Overall, these results demonstrated the potential of using FIELD information as indicator traits for the indirect genetic improvement of LAB measures. In the second approach, we included genotype information for 1,011 cows from the LAB dataset, 1,493 cows from the FIELD dataset, 181 sires with daughters in both LAB and FIELD datasets, and 540 sires with daughters in the FIELD dataset only. Predictions were obtained using the single-step GBLUP method. A four fold cross-validation was used to assess the predictive ability of the different models, assessed as the ability to predict masked LAB records from daughters of progeny testing bulls. The correlation between observed and predicted LAB measures in validation was averaged over the four training-validation sets. Different sets of phenotypic information were used sequentially in cross-validation schemes: (i) LAB cows from the training set; (ii) FIELD cows from the training set; and (iii) FIELD cows from the validation set. Models that included FIELD records showed an improvement for the majority of traits. This study suggests that breeding programs for difficult-to-measure traits could be implemented using FTIR information. While these programs should use progeny testing, acceptable values of accuracy can be achieved also for bulls without phenotyped progeny. Robust calibration equations are, deemed as essential.The objective of this study was to evaluate the contribution of Fourier-transformed infrared spectroscopy (FTIR) data for dairy cattle breeding through two different approaches: (i) estimating the genetic parameters for 30 measured milk traits and their FTIR predictions and investigating the additive genetic correlation between them and (ii) evaluating the effectiveness of FTIR-derived phenotyping to replicate a candidate bull’s progeny testing or breeding value prediction at birth. Records were available from 1,123 cows phenotyped using gold standard laboratory methodologies (LAB data). This included phenotypes related to fine milk composition and milk technological characteristics, milk acidity, and milk protein fractions. The dataset used to generate FTIR predictions comprised 729,202 test-day records from 51,059 Brown Swiss cows (FIELD data). A first approach consisted of estimating genetic parameters for phenotypes available from LAB and FIELD datasets. To do so, a set of bivariate animal models were run, and genetic correlations between LAB and FIELD phenotypes were estimated using FIELD information obtained at the population level. Heritability estimates were generally higher for FIELD predictions than for the corresponding LAB measures. The additive genetic correlations (r In the omics- era, an emerging field of research is represented by phenomics, which is the study of phenotypes on a genome-wide scale . In animWithin the animal breeding context, studies have shown the potential for using FTIR predictions as indicator traits of novel phenotypes like MPC, fatty acid profiles, and other milk components . Multi-tBesides the infrared technology, genome-wide prediction using the single-step approach has also been recognized as an important tool to predict phenotypes . The keyTherefore, the overall objective of this study was to test the value of FTIR predictions from field data (FIELD) for the genetic improvement of difficult-to-measure traits in dairy cattle. Steps to address this objective were (i) to infer (co)variance components, heritabilities, and additive genetic correlations between 30 LAB-measured and FIELD-predicted phenotypes, divergent in terms of biological meaning, variability, and heritability, related to fine milk composition and milk technological characteristics  and (ii) to use bivariate single-step GBLUP for evaluating the predictive ability of FTIR-derived phenotyping for these traits by using different phenotyping and genotyping strategies.This study did not require any specific ethics permit. The cows sampled belonged to commercial private herds and were not experimentally manipulated. Milk samples were collected during routine milk recording coordinated by technicians from the Breeders Federations of Trento Province  and of Alto Adige/Südtirol .lact1); the whole database was instead used for the genomic analyses (FIELD). The data structure is summarized in In this study, we used two sets of data collected on Brown Swiss cows: (i) a LAB dataset in which laboratory measurements and spectra data for phenotypes related to milk quality and cheese-making were available to develop calibration equations and (ii) a FIELD-FTIR dataset for testing field prediction at the population level. A subset of the FIELD-FTIR dataset including only first lactation records was used for estimating (co)variance components  were collected. Details of the animals used in this study and characteristics of the area are reported in –1, which correspond to wavelengths ranging from 1.99 to 10.81 μm and frequencies ranging from 150.19 to 27.73 THz. Spectra were expressed as absorbance calculated as log(1/transmittance). Two spectral acquisitions were carried out for each sample (collected during the evening milking), and the results were averaged before data analysis . The spectrum covers from the short-wavelength infrared , through the medium-wavelength infrared , to the long-wavelength infrared  regions with 1,060 spectral points from wavenumber 5,010 to 925 cmanalysis .20 (min) was defined as the interval from RCT to the time at which a curd firmness of 20 mm was obtained, and a30 and a45 (mm) were measurements of curd firmness at 30 and 45 min after rennet addition, respectively.Measures of MCP were obtained using two different instruments: a Formagraph (Foss Electric A/S) and an Optigraph  according to t (CFt) was estimated, and details are described in eq, min), estimated from the CFt equation; potential asymptotical curd firmness , representing the maximum potential curd firmness after infinite time in the absence of syneresis; curd-firming rate constant , which is a measure of the rate of CF; syneresis rate constant ; maximum curd firmness ; and time to CFmax .A set of parameters of CF at time The milk pH was measured using a Crison Basic 25 electrode .CURD), of curd DM (%CYSOLIDS), and of water retained in the curd (%CYWATER) as a percentage of the weight of milk processed. Four recovery (REC) traits were calculated as proportions of nutrients and energy of the milk retained in the curd . The energy within the curd was calculated as the difference between energy in the milk and in the whey  and whey proteins, β-lactoglobulin (β-LG), and alpha-lactalbumin (α-LA) were determined using a validated reversed phase high-performance liquid chromatography (RP-HPLC) method (Concentrations of the major casein (CN) fractions (α) method . Each prOnly records with spectra and measured phenotypes available were kept. After data editing and removing observations outside three standard deviations, the final number of records and phenotypes used in subsequent analyses varied from 770 to 1,120 depending on the trait as reported in The FIELD data for our study were provided by the Breeders Federations of Trento Province  and of Alto Adige/Südtirol  as part of the Cowability/Cowplus projects. All milk samples were analyzed using a MilkoScan FT6000 . Spectra characteristics, in terms of wavelengths and way of expression (absorbance), were the same as for the LAB data. Spectra were collected between 2010 and 2017.A preliminary analysis was carried out to identify the outlier spectra based on the Mahalanobis distance from the first five principal component scores. The probability level for the chi-squared distribution of a sample’s Mahalanobis distance was calculated from the incomplete gamma function with five degrees of freedom . SamplesTo detect outliers among the predicted phenotypes, a mixed model was fitted for each trait including the fixed non-genetic effects of (i) the stage of lactation (12 monthly classes), (ii) the combined effect of herd , year of the test day (2010–2017), and two seasons of calving (April to September and October to March) . The permanent environmental effects  and animal additive genetic effects were included as random terms.The residuals of phenotypes outside 3 standard deviations were considered as outliers.The pool of genotyped individuals consisted of (i) 1,011 LAB cows genotyped with the Illumina BovineSNP50 v.2 BeadChip ; (ii) 1,463 FIELD cows which