O. sativa). The architecture of the rice inflorescence which is mainly determined by the length and number of primary (PBL and PBN) and secondary (SBL and SBN) branches can influence NSP. Although several genes controlling panicle architecture and NSP in rice have been identified, there is little evidence of (i) the genetic control of panicle architecture and NSP in different environments and (ii) the presence of stable genetic associations with panicle architecture across environments. This study combines image phenotyping of 225 accessions belonging to a genetic diversity array of indica rice grown under irrigated field condition in two different environments and Genome Wide Association Studies (GWAS) based on the genotyping of the diversity panel, providing 83,374 SNPs. Accessions sown under direct seeding in one environement had reduced Panicle Length (PL), NSP, PBN, PBL, SBN, and SBL compared to those established under transplanting in the second environment. Across environments, NSP was significantly and positively correlated with PBN, SBN and PBL. However, the length of branches (PBL and SBL) was not significantly correlated with variables related to number of branches (PBN and SBN), suggesting independent genetic control. Twenty- three GWAS sites were detected with P ≤ 1.0E-04 and 27 GWAS sites with p ≤ 5.9E−04. We found 17 GWAS sites related to NSP, 10 for PBN and 11 for SBN, 7 for PBL and 11 for SBL. This study revealed new regions related to NSP, but only three associations were related to both branching number (PBN and SBN) and NSP. Two GWAS sites associated with SBL and SBN were stable across contrasting environments and were not related to genes previously reported. The new regions reported in this study can help improving NSP in rice for both direct seeded and transplanted conditions. The integrated approach of high-throughput phenotyping, multi-environment field trials and GWAS has the potential to dissect complex traits, such as NSP, into less complex traits and to match single nucleotide polymorphisms with relevant function under different environments, offering a potential use for molecular breeding.Number of spikelets per panicle (NSP) is a key trait to increase yield potential in rice ( Growing world population and the effects of global climate change are increasing the demand for higher crop yields. To meet rice demand in 2050, annual increase production has to increase from the current 1–2.4% by 2050  covering improved and traditional varieties from all tropical regions. For the present study, the association mapping panel consists of a sub-sample of 225 indica accessions obtained from the International Rice Research Institute (IRRI) seedbank. Among the 225 accessions, 51 originate from Africa, 12 from South and Central America, 120 from South Asia and 42 from West and East Asia (Table The population studied represented the diversity within the indica sub-species (ia Table .The experiments were conducted under irrigated conditions during the dry season (May to August) in CIAT Palmira . The experiment was established under transplanting conditions (Exp1 TR) in 2013 and under direct seeding (Exp2 DRS) in 2014. For both experiments, the soil was a silt-loam soil with particle distribution of 10% clay, 80% silt, and 10% sand. The experimental design was a randomized complete block design with 3 replications and 225 plots. The 225 accessions were sown at the same time and grouped by previously estimated maturity date and plant height to facilitate measurements.2. Plots were maintained under lowland conditions with a water depth of 5 cm, after transplanting until 2 weeks after flowering. Phosphorus and potassium were applied at 59.8 kg ha−1 P2O5 and 116.6 kg ha−1 K2O. A total of 207.4 kg ha−1 N, 20.8 kg ha−1 Fe, and 2.8 kg ha−1 Zn was applied. The top soil contained 27.5 g organic C kg−1 and 1.3 total N kg−1 with pH 8.2.In 2013, seeds from the 225 accessions were sown in plastic trays and seedlings transplanted, 20 days after emergence, at one seedling per hill with a hill spacing of 0.2 × 0.2 m. Plot size was 3.0 × 0.6 m, for a plot density of 25 plants/m2. Sprinkler irrigation was applied after sowing. Fertilizers used were 145.9 kg ha−1 of N, 40.5 kg ha−1 P2O5, 17.6 kg ha−1 Fe, and 2.8 kg ha−1 Zn. Twenty days after sowing the field was maintained under lowland condition with a water depth of 5 cm, until 2 weeks after flowering. The top soil contained 20.5 g organic C kg−1 and 1.18 total N kg−1 with a pH 7.5.In 2014, mechanical sowing was done in dry soil with a plot size of 3.0 × 1.0 m and a plot density of 80 plants/mFor both experiments weeds were controlled manually, and by herbicide applications at pre and post-emergence.Weather data was collected daily, at one-meter distance from the experimental trial, and with a 30 min time step in a data logger connected with radiation (silicon pyranometer sensor (S-LIB-M003), temperature and humidity sensors (S-THB-M002) . Average solar radiation, minimum and maximum temperature, minimum and maximum humidity for each experiment are presented in supplementary table Table .In both experiments, the main stem of two plants in each plot was tagged 30 days after sowing. At flowering tagged stems were harvested with its respective panicles. Each panicle was spread out on a white background and held in place with metal pins under a sticky paper. A total of 1350 panicles were dissected using P-TRAP software   Table .www.R-project.org).The descriptive analysis and analysis of variance were performed with SAS v9.3  with PROC MEAN and PROC MIXED, respectively. ANOVA test was applied considering genotype as fixed effect and block and group as random effect. Means were adjusted for blocks and group factor. Histograms of frequency distribution were conducted with PROC SGPLOT and broad-sense heritability was computed using PROC MIXED model in SAS. Pearson correlation was performed using R v3.1.2 (The panel included in this study is a subset of 329 indica accessions that were genotyped using the genotype by sequencing (GBS) protocol  ≥ 0.05 and observed heterozygosity ≤ 0.01  was applied involving a kinship matrix as a random effect generated using the pairwise identity by state distance implemented in TASSEL v5.2.8.www.R-project.org).Plots representing GWAS results (Manhattan and Quantile-Quantile plots) were performed using the packages QQman in R 3.2.2  were considered as a unique region and defined as a GWAS site. To identify genes potentially linked to the detected SNPs, we used the gene database Gramene, a comparative resource for plants (www.gramene.org).Significance threshold for association detection was set to p < 0.001) for all measured variables between both experiments   Table . The hig1) Table .p < 0.001) correlated with SBN, (iii) PBL was positively and significantly (p < 0.001) correlated with SBL, and (iv) PBL was significantly (p < 0.001) and positively correlated with SBN.Correlations between variables showed similar patterns for Exp1-TR and Exp2-DRS Table : (i) PL Interestingly, PBN was not significantly correlated with PBL, and SBN was not significantly correlated with SBL in any experiment. Suggesting that, considering the same rank of branching, greater branch number was not associated with greater branch length.Secondary branches originate from primary branches therefore it was not surprising that PBL was significantly and positively correlated with SBN Table .p < 0.01) related to both the number and length of branches  within both Exp1-TR and Exp2-DRS; but no significant correlation was observed between NSP and SBL (Table p < 0.05). Since NSP was not significantly correlated with PL, PL was not considered for the GWAS study.NSP was positive and significantly , and 19 GWAS sites were associated with the number of branches . NSP collocated with panicle architecture variables only in the cases of SBN in Exp2-DRS (q-9) and PBN in Exp1-TR q-43)  a gene controlling floral organ identity and flowering time was located within the LD block of q-25 associated with NSPexp1. Osmads6-5 and Lax genes affecting the number of spikelets per panicle and the number of branches were within the LD block of q-12 and q-7 respectively and associated with SBLexp1. Osmads5 was within the LD region of q-27 associated to SBNexp1, OsJAG gene which has a known function on the development of the panicle and the number of spikelets per panicle was near q-1 in chromosome 1 position 1.626.152 bp and associated with PBL in Exp2. Finally, Jmj6 controlling the number and morphology of reproductive organs was within the LD region of q-44 associated with PBNexp1. One GWAS site q-14 was near a gene controlling flowering time, SBLexp1 in chromosome 3 was within the LD block of the gene OSMADS50.Six GWAS sites associated with panicle architecture and the number of spikelets per panicle were located within the LD distance of 6 genes related to floral organ formation Table . NECKLEAThree GWAS sites q-6, q-23, q-26, q-28 associated with the number of spikelets per panicle or the number of primary branches were within the region of genes controlling plant nutrient status . Genes controlling plant size were within the LD region of GWAS sites associated with NSP or with