It has been suggested that traits with low heritability, such as fertility, may have proportionately more genetic variation arising from non-additive effects than traits with higher heritability, such as milk yield. Here, we performed a large genome scan with 408,255 single nucleotide polymorphism (SNP) markers to identify chromosomal regions associated with additive, dominance and epistatic (pairwise additive × additive) variability in milk yield and a measure of fertility, calving interval, using records from a population of 7,055 Holstein cows. The results were subsequently validated in an independent set of 3,795 Jerseys.Bos taurus autosomes (BTA) 5, 14 and 20, whereas SNPs with suggestive additive effects on fertility were observed on BTA 5, 9, 11, 18, 22, 27, 29 and the X chromosome. We also confirmed genome regions with suggestive dominance effects for milk yield  and for fertility . A number of significant epistatic effects for milk yield on BTA 14 were found across breeds. However on close inspection, these were likely to be associated with the mutation in the diacylglycerol O-acyltransferase 1 (DGAT1) gene, given that the associations were no longer significant when the additive effect of the DGAT1 mutation was included in the epistatic model.We identified genomic regions with validated additive effects on milk yield on In general, we observed a low statistical power  for non-additive genetic effects compared with additive effects for both traits which could be an artefact of higher dependence on linkage disequilibrium between markers and causative mutations or smaller size of non-additive effects relative to additive effects. The results of our study suggest that individual non-additive effects make a small contribution to the genetic variation of milk yield and fertility. Although we found no individual mutation with large dominance effect for both traits under investigation, a contribution to genetic variance is still possible from a large number of small dominance effects, so methods that simultaneously incorporate genotypes across all loci are suggested to test the variance explained by dominance gene actions.The online version of this article (doi:10.1186/s12863-015-0241-9) contains supplementary material, which is available to authorized users. Female fertility is of great interest to the dairy industry because impaired reproductive ability can reduce the profitability of a dairy herd, particularly by increased expenses of additional inseminations, veterinary treatments and replacement cows , 2. Seleet al. [et al. [When heritability estimates are low for a trait, one could examine the non-additive part of genetic variation for opportunities to improve the trait of interest. Non-additive genetic variation is the result of allele by allele interactions and involves intra-locus (dominance) and inter-locus (epistasis) interactions. Pedigree based estimates of non-additive genetic variance for fertility related traits have been reported to be as large as or larger than additive variance . Hoescheet al.  observed [et al.  estimateet al. [et al. [The prediction of non-additive genetic effects is not a trivial task and requires complex statistical and computational methods . In tradet al.  showed t [et al.  obtainede.g. [Over the last decade, high throughput genotyping has provided a valuable source of information to study the relationships between phenotypes and genotypes in livestock breeding , 18. Acce.g. ). This me.g. . Known ge.g. –23.The objective of this study was to detect chromosomal regions with additive and non-additive genetic effects for calving interval and milk yield (MY) using a Holstein discovery population. We then attempted to validate these associations in an independent Jersey population of cows. The benefits and limitation of accounting for non-additive effects in genetic analyses are discussed, with examples from the present study.P < 1 × 10−7) and Jersey (P < 1 × 10−5) populations. However, for CI  and Jersey (P < 0.01) cows were set to identify potential associations. Significant associations for MY were found on BTA 5, 14 and 20 whereas suggestive additive SNP effects associated to CI were observed on BTA 5, 9, 11, 18, 22, 27, 29 and X chromosome.Manhattan plots of all additive SNP effects for MY and CI in study populations are presented in Figs  CI Fig.  very fewP < 1 × 10−7) in the Holstein analysis  in the Holstein set which corresponds to an estimated FDR of 30 %, while only 5 of these were found to be significant (P < 0.01) in the Jersey population used for validation, with an estimated FDR equal to 26 % (Table P < 0.01) was 73 with a FDR of 1 %.In the association analysis of MY, 715 SNPs were significant (P < 1 × 10−7 (5 % Bonferroni corrected). Therefore for both traits, SNP effects were tested with a suggestive less stringent threshold of P < 0.0001 in Holstein population and validated in Jersey cows at a threshold of P < 0.01.The Manhattan plots of all dominance SNP effects for MY and CI are shown in Figs. P < 0.0001) in the Holstein discovery population for MY, but only 1 of these was validated (P < 0.01) in Jersey cows with different signs observed in the discovery and validation analyses and with a FDR of 39 % (Table P < 0.01) with a FDR equal to 1 %. For CI, 36 SNPs were found to have significant (P < 0.0001) dominance associations in the Holstein discovery set  and 7  chromosomes, respectively.The magnitude of significant dominance effects were smaller than those for additive effects especially for MY. This was confirmed with large FDRs, such that in the discovery analyses of both traits, these values were calculated to be more than 100 % Table . Forty S % Table . The numet Table . Of thesThere were 255,255 and 9,180 pairwise interaction effects included in the epistasis analyses for MY and CI respectively. The SNPs were selected where they had significant additive effects in the discovery population of Holsteins (Table diacylglycerol O-acyltransferase 1 (DGAT1) gene, we suspected that these interactions may have been due to the DGAT1 mutation effect [DGAT1 effect to see if any of the interactions remained significant. We did this by including an additional SNP effect in the model, this SNP was the highest peak in the DGAT1 region. The absence of significant interactions in this region after including the SNP in high LD with the DGAT1 effect in the model suggests that the identified significant pairwise interactions were picking up the DGAT1 effect by creating haplotype like combinations. That is, the linkage disequilibrium of SNP allele combinations with the DGAT1 mutation was higher than for the individual SNP.Similar to the additive analysis, a larger number of pairwise interactions were found to be statistically significant for milk yield compared with fertility Table . Howevern effect . TherefoP < 0.0001) effects on CI in Holstein analysis with a FDR of 18 %, however none of them was validated (P < 0.01) in the Jersey cows, so we did not report them here.Five additive × additive interactions were found that had significant  by additive effects for MY. The effect of DGAT1 on several production traits including MY has been previously demonstrated in several studies [Four regions were detected that had additive associations with MY, of which 2 were on BTA 5 and 1 each on BTA 14 and BTA 20 (Table e.g. –29). The studies , 30, 31.et al. [epidermal growth factor receptor pathway substrate 8 (EPS8) gene. This gene has also been reported by Raven et al. [protein tyrosine phosphatase, receptor type, O (PTPRO) gene and G protein-coupled receptor, family C, group 5, member A (GPRC5A) gene. PTPRO is located 18 Kbp downstream of EPS8 so it is likely that the same QTL affecting milk production traits is responsible for detected associations in these studies. A candidate gene in the other interval, GPRC5A, is associated with signal transduction between cells and has been reported as having differential expression (up regulation / turning on) during the onset of lactation in bovine mammary tissue [Chromosome 5 contained 2 significant regions for MY (94.5 to 95.0 Mbp and 96.9 to 97.9 Mbp) which extended beyond the previously reported significant regions on this chromosome for milk production traits , 33. Wanet al.  reportedy tissue .Growth hormone receptor (GHR) gene has been suggested as underlying the QTL in this region [The region on BTA 20 for MY was located on the middle of this chromosome which was strongly suggested as having a QTL affecting milk production traits , 36. A ms region .P) = 6.076) located on BTA 22 which also explained the highest proportion (0.137 %) of phenotypic variance for CI by additive effects. Nevertheless, all of the individually validated SNPs were found within the region on X chromosome extending from 139.2 to 139.8 Mbp.Seventeen significant regions suggesting several genes with additive effects on CI were discovered in this study Table . Chromoset al. [et al. [sialic acid binding Ig-like lectin-5 (SIGLEC5) gene. SIGLEC5 was suggested to have a role on the initiation of parturition in Human [SIGLEC5 is positioned in our reported QTL region, so it may be possible that the described intervals are harbouring the same QTL.Most of the identified QTL regions for CI in this study have been previously reported in the literature. Chromosome 18 has been largely investigated in search for QTLs affecting reproduction traits in dairy breeds –39. Saha [et al.  as havinin Human , hence sin Human . Althouget al. [Hoglund et al.  performeStudies for detecting associations on chromosome X for fertility related traits are scarce in the literature and this chromosome is generally discarded in GWA studies mainly due to the use of mixed-sex observations. All of the SNPs that were individually validated in Jerseys for CI were found on the X chromosome, so future studies including data on this chromosome are suggested to search for QTL affecting fertility traits.synapsin III (SYN3) gene. The ATP/GTP binding protein like-4 (AGBL4) gene was associated with both of the most significant SNPs in Holstein discovery (rs43361287) and Jersey validation (rs43363311) populations on the identified region on BTA 3 (97.9 – 98.8 Mbp). AGBL4 was reported as a gene under positive selection in the dual purpose (milk and beef) Normande breed cattle [phospholysine phosphohistidine inorganic pyrophosphate phosphatase (LHPP) gene was reported as a differentially expressed gene in mammary gland of Holstein-Friesian dairy cows affected by the polymorphism in DGAT1 [Of the 7 validated regions with dominance effects on MY, 3 were on BTA 26 and 1 identified on each of BTA 2, 3, 5 and 27 (Table d cattle . Among tcovery rs361287 anMyosin IB (MYO1B) gene. MYO1B associated with one of the individually validated SNPs (rs133868000) with dominance effect on CI in our study and was reported to have differential expression in in vitro culture of mouse blastocysts in suboptimal conditions [potassium intermediate/small conductance