We incorporate population effects of sex and antibodies directed against cyclic citrullinated peptides (anti-CCP) into the linkage analysis of rheumatoid arthritis (RA) with microsatellites data provided by the North American Rheumatoid Arthritis Consortium in Genetic Analysis Workshop 15.The method stems from a generalized linear mixed model that incorporates the marginal population effects of important covariates. The resulting test for linkage is based on a score test in a pseudo-likelihood of this model. The mathematical derivation is given elsewhere but the test has a simple and appealing form: it assigns weights to excess identity-by-descent sharing between pairs of related individuals depending on the individual-specific values of the covariates and phenotypes.Although RA is three times more prevalent in women than in men, the weights derived for male-male, female-male, and female-female affected sib pairs turn out to be very similar and the sex-adjusted analysis hardly differs from an unadjusted analysis. High anti-CCP levels are known to strongly predict RA. Our test assigns very small weights to pairs whose anti-CCP levels are high for the two siblings, sib pairs with two low anti-CCP levels are those most contributing to the evidence for linkage. Comparison of the unadjusted and the anti-CCP-adjusted analyses identifies persisting peaks mapping to regions that can be attributed to a 'dimension' of RA independent of anti-CCP. In linkage analysis of continuous traits, random samples of families are often available. The marginal effect of important covariates such as sex and age is routinely incorporated into the mean structure of the variance components model. For binary traits, families are often ascertained  and estimates of the effect of covariates at the population level cannot be obtained. In such designs, incorporation of covariates is usually based on models in which the identity-by-descent (IBD) probabilities are allowed to depend on those covariates . Externaj = 1, 2, the model is as follows: given some observed covariates Xj with population effect estimates β and some unobserved random effects bj, the disease status of the two siblings are independent random variables Yj = 0/1, with a distribution given by π) of the sib pair at a putative location with linkage effect γ, the unobserved random variables bj are normally distributed with mean 0, variance σ2, and covariance σ2 × [ρ + γ(π - 0.5)] as in the usual variance components model for continuous traits. In principle, the model parameters β, σ2, and ρ require population data on sib pairs in order to be estimated. In fact, estimation is often difficult and we have proposed an approximate ad-hoc method that is fully described by Lebrec and van Houwelingen [γ > 0 versus γ = 0 using a score test for this parameter in a pseudo-likelihood of the previously described GLMM, the result is a simple weighted average of the estimated IBD sharing between the two siblings i = 1,..., N)The GLMM models the probability of RA as a function of a linear predictor (sum of the covariate effects+random effect) via a logistic link. In the case of two siblings indexed by T are set to 0 and the resulting statistic T+ follows the usual 0.5χ0 + 0.5χ1 mixture under the null hypothesis. The weight wi given to a specific sibling pair depends not only on the segregation parameters β, σ2, and ρ but also on its covariate values. The weight wi in the linkage statistic given by Eq. (1) is as follows: in a sib pair with individuals indexed by j = 1, 2, let The actual test is one-sided, so negative values of β, σ2, and ρ. In fact, full maximum-likelihood estimation is often a difficult exercise for this type of data so we advocate the use of an approximate method of estimation which has been applied here [ρ = 0.8, we estimate β and σ2 so as to best reflect prevalence of RA in men and women (0.5% and 1.5%) as well as the overall recurrence risk ratio λs = 6. The choice of those estimates does not affect the asymptotic validity (type I error) of the method, indeed the test statistic has mean 0 and variance 1 under the null hypothesis, and only slightly influences the efficiency of the test.Population data are required in order to obtain estimates of the segregation parameters For anti-CCP levels, we first used the available measurements in NARAC to estimate the distribution of anti-CCP levels in RA patients (we chose one affected sib at random per family) and in healthy individuals  separately. The estimation was carried out separately in the two groups using a nonparametric method (Gaussian kernel). Based on an overall prevalence of 1% for RA, we used Bayes formula to derive the probability of an individual to be a RA patient conditional upon his/her anti-CCP level. Given the very limited data available in healthy patients, the resulting curve exhibited high instability, especially for high anti-CCP levels, so we eventually smoothed the results by fitting a logistic curve.