were genotyped with the BovineLD v2.0 BeadChip ; (iii) 181 sires with both LAB and FIELD daughters genotyped with the Illumina BovineSNP50 v.2 BeadChip or the Illumina Bovine HD BeadChip ; and (iv) 540 sires with FIELD daughters only genotyped as (v). The software FImpute  was used–6). SNPs mapped to the sex chromosomes or with unknown position on the genome were also removed. After editing, the number of markers available for analyses was 37,093.Marker editing was performed using the preGSf90 software . MarkersSeparate models were fitted for each trait considered. We used a Bayesian model (BayesB model) implemented in BGLR , as prev0 is an intercept, {xij} are standardized FTIR spectra-derived wavelength data, jβ are the effects of each of the wavelengths, and εi are model residuals assumed to be independent and identically distributed, with normal distribution centered at zero and variance C_LAB). The calibration equations obtained with this procedure in LAB data were then applied to the spectral population data (FIELD) in order to obtain FIELD predictions for all traits of concerns.where βsoftware . To evallact1).The (co)variance components were estimated using REMLF90 and AIREMLF90 , considee−10 was reached.The program was run until a convergence criterion of 1The model for LAB-measures wasy is the vector of observations for traits of concern; b, a, and e correspond to the vector of fixed non-genetic effects, random animal additive genetic effects, and random residual effects, respectively; X and aZ are the incidence matrices relating each observation in y to b and a. The non-genetic fixed effects included in the model were (i) the DIM of each cow within parity (60 levels) and (ii) herd-test day (83 levels). The random terms were animal additive genetic effects and residual effects. The pedigree file included all phenotyped animals and their ancestors .where where lact1 records wasThe model for FIELDy is the vector of observations for the traits of concern; b, a, pe, and e correspond to the vector of fixed non-genetic effects, random animal additive genetic effects, random permanent environmental effects, and random residuals effects, respectively; X, aZ, and peZ are the incidence matrices relating each observation in y, a, b, and pe, respectively. The fixed non-genetic effects were (i) the stage of lactation (12 monthly classes) and (ii) the combined effect of herd , year of the test-day (2010–2017), and season of calving (April to September and October to March) . The random terms were permanent environmental effects , animal additive genetic effects, and residual effects. The pedigree file included all phenotyped animals and their ancestors . Only first lactation records were utilized to avoid convergence problems. The residuals were considered uncorrelated across the two traits (LAB and FIELDlact1 predictions).where where lact1 was estimated from the variance–covariance matrix of the random additive genetic effect as a1,a2 is the additive genetic covariance between two traits, and σa1 and σa2 are the additive genetic standard deviations for traits 1 and 2, respectively.For each trait, the additive genetic correlation between LAB and FIELDIn order to assess the ability of FIELD data to predict LAB records as phenotypes of interest, a fourfold cross-validation was used. In this setting, the LAB phenotype is considered as the breeding goal while the FIELD record is its correlated trait. The models employed for both LAB and FIELD data were the same as for the variance component estimation, except for the stage of lactation effect in the FIELD dataset that was replaced with a stage of lactation by parity effect , since the whole FIELD dataset was used (not restricting the records to first lactation).Sires with both LAB and FIELD daughters were randomly assigned to four groups, evenly sized based on the number of LAB cows for each sire. Details on the number of records and cows in each set are reported in The cross-validation considered different training sets, either using LAB or FIELD data alone or combined: (i) model “LAB.t” included phenotypes available are from LAB cows that were daughters of the sires in the training set; (ii) model “FIELD.t” included phenotypes available from FIELD cows that were daughters of the sires in the training set; (iii) model “LAB.t + FIELD.t” included phenotypes from LAB and FIELD cows that were daughters of the sires in the training set; (iv) model “FIELD.t + FIELD.v” included phenotypes available are from all FIELD cows ; and (v) model “LAB.t + FIELD.t + FIELD.v” included phenotypes available from LAB cows that were daughters of the sires from the training set and all FIELD cows. Model “LAB.t” assesses the predictive ability when FIELD records are not collected, i.e., no use of FTIR data. Model “FIELD.t” evaluates the impact of FIELD phenotyping the daughters of the bulls in the reference population, with no LAB phenotypes included in the genetic evaluation. Model “LAB.t + FIELD.t” evaluates the impact of including FIELD phenotypes for the daughters of the bulls in the progeny test. In model “FIELD.t + FIELD.v,” progeny testing bulls have daughters phenotyped with FTIR data while in model “LAB.t + FIELD.t + FIELD.v,” the progeny testing bulls have daughters phenotyped with LAB data as well.Accuracy of prediction was quantified asaccx is the accuracy in the validation set x , x, x, and cor refers to the Pearson correlation. Estimated genomic breeding values were calculated using the program BLUPf90  values in order to find those that better maximized prediction accuracy. Firstly, estimates of variance components were obtained from single-trait models . Single-lact1, and FIELD datasets for all the investigated traits. We only observed a slight loss of variability for all the FTIR-predicted phenotypes as demonstrated by the lower standard deviations, compared to for the observed traits.Descriptive statistics for all investigated LAB-measured and FIELD-predicted traits are summarized in lact1 datasets for coagulation traits and milk acidity are reported in C_LAB) and used for FIELD predictions, and the additive genetic correlation (ra) between LAB and FIELD traits are reported in lact1 with respect to LAB data. A similar pattern was reported in other studies , this difference increases particularly for traits recorded at increasing time intervals from milk gelation. This is caused by the decreasing repeatability of the measures recorded by the instrument with the progress of the textural test. Therefore, heritability estimates were comparable between datasets for traits recorded earlier , whereas heritability estimates decreased for later measured LAB traits, but not for FTIR predicted FIELDlact1 traits . Optigraph, yielding an optical prediction and not a mechanical measurement, does not show the same decrease in repeatability and heritability, for traits describing the later part of CF pattern. Generally, heritability estimates of measured and predicted traits were comparable to other studies (Variance components and heritability estimates from LAB and FIELD studies . In part studies .Cheese-making traits. Variance components and heritability estimates of LAB and FIELDlact1 for cheese yield and recovery traits are reported in C_LAB developed on LAB data and the ra between LAB and FIELD traits are reported in lact1 for CYCURD (∼1.2-fold) and CYSOLIDS (∼1.6-fold) and smaller for CYWATER (∼1.2-fold). For all these traits, a ∼1.5-fold reduction was observed in residual plus permanent environmental variances. For CYCURD and CYWATER, heritability estimates were comparable between the two datasets, while the heritability estimate of CYSOLIDS was almost double in FIELDlact1 (0.358), compared to LAB (0.192). Variance components for REC traits had different behaviors: RECPROTEIN and RECFAT had smaller genetic variances for FIELDlact1 compared to LAB traits , while RECSOLIDS and RECENERGY had larger genetic variances in FIELDlact1, compared to LAB (∼1.3-fold). On the other hand, we observed a reduction in residual variance for all traits except RECPROTEIN which had a slightly higher value in FIELDlact1, compared to the LAB trait. Accordingly, heritability estimates for REC traits were comparable or higher in FIELDlact1, with the exception of RECPROTEIN which had a lower value in FIELDlact1 (0.247 vs. 0.563).S1-CN, from 0.873 to 0.065), while residual variances were larger for total CN, κ-CN, total