calcium-activated channel, subfamily N, member 3 (KCNN3) gene. KCCN3 plays a key role in fluid secretion within the bovine oviduct which is essential to provide an appropriate environment for gamete maturation, transport, fertilization and early embryo development [KCNN3 is differentially expressed between oocytes and granulosa cells (GCs) during development of the sheep ovarian follicle [KCNN3 was reported as a gene associated with preterm birth [There were 8 regions identified for CI Table  suggestinditions . Both ofelopment . It has follicle . Similarrm birth .Table 7Br2 (r is the correlation between genetic marker and causative mutation) while detection of dominance or pairwise additive by additive effects depends on r4. This indicates there is a much higher reliance on LD when searching for non-additive effects compared to additive effects, if LD between the markers and QTL is incomplete [One of the critical parameters determining the power of GWAS is the amount of LD between the observed SNP and the unobserved causal variant. In fact, the success of a GWAS in identifying QTLs with additive effects is controlled by complete . This waDGAT1 gene, which has known effect on the trait [DGAT1 mutation than the individual SNPs. This illustrates a problem with testing for epistatic interactions with common SNPs in imperfect LD with causative mutations; SNP by SNP interactions can describe haplotypes that are in higher LD with the causative mutation than the individual SNP, and are therefore significant when there is no true epistatic effect present. Putative epistatic interactions between common SNP should therefore be treated with caution.Although we validated some of the pairwise (putative epistatic) interactions for MY across breeds, a subsequent analysis that included the effect of the he trait , removedThe standard in reporting GWAS results is validation and before genotype-phenotype relationships can be used in selection decisions, they should be replicated in an independent population to confirm generalized effects in multiple populations . ValidatQuantifying non-additive gene actions requires phenotypes that are measured on genotyped individuals. Daughter yield deviations are performance averages typically over hundreds of daughters. However, by definition they cannot capture the dominance deviation in daughters’ phenotypes, so they are not useful for estimating non-additive effects of genes. The only way to estimate non-additive genetic effects in dairy cattle is through large datasets of dairy cows, as they express almost all of the economically important traits in dairying.The number of cows with available genotypes in dairy cattle is less than the genotyped bulls but the trend is towards genotyping more cows. Moreover, the availability of genotyped ancestors of cows enables inferring genotype probabilities for cows that can be then used in estimation of non-additive effects . NonetheWe identified and validated a small number of SNPs with suggested dominance effects on MY and CI in Australian Holstein and Jersey cows. Given our results, identifying non-additive gene actions using single SNP regression in a GWAS setting will require very large datasets to capture the likely very small individual non-additive genetic effects. Alternative approaches that simultaneously use all genomic information in Bayesian methods or in terms of genomic relationship matrices in a BLUP seem more appropriate. As the number of genotyped animals is steadily increasing in dairy cattle breeding, incorporating whole genome sequence could reduce the problem of high dependency on LD in detection of non-additive genetic effects and is suggested as a future approach.The original dataset contained 9,159,969 calving interval and 305 d milk yield records of 3,513,757 Australian Holstein and Jersey cows that were in lactation between 1980 and 2011 and recorded by the Australian Dairy Herd Improvement Scheme . Not all contemporaries in a given herd-year-season were genotyped, and therefore, to accurately remove contemporary group effects from the phenotypes, the records were pre-corrected for the effects of age at calving, herd-year-season, parity and month of calving using the full set of records. The residuals from this model were used as the response variable in GWAS analyses for the genotyped animals. Records that did not have both genotype and phenotype data were discarded, so that the final datasets included 23,198 and 11,091 MY and CI records respectively for 7,055 Holstein and 3,795 Jersey cows. Distribution and descriptive statistics of the Holstein and Jersey populations’ phenotypes are shown in Fig. et al. [et al. [et al. [The genotyped animals were part of the Australian genomic reference population that were previously selected for typing based on completeness of their phenotypic data and having sires in the national Australian genomic reference population. Animals were genotyped with Illumina BovineSNP50 v2 BeadChip  and their 50 K SNP data were imputed to the high density (HD) 800 k panel by using another set of 1,785 animals (including Holstein and Jersey key ancestor bulls and heifers) with genotypes from the Illumina BovineHD BeadChip . The imputation was performed with BEAGLE 3.1 . Qualityet al. : only SNet al.  and the  [et al.  and Haye [et al. .A total of 408,255 SNPs included in the analyses were distributed over 29 BTA as well as the X chromosome, but the distribution was uneven with an average genome-wide distance of 6.52 Kb between SNPs, and a minimum and maximum average distance of 5.40 Kb and 15.37 Kb on BTA 25 and on X chromosome, respectively.y is a vector of phenotypes (CI or MY), 1n is a vector of ones, μ is the population mean term, b is the vector containing relevant additive, dominance or epistatic marker effects as specified below, u contains polygenic effects assumed to be distributed as u ~ N with A being the pedigree based numerator relationship matrix, pe is the vector of random permanent environmental effects with pe ~ N and e is a vector of random residual deviates supposed to be distributed as e ~ N. X is a design matrix allocating records to markers effects  and Z and W are incidence matrices for the random effects. σ2g, σ2pe and σ2e are polygenic additive, permanent environmental and residual variances, respectively. The pedigree files included 29,042 and 15,977 animals for Holstein and Jersey with corresponding average generations of seven and six.A mixed linear model was implemented to test for associations between genetic markers and phenotypic values of both traits (CI and MY) for each breed separately. SNP effects were calculated one at a time using single SNP regression procedure. The model in matrix notation was:X, so that xij(a) = {−2p, (q − p) or 2q} for additive effects of aa, Aa and AA genotypes, respectively, with p and q being the allele frequency of A and a allele at marker j in the population. For dominance effects, aa, Aa and AA genotypes were coded as xij(d) = {−2p2, 2pq and − 2q2}. Then, the contents of Xb varied with the type of the genetic effect being tested. For additive effects, Xb = {xij(a)aj}, where aj is the corresponding additive effect. For dominance, Xb = {xij(a)aj + xij(d)dj}, where dj is the dominance effect of marker j. In the epistasis model, j and j’, j’ marker and j and j’. The models were fitted to the data with ASReml v3.0 [The original marker covariates  were corrected for allele frequencies  to buildeml v3.0 .To discriminate between true discoveries and false positive SNP effects, and also to confirm significant SNPs that were consistent between breeds, results from the Holstein and Jersey data sets were compared. The larger Holstein population was assigned to the discovery set and results from Holstein analyses were validated in the Jersey breed in two different ways. First, if a significant SNP was found in the discovery process, we examined whether it was also significant in the validation population. Second, for each significant SNP in the discovery population, we searched for significant SNPs in the validation population within the region 500 kb downstream and upstream of the identified SNP. We call the latter segment validation which accounts for the possible difference in allele frequency of markers in LD with the causal mutation in the different population, that may cause different markers in the same region are tagging the same causal mutation in different populations. The window size was chosen by considering the long range of strong LD between SNPs in the Holstein and Jersey breeds .et al. [P is the P-value threshold in F-test, S is the number of significant SNPs according to this threshold and T is the total number of tests. This FDR can be used to provide an expectation of the number of true positives at the probability thresholds.The false discovery rate was calculated following the approach proposed by Bolormaa et al. .2\documeP-value level used to decide on significance of a main or interaction effect was the corresponding Bonferroni correction of the nominal P-value of 0.05 as: P-value threshold in the analysis including all SNPs was equal to P < 1 × 10−7. In the case that no significant SNP effects were identified at this threshold, an arbitrary P-value threshold of P < 0.0001 in the discovery dataset (i.e. Holsteins) and P < 0.01 in the validation population (i.e. Jerseys) was used. Although this might be arbitrary and some false positives may arise using this approach, it is highly unlikely for significant effects to arise simultaneously in two completely independent populations and our ultimate standard is across breed validation.The P-value of the F-test of the additive model in the Holstein discovery set were included. Therefore, n(n-1)/2 pairwise interactions were tested where n is the number of SNPs whose main additive effect is significant.For additive and dominance models, all of the markers in the final HD panel were used. To reduce the dimension of SNP combinations tested in the epistatic models, only significant SNPs determined using the σa2) or dominance (σd2) variance of each SNP was estimated as follows:pi and qi are the frequency of A and a alleles, and ai and di are respectively the estimated additive and dominance effect of the ith SNP obtained from model (1) and model (2). For most strongly associated additive or dominance SNP effects, these variances were expressed as a fraction of total phenotypic variance (σp2 = σg2 + σpe2 + σe2) where each variance component was estimated based on model (1) without fitting SNP covariates.The additive (www.ncbi.nlm.nih.gov) were used to determine if the significant SNPs were positioned inside known genes. Animal genome QTL database  was used to compare the results of present study with the reported QTL regions in the literature.Manhattan plots were created using qqman 0.1.1  in R 3.1