SBL . The sites q-2, q-3, q-17, q-20, q-36, q-37 were within the LD regions of genes controlling grain size, pollen development or seed starch content suggesting a linkage between the genetic control of panicle architecture and grain formation.Therefore, for all the panicle traits dissected with image analysis , we found significant associations at sites where known genes with relevant function were reported.Thirty one GWAS sites were associated with variables measured in Exp1-TR and 17 GWAS sites were associated to variables measured in Exp2-DRS. Only 2 GWAS sites, namely q-13 and q-46 were detected in both experiments  the role of each panicle architecture component trait and their mutual compensations, (ii) the genetic architecture of panicle component traits, and (iii) the stability of the panicle component traits across contrasting environmental conditions.The present study combined image analysis, GWAS and field trials under contrasting management conditions (transplanting vs. direct seeding) for the phenotypic and genetic dissection of the number of spikelets per panicle in rice. It was expected that the phenotyping of panicle architecture traits would provide further insight into trait-trait correlations and trade-offs defining the total number of spikelets per panicle, while the analysis of two contrasting conditions would provide insights into environmental and genetic control.New open access image analysis tools such as the one used in this study  and length (SBL) of secondary branches. Previous studies reported a positive correlation between SBN and NSP  were not significantly correlated with variables related to the length of branches (PBL), suggesting two independent ways to increase the NSP, either with a high number of branches or with long branches, involving trade-offs between them. The number of spikelets per panicle can be increased; either by increasing the number of branches  were significantly and positively correlated with PL under both environmental conditions. This suggest that PL is not a simple trait and can be affected in a given genotype, by several component traits  that are physiologically interacting and may involve environment dependent trade-offs. Thus, the low correlation observed between PL and NSP in this study can be explained by the effect of the growing conditions on PL and/or the different ways a genotype can achieve a large number of spikelets per panicle (either with long panicles or with short but dense panicles).p < 1.00 E−4) with panicle architecture traits. Furthermore, SNPs with high association probabilities were more likely to be close to previously identified candidate genes, e.g., Osjag in q-1 and OsCKX2 in q-3 with p values of 7.70E−5 and 1.54E−5 respectively. Besides, image analysis allowed us to measure new variables, such as SBN, that were related with the number of spikelets per panicle and associated with new GWAS sites, some of which related with known genes . Thus, this GWAS study identified many true genotype-phenotype associations, and detected GWAS sites that were associated to already known genes with a highly significant effect on the number of spikelets per panicle  compared with other studies  or floral organ identity  and two genes with a function on tillering ability  or carbon and nitrogen content .Globally, in our study only 14 GWAS sites out of 50 were significantly associated with NSP only. Four out of the 14 GWAS sites for NSP were related to known, cloned genes; two GWAS sites were associated with genes with a function affecting panicle density  but did not have a significant effect on NSP. This result supports the idea that the length of the branches has a smaller effect on the number of spikelets per panicle (Ando et al., Site q-46 was also stable in Exp1-TR and Exp2-DRS and controlled both SBN and NSP. Thus, new variables measured in this study using image analysis led to the discovery of new genetic regions with a significant effect on NSP across two different rice growing conditions.Hence, despite the strong environment effect, some genomic regions associated with multiple traits point to the potential for improvement of yield potential through increased number of spikelets per panicle for both transplanting and direct seeding conditions. But overall, it appears that molecular breeding for increased NSP can build on more relevant loci when targeting a specific environmental and cultural practice.MR designed the project, MR and AP analyzed and interpreted the data, also they wrote the manuscript. MD led the GRiSP Global Rice Phenotyping Network which this study was part of. All authors made important intellectual contributions. JD and DC performed the bioinformatic analysis of the GBS data.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.


Dogs were followed-up for 3 years after birth, classified regarding their CHD phenotype using the scheme of the Fédération Cynologique Internationale, and genotyped for the 17 single nucleotide polymorphisms (SNPs) constituting the CHD test in question. Individual SNP genotypes were combined into animal-specific genomic breeding values (GBVs), calculated as the weighted sum of SNP-wise scores as laid down in the patent specification. Logistic regression analysis revealed that, unexpectedly, the odds ratio for CHD decreased, rather than increased, by a factor of 0.98 per unit increase of the GBV. Nevertheless, since this effect was not statistically significant (95% CI: 0.93–1.03), and the area-under-curve of the test was only 0.523, it must be concluded that the genetic test patented by Distl et al. (2009) is unsuitable for individual CHD risk assessment.Genetic testing has been propagated as a suitable means to specify individual risks for canine hip dysplasia (CHD). However, the current lack of validation of most genetic CHD tests has left dog owners and breeders in the dark about their practical utility. Therefore, the Society for German Shepherd Dogs  initiated a prospective study of 935 animals to assess independently the value of a genetic CHD test (European Patent Specification EP 2 123 777 B1) that was developed by Distl  Traditional classification of canine hip dypslasia (CHD) is reliant upon phenotypic assessment, namely by radiography and Norberg-Angle measurement, of the hip joints of full-grown animals. Drawing upon the outcome of these examinations, most European breeding organizations have adopted a classification scheme established by the Fédération Cynologique Internationale (FCI) that specifies five grades of CHD severity (A-E). Class A corresponds to dogs with no signs of hip dysplasia whereas class E indicates presence of severe hip dysplasia. The classification process is laborious and costly but currently represents the only means to acquire useful information for animal selection aimed at reducing the incidence of CHD.Breeding registers gather data from confirmed pedigrees and combine the CHD classification of individual animals with that of close relatives to yield so-called ‘estimated breeding values (EBVs)’. EBVs are specific to a phenotypic trait of interest and express the genetic merit of a given animal in units of that trait, relative to a certain base. For selection purposes, the absolute value of an EBV is usually not important but rather the differences in EBV between animals. An EBV-based selection program to combat CHD was started in 2002 by the Society for German Shepherd Dogs  for all their stud animals. Phenotype evaluation has been mandatory in the program if studbook-documented breeding was aspired to, and only dogs rated grade A to C got unrestricted breeding permission. Among the dogs enlisted in the EBV-based selection program, the prevalence of CHD class A animals had increased from 62% to 75% by the end of 2016.et al.  of the patent contains a description of how to use the markers and GBVs to predict CHD in the prospective offspring of pairs of genotyped dogs as well. To this end, the patent proposes calculation of the probabilities of all possible offspring genotypes, assuming Mendelian inheritance, followed by subjecting the potential offspring genotypes to the same CHD risk assessment as described for experimentally determined genotypes. The weighted average of these genotype-specific risks is then taken as the overall CHD risk of prospective offspring. Since the same method of CHD risk assessment is used in both instances, however, the feasibility of risk calculation for prospective offspring would require, at the very least, the feasibility of risk calculation for singletons.Over a period of three years (2012–2015), a total of 1110 purebred German Shepherd Dogs from the SV breeding population were included in the study. To qualify for participation, dogs had to have a starting age of 12 to 15 weeks at that time of inclusion, and the dog owner had to commit themselves to filling out a monthly questionnaire until the animal reached 15 months of age. A maximum of two dogs per owner were included to ensure population representativeness. Animals were radiographed by SV-approved veterinarians when the dog was 12 months or older, and a blood sample was taken. The timing of these examinations was exactly as in the original association