ρ = 0.8, the segregation estimation lead to a variance σ2 = 2.5 and sex effect β =. Taking male-male pairs of affected individuals as the reference, the relative weights were 0.97 in female-female pairs and 0.99 in male-female affected pairs. Thus, there was little difference in weighing of pairs of different kinds. Discordant pairs provided very little information for traits with a prevalence like RA . The results of the analysis hardly differed from an unadjusted analysis that only incorporated affected pairs and are therefore not presented.For a correlation between random effects ρ and σ2 as for sex, the logistic curve describing the effect of anti-CCP level X on the probability of developing RA was estimated as Based on the same parameters The test yielded very extreme relative weights see Fig.  in whichA test derived to explicitly incorporate population effects of covariates into linkage analysis of binary traits was applied to the mapping of genes responsible for RA. The covariates were both categorical (sex) and continuous (anti-CCP levels), and individual-specific. Adjustment for sex (moderate effect) appears to have a negligible effect in the case of a relatively rare condition like RA. The analysis adjusting for anti-CCP levels (very strong covariate effect) has a substantial effect on the analysis as demonstrated by the relative weights given to different pairs. This is consistent with the theoretical results derived by Lebrec and van Houwelingen . A simulp-values by gene dropping conditional on the test's weights.Usual approaches to adjusting for covariates in linkage analysis for binary traits usually boil down to letting the IBD sharing vary depending on covariate values of the data . The effIn conclusion, for a relatively rare disease like RA, allowance of covariates with only moderate effects like sex brings little added value compared to an unadjusted analysis. Only covariates with very strong effect on the probability of developing the disease can improve power. In the case of a covariate like anti-CCP, which is known to be biologically involved in RA, some regions that are likely related to anti-CCP could be identified . However, the original unadjusted peaks on chromosomes 1, 9, and 10 were only suggestive for linkage so care should be taken in interpreting our findings. Direct linkage of anti-CCP levels to those regions would add strength those findings. In that case, further fine mapping for genes responsible for RA on those chromosomes could be done by directly studying anti-CCP levels as a phenotype. For other highlighted chromosomes , one promising fine-mapping strategy might be to use individuals with low anti-CCP levels only.The author(s) declare that they have no competing interests.


Multiple testing is a problem in genome-wide or region-wide association studies. In this report, we consider a study design given by the Genetic Analysis Workshop 15 (GAW15) Problem 3 – nuclear families (parents with their affected children) and unrelated controls. Based on this design, we propose three two-stage approaches to deal with the problem of multiple testing. The tests in the first stage, statistically independent of the association test used in the second stage, are used to screen or select single-nucleotide polymorphisms (SNPs). Then, in the second stage, a family-based association test is performed on a much smaller set of selected SNPs. Thus, the problem of multiple testing is much less severe. Our simulation studies and application to the dense SNP data of chromosome 6 in the GAW15 Problem 3 show that the two-stage methods are more powerful than the one-stage method (using the family-based association test only). Most multiple-testing adjustment approaches, including Bonferroni correction for controlling the family-wise error rate and the method proposed by Benjamini and Hochberg [Genome-wide or region-wide association is a promising approach to mapping complex disease genes ,2. HowevHochberg  for contIn case-control studies, several authors have proposed a two-stage design that utilizes two independent samples ,6. The fIn this article, we propose several two-stage methods to test association for qualitative traits by using nuclear families  or nuclear families and unrelated controls. To analyze the data set of nuclear families, we compare the allele frequency in affected parents with that of unaffected parents (test I) to screen and select SNPs. Then the pedigree disequilibrium test (PDT)  is used n nuclear families and N unrelated controls. Suppose that we have genotyped M markers across the genome or in a candidate region for each sampled individual. Also, all children in the nuclear families are affected and the disease status of the parents is available. The reason for considering this kind of sample is the design of the GAW15 Problem 3 data set. To detect disease susceptibility loci, based on the sample structure, we proposed three methods. All three methods are two-stage approaches – the methods in the first stage are used to screen and select SNPs and those in the second stage are used to test the association on the selected SNPs.Consider a sample of N1 cases and N2 controls, and each sampled individual has a genotype at a bi-allelic marker with two alleles A and a. To test the association between the marker and the disease, one can use the statistic:The three approaches we propose for the first stage are based on a test statistic for a case-control study. Consider a case-control study with p0 is the sample allele frequency of allele A in the whole sample. Under the null hypothesis of no association, this test statistic asymptotically follows a standard normal distribution. When the absolute value of T is large, we reject the null hypothesis of no association. Based on the test statistic T, we propose the following three tests that can be used in the