Kinship-based INference for Genome-wide association studies (KING). Overall, both methods identified familial relationships in NHANES III and NHANES 1999–2002 for all three subpopulations, but little concordance was observed between the two methods due in major part to the limited SNP data available in Genetic NHANES. Despite the lack of genome-wide data, our results suggest the presence of cryptic relatedness in this epidemiologic collection and highlight the limitations of restricted datasets such as NHANES in the context of modern day genetic epidemiology studies.Epidemiologic collections have been a major resource for genotype–phenotype studies of complex disease given their large sample size, racial/ethnic diversity, and breadth and depth of phenotypes, traits, and exposures. A major disadvantage of these collections is they often survey households and communities without collecting extensive pedigree data. Failure to account for substantial relatedness can lead to inflated estimates and spurious associations. To examine the extent of cryptic relatedness in an epidemiologic collection, we as the Epidemiologic Architecture for Genes Linked to Environment (EAGLE) study accessed the National Health and Nutrition Examination Surveys (NHANES) linked to DNA samples (“Genetic NHANES”) from NHANES III and NHANES 1999–2002. NHANES are population-based cross-sectional surveys conducted by the National Center for Health Statistics at the Centers for Disease Control and Prevention. Genome-wide genetic data is not yet available in NHANES, and current data use agreements prohibit the generation of GWAS-level data in NHANES samples due issues in maintaining confidentiality among other ethical concerns. To date, only hundreds of single nucleotide polymorphisms (SNPs) genotyped in a variety of candidate genes are available for analysis in NHANES. We performed identity-by-descent (IBD) estimates in three self-identified subpopulations of Genetic NHANES  using PLINK software to identify potential familial relationships from presumed unrelated subjects. We then compared the PLINKidentified relationships to those identified by an alternative method implemented in  Epidemiologic cohorts are a valuable resource for genotype–phenotype studies given their large sample size, racial/ethnic diversity, and wealth of phenotypes, traits, and exposures. Though typically ascertained for specific phenotypes, the breadth of phenotypic and environmental variables makes these cohorts particularly well-suited for inclusion in secondary analyses. With the addition of genetic data such as genotypes, these epidemiologic cohorts are positioned for inclusion in genetic association or linkage studies. Some examples of well-characterized studies that have genetic data include the Framingham Heart Study , Women’sSome epidemiologic cohorts specifically seek related individuals during the ascertainment process in order to study the heritability of certain traits in a similar genetic background or minimize certain environmental differences between individuals; for example, the Framingham Heart Study recruited participants from a Massachusetts town and subsequently enrolled their offspring in later phases of the study to identify factors that contribute to cardiovascular disease , whereasGenetic association studies are susceptible to confounding, through population substructure and cryptic relatedness . PopulatSeveral methods have been developed to infer familial relationships primarily for linkage studies, including Graphical Representation of Relationship errors GRR;  and multKinship-based INference for Genome-wide association studies (KING) was recently developed to infer relationships using kinship coefficients  using a combination of identity-by-state (IBS) between individuals and allele frequency at each single nucleotide polymorphism (SNP), assuming Hardy–Weinberg Equilibrium . At a gificients . A kinshficients . Both ofn = 6,634), non-Hispanic blacks , and Mexican Americans . Genetic NHANES has been genotyped for hundreds of SNPs (range n = 364–784) mostly selected to replicate and generalize genome-wide association study findings in diverse populations as part of the Epidemiologic Architecture for Genes Linked to Environment (EAGLE) study, a study site of the larger Population Architecture using Genomics and Epidemiology (PAGE) I study  and NHANES 1999–2002, and Genetic NHANES consists of several racial/ethnic subgroups: non-Hispanic whites  and for 7,839 participants  in NHANES 1999–2002 . Written informed consent was obtained from all participants. The CDC Ethics Review Board reviewed the present study, and the de-identified NHANES data were considered non-human subjects research by the Vanderbilt University Institutional Review Board.The National Health and Nutrition Examination Surveys are population-based surveys conducted across the U. S. by the National Center for Health Statistics (NCHS) at the Centers for Disease Control and Prevention (CDC). NHANES began in the 1960s; the Third NHANES (NHANES III) was performed from 1988 to 1994 and included 33,994 participants. From 1999, NHANES surveys have been performed continuously. NHANES 1999–2002 included 25,316 participants. NHANES capture self-described race/ethnicity on all participants. Oversampling of Mexican Americans, non-Hispanic blacks, children, and the elderly were performed to create nationally representative samples. DNA is available for 7,159 participants over age 12 in NHANES III .Single nucleotide polymorphisms were selected for either candidate gene studies , 2015 orp < 0.001). To obtain a set of independent SNPs, we further excluded SNPs that were in high linkage disequilibrium (LD) with each other (r2 > 0.60) using the –indep command in PLINK. Two different programs, PLINK  for PLINK (Table 1). The –kinship command with additional parameters of –homo and –show-IBD were used to calculate IBD estimates using KING. Kinship coefficient ranges were used to identify potential familial relationships in KING (Table 1). Further classification of first degree relationships from KING were obtained by evaluating the IBD0 values; parent/child relationships will have IBD0 = 0 except for instances of genotyping error. We compared the ability of the software programs to identify cryptic relatedness within NHANES racial/ethnic groups using less than 1,000 SNPs. Due to the data use agreement with the CDC, any participant counts < 5 are suppressed for confidentiality concerns.The –genome command was used to calculate the IBD estimates using PLINK. We pre-specified the classification scheme for potential familial relationships based on ranges of n = 6,811) and NHANES 1999–2002  non-Hispanic whites, non-Hispanic blacks, and Mexican Americans using PLINK and KING software. In both NHANES III and NHANES 1999–2002, the majority of the participants were women . In each NHANES dataset, non-Hispanic whites comprised the largest subgroup (Table 2). The median age in NHANES III was lower (median age = 38.00) than in NHANES 1999–2002 . Household size ranged from 1 to 10 participants in NHANES III and 1–7 participants in NHANES 1999–2002. In both surveys, two-person households were the most common overall, though there were differences by subgroup (Table 2). Mexican Americans had the largest median household size (n = 4) and widest range for household size in both NHANES .We calculated IBD estimates and potential familial relationships in NHANES III (Table 3) using either program; however, we observed no concordance between the potential duplicates/MZ twin pairs . A number of first degree relationships (parent/offspring and full sibling) were calculated with both methods. PLINK calculated the greatest number of potential first degree relationships in non-Hispanic whites  and the majority of these relationships were parent/offspring , while Mexican Americans full sibling pairs were the most common first degree relationship calculated with KING . Across all subgroups, most first degree relationships were categorized by PLINK as parent/offspring and by KING as full sibling (Table 3). The greatest number of second degree and third degree relationships was observed in non-Hispanic blacks using PLINK  and in non-Hispanic whites using KING . We found little concordance (<20% same relationship identified for a given participant pair) between the methods to identify the same participants’ relationships, though 60% of non-Hispanic white parent/offspring pairs calculated with KING were classified as parent/offspring pairs with PLINK . We observed similar concordance/discordance among the results for non-Hispanic black parent/offspring pairs (50% concordant) and Mexican American parent/offspring pairs . Within the discordant results in each subgroup, a number of each potential familial relationship identified through one method was classified as a different familial relationship using the other method. Where the methods yielded a different potential familial relationship for a given participant pair, we found PLINK calculated the pair as more related . This observation held across all subgroups and familial relationships, except second degree relationships in non-Hispanic blacks and Mexican Americans, where KING-calculated second degrees were more frequently classified as PLINK third degrees than any other relationship. Broadly, PLINK and KING identified numerous potential first, second, and third degree relationships in NHANES III; however, there was little concordance between the results.In NHANES III, PLINK calculated more potential familial relationships than KING in all subgroups. We identified few instances of potential duplicate samples/monozygotic (MZ) twins (Table 4). There were few instances of MZ twins/duplicate samples among the three subgroups and the participant pairs were concordant between the two methods . Fewer overall first degree relationships were calculated in NHANES 1999–2002 than in NHANES III (Tables 3 and 4). Similar to the trends observed in NHANES III, KING identified fewer instances of first degree relationships than PLINK (Table 4). PLINK calculated the greatest number of first degree relationships in non-Hispanic blacks (n = 498) and the majority of these were parent/offspring (n = 493), whereas Mexican American full sibling relationships were the most numerous relationship calculated by KING . The greatest number of second and third degree relationships were observed in non-Hispanic whites  using PLINK, and in non-Hispanic blacks  using KING (Table 4). As with the NHANES III results, we found little concordance (<25%) between the participant pairs identified within each potential familial relationship with the exception of parent/offspring pairs across the three subgroups, in which >95% of parent/offspring pairs identified with KING were also identified with PLINK . In addition, we observed a similar trend within discordant pairs, where PLINK calculated the pair as more related than with KING, with the exception of non-Hispanic white second degree relationships which were more often classified as third degree relationships in PLINK. Overall, we