whey, β-LG, and α-LA, smaller for αS1-CN and αS2-CN, and comparable for β-CN. Heritability estimates were lower in FIELDlact1 for all protein traits, ranging from high-moderate (ranging from 0.182 to 0.678) to moderate-low  to 0.953 . In general, estimates of ra for milk coagulation and cheese-making traits were high (>0.75), except for kCF and kSR which displayed moderate-high estimates (>0.60). On the other hand, only two milk proteins showed ra smaller than 0.6: αS1-CN (0.396) and αS2-CN (0.535). These two traits were those with the lowest rC_LAB among all traits tested . On the other hand, a values compared to those in our study (0.62–0.97), which might be ascribed to differences in population  and/or in the analytical technique used for milk protein investigation (capillary electrophoresis vs. HPLC). The reliability of calibration rC_LAB was associated with the decrease in genetic variance between LAB and FIELDlact1 traits (R2 = 0.45). In particular, lower rC_LAB corresponded to larger decrease in genetic variance . A positive relationship (R2 = 0.26) was observed between rC_LAB and ra: a higher reliability of the calibration model corresponded to a higher additive genetic correlation between the LAB-measures and FIELDlact1 predictions (a > rC_LAB). So, even calibrations with a relatively small predictive ability could be exploited in selective breeding, if their ra between measured and predicted traits is sufficiently high.To assess the reliability of calibration equations in the animal breeding context, we estimated, besides the rvariance . A weakedictions . Beyond eq, kCF, and tmax showed values of accuracy above 0.10. CFp and Cmax showed null values, which is in agreement with the low (∼0.1) heritability estimates. Optigraph traits showed a different trend, with RCT reporting the strongest prediction accuracy (0.168) but not the largest heritability. Prediction accuracies were below 0.1 for all CY traits, for which heritability estimates barely reached the value of 0.2. Prediction accuracy was largest for RECPROTEIN among recovery traits, and its heritability estimate was the largest in the group (∼0.55). A similar scenario was found among casein fractions, where whey proteins, β-LG, and β-CN showed one of the strongest prediction accuracies  and the largest heritability (above 0.50). Surprisingly, αS1-CN showed a strong predictive ability (0.165), yet not the largest heritability estimate (∼0.50). Prediction with only LAB information can be considered unreliable from a genetic evaluation standpoint, given the limited size of the dataset and the relative cost needed to acquire each single record. However, this scenario was included as a reference for the other, more reliable, models.In the LAB.t scenario, daughters of progeny testing bulls are not phenotyped and FIELD information is not included and the genetic evaluation is based on a single-trait model. The predictive ability for the different traits followed, to a large extent, the trait heritability . Among M20, a30, and a45 having prediction accuracies of 0.208, 0.190, and 0.181, respectively (compared to null accuracies in LAB.t); Optigraph a30 prediction accuracy increased from 0.037 to 0.242; and CFp increased from 0.038 to 0.235. Among protein composition traits, κ-CN increased from 0.051 to 0.330, while αS1-CN did not increase (being the only trait not showing any increase). For all the abovementioned traits that showed an increase, the optimal value of genetic correlation appeared to be 0.9, which corroborates the relevance of FIELD information for accurately predicting LAB breeding values and phenotypes. The values of correlation for the calibration model used for infrared prediction (rC_LAB) and additive genetic correlations (ra) estimated from the data were large for these traits but not the largest found.The LAB.t+FIELD.t scenario mimics a genetic evaluation where both LAB and FIELD information of proven bulls is included. The comparison with the LAB.t scenario proves the value of including FIELD.t information, which highlights the importance of the construction of FTIR calibration equations and the collection of data at the population level on daughters of proven bulls. Still, the genetic merit of bulls can be predicted at birth under this scenario. The genetic evaluation leverages a bivariate model. Overall, prediction accuracy showed a strong increase, compared to the previous scenario. The largest increases in prediction accuracy were observed for curd firming traits, with MCP k20 (from 0.250 to 0.302), CYWATER (from 0.203 to 0.242), and casein proportion (from 0.198 to 0.230). Traits that did not show an increase were αS2-CN, whey proteins, α-LA, and β-LG.The LAB.t+FIELD.t+FIELD.v scenario mimicked a genetic evaluation based on a progeny testing scheme, which implies the collection of FTIR spectra information on the daughters of progeny testing bulls (FIELD.v). Here, genetic merit of bulls cannot be estimated at birth but collection of FIELD phenotypes is needed as in traditional progeny testing. As compared to a previously discussed scenario, the advantage of the FIELD.v data seemed marginal, showing a maximum of 1.2-fold increase and often a decrease in prediction accuracy. Traits that benefited the most were OPT kS1-CN that showed a dramatic decrease from 0.165 to 0.055 when LAB information was removed. This is due to the low quality of the calibration model used for FTIR predictions (rC_LAB = 0.60 and ra = 0.40). The comparison of the LAB.t+FIELD.t+FIELD.v scenario to the FIELD.t+FIELD.v allows us to further prove the value of LAB phenotypes when FIELD information is also recorded in daughters of progeny testing bulls. Again, changes were negligible for most traits, confirming the low relevance of LAB information when solid FTIR calibration equations are used. The relevance of FIELD.v information is assessed in the comparison of FIELD.t and FIELD.t+FIELD.v, when LAB information is absent. While the increase was negligible in the presence of LAB information (maximum of 1.2-fold increase in accuracy), in this case the fold increase reached 1.25 with several traits being about 1.1. This supports the hypothesis that progeny testing could be beneficial for most traits, but probably the gain in accuracy would not match the cost of delaying the candidate bull’s evaluation. It should be considered that generation interval can be dramatically reduced when FIELD.v information is omitted, compromising prediction accuracy, but probably not sufficiently to justify progeny testing cost.Scenarios FIELD.t and FIELD.t+FIELD.v mimic a breeding scheme where LAB information is not included in the genetic evaluations. Still, LAB information is used to obtain FTIR phenotype prediction equations. The underlying model is a bivariate model that produces LAB breeding values, although LAB records are not included. Comparing the LAB.t+FIELD.t scenario to the FIELD.t scenario allows the evaluation of the contribution of LAB information when FIELD information is recorded on the daughters of proven bulls. Here, differences were negligible, except for αS1-CN, which showed a poor FTIR calibration equation, all traits showed an advantage in the inclusion of FIELD information, supporting the need for well-constructed calibration equations that allow us to obtain predicted phenotypes at the population level. Furthermore, an increase in prediction accuracy was found with the inclusion of FIELD.v information rather than just FIELD.t, either with or without the presence of LAB.t phenotypes. Scenarios that included all FIELD information outperformed scenarios that just included FIELD.t, with the exception of αS2-CN. This would lead to further speculation on the need for conducting progeny testing for new bulls, but the gain in accuracy of prediction is probably not translated into gain in genetic progress due to increased generation interval. It should also be noted that for some traits, i.e., k20, kCF, kSR, βCN, pH, αS1-CN, and α-LA (not necessarily those with low FTIR prediction accuracy), the trend of prediction accuracy over the values of assumed genetic correlation was sometimes null if not negative.With the exception of αS1-CN, for which the quality of the FTIR calibration equation was particularly low, followed by the low FIELD heritability and low genetic correlation with LAB measures. All other traits benefited from the inclusion of FIELD information and the accuracy gained