follows a MVN , 22.m be the number of markers, Si be a statistic for the ith marker and Σ={Cov} be the m×m covariance matrix between the statistics. Assuming the following linear model, we can derive the covariance matrix for the MVN: Below, we show how to obtain the covariance matrix of the MVN. Let n is the number of individuals, μ is a mean of the phenotypic values, 1n is a vector of n ones, Y is a vector of length n with the phenotypic values, Xi is a vector of length n with the genotypic values of the ith marker, βi is their coefficients and e is a vector of length n sampled from Y and Xi are normalized as mean 0 and variance 1. Then, the phenotype follows a MVN with a mean and variance as follows: Here, β for the ith and jth markers are as follows: The ordinary least-squares solutions of The statistics of the two markers are computed as follows: μ, e and σ for the ith marker are as follows: Here, the estimated values for and Si,Sj), is equal to the correlation between the genotypes, rij, as follows [Then, we can prove that the covariance of the two statistics, Cov asymptotically follows a MVN with mean 0 and variance Σ. Given a pointwise p value u, let R(u) be the m-dimensional rectangle with corners Φ−1(u/2)1m and Φ−1(1−u/2)1m, where Φ is the cumulative density function of the standard normal distribution and 1m is the vector of m ones. Then, the significance level pα is approximated as the outside-rectangle probability as shown in Fig. Using the properties of Eq.  theorem , if the tistics S,…,Sm asyα, the per-marker threshold can be approximated by searching for a pointwise p value u whose significance level pα is α.Thus, given an overall significance threshold p values.We first set up the gold standard approach of multiple testing in LMM, which is the equivalent of the permutation test for LMM. We emphasize that the traditional permutation test and its variations do not work for LMM. The idea underlying permutation testing is that each permutation is a sample from the null distribution, which is not the case in LMM, because the permutation alters the dependency of the phenotype on the relatedness structure. If we permute phenotypes, the relatedness structure between the individuals and its effect on phenotype are ignored, which can lead to an inflation of n vectors of null phenotypes from the distribution from MVN with the covariance matrix n vector of those null phenotypes, we compute null statistics . This parametric bootstrapping approach can be thought of as the permutation-equivalent for LMM. Similar approaches were used in previous studies [We propose a resampling-based multiple hypothesis testing approach for LMM, which utilizes the parametric bootstrapping strategy. Figure 13 studies , 53, 54,As described in the previous section, the parametric bootstrapping strategy is impractical due to its high computational cost. To make the procedure efficient, we propose a new approach, MultiTrans. MultiTrans alternatively samples statistics directly from MVN without needing to generate any null phenotypes. Figure 13For LMM, Eq. μ is the mean of the phenotypic values, 1n is a vector of n ones, Y is a vector of length n with the phenotypic values, Xi is a vector of length n with the genotypic values of the ith marker, g is a vector of length n sampled from K is a n×n matrix that explains the correlation between the individuals induced by population structure, and e is a vector of length n sampled from To derive the covariance matrix, we assume a LMM instead of the linear model as follows: ith marker and jth marker are as follows: Given the observed data, it is straightforward to fit LMM and estimate parameters The statistics are computed as follows: Accordingly, the correlation between the statistics changes from Eq. S1,S2,…,Sm), to approximate MVN and correct p values by integrating over the outside of the rectangle, as in Eq. Utilizing the covariance matrix estimated from transformed genotypes, we can generate a large number of samples,  from MVN using Cholesky decomposition [p values accurately [f be the joint probability density function of the statistics. Under the local linkage disequilibrium assumption, the statistics at distant markers are uncorrelated. Thus, given a window size w, we can assume that Si is conditionally independent of S1,S2,…,Si−w−1 given Si−w,Si−w+1,…,Si−1. Utilizing the chain rule, If position  is compuposition , 23 usedposition . Thus, wcurately . Let f and efficiently generate a large number of samples.Thus, we can sample σg and σe, estimating the inverse square root of the covariance matrix, O(n3+n2m) where n is the number of individuals and m is the number of markers. The most computationally expensive step of both of the methods is the sampling process, which causes the main difference in running time between the two. For parametric bootstrapping, we need to sample null phenotypes from MVN with n×n covariance matrix O(n3). Then we calculate the test statistic using LMM. We can reduce the time for calculating the test statistic by using pre-estimated O(n2)) and using pre-computed transformed genotypes, O(nm). Thus, the total complexity excluding LMM fitting is O(s(n3+n2+nm)) where s is the number of repeats. On the other hand, MultiTrans needs