identified potential cryptic relatedness in NHANES 1999–2002 using PLINK and KING, though concordance between the two methods was generally lacking.In NHANES 1999–2002, we again observed PLINK calculated a greater number of potential familial relationships than KING for non-Hispanic whites and Mexican Americans; KING calculated a greater number of familial relationships in non-Hispanic blacks  may lead to spurious results and/or inflated effect estimates in population-based association studies where an underlying assumption is that the individuals are unrelated. Additionally, specifically testing the influence of multiple interactions on heritability estimates requires known relatedness between individuals . EpidemiWe estimated likely familial relationships in NHANES III and NHANES 1999–2002 using ∼730 and ∼370 SNPs, respectively, and two methods, PLINK and KING. Using PLINK, which estimates IBD by calculating IBS and allele frequencies at each SNP, we observed many potential first degree relationships in NHANES III across the three population subgroups. The majority of these first degree relationships in PLINK were likely parent/offspring pairs. In NHANES 1999–2002, we observed fewer likely first degree relationships than in NHANES III. Thousands of potential second and third degree relationships were calculated using PLINK in both NHANES III and NHANES 1999–2002. Using KING, which estimates IBD using kinship coefficients, we observed far fewer first degree relationships in NHANES III and NHANES 1999–2002 than with PLINK. The majority of the first degree relationships calculated by KING were full sibling pairs, in contrast to the parent/offspring majority identified with PLINK. In NHANES 1999–2002, the majority of first degree relationships were full sibling pairs. We identified numerous potential second and third degree relationships using KING. Using both PLINK and KING, which calculate familial relationships with different statistical methods, we observed relatedness in NHANES III and NHANES 1999–2002 across non-Hispanic white, non-Hispanic black, and Mexican American subgroups.®) and found evidence of first and second degree relationships  at fifteen DNA loci used in forensic investigations  to calculate IBD; the more markers are used in the calculation, the greater the stability and accuracy of the IBD estimates , and theMost epidemiologic studies with DNA have GWAS data, allowing investigators to more accurately assess the level of relatedness in the dataset, contrasting with the problem of assessing cryptic relatedness in genotype-limited datasets such as NHANES. Per CDC data use agreements, GWAS-level genotyping is not permitted at this time by investigators outside of CDC or without a CDC contract. While there are multiple programs for accurately estimating IBD given thousands of SNPs, there are relatively few options for epidemiologic collections with hundreds or fewer genotyped SNPs. Recently, a new R package, CrypticIBDCheck, was published demonstrating the ability to calculate IBD with as few as 60 candidate genes (∼300 SNPs) which have not been LD pruned for independence . Future Another limitation of the current study is the lack of pedigree data available in NHANES, which unlike simulated data with known pedigree structures used to originally compare PLINK and KING , prohibiIn summary, we have estimated familial relationships in Genetic NHANES, an epidemiologic cross-sectional study with sparse candidate gene SNPs available for genetic association studies. We implemented the commonly used PLINK and compared these familial relationships to those estimated by a second method implemented in KING. Familial relationships were identified in Genetic NHANES using both methods, but little concordance was observed between the methods. In absence of pedigree data, it is not possible to determine which of the two methods is more accurate in estimating familial relationships in this collection of cross-sectional surveys. In absence of GWAS-level data, basic quality control will continue to be a challenge for NHANES and similar epidemiologic collections. Further research is needed to identify alternate approaches to identify cryptic relatedness using sparse SNP data such as those available in Genetic NHANES.The listed authors provided substantial contributions to the conception or design of the work , the acquisition (DC), analysis , or interpretation of the data  for the work; drafted the work (JM) or revised it critically for important intellectual context ; gave final approval of the version to be published ; and agreed to be accountable for all aspects of the work in ensuring that questions related to accuracy or integrity of any part of the work are appropriately investigated and resolved .The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


A three-component t-mixture model has been used for the parametric empirical Bayes (PEB) method. Inferences have been obtained using Expectation/Conditional Maximization Either (ECME) algorithm. A simulation study has also been performed and has been compared with a nonparametric empirical Bayes (NPEB) alternative.Genome-wide association studies (GWAS) have identified hundreds of genetic variants associated with complex human diseases, clinical conditions and traits. Genetic mapping of expression quantitative trait loci (eQTLs) is providing us with novel functional effects of thousands of single nucleotide polymorphisms (SNPs). In a classical quantitative trail loci (QTL) mapping problem multiple tests are done to assess whether one trait is associated with a number of loci. In contrast to QTL studies, thousands of traits are measured alongwith thousands of gene expressions in an eQTL study. For such a study, a huge number of tests have to be performed .The results show that PEB has an edge over NPEB. The proposed methodology has been applied to human liver cohort (LHC) data. Our method enables to discover more significant SNPs with FDR<10% compared to the previous study done by Yang et al.  as the threshold. This method controls false positive rate. Genome-wide association studies (GWASs) have done a remarkable progress in searching for susceptibility genes. In GWAS, instead of one gene at a time, variation across the entire genome is tested for association with disease risk. GWASs exploit the linkage disequilibrium (LD) relationships among single nucleotide polymorphisms (SNPs), making it possible to assay genome by testing a finite number of SNPs. Till date, the signals that can be discovered through GWAS has not been reported exhaustively. It is important to annotate SNPs information on expression for the better understanding of the genes and mechanisms driving the association. In many situations, there are more common variants truly associated with disease. These variants are highly likely to be expression quantitative trait loci (eQTLs). eQTLs are derived from polymorphisms in the genome that result in differential measurable transcript levels. Microarrays are used to measure gene expression levels across genetic mapping populations. For at least a subset of complex disorders, gene expression levels could be used as a surrogate/biomarker for classical phenotypes. The gene underlying the eQTL is considered to be an excellent candidate for phenotypic QTL.eQTL mapping is a statistical technique to locate genomic intervals, that are likely to regulate the expression of each transcript, by correlating quantitative measurements of mRNA expression with genetic polymorphisms segregating in a population. In a GWAS, millions of SNPs are tested at once. Associations that initially appear to be significant must be statistically adjusted to account for the large number of tests being performed. A large number of false positives will result in if this correction is ignored. The multiple-testing correction, however, sets a very high threshold for genome-wide significance, on the order of al. [al. [Two closely related inferential procedures for multiple testing have been discussed in this work-afrequentist approach based on Benjamini and Hochberg's  false dal. -10, Gelfal. [al. . Hierarcal. [al.  or lognoal. [al.  are usedal. [al. . The appal. [al. ) technolOne of the fundamental statistical problems in microarray gene expression analysis is the need to reduce dimensionality of the transcripts. This can be achieved by identifying differentially expressed (DE) genes under different conditions or groups. Regulatory network can be obtained by associating differential expressions with the genotype of molecular markers. It is possible to have a large number of DE genes that influences a certain phenotype while their relative proportion is very small. It is very important to identify these DE genes from among the number of recorded genes ,9,14,15.The development of the empirical Bayes methodologies that improve the power to detect DE genes essentially reduces to the choice of whether gene-specific effects should be modeled as fixed or random . Both meThe paper is organized as follows. In the Methods section we introduce the necessary notations for our additive genetic model along with the notions of false discovery rate (fdr). In this section we have tried to establish the relationship between fdr and empirical Bayes. Methods section also describes, the proposed Expectation/Conditional Maximization Either (ECME) (Liu and Rubin ) in detaii G= 1.....l as the genomic marker(i.e. SNP), and jT(j = 1......J) as the transcripts. The identified eQTLs refer to the significant Gs that are associated with Ts. These associations can be found using a test statistics based on all al. [In a microarray experiment, we obtain several thousand expression values, one or many for each gene. These studies offer an unprecedented ability to do large-scale studies of gene expression. Let us define  analysis. The preysis[al. . The testh percentile of all al. [where n el al. ).When expression measurements between two groups are compared for any transcript, the observations are partitioned into two user defined groups of sizes i Fbe the minor allele frequency of the ith SNP then we model the distribution of ij Zas a mixture model of the form:where ij Zfor nonzero associations between where For any transcript and any SNP there may be three possible relations: no association, positive association and negative association. Extending the idea of two component mixture model, the distribution of the test statistics is modeled by the following mixture model:Wherei. with d Matsui , have usa-priori models in favor of data-based investigations [Full Bayesian analysis of (4) will require prior specifications of igations .False discovery rate (fdr) is defined as the expected proportion of errors committed by falsely rejecting null hypotheses. Benjamini and Hochberg's fdr criteThe empirical Bayes approach suggests a local version of the fdr called local false discovery rate , and henceal. [n et al. ) and poiAll other parameters will be