first stage to screen SNPs:where T based on this sample is denoted by Tcc. The Tcc only uses the nuclear families (does not need the unrelated controls).1. Consider affected parents of the sampled nuclear families as cases and unaffected parents of the sampled nuclear families as controls. The test statistic n sampled nuclear families as cases and the N sampled unrelated controls as controls. The test statistic T based on this sample is denoted by Tpc. If A is a high risk allele, the frequency of A among the parents should be higher than that in the controls, because each pair of parents has at least one affected child.2. Consider all the parents of the Tpc and Tcc. The test statistic of this approach is Fisher's combination of the p-values of the two tests and is given by Tcb = -2(log P1 + log P2), where P1 and P2 are the p-values of the tests Tpc and Tcc, respectively. Under the null hypothesis of no association, Tcb will follow a χ2 distribution with 4 degrees of freedom [3. The third approach is a combination of the  freedom .ni affected children in the ith family.For a biallelic marker with two alleles A and a, we code the three genotypes aa, Aa, and AA as 0, 1, and 2, respectively. Let Xij, XiF, and XiM denote the codes of the genotypes of the jth child, father, and mother in the ith family. Let We use the PDT  to test Then the test statistic of the PDT is given by Tpc, Tcc, or Tcb to each of the M markers and get M p-values. Select L markers with the smallest p-values (we will discuss later how to choose L). Then, we apply the PDT to the L selected SNPs, and declare a SNP as significant if the p-value of the PDT at this marker is less than a threshold δLα . The threshold δLα is determined by controlling the FDR, the ratio of the number of falsely rejected null hypotheses to the total number of rejected null hypotheses, at level α. To control the FDR we can choose the cut-off δLα as follows [p(1),...,pL) . The data contain 100 replicate data sets. In each replicate data set, there are 1500 nuclear families, 2000 unrelated controls and two affected children in each family. Each individual has genotypes at 17,820 SNPs on chromosome 6. From the answer provided with the data set, we know that there are three trait loci: Locus DR, Locus C, and Locus D on chromosome 6. Locus DR affects the risk of rheumatoid arthritis (RA). Locus C increases RA risk only in women. These two loci are in the same position. The typed SNP 3437 on chromosome 6 is in the same position as Locus DR and Locus C, that is, the recombination rates between SNP 3437 and Locus DR and between SNP 3437 and Locus C are both zero. The rare allele of Locus D increases RA risk five-fold. In the dense SNP panel of chromosome 6, the SNP that is nearest to Locus D is SNP 3917. The genetic distance between locus D and SNP 3917 is 0.00171 cM, and the physical distance is 1565 bp.r = 0.36 and D' = 0.45. The results of the power comparison for detecting SNP 3455 using a smaller sample size are summarized in Table Tpc and Tcb, which use both family data and unrelated controls, are more powerful than the PDT, especially when α is 1%, 5%, or 10%. However, the two-stage approach Tcc is not as powerful as the PDT when α is less than 0.3. When α is between 0.5 and 0.8, the Tcc is slightly more powerful than the PDT (results not shown).We first compare the power of the four methods to detect SNP 3437. The association between SNP 3437 and RA turns out to be very strong, such that the power of the four methods is all 100%. In order to do the power comparison, we reduce the sample size and, instead of detecting SNP 3437, we detect SNP 3455. SNP 3437 and SNP 3455 are in linkage disequilibrium with α > 0.05. When the value of α is between 0.05 and 0.1, the Tcb is much more powerful than the PDT. In the case of two children in each family, the Tcb is also more powerful than the PDT when α > 0.01. The other two two-stage approaches, the Tpc and Tcc, are only slightly more powerful than the PDT when α ≥ 0.05.The power of the four methods to detect SNP 3917 is summarized in Table Tcb using family data and unrelated controls is more powerful than the PDT, and in several cases the Tcb can double the power of the PDT. How to choose the value of the threshold α is a problem. From our simulation studies, one can see that the value of α around 0.01 may be a good choice for the Tpc and Tcb. If only the family data are available, we would use the two-stage approach Tcc. In the case of one child, the value around 0.1 may be a good choice for α. In the case of two children, the Tcc does not benefit much. In general, we need further investigation for choosing the value of α.In this report for genome-wide or region-wide association studies, we proposed three two-stage approaches to analyze family data or data sets that contain family data as well as unrelated controls. Based on our simulation studies and applications of the data sets of the GAW15 Problem 3, we are able to demonstrate that, in the case of one child in each family – the typical data set of the TDT design – all three two-stage approaches are more powerful than the PDT. In almost all the cases we considered, the Our simulation and the GAW15 data analysis results show that the three proposed two-stage methods have correct type I error rates and, in most cases, are more powerful than the PDT.The author(s) declare that they have no competing interests.