study that led to both, the identification of the patented marker set and the development of the GBVs . RadiogrBy drawing upon data that would have been generated anyway, the study aimed at avoiding any unnecessary interference with the well-being of animals. SV members were informed about the study and its design through SV-internal media. Participation in the study was on a strictly voluntary basis and consent was obtained for any necessary processing of personal data (i.e. for study registration and filling-out of the online questionnaires). All animal work, including immobilization, radiography of hip joints and blood sample collection for DNA typing was part of the regular CHD/CED assessment for breeding capability and was not carried out for the purpose of the study. All animal treatment was conducted by trained veterinarians from an SV-accredited pool of experts. This approach obviated the need for explicit ethics committee approval.PCR primers for the amplification of 17 CHD-associated markers were designed according to the specification of patent EP 2 123 777 B1 . However™ 1-Step DNA Isolation Systems kit  according to the manufacturer’s protocol. The identity of each DNA sample was verified in the course of the routine SV program for DNA profiling and paternity analysis. Purified DNA was SNP-genotyped using KASP™ technology . For each of the 17 CHD-associated SNPs, DNA was added to a KASP assay mix containing two allele-specific primers and a common reverse primer. Sample DNA was stored in 96 well master plates and daughter plates were prepared for each marker for genotyping. KASP assay master mix was added by automated pipetting.DNA was isolated from EDTA blood samples using the nexttecPrior to its use in the present study, each KASP assay was tested for its genotyping accuracy by a comparison of assay-derived genotypes with the results of direct Sanger sequencing. To this end, controls were included on each plate that had been genotyped for all CHD markers before by Sanger sequencing. To bolster the trustworthiness of KASP typing even further, a mutation in the SOD-1 gene associated with degenerative myelopathy  was alsoAll animals in our study were genotyped for the 17 SNPs listed in www.medcalc.org). Logistic regression analysis was carried out, and the area-under-curve (AUC) determined for predictive models, with SAS procedure LOGISTIC. Box plots were prepared with SigmaPlot 8.02 .Differences in terms of GBV or GBV(S) between different phenotypic groups were assessed for statistical significance using a Kruskal-Wallis test as implemented in SAS 9.4 procedure NPAR1WAY . Odds ratios (OR) and relative risks  were estimated using the MedCalc software . Virtually identical results were obtained for GBV(S) (data not shown). In the case of CED, the results were also negative as expected in that the median GBV was 1.378 (IQR: 3.090) for affected and 1.320 (IQR: 3.670) for unaffected animals .As was to be expected owing to the order-preserving nature of standardization transformations, no notable differences in terms of GBV or GBV(S) were observed between affected and non-affected animals for either disease. Thus, the median GBV value was equal to 1.018 (inter-quartile range IQR: 4.055) among dogs diagnosed with CHD, compared to 1.442 (IQR: 3.346) in the unaffected group. Contrary to expectation, the genomic breeding value GBV, which is supposed to be positively correlated with CHD risk, was therefore decreased rather than increased in affected animals, although the difference between the two groups was not statistically significant . Moreover, the AUC of the predictive test based upon the logistic-regression-derived CHD risk amounted to a minuscule 0.523.post hoc AUC: 0.622) for severe CHD, but only after inverting the interpretation of the test result.Upon closer inspection of the relationship between the phenotypic classification and GBV, a notably negative trend became apparent for CHD , but notIn view of the poor performance of GBV and GBV(S), we tried to develop a post hoc predictive model for CHD, based upon the genotypes available for the 17 SNPs in question. To this end, each marker genotype was encoded by a combination of two variables, namely the dosage of the respective CHD-associated allele  and a covariate for the dominance effect equal to 1 for heterozygotes and 0 for homozygotes.2 = 5.794, 1 d.f., p = 0.016) and TiHo26 . The estimated OR per HD-associated allele was 0.78 (95%CI: 0.61–0.95) for TiHo25  and 1.41 (95% CI: 1.14–1.75) for TiHo26 . No other significant additive or dominance effects were observed. The post hoc predictive utility of the final model was however found to be poor (AUC = 0.567).Even the full predictive model including all additive and dominance effects of the 17 markers yielded only minor predictive utility for CHD (AUC: 0.610). Stepwise selection of predictors as implemented in SAS procedure LOGISTIC, and employing a significance threshold of 5%, the final model comprised only the allele dosage of markers TiHo25 , with an estimated per-allele OR of 0.54 (95%: 0.33–0.88). In addition, two highly significant dominance effects were observed, namely for TiHo12  and for TiHo18 . Taken together, the three genetic risk factors yielded moderate to high predictive utility (post hoc AUC: 0.793). The two dominance effects were indeed remarkable. Whilst none of the 21 wild-type homozygotes for TiHo12 and only 9 of the 660 homozygotes for CHD-associated allele T developed severe CHD, this was true for 16 of 254 heterozygotes. Considered post hoc, this would imply a relative CHD risk of 4.77 (95% CI: 2.13–10.65) for genotype TC. For GC heterozygotes at marker TiHo18, a relative CHD risk of 2.94 (95% CI: 1.28–6.75) became apparent.An analogous analysis carried out for severe CHD (class 5) also included the allele dosage of TiHo25 in the final model , a prognostic study was therefore performed to investigate the predictive capability of the patented SNP panel for CHD in a large, independent and population-representative sample. The primary intention of the study was to assess the capability of the SNPs to predict individual CHD development. An extension covering the prediction of CHD in the offspring of genotyped dogs was scheduled for after successful completion of the first study phase, but was later abandoned.In addition to the technicalities of the CHD-associated SNPs involved, the patent specification also contains instructions for calculating a standardized genomic breeding value ‘dev’ (here abbreviated as GBV(S)) from a given SNP profile, which in turn can be used to quantify the individual risk of developing CHD by gauging GBV(S) against a reference curve that was also included in the patent description. According to the instructions given, GBV(S) is expected to range from—0.5, reflecting the most beneficial genetic disposition, to +0.5 for animals at the highest disease risk. Such a range would result if the non-standardized breeding value GBV followed a symmetrical distribution. In our study, by contrast, GBV(S) was found to range from -0.613 to +0.387 owing to the pronounced skewness of GBV as observed in the data. Most importantly, however, neither GBV nor GBV(S) was found to bear any appreciable statistical relationship to phenotypic CHD.et al. [et al. [The utility of a predictive test with a continuous outcome such as, for example, GBV or GBV(S) can be assessed by way of the so-called ‘receiver-operating characteristic curve’ (ROC). The ROC relates the probability of true positive results to the probability of false positive results that would ensue from using distinct thresholds to dichotomize the test outcome. The AUC sensibly ranges from 0.5  to 1.0 (perfect prediction) and is independent of the prevalence of the disease in question. According to Janssens et al. , an AUC  [et al.  achievedconditio sine qua non of any practical use of tests exploiting such relationships. While emphasizing their potential usefulness, Wray et al. [With hindsight, our results may not have been surprising because, despite the uncontested prospects of genomic selection in livestock and plant breeding , the vasy et al.  also higy et al.  would haet al. [Instead of basing CHD prediction upon a small number of pre-selected markers, Guo et al.  proposedet al.  also suget al.  and therIn a three years prospective study of nearly 1000 animals, we have evaluated and shown invalid a prognostic, SNP-based test for canine hip dysplasia (CHD) that was patented  based upOur assessment of an alleged genetic test for CHD is the first systematic and independent attempt to validate a DNA-based predictive procedure meant for practical use in a non-human mammal species. In this respect, we regard our work as exemplary for the caution required towards any genetic test claimed to predict complex multifactorial traits in the field. Whatever evidence apparently underpins its predictive capability in the original report, a predictive test should be considered fit for practical use only after it has been tested successfully and independently in the intended target population.S1 Table(XLSX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.S1 Text(PDF)Click here for additional data file.