only to estimate the covariance matrix of the transformed genotypes, which takes O(nm2), and to sample statistics directly from MVN with m×m covariance matrix, which can be performed efficiently using the sliding-window approach described in section “O(w3m), where w is the window size used in the sliding-window approach. As a result, we can reduce the sampling process of parametric bootstrapping, O(s(n3+n2+nm)), into O(sw3m). We note that the time complexity of each step could be reduced using various special mathematical techniques [Both parametric bootstrapping and MultiTrans require fitting the data to LMM to estimate the variance components of LMM, chniques , 67–69.We evaluated our approach using a HMDP (high-resolution association mapping) mouse dataset  that conTo show how our normality assumption of phenotypes affects the results of test statistics, we computed test statistics using a gut microbiome dataset from 592 mice from 110 HMDP strains, which does not follow a normal distribution . The stuWe evaluated our approach utilizing a yeast dataset  that conWe evaluated our approach utilizing a HapMap Phase 3 dataset  that conhttp://hapmap.ncbi.nlm.nih.gov/.The HMDP dataset  is avail7 samplings were performed. For the parametric bootstrapping results in section “5 samplings were performed. To evaluate our method for various ranges of heritabilities, we applied it for four different heritabilities, 0, 0.2, 0.5 and 0.8. The kinship matrix was estimated using all the SNPs in each dataset. However, several techniques can estimate a kinship matrix [p values and the variance components . For details of the license, see https://www.gnu.org/licenses/why-affero-gpl.html.The software and the source code are available at Multiple hypothesis testing is an essential step in GWAS analysis. Although the correct per-marker threshold differs as a function of species, marker densities, genetic relatedness, and trait heritability, no previous multiple testing correction methods can comprehensively account for these factors. In this paper, we describe MultiTrans, an efficient and accurate multiple testing correction approach for linear mixed models. Our method performs a unique transformation of genotype data to account for genetic relatedness and heritability under linear mixed models, as well as to efficiently utilize the multivariate normal distribution. We were able to estimate per-marker thresholds as accurately as the gold standard approach applying to mouse, yeast, and human datasets, while reducing the time required from months to hours. We further provide an intuition about the relationships between per-marker threshold, genetic relatedness, and heritability, based on our observations in real data.


As the availability of cost-effective high-throughput sequencing technology increases, genetic research is beginning to focus on identifying the contributions of rare variants (RVs) to complex traits. Using RVs to detect associated genes requires statistical approaches that mitigate the lack of power with the analysis of single RVs. Here we report the development and application of an approach that aggregates and evaluates the transmissions of RVs in parent-child trios. An initial score that incorporates the distortion in transmission of the observed RVs from the parents to their offspring is calculated for each variant. The scores are analyzed using a support vector machine that handles these data by mapping the transmission distortion of the multiple RVs into a one-dimensional score in a nonlinear fashion when parent-child trios with affected and nonaffected children are contrasted. We refer to this approach as Trio-SVM. A total of 275 trios were available in the Genetic Analysis Workshop 18 data for analysis. Because of their nonindependence and the extended linkage disequilibrium (LD) within pedigrees, Trio-SVM was vulnerable to type I errors in detecting association. Using the GAW18 data with simulated trait values, Trio-SVM has an appropriate type I error, but it lacks power with a sample of 267 trios. Larger samples of 500 to 1000 trios, derived from combining the simulated data, provided sufficient power. Two chromosome 3 candidate genes were tested in the real GAW18 data with Trio-SVM, and they showed marginal associations with hypertension. Genome-wide association studies (GWAS) of common variants have not explained the heritability estimates of common complex disorders . In respUsing Trio-SVM, all members of the trios are sequenced for RVs, and the observed RV transmissions are compared with what is expected, given the parental RV genotypes. Transmission distortions in a gene are combined using SVM. The area under receiver operating characteristic (area under the curve [AUC]) was generated by SVM when contrasting the transmission between affected and unaffected children is estimated for each gene under analysis and used as the test statistic. The strength of Trio-SVM is that it allows for each RV to either confer risk or to be protective and contribute to an overall score in which the direction of the effect for each RV is not a factor in the score.One potential concern is the availability and choice of control groups for the SVM. First, the control sample should be beyond the age