Accounting for and quantifying the associative effect of each animal could improve both welfare of animals and response to selection. Because of the limitation of REML, Gibbs Sampling could be an alternative technique to estimate the variance component of the associative effect. The objective of this study was to investigate the estimation accuracy of the variance component of associative effect by using simulation via Gibbs Sampling. The simulated data comprised five generations of pigs. The breeding animals of each generation were selected randomly. In the simulation, variations were introduced for the methods of assigning pens , the number of pigs per pen (5 or 10), the number of breeding animals per generation (162 or 324) and the correlation between genetic direct effect and genetic associative effect . Each set of simulation was run for 30 replications.Random assignment or mixed sib assignment resulted in bias of estimated variance components in only 3 of 24 combinations. Furthermore, these 3 cases occurred with 162 breeding animals. With full sib assignment, 9 out of 12 groups of estimates significantly deviated from the true parameter value. The Root Mean Square Errors obtained with the full sib assignment were higher than with the other two methods of pen assignment in most of the cases. The Root Mean Square Errors obtained with datasets with 324 breeding animals were notably smaller than the datasets from 162 breeding animals. Within each method of pen assignment, the relative bias of the associative effect was significantly smaller with group size 10 than with group size 5.Full sib assignment caused difficulties to estimate variance components in most of the cases, due to a lack of identifiability. With random and mixed assignment, most data structures yielded unbiased results but increasing the number of breeding animals or group size improves the estimation. Thus to get identifiable and unbiased estimates of the genetic associative effect, it is recommended to avoid close genetic relationship between animals within one pen and to use sufficient numbers of breeding animals and sufficient group sizes. Social interactions are commonly observed among group housed livestock and some of them have negative effects, such as: aggressive behaviour for social rank and competition for limited resources . These interactions may become more important when resources are more restricted leading to increase of injuries and decrease of productivity ,2. ArtifAccording to Griffing , the intImplementation of Bayesian method may provide a valuable alternative. Bayesian Markov Chain Monte Carlo (MCMC) methods have been introduced to quantitative genetics since the early 1990s . HoweverThe objective of this study was to investigate the accuracy of the posterior means of variance components in relation to the (genetic) relationships among penmates, the number of pigs per pen and the variation of the number of breeding animals.In this study, datasets were simulated for 36 combinations of parameters. Each set of parameters was replicated 30 times. Simulations were programmed in R 2.5.1  and perfInitial tests indicated that a total length of the Gibbs chain of 550000 was sufficient. The burn-in period was fixed at 50000, which means that the first 50000 samples were discarded. To reduce the correlation between Gibbs samples, a conservative thinning rate of 500 was used. Therefore, 1000 Gibbs samples of each chain were saved. Geweke and Gelman diagnostics were used to access the convergence of Gibbs Samples. With respect to full sib assignment, less than 33% of the replications gave a diagnostic value around 1.2, whereas 95% of the replications with the random and mixed sib assignment had a diagnostic value around 1.02.The density plots of Gibbs samples of the variance of the genetic associative effect from two chains were shown in figure e) yielded σad = 140, Estimation with a model considering only genetic direct effect  from 30 replications were presented in table 324 , a correlation of 0.5 and group size of 5. Moreover, most of the standard errors calculated from the combinations with full sib assignment were high compared to the other two methods of assignment.The mean and the standard error of estimated values . This occurred with the following combinations: random pen assignment, correlation 0.1 and group size 5; mixed sib assignment, correlation 0.1 and group size 10; mixed sib assignment, correlation -0.5 and group size 5.With S324 compared to the cases with S162, but not significantly different . Within the same number of breeding animals, the RMSE obtained from group size 5 were significantly higher than the cases from group size 10 . Within the same level of group size, the RMSE of random sib assignment (p1) are not significantly different from the mixed sib assignment (p2) .The RMSE of the variance of associative effect obtained from 36 parameter sets were shown in figure 324, correlation -0.5; S324, correlation +0.1; S162, correlation +0.1; S162, correlation +0.5. The RMSE from the full sib assignment depended on correlations, indicating that there may be an association between full sib assignment and "correlation" (between d &a) on the uncertainty of estimates for the associative