Mendelian randomization (MR) is a framework for assessing causal inference using cross-sectional data in combination with genetic information. This paper summarizes statistical methods commonly applied and strait forward to use for conducting MR analyses including those taking advantage of the rich dataset of SNP-trait associations that were revealed in the last decade through large-scale genome-wide association studies. Using these data, powerful MR studies are possible. However, the causal estimate may be biased in case the assumptions of MR are violated. The source and the type of this bias are described while providing a summary of the mathematical formulas that should help estimating the magnitude and direction of the potential bias depending on the specific research setting. Finally, methods for relaxing the assumptions and for conducting sensitivity analyses are discussed. Future researches in the field of MR include the assessment of non-linear causal effects, and automatic detection of invalid instruments. Observational epidemiological studies made important contributions to our understanding of common diseases by identifying important risk factors. Although causal inference is of major interest as it builds a basis for intervention and prevention, it is difficult to perform using observational data from cross-sectional studies. Supposed causality was often revised e.g., by randomized controlled trials (RCTs) . PossiblOn the other hand, RCTs are often subject to long duration and ethical problems. Furthermore, confounding and selection bias is still a problem after the initiation of a RCT. This includes compliance problems or missing of follow-up information depending on treatment effect which may induce missing not at random problems.During the last decade, huge efforts were undertaken searching for genetic risk factors underlying common traits and diseases. Genome-wide association studies (GWAS) revealed thousands of genetic associations predominantly based on single nucleotide polymorphisms (SNPs) including more than 950 related to cardiovascular diseases and measurements (by April 2018) and were made publically available , and thuX on an outcome Y using (one or more) genetic instruments Z for X  alleles.The general aim of the MR approach is the estimation of a causal effect of an exposure  Z for X . BasicalY and assuming linear effects between X and Y without interaction, the causal estimate of the exposure X on Y can be estimated through a 2-stage least squares (2SLS) regression. This method performs both steps described before implicitly. In the first step, the exposure X on Z. In the second step, the causal effect estimate Y on Z and tsls of the package SEM, or by the STATA software (https://www.stata.com/) using the command ivregress. The 2SLS was included in an MR of testosterone with cardiometabolic risk factors, but the single study analysis limited the statistical power substantially . By this means, genetic associations revealed through large-scale GWAS meta-analyses can be used as In contrast to the 2SLS which has to be performed using data of a single sample (one-sample MR), different sample sets can be used for conducting the triangulation: the effect estimates of the IV on exposure Y is dichotomous, i.e., an indicator of a disease status. In this case, log-linear effects without interaction on Y and an approximately normal distribution of X are required. Causal effect estimates on the odds ratio (OR) scale can be calculated by performing a logistic regression analysis using the disease as outcome. This model was also applied in most GWAS. To estimate causal OR using triangulation, the rare disease assumption  has to be fulfilled. Alternatively, estimates of a causal risk ratio may be calculated using a log-linear model instead of a logistic regression  confounder U of the exposure-outcome association. In the second step, a logistic regression of the outcome Y on X is performed, adding the residuals of the first step as a covariate to the model. By adding the residuals of the first step into the model, the effects of U on Y will be controlled. Thus, the effect of X on Y of the second regression corresponds to the causal effect estimate. In case a linear regression is conducted in the second step , the control function estimator is equivalent to the 2SLS estimator  of the exposure-outcome associationThe genetic variant is independent of factors (measured and unmeasured) that confound the exposure-outcome relationshipThe first condition is required because within the MR the (unconfounded) exposure will be estimated using the allele distribution of the IVs. This assumption can be easily tested, and is considered as fulfilled if the SNP-exposure association has an F-statistic >10 .GCKR exemplarily as instruments for kidney function to assess a causal effect on blood pressure would result in an invalid IV as there are effects of GCKR on blood pressure likely that are independent of kidney function, e.g., by the known associations of GCKR with serum lipid levels. Another violation would occur if the sample consists of a population substructure with different allele distributions, and which is also associated with the outcome. In this case, the substructure would be a common cause of both SNP and outcome opening a pathway from SNP to outcome not mediated by the exposure. Several examples of different scenarios violating the exclusion restriction are provided in the work of Glymour et al.  SNPs into a 2SLS model can increase the statistical power but might also increase the relative bias if weak instruments are added .Z is calculated per individual as the weighted or unweighted sum of the number of risk or trait increasing alleles iZ of each SNP i, whereas the effect X is used as weight:Alternatively, an allele score can be generated from the instruments and included as a single variable in the association model. This allele score  weights .metafor. Alternatively, the following simplification of this calculation can be used (A third method for taking advantage of multiple IVs is to combine ratio estimates (triangulation) of single instruments using inverse variance weighting . The met be used :gtx.with its approximated However, it is crucial that the effects of all IVs used in the calculation are corresponding to the allele referring to the same effect direction on the exposure . In theory, problems of missing data may occur especially when using multiple IVs. Nowadays well established methods for imputing missing genotypes based on the linkage disequilibrium structure of the human genome are available to circumvent this problem .U on exposure and outcome will not vary by chance but systematically because of the non-zero effect of the instrument Z on U. Thus, an increasing sample size will not remove the bias because mean implies that there is at least a partial effect of the instrument on the outcome not mediated by the exposure, i.e. αZY≠0 . Dependil+αZYβZX . The biaY are zero. However, it will be sufficient for the bias term to equal zero if all pleiotropic effects X  is zero. This independence between the genetic effects Pleiotropic effects equation  will resestimate . The pri the IVs .http://cnsgenomics.com/shiny/mRnd/. A tool for estimating statistical power of complex MR settings based on simulations is MR_predictor  GWAS sample size N, and its z-statistics z  through the formula . If the outcome is a binary trait, e.g., a disease with prevalence p in the sample, then When conducting two-sample MR, the causal effect corresponds to the unit of the outcome on a per unit change of the exposure that was used in the respective genetic association study of the IV with the corresponding trait . Some GW formula : β^≈ z⋅σMR provides a method for testing causality of different traits using cross-sectional data and genetics. Although large sample sizes are required to achieve sufficient statistical power for revealing causal effects, it is often possible to overcome this limitation by using the publically available genetic association results of large GWAS meta-analyses conducted during the last decade.TwoSampleMR, including the methods discussed in this article  , or to cThe methods summarized in this review assume linear effects between exposure and outcome (or log-linear in case of a binary outcome) without effect modifications by the variables. Addressing these limitations is subject to future research. A method for successfully revealing non-linear causal effects was provided in an example for alcohol intake on cardiovascular traits, but this approach is restricted to additional assumptions and limitations . With reAT designed and wrote the review.The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The purpose of this investigation was to determine the impact of heritability on third molar agenesis in twins. The study sample consisted of 284 same sex twins (172 monozygotic and 112 dizygotic), whose mean ages were 19.7 ± 4.3 and 18.9 ± 4.8 years, respectively. The monozygotic group consisted of 36.3% males and 63.7% females, while the dizygotic group consisted of 50.1% males and 49.9% females. The zygosity of the twins was established using 15 specific DNA markers. The prevalence of third molar agenesis in monozygotic twins was 19.6%, which was higher than in the dizygotic twins group (15.50%) (p = 0.004). In both groups, third molar agenesis was more frequent in the maxilla than in the mandible (p = 0.000). Agenesis of the maxillary third molars was mostly affected by additive genetic factors (62–63%), with the common environment and the specific environment accounting for up to 25% and 13%, respectively. In contrast, agenesis of the lower third molars was associated with a higher additive genetic determination (81–83%), with the specific environment accounting for 17% to 19%. The study’s conclusion is that the formation of the third molars follicle is strongly controlled by additive genetic factors. Recently, discussions regarding the influence of the third molars on dentition have become highly important from several aspects, including their development, formation and retention and their effect on