of risk for the disorder under analysis and have appropriate environmental exposures when those are known to be important. Second, to provide an opportunity for transmission of RVs from parents to their children, ethnic matching, although not necessary, may be helpful. An interesting choice might be the unaffected siblings from the trios in the study because they would have the same opportunities to inherit the RVs that are transmitted to their affected siblings.M predictors.The purpose of the SVM is to discriminate between two groups using a set of variables. It is particularly useful when the number of variables is greater than the number of individuals in the data set. SVM is based on a model with N ordered pairs w and the offset b are estimated to maximize the separation of w and b, where If "." denotes the dot product and "^" the parameter estimate, SVM constructs two hyperplanes in space, w is based on the support vectors. An additional advantage is the relaxation of linear mapping by using a kernel function K that corresponds to a nonlinear function φ such that C) is added for a generalization of the optimal hyperplane when the data do not allow the two groups to be completely separated, which limits the Lagrange multipliers to range between 0 and C.SVM provides the advantage of allowing 0: θ <= 0.5 vs Ha: θ > 0.5 is used to represent the composite scores for distorted transmission within a gene over the sample of trios comparing those who are affected with those who are not. Accepting that θ is greater than 0.5 indicates the combined RVs in the gene are transmitted with greater distortion from that which is expected in the cases when compared with the control participants. The test is one-sided because each group is assigned to a fixed vertex; the statistic Trio-SVM analyzes a set of N parent-child trios, in which each child is described by a coordinate t (FBAT) . At eachn = 464) was sequenced at 8,348,674 sites, and imputation of nonsequenced individuals was performed using the GWAS data, thus providing each individual with a constellation of RVs. Blood pressures were taken longitudinally at from 1 to 4 exams for 932 participants. Hypertension was assigned based on systolic blood pressure (SBP) greater than 140 mm Hg, diastolic blood pressure (DBP) greater than 90 mm Hg, or use of antihypertensive medications.For the GAW18 data, Trio-SVM was used to combine all observed RVs for a given gene, by selecting all affected and unaffected individuals having both parents in each pedigree and treating them as independent. A total of 275 such trios were derived from the 959 individuals in 20 GAW18 pedigrees ascertained for type 2 diabetes (T2D). The pedigree members were genotyped at 472,049 SNPs on GWAS platforms. Half of the sample  [UBE2E2 (3p24.2) [Analyses were focused on chromosome 3, as suggested by the GAW18 organizers. Two T2D GWAS candidate genes, (3q21.1)  and UBE2MAP4, and the type I errors were assessed for the nonpredisposing gene, ARL13B (93.8 Mb), located between RYBP (72.5Mb) and B4GALT4 (118.9Mb), where both influenced DBP or SBP. To evaluate the power in a larger sample size, 500 and 1000 trios were drawn from the 200 replicates using bootstrap sampling.Two hundred replicates of the genotyped data in the GAW18 pedigrees with the trait simulated under specific genetic models were available for assessments of type I and II statistical errors. The genes on chromosome 3 that were predisposing and nonpredisposing in the simulated models were tested. RVs were included in the analysis when their frequencies were less than 0.01 and less than 0.03 in two separate assessments. These analyses were performed on the simulated trait, hypertension, defined in two ways: (a) adjusted by age, age × gender, gender, and use of antihypertensive medications and (b) not adjusted. Covariates were included using linear mixed models with a random effect to account for the intrapedigree correlation. The traits were adjusted to age 38, no medications, and male gender. Power analyses were based on evaluating the predisposing gene Trio-SVM was evaluated using a Gaussian kernel (p-values of 3.2E-04 for ADCY5 at 3q21.1 and 0.035 for UBE2E2 at 3p24.2. For this analysis, genes were selected on both arms of chromosome 3 because we wanted to see if we could detect independent signals given the poor resolution because of LD in pedigrees. Association in the set of 108 founders, in which 58 independent cases were compared with 50 independent control participants, was not detected. However, this limited sample provides very low power. A significant p-value for the AUC statistic has two possible interpretations. Either a consistent set of SNPs is responsible for the signals in a gene or different variants are contributing to the signals in the different pedigrees [Table edigrees . HoweverTable Applications of machine learning methods in genomic data are just beginning -9. UsingThe authors declare that they have no competing interests.ATL and RMC designed the overall study and drafted the manuscript. ATL wrote the code of Trio-SVM and conducted statistical analyses. RMC coordinated the conception of the study and wrote the final draft of the manuscript. All authors read and approved the final manuscript.