with FIELD information greatly depended on the genetic correlation between LAB and FIELD traits. Nonetheless, it was not possible to declare a breakeven value of genetic correlation which deemed the use of FIELD information advantageous. Breakeven values of genetic correlations for indicator traits were found to be 0.5 by Despite the large number of traits involved, this study does not allow us to declare a breakeven value for any genetic parameter that would serve to predict the value of FIELD vs. LAB information. The only trait that did not benefit from FIELD information happened to be αThe present study reported two approaches for assessing the contribution of FTIR calibration equations at the population level for dairy cattle breeding. With the first approach, results indicate that FIELD predictions can be used in breeding programs for the genetic improvement of difficult-to-measure traits and that indirect selection for FIELD predictions will provide satisfactory responses. With the second approach, for the first time we highlighted the utility of FTIR predictions for breeding purposes using real data to simulate different genetic evaluation scenarios, where FTIR-derived phenotypic information is dosed into (single-step) GBLUP to predict wet-lab measured performance of daughters of progeny testing bulls. Collection of FIELD measures for progeny testing bulls appears to be advantageous for increasing the predictive ability for most of the traits studied, but the increase in generation interval due to progeny testing does not justify the increase in prediction accuracy. LAB information from proven bulls’ daughters could be included in the genetic evaluations without a detrimental effect. As there is no evidence of a clear advantage to including FIELD information for progeny testing bulls, progeny testing schemes could be replaced by the construction of robust calibration equations together with more vast collection of FIELD measures on daughters of proven bulls.In general, the increase in predictive ability observed with the inclusion of FIELD information is very favorable and reaches moderate values for 12 traits. While further research is needed in the modeling of FTIR-predicted data, results are promising. Once calibration equations are developed, the cost of collecting FIELD is virtually null, provided that routine spectra acquisition within milk recording schemes is performed and available for breeders. Yet, the cost of developing robust calibration equations should be factored into the total cost of implementing (genomic) selection that includes FIELD data. Thus, an economic analysis should be performed before progressing its use in breeding programs for difficult-to-measure traits.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.AC conceived the study, contributed to set up the objectives of this study, drafted the first version of the manuscript, and supervised the project. HT-A performed the statistical analysis together with FT. SP contributed to the critical interpretation of the results and to manuscript drafting. GB and CM contributed to the critical revision of the manuscript. FT conceived the study with AC, contributed to the critical interpretation of the results, and to manuscript drafting. All authors have read and approved the final manuscript.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.


For outcomes that studies report as the means in the treatment and control groups, some medical applications and nearly half of meta-analyses in ecology express the effect as the ratio of means (RoM), also called the response ratio (RR), analyzed in the logarithmic scale as the log-response-ratio, LRR.τ2, (measured by bias and coverage) in assessing heterogeneity of study-level effects, and also the performance of related estimators of the overall effect in the log scale, λ. We obtained additional empirical evidence from two examples.In random-effects meta-analysis of LRR, with normal and lognormal data, we studied the performance of estimators of the between-study variance, τ2 had considerable bias or were unreliable, and interval estimators of τ2 seldom had the intended 95% coverage for small to moderate-sized samples (n<40). Results for estimating λ differed between lognormal and normal data.The results of our extensive simulations showed several challenges in using LRR as an effect measure. Point estimators of n≥40) and its companion interval (when n≥10). Normal data posed greater challenges. When the means were far enough from 0 , SSW was practically unbiased, and its companion interval was the only option.For lognormal data, we can recommend only SSW, a weighted average in which a study’s weight is proportional to its effective sample size, (when  Users of meta-analysis assemble estimated effects from several studies in order to assess their heterogeneity and obtain an overall estimate. Here we focus on the measure of effect known as the response ratio , analyzed in the logarithmic scale as the log-response-ratio, LRR. In ecology almost half of all meta-analyses use this outcome measure , 2. WhenThe RR was introduced by Hedges et al.  and rediτ2, is often used in estimating the overall effect (the mean of the distribution of random effects). In studying estimation for meta-analysis of LRR, we focus first on τ2 and then proceed to the overall effect, which we denote by λ.The fixed-effect (FE) model regards the studies as sharing a single true effect, whereas the random-effects (RE) model regards those true effects as a sample from a distribution. The variance of that distribution, usually denoted by τ2 and its uncertainty. However, they study only “methods that can be applied for any type of outcome data.” As we show elsewhere . In . In nij mentclass2pt{minimτ2 or λ at the 95% confidence level was roughly For each combination of parameters, we used a total of 10,000 repetitions. The resulting simulation standard error for estimated coverage of We programmed the simulations in R version 3.3.2 using the University of East Anglia 140-computer-node High Performance Computing (HPC) Cluster, which has a total of 2560 CPU cores, including parallel processing and large memory resources. For each configuration, the 10,000 replications consisted of 10 parallel sets of 1000 replications.I2 underlying our simulations. Figures A3 and A4 in Additional File I2=100τ2/(τ2+s2) versus τ2∈ for LRR when n = 20, 40, 100, and 250, with traces for λ = 0, 0.5, 1, 1.5, and 2. As indicated by the definition, I2 increases as τ2 increases. The value of n also has a substantial impact (larger n yields higher I2). Importantly, for LRR I2 increases as λ increases, especially for the smaller n, contrary to the scale-invariance criterion of Higgins and Thompson [I2, for reasons that include those mentioned here.A reviewer inquired about the values of Thompson . We emphτ2) of bias or coverage of estimators of τ2 or estimators of λ, corresponding to four values of n and three values of K. The summary below is illustrated by Figs. We report our full simulation results under the normal and lognormal distributions in e-prints , 33. ThoBias The main feature is a negative relation between bias and τ2. When μC=1 and n=4, all four estimators have definite positive bias at τ2=0 . As τ2 increases, the bias trends downward, roughly linearly, and it can reach substantial negative values . When n=10, the bias at τ2=0 is less than 0.05, and it goes to 0 as n increases. Also, the slopes of the traces decrease in magnitude, and the traces separate  generally does not reduce the biases, but the traces separate when n≤20, especially when n=4. As λ increases, the biases at τ2=0 decrease slightly, and the magnitudes of the slopes decrease substantially  MP often has the least bias, followed by REML, and J and DL have the most bias.n. As expected, bias-correction does not have any effect for large n.Bias increases when the bias-corrected estimator Coverage When μC=1, coverage of τ2 depends strongly on K. Counterintuitively, all four methods have coverage close to nominal when K=5, somewhat below nominal when K=10 (unless n>100), and often far below nominal when K≥30 (in problematic patterns when n=4). At τ2=0 coverage is noticeably above nominal when n≥10 . When n≥100, QP and PL generally have coverage reasonably close to nominal, even for K=30, and QP is sometimes closer; when K=30, the coverage of BJ and J decreases sharply as τ2 increases (except when λ=2)  . When λ≥0.2, the bias is negative at small τ2, with magnitude exceeding 0.12 when λ≥1 and n≤10; it becomes positive as τ2 increases. The bias can be large for small sample sizes, and it decreases to zero only for very large sample sizes. The bias depends very little on K. The bias of SSW is positive, though considerably less than the bias of the IV-weighted methods, and it decreases much more rapidly as n increases  is roughly constant across the range of τ2  Fig. , row 1. ses Fig. , row 4.  