teeth crowding4. Consequently, understanding of the regulatory mechanisms of third molar development variability is of great clinical importance for making decisions on the timing of third molar surgical removal, autologous transplantation, orthodontic treatment planning and chronological age estimation for medico-legal purposes5.Third molars, or wisdom teeth, are the last teeth that erupt into the oral cavity. Interestingly, third molars are unique teeth, as their eruption time may vary from 17 to 24 years, depending on the ethnographic region and race6. Furthermore, the prevalence of third molars agenesis was found to be considerably higher than for the agenesis of other teeth, varying from 10% to 41% among different countries8. The lowest values for the agenesis of these molars were found in black Africans and Indians, exhibiting a prevalence of 10–11% of the population10, while in the Iranian population, the prevalence rates for the third molar absence approached 34.8%11. The highest values of the third molar absence were reported in Koreans (41%)12. These large differences could be explained by different methodologies and different ethnical backgrounds13.In general, agenesis is considered to be the result of disturbances during the early stages of tooth development14. However, even then, this method did not yield very high accuracy rates. In subsequent years, another method, which uses the highly polymorphic regions of DNA obtained from blood or buccal cells, has been used to determine the zygosity of twins with an accuracy rate greater than 95%15. However, a major limitation of twin studies is that they do not represent the whole society as a general unit16. Nevertheless, these studies are useful for the evaluation of the importance of genetics and environment on the manifestation of physical traits or certain illnesses17.For analyzing the influence of genetics and environment on teeth agenesis, the most informative studies were performed using a classical twins study model, which could informatively present the effect of genetics. The earlier twin studies had some bias related to the difficulty in ensuring accurate zygosity determination. The situation changed when serum and enzyme polymorphism analyses were introduced19. However, these studies did not clearly reveal the influence of heredity on the formation of the third molars, which could be highly different from the other teeth because of their unique development1.Previous studies showed that genetics played a crucial role in the agenesis of lateral central incisors or second bicuspids using dental casts20. Second, evaluation of third molar agenesis needs a radiological evaluation of tooth germs, as they must attain a certain level of mineralization to be visible in the radiographs. Consequently, Rakhshan recommended that only individuals over 12 years of age could be used to analyze the formation of these teeth and for the precise determination of their mineralization stages21.First, these teeth begin their development later. The formation of the third molar follicle begins approximately 7 years of age, exhibiting an unusually long developmental stage, and these teeth do not have a primary counterpartFinally, it would be interesting to determine whether genetics or environment is the dominant factor in the agenesis of the third molars. The hypothesis for this study was that the dominant factor for the agenesis of the third molars was genetics.The approval for the study was obtained from the Regional Biomedical Research Committee (No. BE-2-12). The study was conducted in accordance with relevant guidelines and regulations. Furthermore, informed consents were obtained from each participant and from the parents/guardians of any participant younger than 18 years old. Each participant was individually informed regarding the project upon the human subject information consent.Subjects were randomly selected from the National Twin Center and stratified according to zygosity. The study sample consisted of the same sex twin pairs with normal growth and development according to human growth curves using anthropometric measures, such as height and weight. Criteria for inclusion were the following: Caucasian twin pairs of the same sex, twins older than 12 years of age, no congenital anomalies or syndromes, no missing teeth, no teeth extractions, no previous orthodontic treatment and good quality pretreatment digital panoramic radiographs that were made at the first visit of the twin pair to the National Twin Center. The selected radiographs were not older than 5 years during the analysis. Exclusion criteria were twins younger than 12 years, the presence of craniofacial syndromes, a history of orthodontic treatment and poor quality panoramic radiographs. Digital panoramic X-rays were used to minimize the radiation dose following standard radiation safety principles. Every digital panoramic radiograph was evaluated by one orthodontist who had received additional training for teeth bud mineralization assessment in panoramic radiographs. The investigations were conducted twice in a 2-week interval for the evaluator’s calibration. Intra-examiner reliability was assessed by means of Kappa statistics, which showed perfect agreement .17. The more precise determination at the level of 99.99% requires analyze at least 15 highly polymorphic regions of DNA. Ming-Jie Yang found that with the DNA-based 15 STR analysis amplified in a multiplex PCR, the determination of the zygosity is not only cost and time saving but also shows greater sensitivity and precision than conventional methods18. Thus, the zygosity was determined using DNA tests with the polymerase chain reaction set for the amplification of short tandem repeats with 15 specific DNA markers , as well as the Amel fragment of the amelogenin gene for comparison of the genetic profiles.A genetic analysis was performed using maximum likelihood genetic structural equation modeling (GSEM). More recently, the use of highly polymorphic regions of deoxyribonucleic acid (DNA) derived from blood or buccal cells raised accuracy of zygosity in up to 90–95% of cases17. The data were analyzed with the the OpenMx package (http://openmx.psyc.virginia.edu) for the relative influences of the additive genetic factors (A), non-additive genetic factors (D), common or shared environments (C) and unique environment factors (E)22. Using Open Mx to apply sophisticated modelling methods to multivariate and longitudinal sets of dental data from twins offers great potential for clarifying how genetic and environmental factors influence development of the human dentition16. This analysis allows estimation of the significance of the different components of variance: the additive genetic factor (A), the shared environment (C), the non-additive genetic factor (D) and the unique environment (E). The Akaike information criterion (AIC) statistics and the difference in the chi-square (χ2) value relative to the change in degrees of freedom provided an indication of the models’ goodness of fit23. The most parsimonious model  to explain the observed variance was selected. Additive genetic factors (A) refers to the deviation from the mean phenotype due to the inheritance of a particular allele and this allele’s relative (to the mean phenotype of the population) effect on phenotype. Dominant genetic variance (D) involves deviation due to interactions between alternative alleles at a specific locus. The general environmental variance (C) is attributed to the nongenetic sources of variation between individuals that are experienced by multiple individuals in a population. This variance is typically the largest component of variance in populations in natural conditions. While specific environmental variance (E) is determined by the variation within replicated genetic lines, to obtain an estimate of general environmental variance, replicates of each of the genetic lines need to be assessed in each natural or experimental environment of interest24. However, this analysis should be estimated with caution, as it is prone to difference in methodologies , which may limit the chances of finding diverging models27.The twin studies, combined with structural equation modeling, can provide estimates of the proportion of the total phenotypic variation attributable to additive genetic effects, shared or common environments, and unique environmental componentsStatistical analyses were performed using SPSS Statistics for Windows, Version 17.0. The hypotheses of interrelations between characteristics were verified using the chi-square criterion and Spearman correlation coefficients (r). The justification that correlations between monozygotic twins are of a different degree than those in dizygotic twins was assessed by checking for the significance of difference between correlations using ANCOVA. A p-value smaller than 0.05 was considered to be significant. The post hoc analysis of the power of the study showed a level of 0.8.The data will not be available for protection of the twins rights.The study sample consisted of 284 twins (172 monozygotic and 112 dizygotic) whose mean ages were 19.7 ± 4.3 and 18.9 ± 4.8 years, respectively. The monozygotic group consisted of 36.3% males and 63.7% females, while the dizygotic group consisted of 50.1% males and 49.9% females.The prevalence of third molar agenesis in monozygotic twins was 19.6%, which was higher than in the dizygotic twins group (15.50%) (p = 0.004). Females had a tendency to have third molar agenesis more frequently than the males in both groups, but these differences were likewise statistically insignificant  were counted18. The main paths of interest are those which get a start value of 0.520. The analysis of these findings with the Open Mx program showed that the best fitting model for the agenesis of the maxillary third molars was ACE; however, in the mandible, a higher significance was seen using the AE model. The agenesis of the maxillary third molars showed the highly additive genetic determination a2, which accounted for 62 to 63% of the total variation, with the common environment accounting for up to 25% and the specific environment