Mendelian randomization is a popular technique for assessing and estimating the causal effects of risk factors. If genetic variants which are instrumental variables for a risk factor are shown to be additionally associated with a disease outcome, then the risk factor is a cause of the disease. However, in many cases, the instrumental variable assumptions are not plausible, or are in doubt. In this paper, we provide a theoretical classification of scenarios in which a causal conclusion is justified or not justified, and discuss the interpretation of causal effect estimates.A list of guidelines based on the ‘Bradford Hill criteria’ for judging the plausibility of a causal finding from an applied Mendelian randomization study is provided. We also give a framework for performing and interpreting investigations performed in the style of Mendelian randomization, but where the choice of genetic variants is statistically, rather than biologically motivated. Such analyses should not be assigned the same evidential weight as a Mendelian randomization investigation.We discuss the role of such investigations (in the style of Mendelian randomization), and what they add to our understanding of potential causal mechanisms. If the genetic variants are selected solely according to statistical criteria, and the biological roles of genetic variants are not investigated, this may be little more than what can be learned from a well-designed classical observational study. Many investigators have taken two such traits and considered the statistical question of whether genetic variants that are associated with trait A (often taken to be a risk factor and viewed as a putative cause) also show an association with trait B (often taken to be a disease outcome), for example, under the heading of Mendelian randomization 21.A is a cause of B, and all causal pathways from the genetic variant(s) to B pass through A;2.A is a cause of B, but there are alternative causal pathways leading from the genetic variant(s) to B which do not pass through A;3.A is not a cause of B—the genetic variant(s) are independently associated with A and B.We consider the following classification of possible scenarios for the relationship between two variables A and B such that genetic variant(s) associated with A are also associated with B. An interventional definition of causality is presumed; A is a cause of B means that intervention on the distribution of A results in changes to the distribution of B Diagrams representing the relationships between the variables in each case are given in 2.11.The set of genetic variants is associated with the risk factor A;2.Each genetic variant is independent of confounders of the association between A and B;3.If the risk factors were kept constant, intervention on the genetic variant(s) would not have an effect on the outcome.To infer a causal effect of A on B, it is necessary that genetic variants used in the analysis satisfy the assumptions of an instrumental variable A diagram corresponding to these assumptions is given in www.jclinepi.com. The assumptions require that genetic variants used for the assessment of the causal nature of a risk factor must be specific in their associations with the risk factor, although they may also show associations with other variables via downstream effects of the risk factor. For example, genetic variants that are candidate instrumental variables for body mass index (BMI) may show associations with C-reactive protein (CRP), because of a causal effect of BMI on CRP These assumptions imply that all causal pathways from the genetic variant(s) to the outcome pass through the putative causal risk factor, and there are no alternative pathways not via the risk factor If we seek to assess whether there is a causal effect of A on B, but not to provide an estimate of a causal effect parameter, then only the three instrumental variable assumptions listed previously are required. Under these assumptions, an association between the outcome B and genetic variants which are instrumental variables for A implies a causal effect of A on B Mendelian randomization can be understood as being similar to a randomized controlled trial, in which genetic variants play the role of random assignment to a treatment group •P-values, as they are more informative P-value does not achieve conventional levels of statistical significance, a point estimate with a confidence interval allows the reader to judge in a quantitative way whether the null result reflects a lack of evidence or a genuine negative finding in comparison with either the observational association, or with a minimal clinically relevant effect. If the confidence intervals for the causal effect exclude the minimal clinically relevant effect, then the causal effect for all practical purposes is null, particularly as Mendelian randomization estimates often overestimate the effects of intervening on risk factors in practice (as they represent life-long effects) Generally in epidemiology, estimates with confidence intervals are preferred to hypothesis tests with •If several genetic variants are valid instrumental variables for the same risk