estimated by EM algorithm assuming The main difference between parametric empirical Bayes (PEB) and nonparametric empirical Bayes (NPEB) is the way in which n et al. .t distribution the mean parameter To fit a mixture model, EM algorithm is widely used. In case of d Taylor . But thid Taylor ) and an d Taylor  as ECM ad Taylor . Incidend Taylor  propose For the whereand t distribution. In ECME algorithm, this result has been extended to cover the present set up of a 3-component mixture of t distribution. For the sake of brevity, in this section we omit the suffix ij for all the variables. To define t distribution with mean McLachlan and Krishnan  have alrthen marginally, Following the above definition, the complete data likelihood whereandTo compute the E-step of the proposed algorithm, at (t+1)th step we need to calculate whereandwhich is the posterior probability that Similarly,WhereIn usual M-step parameters and To get an efficient algorithm, let us partition CM-Step 1. Keeping CM-Step 2. Now fix Furthermore to make the algorithm more efficient, after the first CM-step, we replace the E-step with To assess the proposed methodology, a small sample simulation study has been performed. This gives an idea whether or not the parameters are well estimated and most importantly, they provide information of false discovery rates.First we simulated a dominant model with 10,000 transcripts and 10 SNPs. The equivalently expressed (EE) transcripts are generated from N after log-transformation. We have simulated the data under three choices of proportions of differentially expressed (DE) transcripts  on the distributions under null has also been studied. Under null, for a t-distribution, the only parameter to be estimated is its degrees of freedom. The comparison has been made by computing different quantiles for six choices of MAFs. For the lower quantiles, they almost overlapped with each other. Very small deviations are observed for upper quantiles Figure .For the 10 SNPs, we fitted the null distribution using permutation method in a balanced way. From each group, randomly selecterd 35 samples are shifted from one group to the other and the value of the statistic is noted. This process is repeated 40 times and histograms are plotted. From the histograms, the degrees of freedom corresponding to the null distribution for eack SNP is estimates. To get an idea about the goodness-of-fit, Q-Q plots are done  are estimated using proposed ECME algorithm after estimating the null distribution using permutation method. Then FDR is computed under both proposed parametric empirical Bayes and nonparmetic empirical Bayes setup and the result is given in Table It is evident from the above table that the nonparmateric empirical Bayes is much conservative compared to its parametric alternative. For parametric set up, the true FDR is very much close to the controlled one, whereas, for nonparametric empirical Bayes these values are not so close as the true fraction of DE transcripts increases.-5,) we are left with 173 samples, 472,000 SNPs and 30,000 expressions.We applied the empirical Bayes model to analyze a sequencing data publicly available. In the current study, we have started with liver tissue data of 213 Caucasian samples from apreviously described human liver cohort (LHC) . To getThe distribution of minor allele frequency (MAF) over SNPs is given in the histogram Figure . For allTo compare our result with , we focuIn contrast to previously available methods based on p-values, the empirical Bayes method uses local false discovery rate (lfdr) as the threshold. This method controls false positive rate. For a particular SNP, the lfdr is computed for the site-specific evidence whereas the FDR averages over other sites with stronger evidence. There are some limitations of using FDR which may result in misleading inferences in genome studies. In such a situation, it is better to use lfdr which is a bit difficult to estimate compared to FDR.However there is still one computational problem which needs much attention. Due to the high dimensionality in the data, sometimes existing algorithms fail. This necessitates the need to find some more efficient algorithms. The choice of threshold FDR value is an important deciding factor in such studies. It would be interesting to see, how number of cis-SNPs vary with the change in FDR threshold. In this way FDR criterion can be used to estimate number of SNPs that we may need to consider.The authors declare that they have no competing interests.


The use of genetic markers as instrumental variables (IV) is receiving increasing attention from economists, statisticians, epidemiologists and social scientists. Although IV is commonly used in economics, the appropriate conditions for the use of genetic variants as instruments have not been well defined. The increasing availability of biomedical data, however, makes understanding of these conditions crucial to the successful use of genotypes as instruments. We combine the econometric IV literature with that from genetic epidemiology, and discuss the biological conditions and IV assumptions within the statistical potential outcomes framework. We review this in the context of two illustrative applications. This is often problematic, as observed associations are not necessarily causal, with confounding being an important concern. Randomization of treatment, as in a Randomized Controlled Trial (RCT), is one way to infer causality. However, such experiments are not always possible or feasible. An approach commonly used in the economics and econometrics literature is that of Instrumental Variables (IV). This introduces a third variable (the instrument) that is robustly associated with the risk factor of interest, but not with the outcome variable, other than through its effect on the risk factor. This instrument can then be exploited to make causal inferences about the effect of the risk factor on the outcome.Recently, epidemiologists, statisticians, economists and other social scientists have become interested in using genetic variants as instruments. ‘Mendelian randomization’ refers to the random assignment of an individual's genotype at conception . Under cThe contribution of this paper is to discuss these conditions within the well-known statistical potential outcomes framework. We use the work by These examples are pertinent for several reasons. For our social science application for example, obese children are more likely to be absent from school, have sleep disorders, and be treated differently by teachers, parents and peers. All these may affect children's (learning) environment and educational outcomes. However, an observed association between fat mass and academic achievement is not necessarily causal. There are likely to be many confounders, and one can never be sure that all relevant ones are accounted for. For our medical application, there is evidence that even relatively small reductions in weight can reduce blood pressure and hypertension risk . HoweverAlthough Mendelian randomization is widely used in the medical and epidemiological sciences, with its findings being fed into pharmacotherapeutic development, it is very controversial within economics. This mainly stems from the credibility of the ‘exclusion restriction’: the assumption that the variants do not directly affect the outcome of interest. Indeed, there are many situations that may violate this assumption, invalidating the instruments and biasing the estimates. One of the issues is that we have very limited knowledge and understanding of the specific functions of genes, and studies that directly examine gene-function are often underpowered. Hence, we can never be certain that the exclusion restriction is satisfied. We discuss this in detail, and highlight the specific  pathways through which the use of genetic variants as instrumental variables may lead to invalid inferences, including the potential for variants to have multiple functions, or to be correlated to other variants that affect the outcome of interest. We also consider the implications of gene–gene and gene–environment interactions for Mendelian randomization. Finally, it is worth noting that the uncertainty of the exclusion restriction is not specific to Mendelian randomization. Indeed, any IV analysis relies on this untestable assumption, and one generally assesses such studies based on whether the available evidence suggests that the assumption is likely to hold see also . We discSection 2We start by discussing the links between Mendelian randomization and other approaches used in the medical and social science literature. We then build on the Potential Outcomes Framework by 2.1We discuss Mendelian randomization from a statistics and economics perspective in the context of a social study, with the aim of making causal inferences about the effect of a treatment on an outcome of interest. Depending on the discipline, the terms ‘treatment’, ‘risk factor’, ‘exposure’, ‘predictor’, or ‘intermediate phenotype’ have all been used to denote the variable of interest that potentially causes the outcome. To avoid confusion, the remainder of this paper uses either the term ‘treatment’ or ‘risk factor’.The concept of Mendelian randomization is closely linked to Randomized Controlled Trials (RCTs), where the allocation of treatment is randomized over all eligible individuals . Indeed,The idea is similar for the social context in our application: individuals ‘select’ their treatment – fat mass – through lifestyle choices, such as diet and physical activity, which are likely to be related to their study outcome . In a well-conducted RCT of an intervention aimed at reducing fat mass, the random allocation effectively balances these lifestyle choices between groups. Comparing groups based on the original random allocation (‘intention to treat’) maintains this balance, whereas comparing groups based on what treatment was actually chosen by the participant  is likely to be biased due to non-ignorable non-compliance. In other words, treatment by choice (as opposed to treatment by randomization) is likely to be related to the outcome through characteristics such as social class, income, diet, etc.There are many cases, however, where RCTs are infeasible  or unethical . In such cases, quasi-experimental designs such as Mendelian randomization experiments can provide a useful alternative approach.As in RCTs, Mendelian randomization assumes that characteristics such as social class, income and diet are balanced across the genotypes. This assumption exploits the fact that there is an equal probability that either parental allele see  is transInterventional studies such as RCTs, where treatment is introduced at a certain age, identify the effect of differences in treatment from that point in time. By contrast, estimates from Mendelian randomization experiments exploit differences in treatment throughout life, estimating the long term (cumulative) effects of the treatment on