Genetic correlations between fat-related traits and the glucose level vary between 0.35 and 0.74 and show a strong correlation between adipose tissue and impaired glucose metabolism. Our power calculations showed a minimum of 80% power for QTL detection for all phenotypes. We revealed genetic correlations at population level, for the first time, for several difficult to measure and novel OOR traits and diseases. The results underpin the potential of the established F2 pig resource population for further genomic, systems genetics, and functional investigations to unravel the genetic background of OOR traits.Obesity is a rising worldwide public health problem. Difficulties to precisely measure various obesity traits and the genetic heterogeneity in human have been major impediments to completely disentangle genetic factors causing obesity. The pig is a relevant model for studying human obesity and obesity-related (OOR) traits. Using founder breeds divergent with respect to obesity traits we have created an F2 pig resource population (454 pigs), which has been intensively phenotyped for 36 OOR traits. The main rationale for our study is to characterize the genetic architecture of OOR traits in the F2 pig design, by estimating heritabilities, genetic, and phenotypic correlations using mixed- and multi-trait BLUP animal models. Our analyses revealed high coefficients of variation (15–42%) and moderate to high heritabilities (0.22–0.81) in fatness traits, showing large phenotypic and genetic variation in the F2 population, respectively. This fulfills the purpose of creating a resource population divergent for OOR traits. Strong genetic correlations were found between weight and lean mass at dual-energy x-ray absorptiometry scanning (0.56–0.97). Weight and conformation also showed strong genetic correlations with slaughter traits (e.g.,  Obesity is a growing worldwide public health problem with a prevalence that has almost doubled between 1980 and 2008  have been performed to identify common genetic variants contributing to OOR traits and diseases. Using a GWAS-approach, 6–11% of the genetic variance could be explained in body mass index (BMI) by the identification of 32 loci, while heritability was estimated at 40–70%  as well as biologically relevant pathways and networks  mapping or GWAS in resource populations, a thorough knowledge on (additive) genetic variance of each trait and (genetic) relationships amongst them are investigated, particularly if such parameters for novel traits have not yet been reported elsewhere. For instance, genetic parameters for 16 different trypanotolerance traits were estimated  and Duroc (DD) sows from a DanBred breeding herd and Göttingen minipig (MM) boars from Ellegaard A/S in the parental generation. The production pig breeds have been selected for leanness and growth among other traits during the last 60 years, whereas Göttingen minipigs are prone to obesity and bred principally for their small size and ease of handling. They are also known to share the metabolic impairments seen in obese humans , resulting in 14 full-sib F1 families. In total, 127 F1 animals were produced: 60 males and 67 females, from which 81 F1 animals were randomly selected to produce the F2 generation. A total of 29 Minipig-Yorkshire (MY) and 24 Minipig-Duroc (MD) gilts were mated to respectively 15 MY and 13 MD non-litter mate boars (each boar used once or twice) to produce the F2 generation, so all F2 animals were a combination of Minipig × Yorkshire or Minipig × Duroc . A total of 474 piglets were born in three different groups, specified by season of birth (SOB), whereby the first SOB consisted of approximately 250 piglets born in June or July, the second SOB consisted of approximately 125 piglets born in August, September, or October, and the third SOB consisted of approximately 100 piglets born in December or January. Litters in the F2 generation consisted on average of eight piglets per litter and ranged from 2 to 12 born piglets. Piglets were weaned at 6–8 weeks of age. In total, the F2 generation consisted of 474 born piglets, 469 of which were still alive at 5 weeks of age and used in further analyses. The complete pedigree consists of 563 animals.® 50 Vet., ChemVet, Denmark), ketamin , detomidin , and buthorphanol . This full sedation is approved and granted by the Experimental Animal Inspectorate on July 1 2011 . Body composition was determined using dual-energy x-ray absorptiometry (DXA) scanning . The scanning was performed with the pigs in ventral recumbency with the front and hind limbs stretched backwards , 5 weeks (34–38 days), 2 months (64 ± 11 days), 125 days (115 ± 27 days), and 7 months (220 ± 45 days). After weaning, at approximately 2 months of age (64 ± 11 days), the piglets were anesthetized with 1 ml/10 kg of a mixture containing zolazepam and tiletamin  with an average of 15 piglets of the same sex per pen. Pigs were fed ad libitum with standard production pig feed  and with free access to water. All pigs were weighed two to four times within the period from 2.5 months to slaughter at approximately 80–100 kg. At the time of weighing, body conformation measurements were recorded  and placed in pens 2, whereby length is the length of the body from rump to the front of the shoulder blade 1.5, where the abdominal circumference is illustrated in Figure For subsequent data analysis some variables were calculated using the recorded measurements. Average daily gain was estimated over the whole growth period (from birth to approximately 7 months of age), and as daily gain pre- and post-weaning. In human studies, BMI is a commonly used indicator of obesity  were not normally distributed and therefore, the first four were transformed using logGENDER is the fixed effect of the sex i of the animal (two classes), SOB is the fixed effect of the SOB j when the pigs were born (three classes), AGE is the age k of the pig in days at the time of measurement as covariate, and kb is the associated fixed regression coefficient. LENGTH is the length of the animal in cm at the time of measuring as a covariate and lb is the associated fixed regression coefficient. The latter effect was only included for fat mass, lean mass, total mass (at DXA scanning) and weight of leaf fat at slaughtering. Random effects included were ANIMAL, the additive genetic effect of the animal l, and e, the error term. The following (co)variances among random effects were fitted:A is the additive genetic relationship matrix and I is an identity matrix. The animal and residual terms were assumed to be An univariate animal model was fitted to the data using ASReml variances as specified above.In order to estimate heritabilities and genetic and phenotypic correlations, we fitted a series of bivariate animal models for all combinations of traits. The bivariate animal model can be represented as follows:All analyses were implemented using ASReml  and Duroc or Yorkshire pigs  as founder breeds. This resource population has been comprehensively phenotyped for several OOR traits with the aim to conduct, among other things, QTL mapping, and GWAS. Table Dual-energy x-ray absorptiometry measurements of fat percentage in the F2 resource population showed an average of 18.6% (SE = 2.9). Previous research showed that DXA is an accurate method for estimating body fat, lean mass, and BMC in pork carcasses  and at 125 days , and slightly lower at 7 months . Huisman et al.  used twoThe heritability of average daily gain was 0.54 (SE = 0.14), while the heritability of pre-weaning daily gain was 0.81 (SE = 0.14) and post-weaning gain was 0.60 (SE = 0.14). Estimation of heritabilities for daily gain for different production breeds and crosses ranged between 0.20 and 0.31 . In addition, our results cannot be directly compared with results based on field data and production pigs.The CVs show a wide range of phenotypic variation: 15–45% for traits directly related to OOR traits. Heritabilities  showed that most of this overall variation is due to additive genetic effects, as expected from the F2 intercross. This was further investigated by plotting the distributions of estimated breeding values (EBV’s) for DXA%fat and FGL, as presented in Figure A multi-trait model that analyzes several traits simultaneously  and DXA scanning results, as expected Table . PreviouIn human research, BMI is popular due to simplicity of measurement and proven association with obesity. However, it is also known that BMI has many shortcomings Heber, . For exaP = 0.09); however, females have a slightly higher BMC and BMD than males, which is not in line with human research. Conversely, a study in a Duroc × Pietrain crossbred population shows no gender effect for BMD and BMC , and a negative genetic correlation with meat characteristics (between −0.45 and −0.76), which shows that an increase in weight of the pigs mainly results in an increase of fat Table , which iwww.biochild.ku.dk) and UNIK projects. Moreover, several tissues were collected at slaughtering, of which some will be used for RNA-sequencing to study transcriptomic profiles in extremely obese vs. lean pigs, as identified by the quantitative genetic analysis results reported here. In conclusion, the creation of this pig resource population resulted in a great potential to study the genetic architecture of OOR diseases.In the current paper we describe a unique resource population consisting of 450 F2 pigs created by using divergent breeds (Yorkshire/Duroc × Göttingen Minipig) as founders. The population was designed with the purpose of establishing a pig model in which the genetic background of OOR and associated traits can be studied. The statistical analyses made on the phenotypic traits recorded in the population clearly demonstrate that potential QTL’s causing variation in the traits of interest are likely segregating in the F2 pig resource population. This study considered a total of 563 animals  for estimation of genetic parameters. While this may be argued as low number of animals for parameter estimation, several other studies used fewer number of animals  to estimate genetic parameters, e.g., by Van Der Waaij et al. . The estQuantitative trait loci mapping or GWAS requires a thorough knowledge on genetic variances and any (genetic) relationships amongst traits that are investigated, particularly if such parameters for novel traits have not yet been reported elsewhere. This study has contributed to creating such knowledge for the established F2 pig resource population and provided a strong support for genomic investigations of OOR traits via GWAS and/or QTL mapping. Specifically, high heritabilities and strong correlations between weight, conformation, DXA, and slaughter traits between the different traits were reported here. This study, to the best of our knowledge, is the first experimental study in pigs in which a wide range of obesity traits, including novel DXA scan traits, information on different fatness traits at slaughter, and FGL have been measured in a large number of experimental animals. Consequently, it is the first study to report quantitative genetics characteristics on these novel OOR traits (in terms of estimated heritabilities and genetic correlations). In conclusion, the established F2 population gives a good rationale for further genome-wide and systems genetics approaches for detecting DNA variants, pathways, and gene networks affecting human obesity.Merete Fredholm was the experimental project leader who originally conceived the F2 experiment and collected/supervised the measurements on all pigs. Haja N. Kadarmideen was the statistical genetics analysis project leader who originally conceived the quantitative genetics design, models, and analysis part and supervised Lisette J. A. Kogelman in the analyses. Lisette J. A. Kogelman collated, edited, and analyzed the data. Lisette J. A. Kogelman wrote the first draft of the manuscript with contributions from Haja N. Kadarmideen, Thomas Mark, and Merete Fredholm. Peter Karlskov-Mortensen, Camilla S. Bruun, Susanna Cirera, Thomas Mark, Mette J. Jacobsen, and Claus B. Jørgensen contributed to pedigree development and phenotypic measurements of the pigs. All authors read and approved the final version of the 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.http://www.frontiersin.org/Livestock_Genomics/10.3389/fgene.2013.00029/abstractThe Supplementary Material for this article can be found online at Supplementary Table S1Phenotypic and genetic correlations of all analyzed variables. Excel file including all phenotypic and genetic correlations, with their standard errors.Click here for additional data file.