factor, greater power to detect a clinically relevant causal effect can be obtained using information on all the variants simultaneously rather than that using the variants individually •Although a causal estimate from a Mendelian randomization investigation will not correspond precisely to the expected effect of a intervention in the risk factor (which will in any case differ between interventions), it does represent the outcome of a well-defined intervention, namely in the genetic code at conception. As such, it will be a more relevant indicator of the predicted effect of a clinical intervention in the risk factor if the intervention acts in a similar way to the genetic variant; for example, if the genetic variant and the intervention affect the same biological pathway, if the magnitudes of change in the risk factor are similar, and if long-term changes in the risk factor are considered.For this reason, some authors have questioned whether causal effect estimates should ever be presented as part of a Mendelian randomization analysis In summary, if the only causal pathways from the genetic variant(s) to the outcomes are via the risk factor of interest, then the causal hypothesis of the risk factor on the outcome can be reliably assessed, although a numerical causal estimate will be at best an approximation to the effect of intervening on the risk factor in practice.2.2Often, the associations of a genetic variant are not restricted to the risk factor of interest. “Off-target” genetic associations, including pleiotropic effects and associations arising from linkage disequilibrium, may lead to violation of the instrumental variable assumptions by providing an alternative pathway from the genetic variant(s) to the outcome not via the risk factor We consider an alternative set of assumptions  and with coronary heart disease risk IL6R gene region were assumed to be instrumental variables for CRP, then the false conclusion would be reached that CRP was causal for coronary heart disease risk. Although in this case, the use of variants in the IL6R gene region as instrumental variables for CRP would be an elementary mistake, in cases where the causal gene and the biological pathway it affects are not known, misleading conclusions could be reached.If the instrumental variable assumptions are not satisfied, genetic variants may be associated with a risk factor and an outcome without a causal effect of the risk factor on the outcome. For instance, genetic variants may be associated with a common cause of the risk factor and outcome. Variants in the Even if the risk factor would seem logically to take the role of the cause and the outcome of the effect, a reverse causal explanation is possible. For example, although inflammatory biomarkers may be thought of as a potential cause of coronary heart disease, it may also be that subclinical disease leads to elevated levels of the biomarkers It is also important to appreciate that the causal question addressed by a Mendelian randomization is whether long-term elevated (or reduced) levels of a risk factor will affect the outcome. For example, the null causal effect of CRP on coronary artery disease risk estimated using genetic variants having modest associations with CRP levels Distinguishing scenarios 1 and 2, where the risk factor is a cause of the outcome, from scenario 3, where the two have common genetic predictors but are otherwise independent, is not empirically possible and requires biological knowledge. As such, if the instrumental variable assumptions in a particular applied investigation are uncertain, a more tentative conclusion is appropriate. In practice, the distinction between more plausible Mendelian randomization investigations and less plausible ones will be a subjective assessment and will give a continuous scale of evidential quality rather than a dichotomy of “good” and “bad” studies. In the next section, we consider some criteria to help judge the plausibility or otherwise of a Mendelian randomization investigation.3Justification of the instrumental variable assumptions can be provided using biological knowledge and statistical testing. In HMGCR and PCSK9 gene regions associated with low-density lipoprotein cholesterol and coronary heart disease risk suggest that inhibition of 3-hydroxy-3-methylglutaryl-coenzyme A reductase (HMGCR) and of proprotein convertase subtilisin/kexin type 9 (PCSK9) would reduce low-density lipoprotein cholesterol levels and therefore be protective of coronary heart disease risk; the former mechanism is how statin drugs act The Bradford Hill criteria also suggest that variants from candidate gene investigations, where the function of the genetic variant(s) is well-understood, will have more credibility for use in Mendelian randomization studies than variants with unknown functional relevance, such as those often discovered in genome-wide association studies. Additionally, the utility for translational research of such an analysis will be increased, as a genetic variant with well-understood biology associated with a causal risk factor often indicates a potential pathway for intervention on the risk factor Although