accounting for 13%. In contrast, the agenesis of the lower third molars was associated with higher additive genetic determination (81–83%), while the specific environment accounted for the remaining 17 to 19%  for complex traits, it is worthwhile to show that there is a significant component of genetic variation present28. The results of our study revealed several findings that were different from other studies.This study tested the hypothesis that genetics plays a key role in the agenesis of the third molars using the genetic model of twins. Martin et al. revealed that females had higher values of third molar agenesis than males29. In contrast, the present study showed that the frequency of the third molar agenesis in males and females was almost the same, and these results were in agreement with a study from Alam et al., which reported that third molar agenesis was not influenced by sex30. This could be due to the differences in the populations.First, examination of the effect of sex on the agenesis of the third molar has been the subject of debate in previous studies. Kruger 31. In contrast, the study by Chung reported that the agenesis of the mandibular second bicuspid was the most frequently observed in Koreans32. Also, a recent study showed that heritability estimates for the third molars had a tendency to be higher in the maxilla than in the mandible.Moreover, the previous findings in the evaluation of the distribution of the missing teeth in the maxilla and in the mandible are confusing. Sisman reported that maxillary lateral incisors were the most frequently absent teeth (27.95%)et al. revealed that third molar agenesis was more common on the right side than on the left6. This tendency was also observed in our study but did not have statistical significance and was in agreement with the study of Silva Meza R., who did not find any differences between missing teeth on the right and left sides33. These disparities may reflect different environmental effects.In addition to these findings, Sujon 7. Interestingly, the structural equation model, which was used in the current study for the calculation of the proportion of the total phenotypic variation attributable to additive genetic effects (narrow-sense heritability), showed that additive genetic determination of the third molar agenesis was the dominant factor. The significance of the heredity in the maxilla was lower than in the mandible. Perhaps the development of these teeth could be affected by several genes and possibly by their interaction with environmental factors as it is seen with other teeth16. Kangas et al. found that dental characters seem to be non-independent and that increasing the levels of expression of just one gene can lead to increases in cusp number, altered cusp shape and position, development of longitudinal crests on teeth, and increases in tooth number in experimental mice34. At the moment, these genes are not clearly identified, and this could be a good field for future investigations.Furthermore, while analyzing the localization of the missing teeth, Fekonja suggested that genes could be the dominant factor for the agenesis in the anterior region, while the posterior teeth could be missing sporadically35. However, the precise nature of these influences is still unclear and they may be due to factors other than differences in methylation of DNA or acetylation of histones. Townsend et al. proposed that they could reflect different responses of odontogenic cells to minor variations in the spatial and temporal expression of local signalling molecules passing between cells during development and can lead to quite major differences in the final appearance of the dentitions36.Previous studies support the view that, even though there is a relatively strong genetic basis to other missing teeth, the number or position of affected teeth can be influenced by epigenetic factorsFrom a clinical perspective, knowledge about the development of the teeth could be highly useful for the understanding of the processes in the oral environment and for the preparation of the potential preventive features that could help patients with such pathology avoid different treatment difficulties.In conclusion, the hypothesis that genetics plays the dominant role in the formation of third molars was supported.Dental development is a multilevel process involving interacting genetic, epigenetic and environmental factors over an extended period. The precise analysis of the relationships of these factors warrants longitudinal studies on larger groups. In addition, the underlying assumption of twin studies is that their results can be extrapolated to the singleton population, but this possibility has not been definitively supported.This recent study showed that agenesis of the third molar was strongly affected by additive genetics. However, future studies on larger groups should be conducted to assess the role of genes, epigenetics and environment more precisely.


We demonstrate through extensive numerical studies that the proposed method has competitive performance. Its usefulness is further illustrated with application to genome-wide association analysis of diabetes-related traits in the Atherosclerosis Risk in Communities (ARIC) study. We found some very interesting associations with diabetes traits which have not been reported before. We implemented the proposed methods in a publicly available R package. Multiple correlated traits are often collected in genetic studies. By jointly analyzing multiple traits, we can increase power by aggregating multiple weak effects and reveal additional insights into the genetic architecture of complex human diseases. In this article, we propose a multivariate linear regression-based method to test the joint association of multiple quantitative traits. It is flexible to accommodate any covariates, has very accurate control of type I errors, and offers very competitive performance. We also discuss fast and accurate significance  Over the past ten years, many epidemiologic studies have used genome-wide association studies (GWAS) to identify genetic components of many complex human diseases. These large cohort studies often collected a broad array of correlated traits that often reflect common physiological processes. By jointly analyzing these correlated traits, we can often gain more power by aggregating multiple weak effects and shed light on the mechanisms underlying complex human diseases .p value [p value. A related approach is the trait-based association test using an extended Simes procedure  [There have been many methods proposed recently to detect SNP association with multiple correlated traits . A dp value , which t  that cois (PCA) , principis (PCA) , 14. PCAMultivariate trait testing methods generally perform better than univariate analysis-based approach . Among tp values for the proposed tests based on the F-distributions that offer very accurate type I error control with good finite sample performance. We also exploit the parallel nature of genome-wide association test to develop very efficient numerical algorithms that are extremely scalable to genome-wide association tests of millions of SNPs. We demonstrate through extensive numerical studies that the proposed methods have very competitive performance compared to existing methods. We further illustrate the usefulness of the proposed methods through an application to genome-wide association study of multiple diabetes-related glycemic traits.In this article, we explore an alternative multivariate regression framework to explicitly model the trait correlation and adjust for covariates to test multitrait associations. We compute the analytical We first discuss a multivariate linear regression-based framework for modeling the multiple quantitative traits and then derive the Wald type statistics for testing multitrait associations.m continuous traits Y = T, a covariate vector X = T of length p , and a genotype score G coding the number of minor alleles. Consider the multivariate normal trait model:β0 is a vector of length m, βX is an m × p matrix, β1 is a vector of length m, and the random error ϵ is of length m and is assumed to follow a zero mean multivariate normal distribution with covariance Σ, ϵ ~ N. Multivariate trait association amounts to testing H0 : β1 = 0. Here we have assumed the same covariates for all traits, which is the case for our ARIC study GWAS example (see Application to ARIC GWAS of Glycemic Traits) and many typical GWAS. In the supplementary materials T, X = T, G = T, and design matrix Z =  of dimension n × (p + 2), where 1n = T is a column vector of n ones.Given observations for m × (p + 2) parameter matrix β = . We can check that the maximum likelihood estimators (MLEs) are A = ZTZ. For the MLEs , with n − p − 2 degrees of freedom (DFs) and scale matrix Σ.Denote the vector operator vec, which stacks the columns of a matrix into a vector. Denote the MLEs  of the Mthe MLEs , we can n × (p + 1) design matrix Z0 =  and the corresponding n × n hat matrix H = Z0(Z0TZ0)−1Z0T. Let P = I − H and Ge = PG. Here I is an n × n identity matrix. We can check thatn − p − 1 − m)/mn)Q follows the F-distribution with  DFs F-distribution for the multivariate normally distributed traits and hence has very accurate control of type I errors for any sample sizes without the need of asymptotic approximation; and (IV) it is very fast to compute (see next section for details) and extremely scalable to genome-wide association tests of millions of SNPs.In the supplementary materials, we analytically show that the CCA test approach  is equivβ1. We can derive similar Wald tests under the MLM /n)T and ((n − p − 1 − m)/n)T′ to a t-distribution with (n − p − 1 − m)-DF.Under the null hypothesis, both Z0, denote its singular value decomposition (SVD) as Z0 = UDVT, where U is an n × (p + 1) matrix with orthogonal columns, D is a (p + 1)×(p + 1) diagonal matrix, and V is a (p + 1)×(p + 1) orthogonal matrix. The null MLM hat matrix can then be computed as H = UUT, and Ge = G − U(UTG). Denote the null MLM residual matrix as E = Y − U(UTY), and let V0 = ETE. In .For a typical GWAS with millions