effect.With the method of full sib assignment (p3) and the following combinations, datasets yielded higher RMSE compared to assignment methods p1 and p2: SThe results from MANOVA test of relative bias showed a significant interaction between the number of breeding animals, the method of pen assignment and the correlation . Interaction between pen assignment method and group size  was also significant at the family wise significance level of 0.1 .324 was significantly smaller than the case for S162   . The phenotype of individuals was composed of heritable and non-heritable effects. We assumed the associative effect to be  genetic and expressed in the performance of the penmates. The simulation model included one fixed effect (sex) and three random effects: genetic direct effect, genetic associative effect and random error .b indicated the effect of sex on the average daily gain ; d represented the genetic direct effect; a represented the genetic associative effect, affecting the growth of penmates; e represented the independent random residual of the individual pig; X, Zd, Za were incidence matrix of each effect corresponding to each individual.Y represented the average daily gain of the pig; It was assumed that the random effects follow a multivariate normal distribution:σda was the covariance between d &a; d, a and e. G was the variance-covariance matrix of genetic effects d and a.i, the average daily gain was simulated asFor an individual pig di denoted the genetic direct effect of the individual i; aji denoted the genetic associative effect coming from the jth penmate of the ith individual; p denoted the number of penmates of the ith individual; ei denoted the random residual of the ith individual.d and a were simulated using the partitioned matrix obtained from G multiplied by standard random normal deviates. For the following generations (progeny), d and a were the sum of the average of the d and a of the parents and a random Mendelian sampling term. e was simulated as the deviation of random residuals multiplied by a standard random normal deviate.Based on the Cholesky decomposition , G was sSimulation included five generations of pigs, and breeding animals for each generation were selected randomly. Litter size followed a normal distribution varying from 2 to 20 with mean equal to 9 and standard deviation equal to 2.6. Sex effect was simulated assuming a uniform distribution, i.e. the probability of male or female was 50%. Since litter size was not fixed, the total number of animals in each replication was not fixed.d & a were examined. Three different scenarios were used to assign pigs to pens. The first scenario was to assign pigs randomly (p1). The second one was to assign half of the pens with full sibs and the other half non full sibs (p2) and the third one was to assign full sibs per pen (p3) [162 and S324), two different group sizes (5 and 10) and three different correlations between d & a  were specified.In order to investigate the impact of the data structure on the estimation of variance components, a number of data sets were simulated. The influence of pen composition (assignment of pigs to pens), group size (pigs/pen), number of breeding animals and the covariance (cov) between pen (p3) ,20. WithVariance components were analysed using the Multiple Trait Gibbs Sampler for Animal Models (MTGSAM)  and applTwo Gibbs chains using different sets of starting values were run to check the convergence. The Geweke and Gelman diagnostic ,22 were lated as :θ is the true value used for simulation and n is the number of replications.where d &a simultaneously on the percent relative bias of the four variance components , multivariate analysis of variance (MANOVA) was used  [The accuracy of the parameter estimates was quantified by the percent relative bias. The percent relative bias was calculated as θ^−θθ. To studS 9.1.3) .P1,...,P4, animal B has penmates Q1,...,Q4, and A and B are from two different pens. Based on the statistical model that we used the genetic covariance between A and B was:Ignoring the genetic associative effect (if present in the data) will often result in biases of variances of genetic direct effect  . LookingAAB = 0.25. To make sure that the covariance between A and B is an unbiased estimation of σad and σad and P1,...,P4 and Q1,...,Q4. However, it is unrealistic to assume that all animals are genetically unrelated. Thus the terms related to σad and σad and σad and If we consider A and B to be half sibs, then the genetic relationship between A and B is 0.25, i.e. AAB = 0. If the genetic associative effect is ignored, the variation caused by σad and σad and σad and To investigate the bias of To confirm this, we took the simulation data obtained from the parameter combination of group size 5, correlation 0.5, 324 breeding animals and mixed full sib assignment. The estimation with a model considering only genetic direct effect and random residual was compared to the true value of simulation parameters.JC carried out the simulation study, and drafted the manuscript. SJ conceived the study, participated in its design, and revised the manuscript. NB participated in conception, coordinated it and revised the manuscript. All authors read and approved the final manuscript.