τ2 Fig. , row 2. sed Fig. , row 3. λ does not reflect the biases of the respective estimators, but strongly depends on K, even though the bias in estimation of λ does not. The MSE of SSW is somewhat higher than MSE of the IV-weighted estimators when K=5, can be higher or lower when K=10 and is usually lower when K=30.Astonishingly, the MSE in estimation of Coverage When μC=1, coverage of all IV-weighted methods is considerably below nominal for n≤40   Fig. , row 1. r K Fig. , row 4, Bias When n is very small . This pattern persists for λ≤1; but when λ=2, the slope is essentially 0 . The bias correction for all Fig. , row 1, y 0 Fig. , row 3. the bias   at τ2=0.1 increase; for a given λ both the intercepts and the slopes decrease as n increases. As a result, when λ≥0,5, the bias of SSW usually has smaller magnitude than the IV-weighted estimators. In relative terms, when n<40, the biases are substantial: as much as 10% of λ in some cases. Here SSW has the least bias, about 10% for λ≥1 and n=10, declining to 5% for λ≥1 and n=20  or coverage less than 93% . All other methods have inferior coverage and are not recommended  occurs when an individual’s likelihood of accepting or choosing a potential mate is greater if others regard that mate as attractive. In controlled experiments, human subjects are commonly shown images of model individuals and asked to rate the model’s desirability, interest, or physical attractiveness. Designs differ between female and male subjects. Gouda-Vossos et al.  report tIn one meta-analysis Gouda-Vossos et al. combined data from 17 studies of female choice in which the experimental manipulation was the addition of a female cue; that is, the female subject viewed images of male targets presented with (vs. without) a female. The data are available from the supplementary material in Gouda-Vossos et al.  and are entclass1pt{minimaτ2 show clear differences. DL provides the highest value at 0.0158, followed by J at 0.0119, REML at 0.0091, and MP at 0.0080, half the size of DL.Table λ=0,τ2=0 and 0.1, and n=40 and n=100. Under these conditions for both normal and lognormal distributions, all methods overestimate τ2 at zero, but we do not have results for positive values of τ2 below 0.1. Our results show that for small τ2>0, the standard methods overestimate λ=0, and only SSW provides nearly unbiased estimates of λ under both normal and lognormal distributions. These results agree with our findings for this example. The SSW estimate of λ, 0.0528, is lower than all IV-weighted estimates .The closest simulation scenarios are for τ2 have considerable effect on the width of the confidence intervals for λ.As the sample sizes are moderate to large, the differences in estimated λ that did not include 0. These reflect the combination of a positively biased estimate of λ and the low estimate of τ2. The original meta-analysis used REML. Interestingly, the HKSJ confidence intervals based on MP and DL also do not cross 0. For HKSJ (DL), this happens because it is actually shorter than the DL interval for these data. The SSW MP CI is wider than the HKSJ confidence intervals, and it includes 0.Among the IV-weighted methods, only REML and MP produced confidence intervals for As the sample sizes are moderate to large, the bias correction is not needed. It is not recommended for normally distributed data in any case.λ, and the HKSJ MP interval to provide correct coverage. Therefore, we do not consider the effect of MCC in women to be significant.Because, in our simulations, the IV-weighted methods tend to give positively biased results, we consider the SSW point estimate to be close to the true value of μg/kg of body weight per minute) with placebo or no therapy, Friedrich et al. [Controversy surrounded the use of low-dose dopamine (a catecholamine with dose-dependent effects) to promote kidney function in several categories of patients . In a systematic review and meta-analysis of randomized controlled trials that compared low-dose dopamine . In both analyses, all methods find a significant effect of dopamine, with SSW MP providing the widest confidence intervals.Table λ=0.2,K=30,τ2 between 0 and 0.1, and n=10 to n=100. Under these conditions for both normal and lognormal distributions, all methods overestimate τ2 when n=10, but are almost unbiased for n=40. We expect that all methods would provide coverage of τ2 that is too low, with QP being the best. We do not expect the bias correction to improve bias or coverage. Our results show that λ=0.2 is overestimated by the standard methods for small τ2>0, and only SSW provides nearly unbiased estimates of λ for both normal and lognormal underlying distributions. This agrees with our findings for this example. The SSW estimate of λ, 0.210 (or 0.209 after bias correction), is lower than all IV-weighted estimates.The closest simulation scenarios are for τ2 are higher, at 0.093 for DL to 0.226 for MP. From our simulations, they may be more positively biased, and in these data bias correction reduces estimates of τ2 to 0.088 to 0.166, respectively, probably reducing biases. We expect SSW to provide a nearly unbiased estimate of λ, at 0.270, with other methods positively biased (the highest at 0.314 for MP). Bias correction does not much affect the SSW estimate, but it does somewhat reduce the positive bias of the other methods (0.292 for MP). Coverage of λ should be nearly nominal for SSW MP  and lower than nominal for HKSJ MP, with the IV-weighted methods providing considerably lower coverage. In summary, the IV-weighted methods seem to indicate a significant effect of dopamine, whereas SSW MP does not.For the 10 studies in the “Other surgery” subset, estimates of Our simulations raise concern about the current state of meta-analysis of LRR. For that effect measure and some others, the relation between the studies’ estimated effects and their estimated variances has several undesirable results: the performance of all inverse-variance-weighted methods depends on the effect sizes, estimates of overall effects are biased, and their confidence intervals have below-nominal coverage, especially for small sample sizes. Our simulations show this clearly.X/Y is, in general, heavy-tailed and has no moments. It can be approximated by a normal distribution only when both X and Y are independent and have positive means, and their coefficients of variation fulfill some conditions [It is well known that the distribution of a ratio of normal random variables nditions . The logτ2 for very small n, but overall MP and REML are reasonable choices, especially for τ2 farther from zero. QP provides reasonable, though not perfect, coverage. For lognormal underlying distributions, τ2 cannot be estimated reliably for sample sizes smaller than 100; but once more, MP is a good choice for larger sample sizes.For normal underlying distributions, we found considerable biases in all methods of estimating Most applications of meta-analysis aim primarily to provide point and interval estimates of an overall effect. For general use, a point estimator should be unbiased, and a confidence interval should have (close to) nominal coverage.