of SNPs, rather than fitting a MLM for each SNP, we developed very efficient algorithm to estimate the MLMs for all SNPs using matrix decomposition tricks following the line of Voorman et al.  as follo ETE. In , we haveINK tool  to test INK tool . TechnicQ is the omnibus test, and T and T′ are the 1-DF test assuming common or common scaled effects. The GEE-based approaches of He et al. [Qs, Ts, Ts′), which are the m-DF omnibus test and 1-DF tests assuming a common effect or common scaled effect.We consider three forms of Wald statistics: e et al.  are compe et al.  and otheX1 and a Bernoulli covariate X2 with probability of 0.5. The SNP genotype score G is simulated from a Binomial distribution, Binom, where the minor allele frequency (MAF) f0 = p0 + p1X2. Here X2 is essentially a population indicator and we have simulated SNPs under population stratification.We consider a standard normal covariate m = 2,4, 8 related traits of 1,000 unrelated individuals, respectively. Each time, we simulate the m traits from a multivariate normal distribution with a compound symmetry correlation matrix with correlation ρ. The first trait has a variance of 2 and all the other traits have unit variance. We set E(Yi) = 1 + 0.5X1 + 0.5X2 + γiG for i = 1,3,…, m − 1, and E(Yk) = 1 + X1 + X2 + γkG for k = 2,4,…, m.We conducted simulations for testing 5 experiments to evaluate the power under various combinations of . We conducted simulations for p0 = , p1 = 0.1, and ρ = 0,0.2,0.5,0.8. Here we report the results for m = 2,8, ρ = 0,0.5, and p0 = 0.1. The conclusions remain the same for other settings (data not shown).We used 10 million experiments to evaluate the type I error and 10m = 8). In general, the proposed Wald tests follow the exact F-distribution under the null hypothesis and hence the type I errors are well controlled under all settings. The GEE tests rely on the large-sample asymptotic distribution and therefore generally we need large sample size to have better control of type I errors, especially for a larger number of traits (containing more model parameters).Tables m = 2 and m = 8, respectively. T is the most powerful when γj are close to each other, and T′ is the most powerful when γj/σj are close to each other. In general, the proposed MLM-based Wald tests perform better than the corresponding GEE-based score tests, especially when testing a large number of traits. This agrees with the general principle that the Wald test is typically more powerful than the GEE-based test.Tables n − p − 1)/n)Q is commonly used in practice and referred to an m-DF chi-square distribution to compute multitrait association test's p values, which can lead to significantly inflated type I errors at stringent genome-wide significance levels. p values computed using the chi-square distribution and F-distribution, respectively. We can see that the type I error based on the chi-square distribution is inflated: more so for larger number of traits, smaller significance level, and smaller sample size. For example, when testing m = 8 traits with p = 2 covariates and n = 500 samples, under genome-wide significance level 5 × 10−8, the actual significance level of chi-square distribution p value is 3.42 × 5 × 10−8 = 1.7 × 10−7. Using the chi-square distribution to compute p values will lead to very small inflation only when the sample size is large, such as in the meta-analysis of multiple GWAS studies. For typical GWAS with small-to-medium sample sizes, we recommend using the appropriate F-distribution to compute significance p values to reduce false positive findings.The chi-square statistic ((R2 ≥ 0.3.The Atherosclerosis Risk in Communities (ARIC) study  is a popT′ identified 104 significant SNPs, T identified 103, Ts′ identified 102, Ts identified 101, and Q and Qs identified the same set of 95 SNPs at the genome-wide significance level 5 × 10−8. Analyzing each glucose measure separately identified 34, 84, 37, and 64 genome-wide significant SNPs at visits 1, 2, 3, and 4, respectively. All the identified SNPs by different methods are genome-wide significant in the MAGIC Consortium, a meta-analysis of 21 fasting glucose GWAS which together included 46,186 nondiabetic participants [As a proof of concept, we first analyzed four fasting glucose levels in 5947 nondiabetic ARIC white participants measured at four visits (visits 1–4) conducted approximately three years apart. The average correlation of glucose levels is 0.55. We applied an additive genetic model with imputed dosage as a covariate and adjusted for age, gender, and study center in all tests. By analyzing four fasting glucose measures jointly, icipants .Ts′, the two additional SNPs identified by T′, rs780093 and rs780094, had p values of 4.8 × 10−8 and 4.8 × 10−8 using T′. Their respective MAGIC meta-analysis' p values were 2.9 × 10−13 and 2.5 × 10−12. Compared to Ts, the two additional SNPs identified by T, rs1260326 and rs11688384, had p values of 4.7 × 10−8 and 4.0 × 10−8 using T. Their respective MAGIC meta-analysis' p values were 4.3 × 10−13 and 4.1 × 10−10.Compared to −8). For joint testing of all three traits, Ts, Ts′, T, T′ identified none, Qs identified 139, and Q identified 140 genome-wide significant SNPs, among which 61 and 61 SNPs were reported as genome-wide significant in the MAGIC meta-analyses of fasting glucose, fasting insulin, or 2-hour glucose levels [Second, we jointly analyzed three distinct diabetes-related glycemic traits measured at visit 4 in 5068 nondiabetic white participants measured at visit 4 in ARIC: fasting glucose, fasting insulin, and glucose level 2 hours after an oral glucose challenge. We applied an additive genetic model with imputed dosage as a covariate and adjusted for age, gender, and study center. To account for the skewed distribution of fasting insulin, we adopted the Box-Cox transformation with an estimated power of 0.35 . The thre levels , 33.Qs, Q identified two additional genome-wide significant SNPs, rs4665987 and rs853780, with p values of 4.9 × 10−8 and 4.9 × 10−8, respectively. MAGIC meta-analysis of fasting glucose reported a p value of 2.1 × 10−38 for rs853780. Its MAGIC meta-analyses of fasting insulin and 2-hour glucose p values are 0.054 and 0.477, respectively. For rs4665987 (near GCKR on chromosome 2:27755825), MAGIC meta-analysis' p values for the fasting glucose, fasting insulin, and 2-hour glucose levels are 4.6 × 10−6, 0.04, and 9.3 × 10−5, respectively. This SNP was genome-wide significantly associated with human serum metabolite levels in a GWAS of 8330 Finnish individuals [Q, Qs reported one additional genome-wide significant SNP, rs17540154, with p value of 4.3 × 10−8. The MAGIC meta-analysis of fasting glucose reported a p value of 8.7 × 10−38 for rs17540154. Its MAGIC meta-analyses of fasting insulin and 2-hour glucose p values are 0.101 and 0.720, respectively.Compared to ividuals  and seveividuals –38. CompAmong the identified significant SNPs by joint testing, there were 79 novel genome-wide significant SNPs that have not been reported as significantly associated with diabetes-related fasting glucose and insulin levels before. Among them, one SNP, rs4665987, is located on chromosome 2:27755825 and 78 other SNPs are clustered on chromosomes 15:62132921 to 15:62396389. Interestingly, six of them .Here we have focused on testing a relatively small number of correlated quantitative traits, which have enabled us to develop accurate and powerful association tests without any asymptotic approximations as adopted in the more general though conservative GEE approach, which can be applied to any mix of quantitative and discrete traits. It will be interesting to extend the proposed methods to the phenome-wide association studies (PheWAS) with a large collection of phenotypes –45 and dhttp://www.github.com/baolinwu/MTAR. We provide some sample R codes to install and use the package in the supplementary materials. The developed algorithms are very efficient and extremely scalable to genome-wide association test.In the previous discussions, we have assumed the same set of covariates across all traits. With differing covariates, we provide technical details regarding model estimation and extensive simulation studies to confirm that the proposed methods accurately control type I errors and perform favorably compared to existing methods . In summary, we recommend the proposed multivariate linear regression-based test as a complementary approach to enhancing the power of analyzing multiple quantitative traits in unrelated individuals. Our numerical studies have suggested that the omnibus Wald test generally has robust and good performance. The 1-DF Wald tests can perform well due to reduced DFs, but they could be sensitive to the underlying assumptions. It will be worthwhile to develop adaptive and powerful tests. We have implemented the proposed methods in an R package available at