Both imprinting and maternal effects could lead to parent-of-origin patterns in complex traits of human disorders. Statistical methods that differentiate these two effects and identify them simultaneously by using family-based data from retrospective studies are available. The usual data structures include case-parents triads and nuclear families with multiple affected siblings. We develop a likelihood-based method to detect imprinting and maternal effects simultaneously using data from prospective studies. The proposed method utilizes both affected and unaffected siblings in nuclear families by modeling familial genotypes and offspring's disease status jointly. Maternal effect is usually modeled as a fixed effect under the assumption that maternal variant allele(s) has (have) identical effect on any offspring. However, recent studies report that different people may carry different amounts of substances encoded by the mother's variant allele(s) , which could result in heterogeneity of maternal effects. The proposed method incorporates the heterogeneity of maternal effects by adding a random component to the logit of the penetrance. Our method was applied to the Framingham Heart Study data in two steps to detect single-nucleotide polymorphisms (SNPs) that may be associated with high blood pressure. In the first step, SNPs that affect susceptibility of high blood pressure through minor allele, genomic imprinting, or maternal effects were identified by using the proposed model without the random effect component. In the second step, we fitted the mixed effect model to the identified SNPs that have significant maternal effect to detect heterogeneity of the maternal effects. The phenomenon that a trait follows a maternal or paternal lineage, instead of following the mendelian mode of inheritance, is referred to as the parent-of-origin pattern. Genomic imprinting and maternal effect could give rise to similar parent-of-origin patterns . Hence, A case-parents triad could have 15 possible familial genotype combinations -4. LL-LRUnaffected siblings are also genotyped in many genetic studies. Although unaffected siblings have been incorporated to infer the missing parental genotypes in LL-LRT and PO-LRT , they doOn the other hand, a prospective study like the Framingham Heart Study (FHS) does not specifically recruit subjects with a certain disease, thus the originally recruited cohort could be considered as a random sample of the general population of healthy people and patients with any disease. Therefore, a test using data from a prospective study could utilize both affected and unaffected siblings by modeling their genotypes and disease status jointly. Nevertheless, the disease of interest should not be a rare one; otherwise, the number of patients in the cohort would be too small to be sufficiently informative.In LL-LRT, PO-LRT, and MFG tests, maternal effect is modeled as a fixed effect because it is assumed that maternal variant allele(s) has (have) identical effect on any offspring. This assumption might be invalid if we consider the cause of maternal effect more carefully. Maternal effect refers to the phenomenon that the genotype of a mother is expressed in the phenotype of her offspring, which is usually attributed to maternally produced molecules, such as mRNA that are deposited in the egg cell, and mRNA or antigens that are passed to the offspring during pregnancy. The latter case could arise from a biological process called microchimerism. Microchimerism means that two genetically distinct cells, one being at a low concentration, are present in the same individual. Microchimerism may be due to transfer of cells between mother and fetus or between two twins. Other sources of microchimerism include blood transfusions and organ transplants. Cells transferred from the mother to the fetus are referred to as maternal microchimerism (MMc). Non-inherited maternal antigen coding alleles (NIMA) ,6 withinIn this study, we will discuss a prospective likelihood formulation that will take multiple affected and unaffected siblings into consideration. Further, we will treat maternal effects as random to model heterogeneity. This method will then be applied to the high blood pressure (HBP) trait in the FHS.HBP in an adult is defined as a blood pressure greater than or equal to 140 mm Hg systolic pressure or greater than or equal to 90 mm Hg diastolic pressure. High blood pressure directly increases the risk of coronary heart disease and stroke, especially when it is present with other risk factors. In the FHS, systolic pressure and diastolic pressure of the Original Cohort (the first generation) and their Offspring Cohort (the second generation) were measured at four exams, and were measured once in the Generation 3. Based on the highest measurements among all available ones, there were 1,036 individuals having high blood pressure and 1,724 individuals having normal blood pressure in the Offspring Cohort. In Generation 3, there were 379 individuals having high blood pressure and 3,618 individuals having normal blood pressure. Our analysis was based on these phenotypic data and the genotypes of nuclear families. Families with missing parental genotype(s) were omitted from our analysis because they are not informative for imprinting and maternal effects if both parents' genotypes are missing.Moreover, only one