τ2, customary practice uses an inverse-variance-weighted mean to estimate the overall effect. The origin of the IV-weighted approach lies in the fact that, for known variances, and given unbiased estimates of the study-level effects, it provides a uniformly minimum-variance unbiased estimate (UMVUE). However, in practice, the within-study variances are unknown, and using estimates for them leads to bias in the IV-weighted estimate of the overall effect and below-nominal coverage of the confidence interval. Thus, the IV-weighted approach is misguided; for most measures of effect, it cannot avoid these shortcomings.After estimating the between-study variance t distribution on K−1 degrees of freedom, and the SSW MP interval adopts that choice. We have, however, seen no empirical evidence relating these choices of reference distribution to the sampling distributions of the point estimators, for LRR or other measures of effect. In future work we intend to investigate sampling distributions of estimators of overall effect and τ2.To improve the coverage of confidence intervals systematically, we would like to have a better understanding of the underlying sampling distributions. For the IV-weighted estimators of the overall effect, in this study, we have retained the customary use of critical values from the normal distribution. To remedy the familiar problem of below-nominal coverage, the HKSJ interval uses the A reviewer called attention to a modification of the IV-weighted estimator of the overall effect that takes into account the relative quality of the studies , 39. ThaXiT and XiC differ substantially.The gaps in evidence include the possibility that the unit-level variances in the two arms may differ, which simulations rarely, if ever, reflect. Because of the extent of our simulations, we did not attempt to fill this gap. However, we do not expect the performance of the IV-weighted methods to improve under more-challenging scenarios. Rather they are likely to perform worst in situations where the (within-study) variances of λ uses weights that do not involve estimated variances . Our point estimator SSW uses weights proportional to an effective sample size, t-based confidence interval for λ is centered at A pragmatic solution to unbiased estimation of from Eq. . Finallyλi, works reasonably well for sample sizes as low as 10 in interval estimation of λ, and for n≥40 in point estimation. We recommend this method for further use in applications.For underlying lognormal distributions, SSW, combined with the bias-corrected estimator of λ for very small sample sizes and λ close to 0, and the bias correction is harmful. The response ratio is a rather challenging effect measure, with two additional sources of possible bias: its restricted range near 0 under the normal model, and transformation bias in using the log scale for specification of random effects. Both issues are inherent in the choice of the respective true model and cannot be easily resolved. Farther from 0, SSW is practically unbiased, and we recommend its use, in combination with SSW MP, which is the only feasible option for confidence intervals.Unfortunately, for underlying normal distributions, the use of sample-size-based weights does not avoid all the problems with bias in estimation of τ2 that we included all had considerable negative bias for normal within-study data and very small study-level sample sizes (n), especially when one of the means was close to zero. For lognormal underlying data, τ2 cannot be estimated reliably for n<40. MP had the least bias overall, and DL should not be used.In extensive simulations the four point estimators of τ2 that we included had coverage that often was below the nominal 95%, in various patterns, especially as the number of studies (K) increased. For lognormal underlying data, many situations were quite challenging. The QP and, to a lesser extent, PL interval estimators had coverage close to 95% when n≥100 or when n was moderate and K was small.For normal underlying data, the four interval estimators of λ that use inverse-variance weights had substantial bias, systematically related to τ2, for normal underlying data, but less bias (with weaker relation to τ2) for lognormal data.Point estimators of An estimator whose weights used only arm-level sample sizes (SSW) typically has less bias and is recommended. Additionally, we recommend bias correction for lognormal data, but it is contraindicated for normal data.n≤40) and large numbers of studies (K≥50) its coverage was sometimes low. Interval estimators based on the inverse-variance-weighted point estimators were inferior, in various patterns, and we do not recommend them.We recommend an interval estimator based on SSW. It mostly had coverage close to 95% for both normal and lognormal data, but for small sample sizes (Additional file 1 Q-Q plots for the standardized means in Examples 1 and 2.Additional file 2 R procedures to implement MP SSW, HKSJ MP, and MP IV methods for meta-analysis of LRR.Additional file 3 Relation of I2 to parameters underlying our simulations.


The objectives of the current study were to study the main environmental factors affecting birth weight (BW) and weaning weight (WW), estimate variance components, genetic parameters and genetic trend and to evaluate the variability and relationships among breeding value of BW and WW using principal components analysis (PCA).A total of 16,370 records were collected from 8,271 buffalo calves. Genetic parameters and breeding values were estimated using a bivariate animal model which includes direct, maternal and permanent maternal effects. These estimates were standardized and used in PCA.The direct heritability estimates were 0.06 and 0.41 for BW and WW, respectively whereas direct maternal heritability values were 0.03 and 0.14, respectively. Proportions of variance due to permanent environmental effects of dam were 0.455 and 0.280 for BW and WW respectively. The genetic correlation between BW and WWs was weak approaching zero, but the maternal correlation was 0.26. The first two principal components (PC1 and PC2) were estimated utilizing the standardized breeding values according to Kaiser method. The total variance explained by the first two PCs was 71.17% in which 45.91% and 25.25% were explained by PC1 and PC2, respectively. The direct breeding values of BW were related to PC2 but those of WW and maternal breeding values of BW and WWs were associated with PC1.The results of genetic parameters and PCA indicate that BW and WWs were not genetically correlated and improving growth traits of Egyptian buffaloes could be achieved using WW without any adverse effect by BW. Bubalus bubalis) contributed 39.2% and 45.2% of national total meat and milk production, respectively [Water buffalo are important source of meat, high quality milk and skin as well as other by products, not only in Egypt but also in many countries worldwide. Thus, buffalos contribute significantly in agriculture economy and human well-being in these regions. The total number of buffaloes worldwide is about 195.1 million heads, in which 97% are raised in Asia [Calf birth weight (BW) is one of the main breeding goals of buffalo breeders, because of its positive relationship with production and reproduction performance. Although, MMI Salem and AMS Amin  showed tData were collated from five buffalo experimental herds  belonging to the Animal Production Research Institute (APRI), Agriculture research center (ARC), Ministry of Agriculture and Land Reclamation, Egypt. A total of 16,370 records were available on 8,327 buffalo calves in which 8,271 and 8,099 records for BW and WW, respectively, were included in the analysis. These calves were born between 1980 and 2018 with pedigree having 188 sires and 2,211 dams .The systematic environmental effects on growth performance traits were examined as fixed effects using least squares methods implemented in general linear model procedure of SAS . These fijklmnop, the phenotypic record of BW or WW; μ, the effect of the intercept; Ai, the fixed effect of ith season of calving; Bj, the fixed effect of jth year of calving; Ck, the fixed effect of kth sex; Dl, the fixed effect of lth herd; Gm, the fixed effect of mth gestation length; Wn, the fixed effect of nth WD; Po, the fixed effect of oth parity and eijklmnop, random residual assumed to be independent normally distributed with mean zero and variance σ2e. The significant fixed effects were used to form contemporary groups, which were included in genetic parameters analysis.Where, YVariance components, heritability and breeding values were estimated using the bivariate mixed animal model using Wombat software . The modAnd the assumptions of the variances were as:y, a vector of BW or WW observations; b, a vector of fixed effects with an incidence matrix X; a, a vector of random animal effects with incidence matrix Z; m, a vector of random dam effects with incidence matrix S; c, a vector of random permanent environmental effects of dam with incidence matrix W; and e, a vector of random residual effects. A is the numerator relationship matrix between animals, I is an identity matrix, σ2a is direct additive genetic variance, σ2m is maternal additive