A 11q13.4 Amerindian ancestry association region spans a variant that was previously reported  in a targeted association study of Blood Pressure (BP) traits and variants in the vitamin D pathway. There was no replication evidence supporting an association in the identified 17q25.3 Amerindian ancestry association region. For a region on 6p12.3, associated with African ancestry, we did not identify any candidate variants driving the association. It may be driven by rare variants. Whole genome sequence data may be necessary to fine map these association signals, which may contribute to disparities in BP traits between diverse populations.Admixture mapping can be used to detect genetic association regions in admixed populations, such as Hispanics/Latinos, by estimating associations between local ancestry allele counts and the trait of interest. We performed admixture mapping of the blood pressure traits systolic and diastolic blood pressure , mean arterial pressure (MAP), and pulse pressure (PP), in a dataset of 12,116 participants from the Hispanic Community Health Study/Study of Latinos (HCHS/SOL). Hispanics/Latinos have three predominant ancestral populations , for each of which we separately tested local ancestry intervals across the genome. We identified four regions that were significantly associated with a blood pressure trait at the genome-wide admixture mapping level. A 6p21.31 Amerindian ancestry association region has multiple known associations, but none explained the admixture mapping signal. We identified variants that completely explained this signal. One of these variants had  Cardiovascular disease is a major cause of death in the United States and worldwide. Blood pressure is a strong risk factor for cardiovascular disease and has a known genetic component. Multiple genome-wide association studies (GWASs) have been carried out in populations of European –4, AsianIn the simplest setting, the admixture mapping effect is equal to the effect of a causal genotype within the local ancestry interval (LAI), down-weighted by the difference in the causal genotype’s allele frequencies between ancestries. The admixture mapping effect also relates to the difference in the causal variant’s effect size between ancestries, if exists  Hispanics/Latinos from the HCHS/SOL. We leveraged the background groups of the HCHS/SOL  to fine-map candidate association variants from detected LAIs, which we then followed-up with conditional analysis, to verify that they indeed account for the admixture mapping associations. We assessed replication of four Amerindian variant associations in a population of Southwest American Indians.The HCHS/SOL , 18 is aWe defined and used blood pressure outcomes as in the blood pressure GWAS study , with thFor all outcomes, we excluded 95 individuals with inconsistencies in their measured SBP or DBP (Omron mean and mean of raw measures difference ≥ 5mmHg), 19 individuals with high degree of Asian ancestry (detected and reported in ), 13 indGenotyping and quality control for HCHS/SOL have been described in Conomos et al. 2016) [16 [20]. We applied standardized quality-assurance and quality-control methods  to generHCHS/SOL participants self-identified as primarily associated with one of six background groups: Central American, Cuban, Dominican, Mexican, Puerto Rican, and South American. Based on these groups, “genetic analysis groups” were constructed as described in Conomos et al. 2016) [16 [20]. Local ancestry inference has been reported in Browning et al. (2016) . It was In admixture mapping, we tested the trait associations of LAI counts inherited from a specific ancestry (e.g. African) against a baseline, the other two ancestries. In association mapping, we tested the trait associations of counts of effect alleles against a baseline, the other allele. Comparison between the admixture and the association mapping estimand and power in the scenario of two ancestries and a single causal genotype in an LAI is provided in p-value threshold 5.68 × 10−5 reported by Browning et al. (2016) [Our primary analysis was admixture mapping with secondary association testing employed to fine map specific association loci. For statistical significance of admixture mapping we used the . (2016)  for the . (2016)  based onAfter discovering genome-wide significant LAI associations (at the admixture mapping level), we attempted to fine-map these intervals to detect genotype associations that account for the signals. To determine whether a genotype association explains an admixture mapping signal, it suffices to use the genotype count as a covariate in the same regression analysis as the local ancestry count, to see if the local ancestry association becomes less statistically significant.p-value> 10−7). Based on the power comparison provided in p-value threshold and sometimes differences in effect allele frequencies (EAFs) between the two genetic analysis groups with the highest and lowest proportions of the ancestry of interest. Thus, if an admixture mapping association was discovered in a specific interval comparing the counts of Amerindian ancestry to other ancestries, we considered the EAF  of the Mexican and Cuban genetic analysis groups for variants in the interval. This is a practical alternative to calculating the more interesting quantity, the difference between EAFs in the ancestral populations, for all variants in the LAI, because it is computationally too intensive.Each local ancestry interval corresponds to possibly thousands of imputed and hundreds of genotyped variants in the HCHS/SOL data set, many may not appear to be significantly associated with the trait  we required a difference in EAFs between the Mexican and the Cubans. For relatively low p-values (e.g. ∼ 10−6), we did not make any such restriction, because (1) the number of such variants is low, so stronger filtering is not required, and (2) admixture association may be detected by differences in the variant effect between the ancestral groups, even when the EAF is the same. In practice, we took a step-wise approach in which we relaxed the required p-value by factors of 10 , where for low p-values  we filtered by decreasing differences in EAFs  of the two relevant genetic analysis groups. Finally, when searching for variants in the association analysis results, we utilized the heterogeneity of the HCHS/SOL cohort again by searching in both the results from the meta-analysis of all genetic analysis groups, the meta-analysis of only Caribbean, and the meta-analysis of only the Mainland genetic analysis groups reported in [For relatively high s e.g. ∼ −6, we dip-value in association testing) from each set of correlated variants, defined as the set of variants such that each variant has Pearson correlation of at most 0.4 with at least one other member of the set. We then applied the admixture mapping model while adjusting for these variants in the mixed model , and also calculated the ancestry-specific EAF of these variants using ASAFE software. [Upon generating a list of potential variants associated with the trait, we pruned them to obtain lead variants . There are multiple previously reported BP associations in this region: rs9266359, rs2021783 , rs15637p-value among the Mainland groups only  but EAFs were similar across ancestries, suggesting that in this case there are differences in SNP effect sizes between the ancestries. These variants are in close proximity to rs1790370, previously reported by Wang et al. (2014) [We selected three variants based on association testing results and differences in EAFs between the Cuban and Mexican genetic analysis groups . Interes. (2014)  in a canp-value of the lead admixture mapping interval became 0.002 in the conditional analysis.The selected variants partly explained the admixture peak, as could be seen in p-values were relatively high  estimated as almost monomorphic in the HCHS/SOL Amerindian ancestry (MAF = 0.004), while being quite polymorphic in Pima Indians (MAF = 0.06). The frequency of this variants in the 1000 Genome AMR population was 0.07, as in the Pima Indians.We sought replication of the variants identified under the admixture mapping peaks on chromosomes 6, 11 and 17 in a study of Pima Indians (see methods). Four variants were polymorphic in Pima Indians and genotypic data was available to assess replication. We performed admixture mapping of BP traits in a heterogeneous sample of US Hispanics/Latinos with the intent of identifying novel BP loci. In admixture mapping, counts of local ancestry at intervals are tested for association with a trait, and this approach has the potential to be more powerful than association analysis to identify variants with large EAF differences across ancestral populations  and Caribbean  Hispanic/Latino groups that have different distributions of ancestry proportion, because admixture mapping association can be caused by different effect sizes between ancestries. For one region , we did not find any candidate variants. For the other three associated regions , we proposed a few variants explaining the admixture mapping association. Four proposed variants in the 6p21.31 region completely explained the local Amerindian ancestry association. These variants may tag an associated Amerindian haplotype in the region. In the 11q13.4 MAP Amerindian ancestry association region, one of the candidate variants was associated with MAP only in the Mainland-specific analysis reported in , consistp-values of 0.02 and 0.04 with MAP and SBP, respectively. One-sided testing, where the side was based on the direction of association in the HCHS/SOL, has been shown to be more powerful while still providing better protection from type 1 error than two-sided testing in the replication stage. [Because the identified admixture mapping signals were identified in analyses comparing Amerindian ancestry to other ancestries, we tested the association with BP traits in a study of Pima Indians but these associations did not replicate when accounting for multiple testing. However, one variant in the chromosome 6 association region had replication one-sided n stage.  PossibleIn summary, we detected multiple regions of associations with local ancestry for BP traits. These loci are distinct from genomic regions reported in our recent report of BP GWAS in the HCHS/SOL. Such associations are driven by genetic variants at the local ancestry interval. We provided a systematic approach to identify the underlying variants at each region. However, these variants may not be well tagged by genotyped or imputed variants in the data set. While we were able to detect a few candidate variants driving the Amerindian association regions, and one association had p-value = 0.02 in the replication study, none of the associations replicated after accounting for multiple testing in a small sample of Pima Indians. Unfortunately, we did not have access to any larger or additional sample of American Indians for further replication. We did not detect any variants driving the African Ancestry association region, suggesting that current genotyping and imputation platforms are lacking in coverage for less minority populations or that rare variants drive these associations. Whole-genome sequencing studies in Hispanics/Latinos, American Indians, and African Americans are needed for additional and more complete fine mapping efforts of complex traits.S1 File(PDF)Click here for additional data file.