Several statistical methods have been suggested for genomic selection. Compared to traditional selection, genomic selection can be more accurate which can lead to higher efficiency in terms of time and cost. Herein we applied different genomic evaluation methods on the 14Four different approaches were used for the estimation of EBV of animals for the Quantitative and the Binary Trait (QT and BT respectively). It included two Bayes B types of approaches (BB): using only SNP information (GBB) or SNP and Pedigree information (GPBB); and two genomic BLUP, GBLUP and GPBLUP. Traditional BLUP was also used only for comparison. When using BB methodology, the probability of SNP having an effect on the traits (which include a quantitative and a binary trait) were also estimated. We also performed “standard” QTL mapping approaches including linkage and association analyses to compare them with BB results as a potential QTL mapping tools.r = 0.68). Genomic BLUP estimations (GBLUP and GPBLUP) were less accurate (r = 0.60 and 0.61 respectively). Similar results were obtained for the BT: r were estimated at 0.82, 0.82, 0.71 and 0.70 for GPBB, GBB, GPBLUP and GBLUP respectively. Using traditional BLUP, r was at 0.39 and 0.47 for QT and BT respectively. The genetic correlation between the two traits (approximated by the correlation between EBVs for BT and QT using GBB method) was as high as 0.58.For QT, the best accuracy of EBV (correlation between EBVs and TBVs) for young animals, was obtained by BB methods (r=0.58) which suggested that bivariate analyses may be of advantages. Signal profile by GBB followed well the true QTL patterns, which was consistent with good estimation of EBVs by this method, suggesting its potential value for QTL mapping.Better accuracies were obtained using BB methods, compared to BLUP analyses. Compared to the traditional BLUP, the accuracy of the EBVs was improved about 70% and 50% using BB and GBLUP methods respectively. The benefit of genomic selection was the same for both the QT and BT. Models with and without polygenic effect led to similar accuracies in the estimation of breeding values. The BT and QT were genetically correlated ( Genomic selection can be described as the use of highly dense genotyping in the evaluation of animals, to increase the accuracy of the estimated breeding values (EBV) . SeveralRegardless the approach used for genomic selection, their success would depend on the quality of the SNP map to capture the whole genetic variation, which would depend on several factors such as Linkage Disequilibrium (LD) between loci and the coverage of the whole genome. In order to safeguard against possible problems related to the quality of the SNP panel, the model can be modified to include an extra genetic effect which is explained by the pedigree information. A model combining both source of information may prove to be beneficial.The aim of this study was to compare the results evaluations from using these two methods (a modified Bayes B and genomic BLUP) with and without polygenic in the model to evaluate animals in the QTLMAS dataset. We also compared BB results with “standard” association and linkage analyses, to assess its potential values for QTL mapping.The data used is the simulated dataset distributed by the organisers of the QTLMAS workshop 2010. The population consists of 3226 individuals spanning 5 generations, of which the last 900 individuals have no phenotype for a quantitative and a binary trait (QT and BT). Genome is about 500 Mb long distributed in 5 chromosomes. All individuals have genotype for 10031 SNPs.a priori. Applying these assumptions, two models, with (GPBB) or without polygenic effects (GBB), were fitted:Bayes B (BB) method was first described by Meuwissen et al.. Basicaly is the vector of phenotypes; µ is the population mean for the trait; n is total number of SNP, zi is the vector of genotypes at SNP i; iβ indicates the allelic substitution effect for SNP i; and e is the vector of residuals. The allelic substitution effects β for each SNP were assumed to come from a mixture distribution, with probability of π to have a non-zero effect on the trait, a is the genetic addictive effect explained by pedigree information and assumed to be normally distributed, A is the additive relationship matrix calculated from pedigree information, Z is the incidence matrix. Here, thereafter, the effect associated to the pedigree will be referred as the polygenic effects.where, The models were implemented using Gibbs sampling. The parameters π and For the binary trait a liability threshold model was used.In order to estimate the relative value of the genetic effect explained by the SNP or the pedigree information, the genetic variance explained by genomic information (SNP) was estimated. The simplest approach would have been to sum the variance individually explained by each SNP given their effects and frequencies, but this may be biased because it does not account for the LD between loci. In order to avoid this problem, an approximation based on the infinitesimal model theory was used :r is the accuracy of estimates. The explained additive genetic variance  and the true breeding values (TBV). Alternatively, within each method we compared the model with and without polygenic effect using Bayes Factor (BF)  and likeAdditionally to the estimated SNP effects, BB methods also estimate the probability of SNP having an effect on the trait, which can be used as a criterion for QTL mapping. In order to assess its potential in use, we compared these results with standard association and linkage analyses.Association analyses were performed using the GRAMMAR approach , which cHalf-sib analyses (HS-QTL) were performed as described by Haley et al. , and impAs the population is distributed across several generations creating a complex pedigree structure, a QTL mapping based on a variance component approach (VC-QTL) may perform better than the mapping based on half sibs regressions. Here, we performed this analysis for the quantitative trait. The method is based on a two-step approach : At eachCorrelations between TBV and EBVs estimated by the different methods were shown in Table Table Correlation between EBV for both traits was around 0.58 across the four genomic selection methods Figure . This reBB estimated the probability of a given SNP having an effect on the trait. Locating single SNP or a cluster of linked SNP with a relatively large probability may be used as criteria for mapping QTL. Figures The good performance of the BB, in terms of genomic evaluation of animals, was also reflected in the consistent QTL signals, obtained by the method, compared to the actual simulated QTLs, raising its potential value for QTL mapping.The authors declare that they have no competing interests.JN and RPW carried out the analyses and drafted the manuscript. Both authors have read and contributed to the final text of the manuscript.


Genetic factors are believed to account for 25% of the interindividual differences in Years of Life (YL) among humans. However, the genetic loci that have thus far been found to be associated with YL explain a very small proportion of the expected genetic variation in this trait, perhaps reflecting the complexity of the trait and the limitations of traditional association studies when applied to traits affected by a large number of small-effect genes. Using data from the Framingham Heart Study and statistical methods borrowed largely from the field of animal genetics , we developed a WGP model for the study of YL and evaluated the extent to which thousands of genetic variants across the genome examined simultaneously can be used to predict interindividual differences in YL. We find that a sizable proportion of differences in YL—which were unexplained by age at entry, sex, smoking and BMI—can be accounted for and predicted using WGP methods. The contribution of genomic information to prediction accuracy was even higher than that of smoking and body mass index (BMI) combined; two predictors that are considered among the most important life-shortening factors. We evaluated the impacts of familial relationships and population structure  and concluded that in our dataset population structure explained partially, but not fully the gains in prediction accuracy obtained with WGP. Further inspection of prediction accuracies by age at death indicated that most of the gains in predictive ability achieved with WGP were due to the increased accuracy of prediction of early mortality, perhaps reflecting the ability of WGP to capture differences in genetic risk to deadly diseases such as cancer, which are most often responsible for early mortality in our sample. Agricultural and biomedical research has shown through controlled experiments and familial studies that many complex traits are highly heritable, suggesting that in principle, such traits could be predicted early in life from knowledge of individuals' genotypes. Human longevity is not an exception: empirical evidence from twin and familial studies indicate that approximately 25% of inter-individual differences in human lifespan can be attributed to genetic factors Research with model organisms offers several examples of genetic polymorphisms having a sizable effect on lifespan Several diseases  and biological events  can lead to death, and the genetic architecture  of each of these mortality-related traits is expected to be disorder-specific. Therefore, the genetic architecture of YL is likely to include a large number, perhaps thousands, of possibly interacting genes.Recent articles Whole genome prediction exploits multi-locus linkage-disequilibrium (LD) between quantitative trait loci (QTL) and genome-wide markers  to predict inter-individual differences in a quantitative trait that are attributable to genetic factors. Unlike traditional association studies, in which the association between markers and phenotypes is tested one marker at a time, WGP uses all available markers to regress phenotype onto genomic information. This methodology was first proposed in the field of animal breeding by Meuwissen Hayes and Goddard in 2001 2) and smoking.More recently, research with human height showed that much of the so-called missing heritability of complex traits could be recovered using genome-wide panels of common variants Many outcomes in human-health studies are either binary  or are subject to censoring . And it is well established that ignoring censoring yields biased estimates i = 1,…,n) as the sum of individual-specific means (thj SNP. By combining (1) with the normal assumptions described above, we derived the likelihood function for censored and un-censored individuals , and the rate and shape parameters  assigned to the regularization parameter of the BL. A discussion of how these can be chosen is given in Perez et al. The Bayesian model is completed by assigning a prior density to the collection of model unknownsModels were fitted using a modified version of the BLR package http://www.framinghamheartstudy.org/research/consentfms.html for further details about consent forms). And the current study has been approved by the Internal Review Board of University of Alabama at Birmingham (IRB Protocol Number: X090720002). The criteria for inclusion in the study included being 18 years or older at time of recruitment, having survival information as of 2007, and having complete information for covariates . were from the original  and offspring  cohorts of the Framingham Heart Study. Data and material distributions from this study are made in accordance with the individual consent history of each participant . Other editing and genotyping quality control and imputation procedures were as described in Makowsky et al. Average age at entry was 37 with a standard deviation (SD) of 9.0 years. Of the participants, two thirds  were censored , 55% were female, and 36% never smoked. Mean BMI at first exam was 25.0 with a SD of 4.1 kg/mA-0) includes an intercept, sex, and age at entry; the latter modeled nonparametrically using a 4-df natural spline th, 50th and 75th sample percentiles of the predictor variables. We extended this model by adding smoking and BMI  to 80K; these models were denoted as M(.)