genetic variance, σ2am is the direct × maternal genetic covariance, σ2c is maternal permanent environmental variance, and σ2e is residual variance. Direct and maternal genetic trends were estimated by regressing yearly mean estimates of breeding value of animal and dam on year of calving.Where i = (xi− χ̄)/si, where zi is the standardized value of xi variable, χ̄ is the mean of ith trait, and si is the corresponding standard deviation. Then, the standardized estimated breeding values (SEBVs) were used in the PCA performed using FactoMineR package [The principal component (PC) could be used as index to evaluate animals for multiple traits . First,  package  in R sof package . In the  package . Thus, tij is the SSC for SEBV of ith trait in the jth PC. The principal component scores were calculated as follows:Where SSCjl is the principal component score for the lth animal in the jth principal component, SSCij is the SSC for EBVs of ith trait in the jth PC and SEBVil is the standardised estimated breeding value of the ith trait for the lth animal.Where PCSThe current study assessed the non-genetic factors affected the growth performance (i.e. BW and WW) in Egyptian buffalo . The sexam) effects for BW (−0.16) which was reported by other studies [The direct heritability estimates were 0.06 and 0.41 for BW and WW, respectively whereas direct maternal heritability values were 0.03 and 0.14, respectively . These h studies . This ne studies .2) was higher than h2m for BW and WW, indicating that maternal environmental effect was dominant until weaning [2 and h2m for different beef breeds were close to those obtained in the current study [am) was negative for WW and higher than its value for BW. This negative ram was also found in Australian beef cattle [In the current study, high 0.41) and moderate (0.14) direct and maternal heritability estimates were obtained for WW, respectively indicating that the genetic selection to improve WW is possible with good response of maternal ability . Such lo1 and mod weaning . Estimatnt study . The dirf cattle  and Spanf cattle . The negf cattle .m and maternal permanent environmental rc correlations were 0.262 and 0.003 respectively which were lower than estimated values 0.33 and 0.64 reported in Japanese beef cattle [A low genetic correlation between BW and WW (0.05) found in the current study indicated that selection to improve WW in buffalo may not affect BW in a breeding objectives that include both traits. Such relationship is very important to avoid dystocia which may occur for calves with high BW. High estimates of genetic correlation between BW and WW of Egyptian buffalo calves were reported in other studies  using anf cattle .Remarkable fluctuations in breeding values of calves and dams, and negative direct and maternal genetic trend in some years were found . AverageThe total variance explained by PCs was 71.17% in which 45.91% and 25.25% were explained by PC1 and PC2, respectively . These rPC1 explained most of direct and maternal breeding value variation and was correlated with the direct and maternal breeding values of WW and maternal breeding values of BW. Thus, it could be considered as genetic index to WW and also as maternal index for BW and WW. Only 25.25% of direct and maternal breeding value variation was explained by PC2 which was correlated with direct breeding values of BW and considered as genetic index related BW. Therefore, selection to improve WW could be applied using PC1 separate from selection to improve BW in Egyptian buffalo. These results supported the reported genetic correlation between BW and WW in The PC scores for each animal in the first two principal components were calculated as:The weights of these indices were SSC for each SEBV. The larger the absolute value of the SSC, the greater the relative importance. The 2 PC scores allowing capture the main information in predicted breeding value for BW and WW. Animals with higher PCS1 could be used to improve WW, and animals with higher PCS2 could be used to improve BWs. Thus, selection with previous index could be used in genetic selection programs of Egyptian buffalo. As previously mentioned regarding the use of PCA is very practical technique to reduce the data dimensionality especially with limited number of observations in the dependent variables under the lacking of national recording system in Egypt. Also, under Egyptian breeding programs, it has been difficult to develop the economic indices and if developed they were rarely used because of the difficulty in economic weights for each trait as the Egyptian market is not stable. Thus, we can consider the PCSs as new traits which can be included in new breeding objectives and used as selection criteria under Egypt condition. Meanwhile, in other studies the PCSs can be used to reduces the genetic variance components accounting for selection bias and correlated response in correlated traits .All environmental factors affect BW, and sex, season of calving and herd affected on WW. The results indicated low heritability value for BW, high heritability value for WW and low genetic correlation between BW and WW. Moreover, 2 PCs components were sufficient to capture the breeding value variation of the studied traits. Finally PC1 and PC2 could be considered as new traits representing WW and BW, respectively. These results suggested improving growth traits of Egyptian buffaloes could be achieved using WW without any adverse effect by BW.


A specific class of deep learning-based methods allows for the prediction of regulatory effects per variant on several cell type-specific chromatin features. We here describe “DeepWAS”, a new approach that integrates these regulatory effect predictions of single variants into a multivariate GWAS setting. Thereby, single variants associated with a trait or disease are directly coupled to their impact on a chromatin feature in a cell type. Up to 61 regulatory SNPs, called dSNPs, were associated with multiple sclerosis , major depressive disorder , and height . These variants were mainly non-coding and reached at least nominal significance in classical GWAS. The prediction accuracy was higher for DeepWAS than for classical GWAS models for 91% of the genome-wide significant, MS-specific dSNPs. DSNPs were enriched in public or cohort-matched expression and methylation quantitative trait loci and we demonstrated the potential of DeepWAS to generate testable functional hypotheses based on genotype data alone. DeepWAS is available at https://github.com/cellmapslab/DeepWAS.Genome-wide association studies (GWAS) identify genetic variants associated with traits or diseases. GWAS never directly link variants to regulatory mechanisms. Instead, the functional annotation of variants is typically inferred by  In the era of steadily increasing amounts of available genetic data, we still lack novel and innovative ideas on how to improve fine-mapping of regulatory variants identified by genome-wide association studies (GWAS), especially in non-coding regions. Current approaches for the identification of functional variants conduct functional annotation after the GWAS analysis either using position-based overlaps of each variant with regulatory elements or deep-learning-based methods predicting regulatory effects per variant on cell-type-specific chromatin features. We here present DeepWAS, which integrates these regulatory effect predictions of single variants into a multivariate GWAS setting. Our results provide evidence that DeepWAS results directly identify disease/trait-associated SNPs with a common effect on a specific chromatin feature in a relevant tissue. We can show for multiple sclerosis, major depressive disorder, and body height, that the SNPs identified by DeepWAS are at least nominally significant in classical univariate GWAS analysis of the same cohorts or larger published GWAS. By integrating expression and methylation quantitative trait loci (eQTL and meQTL) information of multiple resources and tissues, we can show that DeepWAS identifies disease/trait-relevant transcriptionally active genomic loci. We demonstrate that DeepWAS identifies both known variants and highlights underlying molecular mechanisms. Genome-wide association studies (GWAS) have been highly successful in identifying genetic variants associated with risk for common diseases and traits. However, going from pure association to mechanistic insight has been a much more