the outcome of interest .As noted by 2.2Z1 and Z2), we observe nine instrumental values, defined by the combination of the number of rare alleles. Without loss of generality, we order the instruments by their mean fat mass, for example: Z with support 1,2,…,9; the full set of instruments are the nine mutually exclusive dummy variables. Let A and Y denote random variables representing, respectively, fat mass and the educational outcome/blood pressure.Our two illustrative applications use a continuous treatment and outcome variable, and 32 independent genetic variants. For ease of exposition, however, we discuss our framework for the case of two genetic variants, though we note that this is easily generalized to incorporate any number of variants. As shown in i when the instrument is set to z. Only one of the 9 possible treatment assignments i that would be obtained if i‘s fat mass, the treatment variable, was set to a and the instrument was set to z. We refer to Let i's potential treatments and potential outcomes are independent of the outcome and treatment status of other individuals. This is also referred to as the Stable Unit Treatment Value Assumption , defined here as Z be ordered such that l < m implies that ωz > 0 and ∑zωz = 1. Hence, it averages the (pairwise) instrument-specific weighted averages of the derivative function, where the weights are proportional to the instrument-induced change in the cumulative distribution function (CDF) of fat mass , the IV estimand that uses the multivalued allelic score reatment . Thus, icompliers), those who do the opposite of their assignment (defiers), those who never take treatment, whatever their assignment (never-takers), and those who always take treatment, regardless of their assignment . In this framework, the IV estimate can be interpreted as a Local Average Treatment Effect (LATE) or Complier Average Causal Effect (CACE): the effect of treatment for those who are induced to take treatmentby the instrument (the compliers). Indeed, LATE or CACE is not informative about effects on never-and always-takers, because (by definition) treatment status for these groups is not affected by the instrument. By virtue of the exclusion restriction, the causal effect of Z on Y for never-takers and always-takers is zero. And by virtue of the monotonicity assumption, there are no defiers. Note that in the case of a continuous intermediate variable as generally used in Mendelian randomization studies , it is unclear what it means to be a complier, defier, always-taker, or never-taker. A detailed discussion on identifying compliers in such cases is beyond the scope of this paper, but for different approaches, we refer the reader to At this point, it may be useful to consider a situation where the instrument and treatment are binary, in which case we can stratify individuals into four latent groups, as commonly used in the econometrics literature e.g. : those w2.3Assumption 1within ethnic groups, separately analyzing the different subpopulations, and/or adjusting for principal components from genome wide data that function as ancestry markers. These approaches then relyon the conditional independence assumption, assuming independence conditional on ethnicity or ancestry.Although genotypes are randomly allocated at conception, the allele distribution may differ for different population subgroups. If these subgroups also have systematically different outcomes of interest, this could lead to an association between the two at the population level without an actual causal relationship. A systematic relationship between the allele frequency and the outcome of interest across different sub-populations is also referred to as ‘population stratification’. For example, allele frequencies can vary across ethnic groups. Any systematic differences in the outcome of interest across these subpopulations that are not due to the genetic make-up may therefore lead to biased estimates of the effect of treatment by violating the independence Assumption 1. In other words, despite the fact that genotypes are randomly allocated and with that satisfy independence, any population stratification can violate this assumption. This can be dealt with, however, by examining the question of interest For a valid causal interpretation of the IV estimand that uses the genetic variants as instruments, we require the above assumptions to hold. However, there are various situations that may violate them, which need to be examined. We discuss these below.given the parental genes, the presence of assortative mating based on genes can violate independence. The cleanest experiment, therefore, is one with biological siblings, examining randomization of genes within families . This can bias studies that examine maternal behaviours that influence the outcome of interest via intrauterine effects. Likewise, it may be a problem in studies where parental behaviours influence the outcomevia affecting their (child's) behaviour.As genotypes are randomly assigned families . Howeverfamilies . One waysee also . It may in utero and its functioning later in the child's life, there is a link from the offspring's genotype (IV) to the outcome (the offspring's liver disease) via maternal genotype and maternal alcohol consumption, violating As an example of the former, if one were interested in the effect of an individual's alcohol consumption on their later life liver disease using a genetic variant that robustly relates to alcohol intake, any intrauterine effects of maternal alcohol consumption during pregnancy on offspring liver development could violate As an example of the latter, if one is interested in the effect of fat mass on education, as we are below, parents who carry ‘fat’ alleles may be discriminated against in the labour market because of their on average higher weights . If thisA second situation relates to the mechanisms through which genetic variants affect the modifiable risk factor. These are often unknown. If the mechanism involves changes in behaviour or preferences that in addition to affecting the risk factor also directly affect the outcome, Thirdly, the genetic instrument may be related to other genetic variants that affect the outcome of interest. Mendel's second law states that the inheritance of one trait is independent of the inheritance of another. However, it has been shown that this does not always hold and that some variants are likely to be co-inherited. This so-called ‘Linkage Disequilibrium’ (LD) does not occur for genetic variants on different (non-homologous) chromosomes, and the degree of LD is partly a function of the distance between the loci (see Appendix A for some of the genetic terms used here). Depending on the effects of the co-inherited variant, LD can bias the estimates. If our instrument is in LD with another polymorphic locus that affects only the modifiable risk factor, the IV estimates remain consistent. However, if it is in LD with a polymorphic locus that directly affects the outcome, Fourth, a biological process that may bias causal estimates in Mendelian randomization studies is ‘canalization’. This refers to the reduced sensitivity of a phenotype to the changes in underlying genetic and non-genetic factors that determine its expression. Hence, a canalized genotype produces the same (or a similar) phenotype in different genetic and non-genetic backgrounds . For exaindirectly; we discuss this in more detail in Section Assumption 3sample correlation exists, sample association with the risk factor  can lead to biased IV estimates  the risk factor of interest. Mendelian randomization can only be used with genetic variants that have been robustly shown to affect the risk factor. This point is especially important, as many initial genotype-risk factor associations fail to replicate . Withoutstimates . It is tThese different potential violations of Assumption 4Whether monotonicity is satisfied relies on knowing each individual's counterfactual and therefore always remains an assumption. Monotonicity may be violated in the presence of gene–environment interactions; i.e. when the effect of the environment on the risk factor differs depending on individuals’ genetic predisposition, or when individuals’ genetic predispositions are expressed differently in different environments. For example, if the expression of a genetic variant that increases fat mass depends on individuals’ awareness of the importance of nutrition for one's health, monotonicity may be violated when the potential fat mass of an individual with the genetic variant in an (e.g. educated) environment is less than the potential fat mass for the same individual in that environment without the genetic variant. However, if the expression of the variant is simply reduced in the educated environment, monotonicity would not be violated, as the potential adiposity of an individual with the genetic variant remains at least as high as the potential adiposity for the same individual without the genetic variant.However, even if a suitable genetic instrument is available, it may explain little of the variation in the observed risk factor. A weak association could result in a biased IV estimate and has implications for statistical power. If the alleles shift the distribution of risk factor by a very small amount, the effect of the risk factor on the outcome is identified only by this small difference, emphasizing the need either for very large sample sizes, especially when the average causal effect of the risk factor on the outcome could be small, or many genetic variants that can be combined into a more powerful instrument. This, of course, is not a problem specific to Mendelian randomization, but refers to a more general problem of weak instruments see e.g. .Assumpti2.4conditional independence and exclusion restriction are more likely to be valid. A second reason for including covariates in many economics and social applications of IV is that it may reduce the residual variability of the dependent variable, leading to more precise estimates.There is a large literature on the use of covariates in IV. Economics and social applications of IV generally include a wide set of control variables; the main motivation being that the conditional independence assumption. The inclusion of further baseline covariates may in addition increase the precision of the estimates. In Mendelian randomization studies, however, there are no baseline covariates. Furthermore, as covariates do not enter the assignment mechanism, assignment is independent of covariates, and we can rely on the unconditional independence assumption. Therefore, conditioning on covariates is not necessary in Mendelian randomization experiments. The exception, however, is when there is population stratification. In this case, the analyses should be done within population subgroups, or should adjust for principal components from genome wide data, relying on the conditional independence assumption.The situation is somewhat