-2.5K, M(.)-5K, M(.)-10K, M(.)-20K, M(.)-40K and M(.)-80K, where (.) was either A or B.Using the specification of equation (3) we generated a sequence of nested models by changing the predictors included in the right-hand side of the linear predictor  and to evaluate the goodness of fit and the Deviance Information Criterion First, in order to account for population structure, we extended the model including age, sex, smoking and BMI as predictors (MB-0) by adding the effects of the first two principal components (PCs) derived from the same set of 80K SNPs used in M(.)-80K. Second, to quantify the relative importance of familial relationships on prediction accuracy we carried out two additional analyses: (a) we extended MB-0 by adding an effect representing a regression on the pedigree. This was done using the standards of the additive infinitesimal model of quantitative genetics B-PED. And (b) we fitted models MA-0K, MB-0K and MB-80K in a 10fold CV where entire families, as opposed to individuals, were assigned to folds; therefore, in this CV predictions are derived from nominally-unrelated individuals.The distribution of genotypes, their allele frequency, levels of LD, etc., can be affected by factors such as population structure, admixture or familial relationships. Therefore, a certain proportion of the prediction accuracy of WGP could be attributed to those factors. To further explore this, a series of additional analysis were carried out. B-0, we estimated an average (± posterior SD) difference in YL between females and males of 3.1 (±0.42) years and between smokers and nonsmokers of −4.1 (±0.44) years. Using estimates from MB-0, we computed the expected YL of a nonsmoking 35-year-old by sex and BMI; the results are displayed in ) and from 12% to 21% for the model including smoking and BMI (MB-(.)).  consistently across folds indicating that SNPs are capturing important and consistent patterns of variability in human lifespan.MB-(.)).  shows  fB-0K and MB-80K. As expected, for both models, the absolute value prediction error was lowest for people dying around median age (80 YL) and increased for people dying early or late in life. Predictions derived from model MB-80K were much more accurate than those of MB-0 for the prediction of YL of people dying early in life; however, the prediction accuracy of the model with markers was slightly higher than that of MB-80K for subjects dying at intermediate ages. This suggests that the overall higher predictive ability of MB-80K is due mostly to improvements in prediction of early mortality.The above results indicate that markers can explain a sizable proportion of inter-individual differences in YL that are not accounted for by age at entry, sex, smoking and BMI. To obtain further insights into the source of this improvement in prediction accuracy, we present in A-0, MB-0, and MB-80K for each of the 8 thresholds . Adding BMI and smoking information to a model that included sex and age (MB-0 vs MA-0) resulted in an increase in AUC(τ) of roughly 5–7%. When 80 thousand SNPs (MB-80K) were added to a model that included age, sex, smoking and BMI as covariates we observed a substantial increase in classification performance for prediction of early stage survival status  of 18%), a more modest increase in AUC(τ) for survival status at ages 65–90 (MB-80K outperformed MB-0 by about 14% for AUC(65) and by 7–10% for AUC(70)–AUC(90)), and no change in AUC(95). These results are consistent with those observed with A-0, MB-0 and MB-80K by fold of the CV. Similar to what we observed for B-0 relative to that of MA-0 such superiority was not consistently observed in every fold. However, for early and intermediate survival status (τ≤85) model MB-80K had a classification performance that was consistently higher than that of models without genetic information (MA-0 and MB-0). For late mortality (τ>85) such superiority was not consistently observed across folds.B-GWPC was 15.77%, this is roughly half the way from the B-0 (11.45%) and that of model MB-80K (21.40%). Results for AUC showed similar patterns. This indicates that a sizable proportion of inter-individual differences in YL could be attributed to genetic differences associated to population structure. On the other hand, the fact that the B-80K was 37% higher than that of model MB-GWPC suggests that genetic factors beyond those associated with population structure account for a sizable proportion of inter-individual differences in YL.The estimated B-PED, which including age at entry, sex, BMI, smoking and pedigree information showed clear signs of over-fitting  and, consequently, had a very poor predictive performance; even worse than our baseline model (MA-0). This is most likely to occur because of two reasons. First, the pedigree is very sparse, with 37% of nominally un-related individuals and most of the remaining individuals coming from relatively small nuclear families . Additionally, in the great majority of nuclear families the offspring have censored YL. Therefore, in this dataset the amount of familial information available for prediction is very limited. To further illustrate this, we counted for every subject in the 10-fold CV where individuals were randomly assigned to folds the number of close-relatives  which were used for prediction . We found that in our CV 41.6 of the observations were predicted without having any direct relative in the training dataset (i.e. in other folds) and 70.75 were predicted without having any un-censored direct relative available for training. Only 10% of individuals had 3 or more direct relatives in the training datasets, and no-one had 3 or more direct relative with observed YL assigned to a different fold.Model MA-0, MB-0 and MB-80K in a10-fold CV where entire families, as opposed to individuals, were assigned to folds. Such setting guarantees that no-direct relatives are used for prediction. The B-0 and MB-80K, respectively) to the ones we obtained when subjects, as opposed to entire families, were assigned to folds . Combining all these results we conclude that in our analysis familiar relationships were not a major factor explaining the prediction accuracy obtained with WGP.Our second approach to quantify the relative importance of family relationships on prediction accuracy consisted on fitting models MOur results suggest that genomic information can enhance prediction of lifespan, mostly by improving prediction of early mortality. This can be due to several factors, one of which may be that SNPs are capturing genetic risk to certain diseases that are most responsible for early mortality. Familial studies suggest that roughly 25% of the inter-individual differences in YL can be attributed to genetic factors When genetic markers were added to a model accounting for age at entry, sex, smoking, and BMI, the increase in As anticipated, our results suggest that the genetic basis of YL involves a large number of variants. The observation that DIC and prediction accuracy improved with marker density suggests that a large number of markers spread across the genome are needed to account for differences at QTLs affecting YL, and this is consistent with what one would expect for a trait that conforms to an “infinitesimal” model p-values derived from single-marker regressions. Although the study by Yashin et al. Our results are also consistent with those of Yashin et al. In addition to demonstrating that a sizable proportion differences in YL can be predicted using genomic information, we found that most of the gains in prediction accuracy obtained with use of genetic information came from increased accuracy of prediction of early mortality. Further examination of the distribution of causes of death by age at death reveled that cancer was the leading cause of death for people dying early in life. Therefore, a possible explanation of our results is that the ability of our WGP to capture cancer risk (indirectly through YL) was higher than for other death-related disorders. Further studies, using disorder-specific responses  and case-control datasets will be needed to confirm this conjecture.The Framingham dataset has a familial design and exhibits some level of population structure, much of which can be described through PCA of genome-wide SNPs. Whole-Genome Prediction exploits multi-locus LD between markers and QTL. These patterns of LD are likely to change across sub-groups in the population and because of this, models fitted using WGP cannot be regarded as ‘universal equations’. The validity across sub-groups of the patterns captured by a WGP model will depend on the extent to which genetic features  present in training samples are also present in those used for validation.Including the first two marker-derived PCs increased prediction accuracy markedly, indicating that YL covariates with ancestry, as described by the first 2 PCs. However, the level of prediction accuracy attained by models using the first two marker-derived PCs was substantially lower than that of the model using 80K genome-wide SNPs, suggesting that the genetic factors affecting YL cannot be fully described by features such as population structure. The effects of familial relationships on the prediction accuracy of WGP are well established Methods S1Describes the Bayesian model used.(DOCX)Click here for additional data file.Figure S1Estimated expected years of life versus Body Mass Index (BMI) by sex .(TIFF)Click here for additional data file.Table S1Cross-validation R-squared and Area Under Longitudinal Receiver Operating Characteristic Curves by model and fold of a 10-fold cross-validation.(DOC)Click here for additional data file.