nuclear family was selected at random to be included in the analysis from each three-generation pedigree. This selection process led to approximately 300 nuclear families (with the number of children in each family ranging from 1-8) for each single-nucleotide polymorphism (SNP).N nuclear families. The ith family has two parents and ni children, i = 1, 2, ..., N. We model the genotypes of all family members and disease statuses of all children jointly. Let Mi and Fi denote the genotypes of mother and father in the ith family.Suppose there are ni children in the ith family. Mi, Fi, and j = 1, 2, ..., n. jth child in the ith family being affected, and 0 indicating otherwise.ith family could be decomposed asThe likelihood for the β parameters) and the maternal effect (the γ parameters):We use the logit model to relate the penetrance to the imprinting effect (part of the jth offspring in the ith family coded in one row: I(Mi = 1), I(Mi = 2)). The parameter vector β0 is the logit of phenocopy rate; β1 measures the effect of the single minor allele inherited from the father; β1 + βim measures the effect of the single minor allele inherited from the mother; βim measures the imprinting effect, with βim < 0 indicating maternal imprinting and βim > 0 indicating paternal imprinting; β2 measures the effect of two copies of the minor allele; γ1 and γ2 measure the maternal effect when the mother carries one or two copies of the minor allele, respectively. Because we assume that different mothers may impose heterogeneous maternal effects, εi measures the deviation of the effect size from the mean; it also introduces correlation among the siblings within the same family. Specifically, εi is assumed to follow N.where β0, β1, β2, βim, γ1, γ2, and σ2 are estimated by maximizing the likelihood using the procedure NLMIXED in SAS.The parameters εi and use the minimum p-value  being ≤ 0.00005 as the criterion to choose the SNPs. We then screen the selected SNPs by checking specific parameter constraints. The assumption that carrying minor alleles would increase the disease risk implies that β1 ≥ 0 and β1 + βim ≥ 0. Furthermore, two copies of the minor allele should have an effect at least as large as a single copy, and thus β2 ≥ max. Estimates of β1 and β2 being significantly less than zero indicates that labels of minor and major alleles should be reversed. SAS does not allow complex constraints such as β1 + βim ≥ 0 and β2 ≥ max in its NLMIXED procedure, and as such we fit a "constraint model" and an "additive model" to check the intended constraints. In the "constraint model", we reparametrize β2 - β1 = β1 ≥ 0 and β1 ≥ 0 and β2 ≥ 0. In the "additive model", we assume an additive effect of the two copies of the minor allele, i.e., β2 = β1 + (β1 + βim), to ensure that β2 ≥ max. In the second step, we fit the mixed effect model to the selected SNPs with significant maternal effect and use the p-value of testing σ = 0 being less than 0.05 and reduced Akaike information criterion (AIC) value as the criterion for identifying heterogeneity of maternal effects.SNPs that may have a minor allele effect, imprinting effect, or maternal effect are selected in the first step and the heterogeneity of maternal effects is detected in the second step. In the first step, we fit the parsimonious fixed-effect model without the random component p-values for testing β1 = 0 or β2 = 0 being less than 0.05 are shown in boldface, which signifies potential minor allele effects. For SNPs that have significant minor allele effect, we further looked at the p-value for testing βim = 0 and inferred maternal or paternal imprinting effect from the sign of p-value for testing γ1 = 0 or γ2 = 0 is less than 0.05, we further tested for heterogeneity of the maternal effects in step two. Results from the second step are shown in Table p-values, and AIC of the fixed effect model, while the second row shows those of the mixed effect model. If the p-value for testing σ = 0 is less than 0.05 and the AIC is reduced by fitting the mixed effect model, we concluded that the maternal effect is heterogeneous. Five SNPs were detected to have various degrees of maternal effects, of which four appears to be heterogeneous among the families (Table We scanned 230 k SNPs on chromosomes 1 to 6 and detected nine SNPs that may be associated with high blood pressure through minor allele, imprinting, or maternal effect. These nine SNPs are shown in Table To summarize and visualize the result, we categorize the nine SNPs into a Venn diagram Figure  accordinIn the Genetic Association Studies of Complex Diseases and Disorders section of the Genome Browser, we found that the association between the nine detected SNPs and blood pressure has been established either in human or in rat (see the third column of Table AIC: Akaike information criterion; FHS: Framingham Heart Study; HBP: High blood pressure; LL-LRT: Log-linear likelihood ratio test; MFG: maternal-fetal genotype incompatibility; MMc: Maternal microchimerism; NIMA: Non-inherited maternal antigen coding alleles; PO-LRT: Parent-of-origin likelihood-ratio test; SNP: Single-nucleotide polymorphism.The authors declare that they have no competing interests.JY and SL developed the methodology and designed the analysis scheme. JY implemented the analysis and drafted the manuscript. Both authors read and approved the final manuscript.