the instrumental variable assumptions cannot be statistically proven, implications of the assumptions can be tested 4Recently, several investigators have considered genetic variants associated with a risk factor and their association with an outcome variable in the absence of biological knowledge about the genetic variants. For example, investigators have taken all the genetic variants associated with height at a genome-wide level of statistical significance and considered whether these variants also predict colorectal cancer risk To distinguish these analyses from well-justified Mendelian randomization analyses, we use the term “joint association study” as the joint association of variants with a risk factor and an outcome is assessed. A non-null finding from a joint association study will still provide suggestive evidence of a causal effect, or of shared causal mechanisms, through the conclusion of common genetic predictors 5If there is insufficient biological knowledge to justify the instrumental variable assumptions for a set of candidate genetic variants, several approaches for the selection of variants can be taken as follows.5.1If the instrumental variable assumptions can be justified or are more plausible for a subset of variants, then the primary analysis should be based on these variants, and a more speculative analysis using more variants  should be viewed as a secondary analysis.5.2If the instrumental variable assumptions cannot be justified biologically, an analysis can be performed using those variants which are associated with the risk factor of interest, but not associated with measured covariates which are potential confounders. Although this approach does not address the difficulty of unknown and unmeasured confounders, sensitivity analyses can be performed to give a sense as to how robust the finding is to violation of the instrumental variable assumptions 5.3Alternatively, a data-driven approach has been proposed on the basis of a heterogeneity test statistic for the causal effect estimates from multiple genetic variants There are several potential pitfalls with such an approach. First, it is necessary to assume that most genetic variants do satisfy the instrumental variable assumptions, so that the outlying variants removed in the stepwise selection are the invalid variants. Second, even if all genetic variants are valid instrumental variables, some heterogeneity in their associations with the outcome would be expected, particularly if the genetic variants influenced the same risk factor via different causal pathways. Third, as with all post-hoc analyses in which the analysis method is determined on the basis of the observed data, there is likely to be bias in the effect estimates. If associations of most genetic variants lie on a straight line with a limited number of rogue variants, then a post-hoc analysis may be a reasonable sensitivity analysis. If there is considerable heterogeneity between variants with no discernible pattern of association, then results from a data-driven analysis will not be reliable.5.4P = 0.028), but BMI was not (P = 0.37) and suggested an inverse effect of low-density lipoprotein cholesterol on hypertension (P = 0.011) and on type 1 diabetes risk (P = 0.018) A final alternative is a whole-genome approach, where genetic variants from throughout the genome are included in an analysis. It has also been suggested that investigations with large numbers of genetic variants may be fruitful 6If genetic variants associated with two traits overlap, this increases the likelihood that the traits have related biological mechanisms. For example, genetic approaches have been used in the nosology of psychiatric disorders to inform the degree to which separately classified diseases may be related However, the complete separation of biological from nonbiological effects using population genetics is not possible. For example, a genetic variant associated with both alcohol consumption and cannabis use has been interpreted as evidence in the hypothesis that alcohol consumption causes increased cannabis consumption Although a joint association analysis can increase or decrease the plausibility of a causal relationship, there are many limitations to such an analysis. This means that the evidential weight of such an analysis in terms of proving or disproving causation should not be as great as that of a Mendelian randomization study in which the instrumental variable assumptions are strongly supported by biological and statistical justification. An analysis where the choice of genetic variants is made solely on the basis of observational data and the biological pathways affected by the variants are not investigated should not carry much more evidential weight for demonstrating a causal relationship than a well-designed classical (nongenetic) observational study.7Mendelian randomization has been defined as “using genes as instrumental variables for making causal inferences” Mendelian randomization has been advocated as providing strong evidence for causal relationships and has been placed in a hierarchy of evidence only below well-designed randomized controlled trials