It is well known that the presence of population stratification (PS) may cause the usual test in case-control studies to produce spurious gene-disease associations. However, the impact of the PS and sample selection (SS) is less known. In this paper, we provide a systematic study of the joint effect of PS and SS under a more general risk model containing genetic and environmental factors. We provide simulation results to show the magnitude of the bias and its impact on type I error rate of the usual chi-square test under a wide range of PS level and selection bias.The biases to the estimation of main and interaction effect are quantified and then their bounds derived. The estimated bounds can be used to compute conservative p-values for the association test. If the conservative p-value is smaller than the significance level, we can safely claim that the association test is significant regardless of the presence of PS or not, or if there is any selection bias. We also identify conditions for the null bias. The bias depends on the allele frequencies, exposure rates, gene-environment odds ratios and disease risks across subpopulations and the sampling of the cases and controls.Our results show that the bias cannot be ignored even the case and control data were matched in ethnicity. A real example is given to illustrate application of the conservative p-value. These results are useful to the genetic association studies of main and interaction effects. In the search of causative agents of human disease, both environmental and genetic risk factors have been identified. Overwhelming evidence indicates that there are reasons to believe that relative common polymorphisms in a wide spectrum of genes may modify the effect of environmental agents ,2. SeverMany association designs have been proposed for studying gene-environment or gene-gene interactions. Recently, Wang and Zhao  found thIn this paper, we investigate the joint effect of population stratification and sample selection in testing null main or interaction effects. Under general sampling, we quantify the magnitude of the PS-SS bias in terms of the baseline disease risks, genotype frequencies, exposure rates, their odds ratios (linkage disequilibrium coefficients), and the effect sizes of the risk factors. Based on this result, we find that matching in ethnicity cannot eliminate bias in association studies. Using the bias, we are also able to derive important conditions under which it is null.The PS-SS bias cannot be estimated, since we don't know how many subpopulations involved in the studied population and/or which subpopulation a person belongs to. Although adjusting for covariates such as principal components can be used to account for PS in genome wide association studies , howeverD with levels D = 1, and 0, indicating the presence and absence of the disease, respectively. Let G = 1(0) represent the presence (absence) of the genotype of interest. H = 1(0) represents the presence (absence) of the environmental exposure or another genotype of interest. Although we only focus on 2 × 2 × 2 table, however, all results can be extended to any number of risk factors or any number of levels. We also assume that the population under study consists of K subpopulations and denote S as the stratification variable, taking values s = 1,..., K. However, K is unknown and S is not observable in our discussion of the PS effect.We begin this section with the notation that will be used throughout this work. Disease status is denoted as To quantify the PS effect, we assume that the risk model is given bys. As usual, we use s = 1, g = 0, and h = 0 to represent the referent subpopulation, genotype and environmental exposure, respectively. For the purpose of identifiability, we define s = 1,..., K, are the subpopulation-specific parameters representing the potential heterogeneity of disease risk across subpopulations. In this model, log-odds-ratio β measures the association between the genotype and risk of disease, log-odds-ratio γ measures the association between the environmental exposure (or another genotype) and risk of disease. The multiplicative interaction δ measures the change of the disease-genotype log-odds-ratios according to different levels of risk factor H. Similar risk models for studying genetic effect under PS can be found in Satten et al. [s, we use s ORto represent the baseline G-H odds ratio (given D = 0). Definewhere the genetic and environmental data are obtained from subpopulation n et al.  and Chenn et al. , for exaG- frequency odds and baseline H- frequency odds s His similarly defined. Also define s Das the baseline disease frequency odds given byas the baseline P(S = s|D = 1) and P(S = s|D = 0) represent the corresponding proportions of subpopulation s in the cases and controls, respectively. However, in real applications, selection bias often happens and sampling may not be done according to the SRS scheme for various reasons. Let the true proportion of subjects in the cases (controls) that are from subpopulation s be denoted by P#(S = s|D = 1) (P#(S = s|D = 0)). We use s DS= s. If there is no selection bias, s DS= 1.In the discussion of PS effect, one often assumes that case and control data are sampled according to the SRS design. Let G and H, we show in the Methods section that given the presence of PS and general sampling, the main effects and interaction are given bySince in the population level we only observe factors whereandβ*), exp(γ*) and exp(δ*) are the bias levels. We note that if sDSs Dis a constant with respect to s, then Kis also a constant and there is no bias of any kind. A sufficient condition for this to hold is when the baseline disease risk is identical across all subpopulations and sampling of the study follows a SRS design. Further, sinceexp(P(D = 1|S = s) and baseline disease risk P are approximately equal in each subpopulation, then bias depends on sDSs Donly through the degree of matching P(D = 1|S = s) ≈ P for all subpopulations is often not true when environmental factor, such as smoking, are involved in causing the disease risk. Under this scenario, even the cases and controls are perfectly matched, the bias can still be large. This conclusion is different from that under the gene-disease association study; see for example, Cheng, Lee and Chen [therefore, if the disease prevalence and Chen . We shalβ*) to the estimation of genetic main effect depends on the variation of the genotype frequencies measured byδ*) to the estimation of interaction depends additionally on the variation of the baseline odds ratio, measured by Here, we give conditions for the null bias and bounds for bias. The bias exp. We first present some conditions for the null bias β* = 0, when the true genetic main effect is null: (1) if the baseline genotype frequency is constant across subpopulations, then the bias β* is zero (can be proved using equation (1) in the Methods section); (2) if the sample selection follows a SRS scheme (DS† = 1), and the disease risk is constant, then the bias is also null. , then the bias is null.Note that the bias is null:  if the bection);  if the sδ* = 0 are: (1) if the baseline G-H odds ratios and G(or H)- frequency odds are constant across subpopulations, then the bias δ* is null (can be proved using equation (2) in the Methods section); (2) if the sample selection of the study follows SRS, and the disease risk is constant, then the bias δ* is also null. However, see Tables When the interaction effect is null, some conditions for the null bias = 0 are:  if the bequation  in the Mβ*) can be expressed asNext, we present bound to measure the largest bias to the estimation of main effect. In the Methods section, we show that the bias exp(s ware some constants satisfying 0 ≤ s w≤ 1 and DS† = 1) is similar to that given by Lee and Wang [where and Wang . Howeverδ*) was bounded above by D† )2 and bounded belowD† )-2. These are the same bounds derived by Wang et al. [δ*) was bounded above byIn the Methods section, we also showed that under SRS, the bias exp frequency odds is small then the bias is also expected to be small.and bounded below by In case-control studies, one often expects that the type I errors of the association tests can be approximately controlled at some predetermined level. However, in the presence of PS or selection bias, the usual test statistic does not have a chi-square distribution under the null hypothesis. Instead, it has a non-central chi-square distribution, with non-centrality parameter depending on the level of the bias. Thus, the usual chi-square test tends to have inflated type I errors.α and let α) percentile of the chi-square distribution with one degree of freedom. Let Suppose that the intended type I error rate of the chi-square test is G = g, H = h and disease status d. Then the true type I error of the usual chi-square test of null interaction is given by α. In the case of testing null genetic main effect, the non-centrality parameter is given bywhere α.The corresponding true type I error of the chi-square test is given by δ(Δβ) but with δ* (β*) replaced by its upper bound βU). Let In most practical applications, one often does not know the true value of the non-centrality parameter and therefore it is difficult to calculate the true p-value of the chi-square test when the PS is present and/or there is selection bias. However, we are able to develop a bound for the non-centrality parameter, and the latter may be estimable in many cases. Define and Chen , a conseβ* and δ* and true type I error rates β αand δ αof the usual chi-square tests when the significance level is 0.05. We assumed that there are two subpopulations (K = 2), β = δ = 0, γ = 0 or 1. G (H-) frequency of the first subpopulation was given by P(G = 1|S = 1) = 0.51 (P(H = 1|S = 1) = 0.19), the first subpopulation disease risk was P(D = 1|S = 1) = 0.05, the proportion of subpopulation 1 in the overall population was 0.7, and case and control sample sizes both equaled to n = 500. We defined LDs =  where LDs was the linkage disequilibrium coefficient between loci G and H in subpopulation s, and considered linkage disequilibrium coefficient LDs = 0 or 0.05. We also assumed that the sampling proportions of the cases followed SRS but those of the controls might not. The rest of the parameter values were determined from the values for the variations G† ,H† ,D† and DS† given in the tables with the assumption that subpopulation 2 has the maximal baseline G (or H) frequency odds, disease risk, and sampling deviation (this implies that P#(S = 2|D = 0) ranges from 0.0585 to o.7163). Finally, we note that in computing the non-centrality parameters, the sample frequencies n × P. The simulation results for G† = 5 were given in Tables G† = 3 can be found from Tables S1 and S2 in Additional file Tables ions K = , β = δ =β αranges from 0.05 to 0.9998 under linkage equilibrium. If the SRS condition holds and γ = 0, the true type I error β αranges from 0.05 to 0.9602 with mean 0.4377 and standard error 0.3298. Under the same conditions but γ = 1, the corresponding range becomes  with mean 0.3822 and standard error 0.2969. On the other hand, if the sampling is not SRS (DS† = 3 or 5) and γ = 0, the range of β αis  with mean 0.6871 and standard error 0.317. Under non-SRS but γ = 1, the corresponding range becomes  with mean 0.6291 and standard error 0.3117. These results indicate that the bias can be quite large and its level may be modified by the sample selection and the level of H-main effect. We also observe that the bias β* may be nonzero under perfect matching. For example, if matching is perfect and H-main effect γ = 1, the largest true type I error is 0.1064, which occurs at the case with G† = H† = D† = 5. This is contrary to our usual belief that matching between cases and controls in ethnicity can eliminate the PS bias. However, except in some special cases, the bias under perfect matching design are smaller than those under other sampling designs.According to the results in Table δ* to the interaction effect is small when the linkage disequilibrium coefficient is small and the sampling is SRS. Our Table δ αin testing null interaction ranges from 0.05 to 0.0659. This agrees with their finding. However, if there is selection bias (DS† = 3 or 5), the true type I error rate δ αhas range , mean 0.101, and standard error 0.056 when γ = 0, and range , mean 0.1053, and standard error 0.0597 when γ = 1. The means and standard errors given here and later were computed based on the results shown in Tables δ αis only between 0.05, and 0.0541.Wang et al.  suggeste 0.05, 0.656, meanγ = 0, the mean of β αis 0.3377 under SRS and 0.5514 under non-SRS (selection bias), and when γ = 1 the mean becomes 0.2716 and 0.4597, under SRS and non-SRS, respectively. On the contrary, the bias to the estimation of the interaction effect increases when the linkage