challenging task. Identification of the true causal variants in the context of a disease or trait from within regions of associated variants is hampered by linkage disequilibrium (LD), as proximal variants are likely to co-segregate in a population. The functional variants can, in most cases, not be easily discerned within long stretches of such correlated DNA, which can span several genes and include hundreds of associated variants.cis-regulatory elements such as promoters and enhancers . It reduces the multiple testing burden of classical GWAS and makes regulatory information on a single SNP level readily available without requiring a second analysis step. We made use of the most recent predictions for SNPs with regulatory potential, which will be constantly growing whenever new data becomes available in the future. For a proof of concept of DeepWAS, we used data from published GWAS of two common diseases, multiple sclerosis (MS) ) to correct for the Inf I/Inf II distribution shift.DNA methylation data was also available for a subset of the KORA study (eviously . Intensin = 319 DE1 MS cases) was performed using lllumina HT-12 v4 Expression BeadChips, as described in [n = 1,002 F4 individuals) gene expression profiling was performed using the Illumina HT-12 v3 Expression BeadChips and described previously in [Gene expression analysis of a subset of the KKNMS cohort (ribed in . For a sously in .R package MatrixEQTL (https://cran.r-project.org/web/packages/MatrixEQTL/index.html), in order to detect cis-meQTLs. Sex, blood cell counts, and MDS ancestry components to correct for possible admixture effects were included as covariates. Significance after multiple testing was adjusted using a false discovery rate (FDR) of 5%.For the MDDC cohort, linear regression models were fit for each CpG site to test the relationship between the whole blood DNA methylation  and proximal SNP genotype (in dosage format) within 1Mb up- or downstream of the SNP using the cis-meQTL analysis in the KORA cohort we used the OmicAbel software (https://github.com/GenABEL-Project/OmicABEL) with age, sex, and blood cell counts as covariates. A total of 1,731 individuals had valid methylation and genetic data available. Significance was defined using Bonferroni correction at a p-value of 1×10−14. To examine the relationship between proximal genetic variation and gene expression, i.e. cis-eQTLs, in KORA , we first derived residuals for gene transcript expression using linear regression of log2-transformed gene transcript levels against sex, age, the RNA integrity number, RNA amplification plate, and sample storage time. Expression residuals were then used as outcome variables in a linear regression model with SNP dosage as the independent variable. Data analysis was performed using MatrixEQTL and significant cis-eQTLs were filtered at an FDR of 5%.For the whole blood cis-eQTL analysis in the KKNMS cohort, we used MatrixEQTL with sex, age, blood cell counts estimated using R package CellCODE (http://www.pitt.edu/~mchikina/CellCODE/), and MDS ancestry components as covariates. Significance after multiple testing was adjusted using an FDR of 5%.For the whole blood i.e. eQTM), downloaded from http://genenetwork.nl/biosqtlbrowser, CMC eQTLs [https://www.synapse.org/#!Synapse:syn4622659, and GTEx eQTLs [https://gtexportal.org/home/datasets, we were able to intersect our dSNPs and their LD proxies (r2≥0.5) with transcriptionally relevant data. The eQTLs obtained from GTEx were filtered on gene p<0.05 and eQTLs obtained from BIOS and CMC were filtered on FDR <0.05. We used permutation tests to determine if dSNPs or their LD proxies were enriched in BIOS QTLs. For each phenotype, we compared the overlap of dSNPs and BIOS QTL SNPs to the average overlap from 1,000 equally-sized sets of regulatory SNPs and BIOS QTL SNPs.Using published QTL data from BIOS whole peripheral blood DNA of 3,841 and mRNA of 2,116 healthy samples  . All DeepWAS results were inserted into the database. The graph structure consisted of genes, transcription factors, CpGs, SNPs, cell lines, and tissues that were connected to each other through dummy nodes representing each dSNP. Dummy nodes are especially important in cases where a dSNP is predicted to be active in more than one FU, e.g., TF1:CL1 and TF2:CL2. In this case, connecting these four elements directly to the dSNP leads to ambiguity about the FU, which can be misinterpreted as TF1:CL2 or TF2:CL1, since the information of the FU would be lost. Using dummy nodes avoids this confusion by providing a SNP-FU link.For the visualization of dSNP-QTL interactions, we set up a S1 FigA) MDD and (B) height dSNPs. Chromatin features are limited to be at least present in two distinct cell lines.The heatmaps show the number of selected chromatin features vs. cell line for ((PDF)Click here for additional data file.S2 Fig(A) Graph-based QTL Network visualization of the DeepWAS results involving the TF MEF2C, which itself is one of the top associated PGC GWAS loci. Two dSNPs are jointly associated with MDD and belong the same FU: MEF2C:GM12878. Edges represent the association relation of dSNPs, chromatin features with or without treatment, cell lines, top-level tissue group, CpGs, and genes. Edges of the FU MEF2C:GM12878 are colored in red. Circular shades mark the corresponding genes or CpGs with are plotted in B and C. (B) Box plot of GTEx frontal cortex eQTL data showing relationship between SPIDR gene expression and dSNP rs7839671. (C) Boxplot of recMDD meQTL data illustrating relationship between cg01650371 methylation and rs10099827 genotype in recMDD samples. Variant rs10099827 is a proxy of dSNP rs7839671 (r2 = 0.8). DSNP rs7839671 exhibits a meQTL effect on the same CpG and was excluded from the original meQTL. analysis, as it is 571 kb away from the CpG site (meQTL distance cutoff≤250 kb).(PDF)Click here for additional data file.S3 Fig(A) Locus-specific Manhattan plot of the dSNP rs2273030 that is a sub-threshold GWAS SNP for MS. The plot is produced using LocusZoom (https://github.com/statgen/locuszoom). with EUR samples of the 1,000 genomes November 2014 reference panel on the hg19 build. Dots represent GWAS p-values and the color of dots indicates LD with the lead variant, grey dots have LD r2 missing. (B) MS-specific three-way QTL interaction network generated by using a graph database and highlighting only the dSNPs with eQTL and meQTL effects that also harbor an eQTM. Edges represent the association relation of dSNPs, chromatin features with or without treatment, cell lines, top-level tissue group, CpGs, and genes.(PDF)Click here for additional data file.S4 FigA) Height-specific three-way QTL interaction network highlighting dSNP rs7146599 on chromosome 14 as one of the moderators of height in eleven cell lines. It affects a cascade of chromatin features (n = 8) and shows meQTL and eQTL effects that, at the same time, harbor an eQTM. The CpG site and the dSNP thus affect the transcriptional level of the same genes. In addition, the network includes rs2871960 on chromosome 3, linked to the ZBTB38 locus and correlated with multiple CpG sites. Edges represent the association relation of dSNPs, chromatin features with or without treatment, cell lines, top-level tissue group, CpGs, and genes. (B) MDD-specific three-way QTL interaction network generated by using a graph database and highlighting only the dSNPs with eQTL and meQTL effects that also harbor an eQTM. It shows that the MDD-specific dSNPs rs163105 on chromosome 5 changes the expression of SKIV2L2 . Edges represent the association relation of dSNPs, chromatin features with or without treatment, cell lines, top-level tissue group, CpGs, and genes.((PDF)Click here for additional data file.S5 FigThe LASSO picked out the smallest number of SNPs (n = 164 SNPs in 708 FU). The EN with penalty weight α = 0.1 (EN01) selected 169 SNPs in 710 FU, EN with α = 0.5 (EN05) selected 174 SNPs in 709 FU and EN with α = 0.75 (EN075) selected 169 SNPs in 706 FU. The single LASSO regression (SLR)  identified 19 SNPs showing a significant association with MS, these SNPs were also part of the sets of selected SNPs by either LASSO or EN.(PDF)Click here for additional data file.S6 FigThe y-axis indicates number of boosting iterations, the x-axis indicates the stability selection probability, and the horizontal line correspond the 0.7 probability threshold.(PDF)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.