different, however, in RCTs/encouragement designs, and in Mendelian randomization studies. When covariates enter the assignment mechanism in RCTs/encouragement designs, such as when randomization takes place within certain strata, these covariates should be controlled for, relying on the which covariates to include in a Mendelian randomization study, as any characteristic is, in principle, a post-treatment variable with respect to the instrument, and – with that – may be affected by the instrument. If the instrumented treatment has multiple causal effects, or if the outcome has a causal effect of its own, adjusting for such post-treatment variables may lead to biased estimates of the causal effect. Indeed, we should not control for any ‘downstream’  covariates that are potentially affected by the treatment or outcome. Thus, we only control for 10 ancestry-informative principal components in our main analyses, though we report the estimates that adjust for further covariates in the sensitivity analysis. Under independence, and when the instrumented treatment and outcome do not affect these covariates, the unadjusted and adjusted IV estimates should be similar, though the latter may be more precise.Although one may choose to adjust for covariates to increase precision, this raises the issue of 2.5direct test for the validity of the exclusion restriction .Similar to other IV studies that use multiple instruments, however, Mendelian randomization allows for potential violations through pleiotropy or LD  to be tested when data is available on a large number of genetic instruments. More specifically, if multiple IV models – each using different combinations of these variants – predict the same causal effect, it is unlikely to be due to some common pleiotropy or LD across the different sets of variants, assuming that the different variants are located on different chromosomes and affect the trait via different pathways . Hence, Alternatively, one can view Mendelian randomization with multiple instruments as analogous to a meta-analysis of separate study results. Just like the IV estimate using multiple instrumental variables is a weighted average of the individual IV estimates, a meta-analysis is a weighted average of multiple studies. In a constant effects model, one can indirectly test whether the exclusion restriction holds using an ‘over-identification’ (Sargan or Hansen) test , provideNote that, although canalization refers to a violation of the exclusion restriction, it cannot necessarily be tested using over-identification tests. Similar to the above, a rejection cannot distinguish between treatment effect heterogeneity and canalization. In fact, there is no (clear) way of testing or correcting for canalization. However, for the complex traits that are largely of interest in Mendelian randomization studies, there is no evidence that canalization occurs in humans .2.6DAT1) and D2 receptor (DRD2), tryptophan hydroxylase (TPH) and cytochrome P4502B6 (CYP2B6). DAT1 and DRD2, their instruments include the dopamine D4 receptor (DRD4), the serotonin transporter (5HTT), monoamine oxidase (MAOA) and cytochrome P4502A6 (CYP2A6). Finally, DAT1 and DRD4 as instruments for BMI and find no evidence of a causal association.The existing economics literature includes three studies that exploit genetic variation to identify the effects of BMIon economic outcomes. The discussion in Section prior knowledge about the association between the genotype and risk factor. The choice of instruments in the studies cited above, however, seems to be data-derived: using either forward stepwise estimation  or selecting those SNPs that have nominally statistically significant sample correlations in the first stage (Fletcher and Lehrer). Furthermore, both Ding et al. and Fletcher and Lehrer acknowledge that there is weak and inconsistent evidence in the medical literature, based on very small unrepresentative clinical samples, of the association between their genetic variants and health status or behaviours. Indeed, the IV strategy is invalid when relying only on such sample associationsand leads to biased results  of England. Women eligible for enrolment in the population-based Avon Longitudinal Study of Parents and Children (ALSPAC) had an expected delivery date between 1 April 1991 and 31 December 1992. Approximately 85% of these mothers enrolled, leading to about 14,000 pregnancies. The Avon area has approximately 1 million inhabitants and is broadly representative of the UK as a whole, though slightly more affluent than the general populationA total of 12,620 children survived past the age of 1 and returned at least one questionnaire. Of these, we exclude 642 children because either their mother or father is of non-white ethnic origin , leaving 11,978 potential participants. Our sample selection process is as follows. First, we select children for whom we observe their genotypes and 10 ancestry-informative principal components, leaving us with 7335 children. Second, we drop children with missing data on fat mass. We further restrict the sample to children for whom we observe their educational outcomes and blood pressure, leading to a final sample size of 4844 and 4047 children, respectively.Attrition in the ALSPAC cohort is known to be correlated with socio-economic position, with children from lower educated, lower income families more likely to drop out . Attriti3.2Our first outcome measure is the child's Key Stage 3 (KS3) score. The KS3 exam is a nationally set exam, taken by all 14-year-olds in English state schools. This measure of children's performance is therefore objective and comparable across all children. Their scores for three subjects  are obtained from the National Pupil Database, a census of pupils in England in the state school system, which is matched into ALSPAC. We use an average score for the three subjects, standardized on the full sample of children for whom data is available, with mean 100, standard deviation 10.Our second outcome measure is the child's blood pressure, measured in millimetres of mercury (mmHg) at age 13. We observe both systolic (maximum) and diastolic (minimum) blood pressure, measured by trained nurses. Blood pressure was measured twice at the clinic; we use the average of the two readings to reduce measurement error.Our main measure for child fat mass, our risk factor of interest, is the child's body fat mass , as measured by a dual-energy X-ray absorptiometry scan (DXA) at age 11. As fat mass is measured two to three years prior to the outcomes of interest, this avoids potential problems related to reverse causation. The DXA scan scans the whole body, dividing it into fat, lean tissue, and bone mass. We standardize fat mass on the full sample of children for whom data are available, with mean 100 and standard deviation 10.For the genetic variants, we use 32 SNPs that have been consistently found to relate to body weight and fat mass  are known to vary by ethnic group  size that is related to their genotype. Hence, it is unlikely to observe any strong responses to increased body weight, such as changing (children's) diets. However, the question remains whether there are any more subtle responses to higher body weights. As it requires large sample sizes and data on different parental preferences and behaviours to explore that in detail, one cannot say with complete certainty that behaviours are unaffected. Nevertheless, we explore this indirectly in our data, testing whether mothers’ behaviours or characteristicsUsing a total of 249,796 individuals from 64 different cohorts of European ancestry, FTO, MC4R) are associated with an increased consumption of fat and energy  our outcomes of interest or its determinants. More specifically, data from the International HapMap Project show that the SNPs that replicate in a large number of independent samples for educational attainment  and blooFourth, for canalization to violate the exclusion restriction, the presence of the fat related variant at conception would have to result in different brain or blood vessel development in order to counter any predicted adverse effect of fat mass on the outcome. We believe this is implausible. Furthermore, there is no evidence in humans that canalization occurs in relation to complex traits such as fat mass.Assumption 3The prior findings of robust associations between the genetic variants and fat mass, replicated in a large number of studies, justify their use as instruments. Using standard statistical tests, we will examine the strength of our instruments in the application below.Assumption 4Finally, with random allocation of genetic variants and the fact that individuals do not know their genotypes, we assume that an individual who carries the risk allele is at least as heavy as the same individual, had she not carried the risk allele, satisfying monotonicity. Although we do not observe individuals’ counterfactuals, the literature tells us that, at a group or population level, those who possess the genetic variants are heavier than those who do not.In summary, we do not know individuals’ behavioural response to their genotype, the specific physiological functions or biological pathways through which the variants affect the phenotype, and whether the variants have multiple phenotypic effects. With that, it is impossible to guarantee that As monotonicity can be violated by gene–environment interactions, we examine this in two ways. First, we explore the issue of such interactions indirectly, testing whether the association between fat mass and our instrument differs in different ‘environments’. Although one can never observe all potentially relevant gene–environment interactions, we explore the importance of a set of environments that have been shown to be important for child development, defined by gender, the child's birth weight, breastfeeding duration, social class, mother's education, income and deprivation. The results (presented in Table S3 in the Web Appendix) show little evidence of gene–environment interactions.FTO and physical activity, though only for adults: for the physically active, the FTO risk allele increases the odds of obesity less than for the physically inactive. They do not find such interaction for children. Using a sample of around 170,000 individuals, a recent study explores whether genetic variants explain the variance of BMI . They conclude that there are no common genetic variants that account for a large proportion of variation in environmental or phenotypic variability, finding no evidence of widespread gene–environment interaction effects for BMI  and 69 (blood pressure) suggests the instrument is strong. Translating the effect size into body weight, a one standard deviation increase in the allelic score increases weight by around 1.3 to 1.5 kg, though the exact amount will depend on which alleles are carried by the individual, as there is much heterogeneity in the variants’ effect sizes on adiposity. For example, each