disequilibrium coefficient increases from 0 to 0.05. Our results show that when γ = 0, the mean of δ αis 0.1642 under SRS and 0.5512 under non-SRS. When γ = 1, the mean becomes 0.1706 and 0.5555, under SRS and non-SRS, respectively. In all, bias δ* seems to become larger when linkage disequilibrium coefficient gets larger. Under stronger linkage disequilibrium, the true type I error δ αcan be as large as 0.1101 even the cases and control were perfectly matched.Linkage disequilibrium between two genes or correlation between genetic and environmental factors play important role in determining the bias level in the studies of interaction. According to results presented in Table H = 1if maternal smoking was yes (0 if no) and G = 1if GSTT1 genotype was null ; see Table A6 of [G × H interaction was 3.2499 and chi-square test had p-value equal to 5.5676 × 10-4, indicating strong interaction effect. Also, from [G† = 4.8762. The range of maternal smoking rate was between 0.101 and 0.244 , our upper bound for the bias exp(δ*) (see equation 2) equals to 1.6149, leading to the conservative p-value equal to 2.0353 × 10-2. This suggests that the maternal smoking effect on the cleft risk can be modified by the GSTT1 genotype even the population stratification and selection bias are both present in the study.Shi et al.  studied le A6 of . Based o244 see -27), giv, givH = The impact of population stratification is considered by many to be important in case-control studies of gene-disease association. Many authors have suggested quantitative methods to control type I errors of the usual association test. The most popular treatments include the "genomic control" method -33 and tDS† = 3), the bias to the estimation of main or interaction effect may become unacceptable. Our suggestion is that the bias should be treated seriously, even when the genetic factors are in linkage equilibrium or the genetic and environmental factors are uncorrelated. Large correlation or strong linkage disequilibrium could make the bias become even larger. Also, small variation in disease risk cannot guarantee small bias, unless there is also small selection bias. In applications, it is important to be able to measure the impact of the bias. In this paper, we drive some bounds for the bias. If these bounds are estimable, then they can be used to make conservative inference. We show one real example that a conservative p-value for testing null interaction can be computed and significance conclusion can be reached even there is bias. Genotype frequencies of the SNPs and their LDs are readily available from international HapMap project. Further, disease prevalence is also available from many nations or from World Health Organization, for example. This information allows us to easily compute bounds and then conservative p-values.In practical applications, the selection bias is not unusual. For examples, when the hospital-based cases (controls) are used in the study and they are not representative of the population-based cases (controls) or when many non-response of the cases or/and controls occur in the study or there are self-selections, then the SRS condition may fail. In this paper, we show that under slight selection bias (β*) (see equation 1) to the genetic main effect also depends on the effect size of other risk factor. We found that if γ = δ = 0 then the residual bias after matching is small. However, if γ = 1, and δ = 0, the residual bias after matching is still quite substantial. A sufficient condition to assure bias β* = 0 under perfect matching is γ = δ = 0. Tables We note that matching in ethnicity between cases and controls has been suggested by epidemiologists as an affective method to control the PS bias in case-control gene-disease association study. However, in a more complicated risk model such as the one discussed here, bias  and testing gene-gene interaction is the main focus, one may follow the idea of genomic control to type extra pairs of null markers and apply the computed interaction levels to control the bias. In principle, if the candidate markers are in linkage equilibrium, the selected pairs of null markers also need to be in linkage equilibrium so that the important characteristics of the bias can be captured. On the other hand, if the candidate markers are in linkage disequilibrium, the paired null markers also need to be correlated. We are currently working to solve this important problem. Another approach for reducing bias is to match the cases and controls in ethnicity. According to our simulations, we find that under perfect matching and weak linkage disequilibrium, the bias to the estimation of the interaction effect is small. However, more study is needed in order to understand the impact of the residual bias when the matching is not perfect.In this paper, the biases to the estimation of genetic main and interaction effects are quantified and their bounds are derived. We find that if there is environmental effect or interaction, the bias to the genetic main effect cannot be ignored even cases and controls were matched in ethnicity. The bias to the estimation of interaction effect also has the same problem. The estimated bound can be used to compute conservative p-value for the association test. The computation of conservative p-value does not require the knowledge on the number of subpopulations involved in the study or the membership of each study subject. In real applications, it is usually not clear that if there is PS or selection bias or both. However, if appropriate information such as the variation of genotype frequencies is known, we always can compute the conservative p-value. If the conservative p-value is smaller than the designated significance level, we can safely claim that the test is significant regardless of the presence of PS/non-SRS.Following the usual Bayesian argument, the disease-risk model implies thats = 2,..., k. As a consequence,where G and H in the control population is given byOn the other hand, the joint frequency distribution of Thus their ratio is given byμ* = log{KΔ},Here, we define Also note that we can expresswhereDefineandw* such that the bias is bounded above bySimple algebra shows that there exists some constant MG(mG) is the largest value of sG.MD, mD, MDS, and m DSare similarly defined. Also note that under SRS, s DS= 1 and therefore according to the definition of exp(δ*)we easily show that it is bounded above by (D† )2 and bounded below by (D† )-2. However, under general sampling design, the bias is expressed asHere β*), we also can derive bounds for exp(δ*).where KFC designed the study, performed the analysis and wrote the paper. JYL performed the Computation and helped in discussion. All authors read and approved the final manuscript.Biases and the true type I errors of the chi-square tests. The file contains two tables showing the biases and true type I errors of the chi-square tests when G† = 3 and LD =  or LD = .Click here for file


Several p-value combining methods have been developed and applied to genetic data; see Dai et al.  are often correlated due to linkage disequilibrium (LD). Other genetic data, including variants from next generation sequencing, gene expression levels measured by microarray, protein and DNA methylation data, etc. also contain complex correlation structures. Ignoring correlation structures among genetic variants may lead to severe inflation of Type I error rates for omnibus testing of p-values. In this work, we propose modifications to the Lancaster procedure by taking the correlation structure among p-values into account. The weight function in the Lancaster procedure allows meaningful biological information to be incorporated into the statistical analysis, which can increase the power of the statistical testing and/or remove the bias in the process. Extensive empirical assessments demonstrate that the modified Lancaster procedure largely reduces the Type I error rates due to correlation among p-values, and retains considerable power to detect signals among p-values. We applied our method to reassess published renal transplant data, and identified a novel association between B cell pathways and allograft tolerance.Rapid developments in molecular technology have yielded a large amount of high throughput genetic data to understand the mechanism for complex traits. The increase of genetic variants requires hundreds and thousands of statistical tests to be performed simultaneously in analysis, which poses a challenge to control the overall Type I error rate. Combining i et al.  for a co From a systems biology perspective, genes, cells, tissues, and organs function as a system through metabolic networks and cell signaling networks. In non-Mendelian inheritance patterns, such as complex disorders, a subset of genetic variants may jointly confer moderate effects in mediating molecular activities. As a result, signals may not be significant in single marker-single trait analysis, but many such values from related genes might provide valuable information on gene function and regulation. For instance, in pathway analysis  of p-values evaluates the pattern (distribution) of p-values instead of selecting p-values less than an arbitrary threshold. Therefore, this method has the potential to identify multiple genes with small effects. If we assume that all individual tests are independent and arise from genetic variants with no effects, then p-values are identically and independently distributed as Uniform . Taking this as a null hypothesis for the pattern of p-values in the global test, one can assess whether p-values, especially small p-values, are generated by chance. The global test of p-values is robust and can be applied to p-values from varying statistical models including t-tests, analysis of variance (ANOVA), linear mixed models, and so forth. Multiple simulation studies and case studies have demonstrated that this approach usually has sufficient power to detect signals of genetic association from a group of genes. For instance, Peng et al. , where p-values might first be transformed by a function H. So far, several statistical methods have been developed to combine p-values. Let ip be independent p-values obtained from n hypothesis tests. Under the null hypothesis (H0) that p-values follow a Uniform  distribution, Fisher (ip) follows a chi-square distribution with 2n degrees of freedom. For a one sided test with a nominal error rate of α, one can reject the null hypothesis when the test statistics exceeds the (1 − α)*100% percentile of χ2n2. Stouffer  for N. Under the null hypothesis, the z-test statistic follows N.One category of global tests of , Fisher  shows thp-values, Littell and Folks  under H0.Although there is no consensus regarding the most powerful method of combining nd Folks , 1973 dend Folks . Subsequancaster  generaliand Bush  proposedz-test. The Bahadur efficiency ratio gives the limiting ratio of sample sizes required by two statistics to attain an equally small significance level. Thus, Bahadur efficiency is an important method to compare test statistics. From the perspective of Bahadur efficiency, the Lancaster procedure asymptotically requires a relatively smaller sample size than other weighted p-value combining methods. This prompted us to focus on modification of the Lancaster procedure for correlated genetic data in this work.In a separate paper, we have proved that the Lancaster procedure achieves the optimal Bahadur efficiency. We further demonstrated that the Lancaster procedure yields higher Bahadur efficiency than the weighted p-value combining methods as compared to smaller genes  to a chi-square distribution, i.e., γ−1iw /2, 2)( (1−ip)~ χ2iw where χ2iw is a chi-square distribution with iw >0 degree(s) of freedom. The parameter iw serves as a weight function to adjust the individual p-values. When p-values are independent, T has an exact chi-square distribution with In this section, we allow p-values, T does not have an explicit analytical form. To address this issue, we consider a Satterthwaite approximation by approximating a scaled T statistic with a new chi-square distribution , we use the Satterthwaite method to match the mean and variance of cT and χ2v, and then solve the equations to derive c and v. Koziol  = α. It follows that the corresponding percentage point for Approximate ET approximation.cT by χ2v then perform saddle point approximation  = Φ (ya) − ϕ(yb−1 − ya−1) for y ≠ 1 and K(t) = −0.5log (1 − 2t), and yt = (y − 1)/2y.Approximate ij is unknown, one can use the permutation approach to estimate ρij by shuffling the phenotype variable among subjects. For the kth permutation , we keep the genetic variants within the subject to preserve the correlation structure, then randomly assign the phenotype variable to subjects. Individual hypothesis testing can be done on all n genetic variants separately to generate the p-value vector kp = t. The permutation is repeated m = 1000 times, and ρij is estimated from .When the covariance ρp-values with varying correlation structures. We consider six different types of correlation structures, including fixed and random compound symmetric as well as random positive definite variance-covariance structures for Σ. Let I be an identity matrix, t be the transposition. In Cases I–V, let Σ = Block ⊗ I20 be compound symmetric variance matrices with 20 blocks of size 5 where The accuracy of the five approximate distributions to the correlated Lancaster procedure is then assessed using T that combines n p-values is renamed as LancasternT in Figure y = x, indicating the limiting distribution for the test statistic in the original Lancaster procedure is less dispersed than the distribution of LancasternT under correlation structures. As a result, the original Lancaster procedure will have severely inflated Type I errors. In contrast, the five approximations  match the underlying distribution of LancasternT. For data with stronger internal correlation, AT, DT, and ET better approximate LancasternT. The Q-Q plots under other correlation structures are similar to Figure The quantile-quantile (Q-Q) plot assessing the accuracy of the proposed methods when the correlation coefficient ρ = 0.3 is shown in Figure q1 and q2 be the minor allele frequencies (MAFs) at loci 1 and 2. Assuming Hardy–Weinberg equilibrium, the genotype at locus 1 can be randomly generated using a binomial distribution. Given the distribution of SNP at locus 1, one can simulate the genotype at locus 2. To do so, let D be a measure of LD. Then the conditional probability for the genotype at locus 2 given the genotype at locus 1 can be expressed as P(A|B) = [A qBq + D]/Bq, P(a|B) = [(1−Aq)Bq −D]/Bq, P(A|b) = [Aq (1−Bq)−D]/(1−Bq), and P(a|b) = [(1−Aq)(1−Bq)+D]/(1−Bq) where A and B represent the minor alleles at the two loci. For a diploid genome, similar idea can be applied and the simulation details can be found at Cui et al. . The variable D = 0, 1.5, and 2 suggests no LD, moderate LD, and very strong LD among SNPs with the corresponding correlation R = 0, 0.71, and 0.95. Six scenarios for disease susceptibility (p) are simulatedWe assess the Type I error rates and power for the proposed correlated Lancaster procedures and compare them to the independent Lancaster procedure ) = β1G1, 2 +β2G1, 5 +β3G1, 7 +β4G1, 8 +β5G1, 12.Case I: ln (p/(1−p)) = β1G2, 2 +β2G2, 4 +β3G2, 6 +β4G3, 2 +β5G3, 3.Case II: ln (p/(1−p)) = β1G3, 2 +β2G3, 4 +β3G4, 1 +β4G4, 3 +β5G5, 1.Case III: ln (p/(1−p)) = β1G1, 1 +β2G1, 3 +β3G1, 7 +β4G1, 8G1, 10G1, 11 +β5G1, 12.Case IV: ln (p/(1−p)) = β1G3, 1 +β2G3, 3 +β3G4, 2 +β4G3, 2G3,4 +β5G4, 3G5, 1.Case V: ln (p/(1−p)) = β1G1, 2 +β2G2, 2 +β3G3, 3 +β4G5, 2 +β5G1, 5G1,7 +β6G3, 3G5, 1.Case VI: ln ( (1−pi) transforms p-value into a variable with χ22 distribution.Weight functions can be used to remove potential bias when combining g et al.  and othen = 200  have well controlled Type I error rates (<0.05).Due to LD, SNPs from the same gene are correlated. We first assess the Type I error rate of the test statistics by testing n = 200 to n = 400.The power of all test statistics was compared for regression coefficient values set at β = 0.4 and β = 0.6, respectively. The results in Tables D = 0, 1.5, 2, and uniform. To save the space, we only show the results for D = 1.5 (Table D = 2 (Tables AT − ET) have well-controlled Type I error rates and power for both moderate and strong LD (Tables We simulate different levels of LD for SNPs with .5 Table  and D = D Tables .AT − ET), the power is increased when a weighting function is used. This confirms that an appropriate weight function is beneficial to the Lancaster procedure.In Table http://www.ncbi.nlm.nih.gov/sites/GDSbrowser?acc=GDS4266). A group of tolerant renal transplant recipients , as defined by stable graft function in the absence of immunosuppression for more than 1 year, were compared to subjects with stable graft function who were receiving standard immunotherapy  as well as to a group of healthy controls . Gene expression profiles of whole-blood total RNA from all subjects were measured by microarray. The goal of the study was to identify genetic variants associated with long-term allograft survival without the requirement for continuous immunosuppression, a condition known as allograft tolerance. Newell et al.  preprocessing methodology, which included background subtraction, quantile normalization, and summarization via median-polish.F-test. This is equivalent to a One-Way ANOVA for each gene except that the residual mean squares have been moderated across genes. P-values from multiple hypothesis testing were adjusted by FDR  as described in Section Correlated Lancaster Procedures to combine p-values from pathways. Combining p-values allows us to integrate small effects in pathway and gain the power of statistical testing. A total of 1454 Gene Ontology human pathway gene sets were analyzed. The size of pathways ranged from 9 genes to 2131 genes, with a median of 27 genes per pathway. Also, the number of probes per gene was highly variable. In order to map genes to pathways, we removed genes without gene symbols from the analysis. Among 21,049 genes with gene symbols, approximately 48% (n = 10161) of genes were interrogated with a single probe, 26% (n = 5389) of genes were queried using 2 probes, 14% (n = 2842) of genes were assessed by 3 probes. There were 3 or more probes for each on the remaining genes (range: 4–17). This finding indicates that larger genes would have more p-values and a stronger impact to pathway analysis. To prevent this bias, we set the weight function as in is the number of probes for the ith gene.To address this issue, we performed the modified Lancaster procedure . The increase in number of significant pathways identified by the traditional approach is primarily due to false positive discovery, and is consistent with the inflation of Type I error rate as presented in Section Empirical Assessments. Thus, by accounting for correlation structures (LD) within pathways and the number of probes per gene, our proposed method minimized identification of larger, non-specific cellular processes pathways, and instead revealed more focused and functionally relevant biological pathways implicating a role for a humoral immune response in immunotolerance to renal transplants , the Satterthwaite approximation (AT) is the most computationally efficient. Other approximation methods  are based on the Satterthwaite approximation. Therefore, we recommend using the Satterthwaite approximation (AT) as the standard procedure to modify the Lancaster procedure. Among other approximation methods, simulation results in Section Correlated Lancaster Procedures show that, for data with stronger internal correlation, DT and ET have better approximation than BT and CT. Our simulation study and the case study further provide evidence that DT tends to have slightly higher power than the Satterthwaite approximation AT. The R code for five approximation is posted at http://d.web.umkc.edu/daih/.Among five proposed approximation methods (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.


The unrelated individuals sample from Genetic Analysis Workshop 17 consists of a small number of subjects from eight population samples and genetic data composed mostly of rare variants. We compare two simple approaches to collapsing rare variants within genes for their utility in identifying genes that affect phenotype. We also compare results from stratified analyses to those from a pooled analysis that uses ethnicity as a covariate. We found that the two collapsing approaches were similarly effective in identifying genes that contain causative variants in these data. However, including population as a covariate was not an effective substitute for analyzing the subpopulations separately when only one subpopulation contained a rare variant linked to the phenotype. Of the 24,487 exomic single-nucleotide polymorphisms (SNPs) in the data, 9,433 (38.5%) occur only once in a single individual and 18,131 (74.0%) occur with less than 1% minor allele frequency (MAF). Phenotypes provided include sex, age, smoking (yes/no), ethnic population, three quantitative traits , and the dichotomous trait Affected. A single genetic model based on additive genetic effects was used for all subjects. For a full description of the data simulation, see Almasy et al. [The Genetic Analysis Workshop 17 (GAW17) unrelated individuals sample is derived from the pilot3 study of the 1000 Genomes Project  from the total 3,205 genes included in the data. This arbitrary threshold was chosen as a compromise between what is typically considered common (MAF ≥ 0.05) and the fact that the sample size in the provided data was modest. After inspecting the generating model, we discovered that 5 out of 39 causative variants for Q1 fell between these two thresholds, as did 2 of the 51 variants for affection status. We used a regression framework to examine the quantitative trait Q1 and the dichotomous trait Affected.We generated two genetic variables based on related collapsing approaches. The first variable was simply a count of how many rare alleles an individual carried for a particular gene. The second variable was dichotomous, indicating whether or not an individual carried at least one rare allele in a particular gene. Both of these collapsing approaches were previously discussed by Li and Leal  as part Because of the sparseness of the information in the unrelated individuals sample, we believed that a single data replicate would likely be underpowered for this analysis. Each replicate contains exactly the same genotypes, making most approaches to combining information from multiple replicates prone to spurious associations. The focus on rare variants in this analysis exacerbates this problem. We chose to perform a meta-analysis of the multiple replicates. For these particular data, this approach provides a scalability feature that allows easy comparisons of differing sample sizes. For the full data, we examined single replicates, and meta-analyzed sequential groups of 10 replicates each  and the first 50 replicates. For the much smaller subpopulation samples, we meta-analyzed sequential groups of 10 replicates each and the first 50 replicates.An initial examination of the quantitative traits indicated that Q4 was largely determined by the covariates Sex, Age, and Smoking. This made Q4 a good candidate to use to evaluate the extent to which combining multiple replicates would lead to entirely extraneous false positives. We therefore performed the same regression analyses and meta-analyses on Q4 as we did for Q1. The use of Q4 as a negative control for false positives allowed us to evaluate the chances of the single set of genotypes giving rise to entirely spurious signals. We note that the use of a negative control lets us evaluate only the extent to which entirely spurious signals might arise from the use of multiple copies of the same genotypes. However, this approach cannot provide an estimate of the extent to which small spurious signals, resulting from such things as rare variants in individuals with extreme phenotypes or modest correlations between a causative gene and a null gene, might be amplified when using multiple replicates.We evaluated two methods for dealing with population stratification: (1) analyzing the strata in separate analyses and (2) pooling data from all strata, using population as a covariate. Through the use of meta-analyses of varying numbers of data replicates, we could also compare results from similarly sized single-population analyses and pan-population analyses.Our analyses for Q1 were based on linear regression using Sex, Age, Smoking, and Population as covariates and one of our two ways of coding the genes (quantitative count or dichotomous indicator) as the predictor of interest. We noted that the dichotomous Affected phenotype was highly correlated with the quantitative traits. As a result, we believed that our top signals from a straightforward analysis of this trait might reveal only genes associated with Q1 or Q2. Therefore, to detect genes associated directly with the Affected phenotype, in our logistic regression analyses of affection status we included Q1, Q2, and Q4 as well as Sex, Age, Population, and Smoking as covariates.We considered the possibility that if a causative variant were found in only one subpopulation, it might be advantageous to analyze that subpopulation separately. To evaluate this possibility, we conducted a second set of analyses, performed separately on each genetically distinct subpopulation. To determine whether any of the samples could be pooled, we first performed an EIGENSTRAT analysis . The resFinally, we note that one of the CEPH subjects (NA7347) was an extreme outlier for Q1 across most of the data replicates. This subject was excluded from our analyses.k individual data replicates and retained the p-values. Then we performed meta-analyses using Fisher’s statistic,Our multireplicate analysis plan proceeded as follows: First, we analyzed k degrees of freedom (df). The nonindependence of the genotypes between the data replicates violates the distributional assumptions. However, our chief goal was to determine whether any of the true signals would stand out from the bulk of the noise in this sparse data.which under the null hypothesis would be expected to have a chi-square distribution with 2−6 as our threshold for statistical significance. All statistical analyses were performed in SAS [Because of the large number of tests performed, we used 10d in SAS .p-values. The high degree of similarity between the two collapsing approaches held true throughout our analyses. As an example, Figure p) values for the genes in a meta-analysis of Q1 using the first 50 replicates. Each point represents the results of meta-analysis of a single gene. The horizontal position is −log(p) from the analysis based on the Indicator variable; the vertical position is −log(p) from the Count variable. The correlation between the values from the two collapsing methods is 0.92. If we eliminate the top four outlying values, the remaining values still have a correlation of 0.85. For this reason, we report only the results from the Count variable in the remainder of this paper.Table FLT1 as its top result, with p < 10−5. The inability of any of these samples to pass the significance threshold was expected because of the small sample size. Results from meta-analyses of 10 replicates at a time are found in Table VEGFA, did not quite pass the significance threshold , it was a true positive, and the next ranked gene was three orders of magnitude less significant. This signal was consistent throughout the replicates and would become significant when more replicates were added to the meta-analysis. In contrast, we note that VEGFA was ranked 406th in the meta-analysis results for the combined population sample  with median p = 4.6 × 10−4.A stratified analysis of the individual populations did not have any results that passed our significance threshold. However, the European sample (CEPH and Tuscan sample combined) had p < 0.05 in the combined population sample or any of the subpopulations. Furthermore, in none of our meta-analyses, even including all 200 data replicates, did we achieve a p-value that passed our significance threshold (10−6) either in the combined data or in any subpopulation.In contrast, our analysis of the negative control phenotype (Q4) resulted in no gene with a median PRKCA on chromosome 17, was significant in meta-analyses of 10 replicates . PRKCA was a causative gene in the model. Another causative gene, PIK3C2B, was ranked 5 out of 2,448 in the meta-analyses of 10 replicates. However, it would not reach significance unless all 200 replicates were meta-analyzed.For the combined population data no gene was significant in the individual data replicates. Only one gene, PRKCA became significant in the Asian sample  and in the Yoruba sample  and was trending toward significance in the Luhya sample . This signal was not seen in the combined European sample .In the stratified analyses none of the subpopulation samples passed the significance threshold, in single replicate analyses or in a meta-analysis of 10 replicates. However, if 50 replicates were meta-analyzed, FLT1, VEGFA, PRKCA) could be detected by an examination of rare variants in the unrelated subjects. However, it turned out that our second goal  gave rise to the most interesting results.Clearly, some contributing genes  Because the signal was present in subsamples representing more than 84% of the data, pooling the data and using population as a covariate maximized power.VEGFA, found in an analysis of the Luhya sample, was not near the top of the list in the combined analysis. It was not until we meta-analyzed 50 replicates of the full data  that this gene surpassed the 10−6 significance threshold (p = 1.4 × 10−14). In contrast, meta-analysis of the first 50 replicates of the Luhya subjects alone  resulted in an extremely low p-value (p = 2.1 × 10−94). This is because the rare variant for VEGFA is private to the Luhya population. As a result, including samples from other populations merely introduces noise into the signal. It is interesting to note that VEGFA corresponds to the highest linkage signal found in a linkage analysis of the family data [In contrast, VEGFA, this need not be the case. This suggests that it might be worthwhile to analyze multipopulation data both ways (stratified and adjusted), despite the multiple testing penalty.We note that the phenotypes were modeled identically for the different populations. As a consequence, one might have believed a priori that a combined analysis (perhaps not even using population as a covariate) might be the most powerful approach. However, as illustrated by the results for In these data we also found that the two tested approaches to collapsing performed similarly, particularly for the top signals. This simply suggests that in these data the outliers in phenotype were not also outliers in terms of the count variable for any genes. Clearly, this cannot be generalized to other genetic models.Finally, although our top signal in each analysis result was a true signal, there were many more highly significant false positives than we would have expected. We learned from the analysis of Q4 that it is unlikely that these spurious results were a completely random effect of using multiple replicates of the same genotypes. Two other possible causes come to mind. First, rare variants carried by individuals with extreme phenotypes could give rise to such results. We tested this idea by performing some analyses that included the individual from the CEPH sample (NA7347) who had an extreme Q1 value (>5 standard deviations above the mean) in nearly every replicate. We found that multiple genes that were not included in the model but for which this individual was the only carrier of rare variants became significant. Second, the signals could actually be in the data, although they were not included in the generating model. We note that many false positives in these data have been reported as consistently arising under a variety of analysis methods. For a detailed discussion of this aspect of the data, see Luedtke et al. .In our analyses we found that in the GAW17 data, the two collapsing methods produced similar results. More important, these analyses showed that even with the identical genetic model applied to multiple subpopulations, sample size is not the only factor that determines power. If rare causative variants are private to a subpopulation, stratified analysis might be more powerful than a combined analysis, despite a considerable decrease in sample size.The authors declare that there are no competing interests.RCC conceived of the study, participated in its design, performed the main statistical analysis, and drafted the manuscript. ALH participated in the design of the study and performed the EIGENSTRAT analyses. BKS participated in the design of the study and helped to draft the manuscript. All authors read and approved the final manuscript.


OXT (rs2740210 and rs4813627) and one polymorphism in the oxytocin receptor gene OXTR (rs237885) in 187 Caucasian mothers at six months postpartum. For OXT, both rs2740210 and rs4813627 significantly associated with maternal vocalizing to the infant. These polymorphisms also interacted with the quality of care mothers experienced in early life, to predict variation in maternal instrumental care and postpartum depression. However, postpartum depression did not mediate the gene-environment effects of the OXT SNPs on instrumental care. In contrast, the OXTR SNP rs237885 did not associate with maternal behavior, but it did associate with pre-natal  depression score. The findings illustrate the importance of variation in oxytocin genes, both alone and in interaction with early environment, as predictors of individual differences in human mothering. Furthermore, depression does not appear to have a causal role on the variation we report in instrumental care. This suggests that variation in instrumental care varies in association with a gene-early environment effect regardless of current depressive symptomatology. Finally, our findings highlight the importance of examining multiple dimensions of human maternal behavior in studies of genetic associations.Individual differences in maternal behavior are affected by both early life experiences and oxytocin, but little is known about genetic variation in oxytocin genes and its effects on mothering. We examined two polymorphisms in the oxytocin peptide gene  Early life experiences including adversity and stress influence development in many mammals. Early social isolation in rats results in a high proportion of mothers who are erratic, less attentive, and show reduced licking and grooming OXT) and the oxytocin receptor gene (OXTR), and variations in human maternal care. The oxytocin system is an excellent candidate gene system in the maternal context. Extensive pharmacological, physiological, and behavioral evidence points to a role of oxytocin in mammalian mothering OXTR genotype and observed maternal sensitivity OXT gene are unexplored in association with human mothering.In the present study, we first explored associations between genetic variation on both the oxytocin peptide-coding gene  = 0.57, p = 0.45). Most subjects reported having a partner (94%). Mean (±SD) maternal age was 31.2 (±4.9); mean maternal education was 4.81 (±2.3) on a scale of zero to ten, where zero is ‘not completed high-school’, and ten is ‘post-graduate degree’.Subjects were part of the longitudinal study on Maternal Adversity, Vulnerability, and Neurodevelopment (MAVAN). The study follows two cohorts of mothers and their infants: one in Montreal, QC, and another in Hamilton, ON, Canada. Behavioral data were available for the Hamilton cohort of mothers; the present study examines this cohort. Ethnic descent in this sample was mostly Caucasian (90%), with 3% mixed ethnicity, 2% African, 1.5% Hispanic, and 1% East Indian; the remainder were unspecified. This ethnic distribution is typical of the greater Hamilton region. Allele frequency distributions can differ across ethnic groups Subjects signed written consent to participate in the MAVAN project. Ethics approval for this study was obtained from the ethics review boards at the University of Toronto, Toronto, ON; and St Joseph’s Healthcare, Hamilton, ON. We assessed mothers and their children through questionnaires, diagnostic tools, and behavioral tasks, during 20 home and lab visits starting at weeks 12 to 24 of pregnancy and continuing until 72 months postpartum. Participants received $25 compensation after each visit.We assessed maternal behavior and maternal sensitivity by video-coding 30-minute in-home mother-infant recordings at six months postpartum. During the first 20 minutes mothers were free to interact with their infants as normal, but without feeding or changing the infants. In the last ten minutes mothers completed self-report questionnaires in the presence of their infants, to assess responsiveness during maternal divided attention.One hundred and fifty-eight of the 187 Caucasian-sample mothers agreed to be recorded. These mothers did not differ significantly from mothers who did not participate in the video recording with respect to having prior children (parity), prenatal household income, maternal age, or maternal education.orienting away from infant (frequency), infant-directed vocalizing (duration), and instrumental care (duration). Orienting away frequency was the number of times a mother’s gaze was directed away from the infant’s head or body. This measure was transformed with the natural log (Ln) transformation due to positive skew. Infant-directed vocalizing was defined as any infant directed speech including motherese, nonsense words, and onomatopoeic sounds. All mothers vocalized during the 20-minute recordings and the measure had a normal distribution. Instrumental care included all maternal grooming and cleaning of the infant’s body and face, as well as adjusting clothes, bibs, soothers, and hats. We corrected the skew in this measure by using the square root transformation. We quantified the following three infant behavioral durations: reaching toward mother, smiling at mother, and crying. These three durations were aggregated to obtain a total duration of infant activity. We later used this measure as a covariate in the regression analyses.The first 20-minutes of the mother-infant interactions were coded by two raters using