risk allele of FTO – the variant that has been shown to have the largest effect size – increases body weight by approximately 1 kg for an average 11 year old, whereas the effect size for GNPDA2 increases body weight by just over 300 g.Panel B presents the first-stage regression results, showing a strong positive relationship between the instrument and child fat mass. The strength of the relationship is shown by the first stage p-value of 0.054 for the Hausman test, there is some support for the IV as opposed to the OLS estimate, though any such judgement should be based on a synthesis of all the evidence, rather than on this one test alone.The second stage IV results are presented in Panel C. Colum 1 shows no effects of fat mass on educational performance. Although the IV estimate is of similar magnitude but opposite sign to that in Panel A, the large standard errors preclude us from rejecting the null of no effect. However, with a Column 2 and 3 show a positive effect of fat mass on both systolic and diastolic blood pressure, with an estimate that is somewhat larger than the OLS estimates in Panel A. The estimates suggest that a one standard deviation increase in fat mass increases systolic and diastolic blood pressure by 0.37 and 0.21 mmHg respectively, though the Hausman test suggests that there is insufficient evidence to reject the hypothesis that the OLS estimate is unbiased.3.6We next report a set of sensitivity analyses, evaluating the robustness of the results. First, we use different specifications of the instrument. We start by specifying the 28 mutually exclusive instruments, indicating the number of adiposity-increasing alleles carried by each child. Panel A of F-statistic, the results are similar.Panel B of FTO and MC4R, the two variants that account for the largest proportion of the variation in fat mass, as the instrumental variables. The estimates are similar, suggesting that the findings are not sensitive to the definition and specification of the instrumentsAs discussed in section 3.3, some of the variants in our analyses have been shown to associate with other, non-adiposity related, phenotypes, such as asthma and schizophrenia. In Panel E, we re-estimate the IV model with the weighted IV score that drops these variants (see Web Appendix) from the instrument set. In addition, Panel F shows the estimates using only F-statistic of approximately 8, 4 and 3 in Panels A, B and C of k (with k = 1). The critical values in F-statistic of 8.3, the size distortion in LIML is less than 10%, and Fuller has a relative bias that is less than 5%. We present the LIML and Fuller (1) results for our specification with the largest number of instruments , their imprecision means we cannot reject the null of no effect. For blood pressure (columns 2 and 3), the estimates confirm that being underweight substantially decreases both systolic and diastolic blood pressure, whilst being overweight leads to an increase.Third, we explore different definitions of the variable of interest: fat mass. As we discuss in the introduction, obese children may have different educational outcomes due to sleep disorders, school absenteeism, or differential treatment by teachers, parents and peers. This would suggest that there may be non-linearities. Hence, it is of interest to study whether there are substantially different effects on education and blood pressure for underweight and overweight children. We examine the child's underweight and overweight status in the IV analysis, defined as being in the bottom and top 15th percentile of the fat mass distribution respectively. We show the results using the (unweighted) allelic score as our instrumental variable, though they are robust to using the different instrument specifications. The results are presented in Next, we explore the existence of heterogeneous effects of fat mass on KS3 and blood pressure by gender. It may be, for example, that girls are more affected by potential peers’ differential treatment related to their adiposity than boys. Finally, we examine the robustness of the estimates to the inclusion of different sets of covariates. As we argue in Section 4Economists have become increasingly interested in the effects of behaviours such as smoking, drinking or excessive food intake on economic outcomes. As these behaviours are endogenous and difficult (if not impossible) to randomize in an RCT, estimating their effects is difficult. Many studies therefore attempt to find instrumental variables, or exploit some natural experiment that shifts the behaviour for some group, but not others, to identify their causal impact. The increasing availability of biomedical data, in combination with a growing medical literature on the effects of carrying specific genetic variants, introduces a different approach to the examination of certain risk factors on different outcomes. This paper discusses the method of instrumental variables using Mendelian randomization, and links this to the statistical potential outcomes framework. Mendelian randomization provides a novel approach to estimating the causal impact, and with that will be of interest to economists to explore.We note that its suitability and applicability depends on a set of  conditions, as well as on the research question and context. We discuss the specific conditions that need to be met for genetic variants to be used as instruments, and relate these to the statistical assumptions necessary for identification of the average causal response using instrumental variables. These conditions have not been well defined in the current social science literature, but understanding them is crucial to the appropriate use of genotypes as instruments for modifiable risk factors.We review these conditions in the context of two empirical applications. First, we examine whether child fat mass causally affects academic achievement, and second, we study whether it affects blood pressure. To study the effect of adiposity on our outcomes of interest, a well-conducted RCT would randomize an intervention that reduces fat mass and compare the outcomes between the group that was treated and the control group. Randomizing adiposity, however, is difficult. We show that, in such cases, quasi-experimental designs such as Mendelian randomization experiments can provide an interesting alternative approach. We use a set of 32 recently identified genetic variants as instrumental variables for fat mass to illustrate the key concepts. In these illustrative examples, we show the systematic approach required to identify genetic variants as instruments. We also use direct measures of fat mass, rather than the generally used BMI. OLS shows that leaner children perform better in school tests compared to their fatter counterparts, and that fatter children have higher blood pressure. Our genetic IV analysis, however, shows no evidence that children's fat mass affects their academic performance, whilst we find that fat mass increases children's blood pressure.Our discussion of the conditions for the suitability of genetic variants as instrumental variables and our application raise some more general issues of the use of genetic variants as instruments. First is the question whether genetic variants are powerful enough to identify causal effects. In the illustrative case we examine, while our instruments are not weak in a statistical sense their effects may be too small to impact on the possible pathways to academic performance. In other words, a 1–2 kg increase in fat mass may not lead to a large drop in self-esteem or an increase in absenteeism. It is, therefore, perhaps not surprising that we find no significant effect on academic performance. In contrast, our results on blood pressure show strong evidence of an increase driven by elevated fat mass. As intervention studies of weight reduction  count of the number of risk alleles. This could increase the explained phenotypic variation and with that, the precision of the estimates. But for the type of physical attributes that economists have been interested in such as fat mass or height, any additional variants are likely to have even smaller effects than those already identifiedHence, if small changes in the risk factor are sufficient to shift the outcome of interest, Mendelian randomization presents an interesting approach. However, if the outcome of interest is only affected by large changes in the risk factor, Mendelian randomization may not be sufficiently powerful, as genetic variants generally shift the risk factor by a relatively small amount. This is particularly relevant for studies in economics, which are often interested in the effects of different intermediate phenotypes  on economic outcomes. In contrast to various examples in the medical literature, finding effects on such A second issue is the credibility of the IV assumptions. Some of these are testable, but others are not. In particular, the validity of the exclusion restriction cannot be tested, and will never be known with certainty, which makes Mendelian randomization a controversial approach within the economics literature. Our paper has discussed this in detail and highlighted the various ways through which the use of genetic variants as instrumental variables may lead to invalid inferences. With our limited understanding of the functions of variants and the pathways through which they affect outcomes, it is unlikely that we will understand their exact function and mechanism in the foreseeable future. Hence, we argue that genetic variants need to be used with care. Their appropriate use requires that several conditions, which have not hitherto been spelt out in the economics literature, are met. However, even if these conditions are met, the sample sizes in data sets that contain both genetic markers and outcomes of interest to economists may be too small to obtain definitive results. Indeed, even with around 4000–5000 observations, our standard errors are relatively large. But with a rapid increase in the number of genome wide association studies, and with a decrease in their costs, this may change. Finally, just as there are good and poor RCTs and studies using any other identification design and methodology, there are good and poor Mendelian randomization studies. By highlighting the potential problems and showing the systematic approach required to identify genetic variants as instruments, we attempt to steer others to carefully consider the different assumptions and conditions needed for valid inference before jumping to their use.Economic and Social Research Council (RES-060-23-0011 and PTA-026-27-2335), the MRC (G0601625 and G1002345), and the European Research Council (grant 269874—DEVHEALTH) is gratefully acknowledged.The UK Medical Research Council (MRC), the Wellcome Trust and the University of Bristol provide core support for ALSPAC. This publication is the work of the authors, who will serve as guarantors for the contents of this paper. Funding from the