the Behavioral Evaluation Strategies and Taxonomies (BEST) coding system  sensitivity using the Ainsworth Maternal Sensitivity Scales A single rater coded the full-length 30-minute videos for maternal We used the Center for Epidemiological Studies Depression Scale CES-D; , a 20-itearly care quality factor early care quality values range from negative (high early life adversity) to positive (low early life adversity). This dimension was the first principal component (of two) derived from principal component analysis (quartimax rotation) with nine input variables from CTQ, PBI, and LHC, and had an eigenvalue of 4.0. Early experience dimensions that loaded highly on care quality were the following: CTQ physical abuse, CTQ emotional abuse, CTQ physical neglect, CTQ emotional neglect, PBI maternal care and PBI maternal overprotection . Missing values in the derived early care quality dimension were imputed with stochastic regression single imputation in SPSS, where the original nine CTQ, PBI and LHC variables were used as predictors  is part of a haplotype block for OXTR, which is significantly associated with pro-social behaviors OXT gene, rs4813627 is 56 kb downstream of the OXT gene, and rs237885 is in the intron region of the OXTR gene. The genotypes of the OXT polymorphisms were determined by the Taqman assay method using the ABI PRISM 7000 . The IDs for on-demand assays available from ABI were as follows: C__16061225_10 (rs2740210), C___2712196_10 (rs4813627), and C___3290319_1_ (rs237885).We collected subjects’ DNA through buccal swabs. DNA extraction and genotyping were carried out at the Center for Addiction and Mental Health (CAMH), Toronto, Ontario, Canada. Because of the relative lack of known functional polymorphisms in the two candidate genes, particularly the genetics package in the open-source statistical framework R (http://cran.r-project.org/). We first tested for main effects of maternal OXT genotype on maternal behavioral outcomes using analysis of variance (ANOVA). OXT SNPs (rs2740210 and rs4813627) were entered in the models both separately and together. The direction of effects was the same, but because of high LD (see above) results are presented for the analyses in which these SNPs are entered together.Hardy-Weinberg Equilibrium tests and linkage disequilibrium tests were carried out with the Next, we used multivariate regression models to test for genotype×early experience (G×E) effects on 1) maternal behavior and 2) maternal mood . We first ran full models with genotype, early experience, and their cross-product as predictor variables; maternal age, education, parity (whether this was the mothers’ first child), and postnatal depression score  as maternal covariates; and infant gender and activity as infant covariates. Model reduction with the F-test enabled the removal of non-significant covariates for the “reduced models”. We present output from both the full and the reduced models in the regression tables.orienting away from infant, infant-directed vocalizing, instrumental care, maternal sensitivity, and infant activity), with the Hmisc package in R. Imputations were performed with predictive mean matching and Bayesian approximation methods over ten iterations, and results were combined with the fit.mult.impute function, which returns likelihood ratio test chi-squared values as a test of overall fit of the test model compared to the null model (intercept only). This function also returns average beta coefficients. Imputations were performed for the following percentages of missing data in the sample (N = 187): 14% for behavioral outcomes, including maternal and infant behaviors; 9% for parity; 14% for maternal education; and 12% for CES-D Depression scores.For the SNP main effect models and the G×E regression models, we used multiple imputation to impute values for missing data in the behavioral outcomes  and Depression Score is maternal CES-D score at 6 months, centered at the standard cut-off score of 16. We used this model to derive path coefficients for a direct effect of early experience  on instrumental care, Y; and indirect paths (A) from early care quality to depression (CES-D) and (B) from CES-D to instrumental care. Each of the three paths was modeled to be potentially moderated by genotype. Regression coefficients and bias-corrected boot-strapped confidence intervals (n = 1000) were derived using the boot and boot.ci functions in the boot package in R. For mediation analyses we used the original rather than the imputed data.Where Finally, path models using prenatal depression as a mediator were also examined, to strengthen any arguments based on the previous model where the mediator (depression) and parental outcome  occur at the same time-point (6 months postpartum). We present the model with prenatal depression in the supplementary materials.OXT SNPs rs2740210 and rs4813627 . When SNPs are in high LD, the individual effects of SNPs in regression models should be interpreted cautiously. Results from haplotype analyses are presented in Sample characteristics and study variables are described in infant-directed vocalizing and frequency of orienting away from the infant (Spearman’s rho (158) = −0.3, p<0.01), and between frequency of orienting away and sensitivity (Spearman’s rho (158) = −0.19, p = 0.02)  = −0.17, p = 0.04), and positively with infant activity (Spearman’s rho (158) = 0.22, p<0.01). There was a trend for a positive correlation between instrumental care and CES-D postnatal depression score (Spearman’s rho (145) = 0.16, p = 0.05). Depression score negatively correlated with maternal education (Spearman’s rho (143) = −0.25, p<0.01) (There was a significant negative correlation between  = 0.02) . Instrum p<0.01) . ANOVAs infant directed vocalizing  = −2.09, p = 0.04 and β = −56.3, t(147) = −2.06, p = 0.04, respectively). Together rs2740210 and rs4813627 genotypes explained a significant proportion of variance in infant-directed vocalizing  = 15.7, p = 0.004) (There were significant main effects of both rs2740210 A/C and rs4813627 A/G genotype (reference group was rs2740210 C/C and rs4813627 G/G respectively) on = 0.004) . Based o= 0.004)  revealedearly care quality on the total duration of maternal instrumental care  on any maternal measure.There were no main effects of early care quality or interactions of care quality with genotype×early care quality interactive effects (for both rs2740210 and rs4813627) on maternal depression score (CES-D) at 6 months  and G/G (rs4813627) were more negative, indicating that early life experience had a stronger moderating effect in this group of mothers than in mothers with other genotypes  (OXTR genotype (rs237885) on depression levels at 6 months postpartum, but when we used a prenatal depression measure, there were significant associations between rs237885 genotype G/G, which explained a significant proportion of the variance  = 11.72, p = 0.003).There were significant 6 months , Table 4In mediated moderation analysis, we compared rs2740210 genotypes C/C with genotypes A/C and A/A, and found direct effects and indirect effects in the model from early experience to instrumental care. For both rs2740210 genotypes, there was a significant negative association between early care quality and postnatal depression (path coefficients are −7.98 (C/C) and −2.40 ) . The dirModels using prenatal depression revealed a similar pattern of effects for the C/C genotype mothers (significant first stage effect (early care depression) and direct effect ), and a similar direction (though not significant) of effects for the alternate genotype . The difOXT), and one which codes for the oxytocin receptor (OXTR) – and found that polymorphisms in OXT (but not OXTR) associate with both infant-directed vocalizing and maternal instrumental care.There is accumulating evidence for the role of oxytocin in the regulation of human mothering OXT SNPs (rs2740210 and rs4813627). Vocalizing to infants is a universal behavior of mothers that includes infant-directed speech, or “motherese”, characterised by exaggerated prosodic cues and is present in all studied languages There was a main effect of genotype on vocalizing for both DRD1 and DRD2) associates with individual variation in human maternal care, including infant-directed vocalizing DRD2 genotypes and haplotypes and maternal infant-directed vocalizing. The link between genetic variation in both the OXT and DRD2 genes and individual differences in the duration of maternal vocalizing to infants is plausible. Oxytocin neurons express DRD2-like receptors in the rat brain We previously showed that genetic variation in the dopamine D1 and D2 receptor genes  displayed shorter overall instrumental care duration with increasing early care quality; for mothers with the other two genotypes for these SNPs, instrumental care duration increased with increasing early care quality  style of mothering sometimes associated with depressed mothers stpartum . HoweverOXT genotype×early life experience influences on mothering.In addition to being intrusive, depressed mothers are sometimes withdrawn - vocalizing less with their infants and looking away more often OXTR polymorphism rs2254298, which associates with depression and anxiety in adults OXT SNPs in our study exhibit gene-gene interactions with the OXTR rs2254298 SNP in the above studies, or if they have similar or overlapping functions. There is an indication that rs2254298 influences amygdala volume, but this effect may be ethnicity-dependent as it is found in Asian, but not Caucasian populations Interestingly, the genotype groups that showed the longest duration of overall infant-directed vocalizing  also shoOXTR polymorphism, rs53576, has previously been shown to associate with maternal sensitivity OXTR gene. We found a notable absence of associations between this SNP and any maternal outcome tested. The previously studied rs53576 is a silent (AG) mutation and along with the SNP we assessed, rs237885, lies in the intronic region of the OXTR gene, with no known effects on expression or protein function. Yet because rs53576 has effects in other association studies, future research should examine this SNP in association with early adversity for effects on maternal behavior.Another sensitivity, a global measure of maternal quality of care; or with orienting away, a measure of maternal responsiveness potentially related to attention. We have previously reported that orienting away associates with dopamine D1 receptor genotype and with genotype at the serotonin transporter-linked polymorphic region (5HTTLPR) OXT SNPs and orienting away is not surprising. Oxytocin seems to have functions centered on sociality and affect, and therefore attention-related dimensions of mothering are unlikely to be influenced by genetic variation in the OXT gene.None of the three SNPs we explored showed associations with maternal One limitation to our study is the use of a retrospective measure of early care quality. However, the subcomponents of our measure were the Childhood Trauma Questionnaire (CTQ) and the Parental Bonding Instrument (PBI), both of which have long-term stability. The PBI has been examined in clinical samples where depressed individuals improved over time; in mothers who were followed from the early postpartum for 30 months OXT in relation to maternal behavior. We examined two polymorphisms in the OXT gene (rs2740210 and rs4813627), and both showed a main effect on maternal vocalizing to the infant; as well as a significant interactive effect with early life experience on maternal instrumental care of the infant. The significant associations for type  but not quality  of maternal care, highlights the importance of exploring multiple levels of behavioral phenotypes in genetic association analyses. Finally, it is important to keep in mind that mother-child interactions may change over time. Thus, they represent a dynamic relationship, which at different times may exhibit different influences from hereditary and non-hereditary factors. Genetic studies should begin to delve into the temporal stability of association between genetic variation and multiple outcomes over time.The present report is the first, to our knowledge, to examine genetic variation in the oxytocin peptide gene Figure S1Path models depicting relationships between early experience, prenatal depression, and maternal instrumental care in two genotypes of rs2740210: C/C and A/C using coefficients from (TIFF)Click here for additional data file.Table S1Sample characteristics and study variables.(DOCX)Click here for additional data file.Table S2OXT haplotypes and regression models with these haplotypes.(DOCX)Click here for additional data file.Table S3Coefficient estimates of path models .(DOCX)Click here for additional data file.Table S4Simple effects of path models .(DOCX)Click here for additional data file.