Genome-wide association (GWA) studies that use population-based association approaches may identify spurious associations in the presence of population admixture. In this paper, we propose a novel three-stage approach that is computationally efficient and robust to population admixture and more powerful than the family-based association test (FBAT) for GWA studies with family data.-6 for 34,625 genotyped SNPs in this paper) are analyzed in the third stage using FBAT, with correction of multiple testing only for SNPs that enter the third stage. Simulations are performed to evaluate type I error and power of the proposed method compared to LME adjusting for 10 principal components (PC) of the genotype data. We also apply the three-stage approach to the GWA analyses of uric acid in Framingham Heart Study's SNP Health Association Resource (SHARe) project.We propose a three-stage approach for GWA studies with family data. The first stage is to perform linear regression ignoring phenotypic correlations among family members. SNPs with a first stage p-value below a liberal cut-off (e.g. 0.1) are then analyzed in the second stage that employs a linear mixed effects (LME) model that accounts for within family correlations. Next, SNPs that reach genome-wide significance (e.g. 10Our simulations show that whether or not population admixture is present, the three-stage approach has no inflated type I error. In terms of power, using LME adjusting PC is only slightly more powerful than the three-stage approach. When applied to the GWA analyses of uric acid in the SHARe project of FHS, the three-stage approach successfully identified and confirmed three SNPs previously reported as genome-wide significant signals.For GWA analyses of quantitative traits with family data, our three-stage approach provides another appealing solution to population admixture, in addition to LME adjusting for genetic PC. Many published genome-wide association (GWA) studies with dense SNP markers are based on study designs with unrelated individuals. It is well known that such designs are prone to spurious association caused by population admixture. A current popular solution to this problem involves identifying axes of genetic variation via principal components (PC) analyses with a large number of SNPs and then adjusting for the PC in the association analysis . HoweverIn the context of GWA studies with family data, we present three basic strategies to handle a family-based design, and then we use the three basic strategies to form a two-stage population-based approach, and a three-stage family-based approach. The two-stage approach is computationally efficient and can account for familial relatedness, whereas the three-stage approach is additionally robust to population admixture. We performed simulations to evaluate the three basic strategies, the two-stage and the three-stage approaches. We also applied these strategies to Framingham Heart Study (FHS) SNP Health Association Resource (SHARe) 550K GWA analyses of uric acid.Least squares regression (denoted LM) is available in many standard statistical software packages and is fast to compute. The latter property is particularly desirable for the latest GWA studies with growing number of SNPs and phenotypes to analyze. The LM model can be expressed asYij and Gij are the phenotype and genotype for the jth person in the ith family, respectively. X(.) is the coding of the genotype and εij's are independent random measurement errors following a Gaussian distribution. β can be estimated via maximum likelihood assuming that Yij's are independent and the p-value of testing genetic association is computed via two-sided t test. However, for family-based design, Yij's from the same family are correlated due to environmental and genetic effects. LM assumes independent Yij's, which could result in inflated type I error due to unexplained phenotype correlations in a family.where Y, i.e.Linear mixed effects (LME) model is traditionally used to model correlated continuous outcomes. LME is a generalization of LM with an additional random intercept that can account for familial correlation in i is the correlation matrix in ith family. Similar to [i is the matrix of the coefficient of relationships or twice the coefficient of kinships, thus where milar to , we assuanalyses , in whicFBAT statistics  are basei Pare the parental genotypes of the th ifamily, X(Gij) is the score of the th jchild's genotype in the th ifamily, and E(X(Gij)|Pi) is the expected score of the child's genotype given parental genotype data. The p-value of testing genetic association is computed via two-sided Z test.where 1 . This approach uses every genotyped and phenotyped individual and accounts for differential pedigree structures in the data. In addition, the first stage's screening makes this approach more efficient when applied to GWA studies. However, it is subject to the confounding due to population admixture.We propose a two-stage population-based approach for family data. The first stage is LM ignoring the familial correlations. The second stage uses LME on SNPs with first stage LM p-value less than αn is the number of SNPs detected at the second stage LME. When FBAT is not included, the strategy reduces to two-stage approach.To control for population admixture, we further propose a three-stage family-based approach. The first two stages are identical to the two-stage approach proposed above. In the third stage, FBAT is conducted on SNPs with second stage p-value less than a specified threshold. FBAT p-value with multiple testing correction (such as Bonferroni correction) that only pertains to SNPs entered the third stage is used as final p-value for this approach. SNPs that did not enter the third stage are deemed as not associated with the phenotype of interest. This approach can be viewed as a special case of weighted FBAT approach , where SWe conducted simulation studies to evaluate the type I error and power of each of the introduced approaches. We simulated phenotype and/or genotype data, based on the real pedigree structures of 8,481 individuals from 1,494 pedigrees in the FHS SHARe project. Continuous traits are randomly generated following a multivariate normal distribution by using the program SOLAR [For the basic strategies and the two-stage approach, combinations from the following simulation parameters are considered for evaluating type I error rates Tables , 2 and 3r2 between any two SNPs on chromosome 1 was computed using R "genetics" package [r2 between rs1570092 and other chromosome 1 SNPs for studying the power under different r2s . We used simulated normal phenotypes with QTL variance 0, polygenic heritability 0.3 and 0.6, to estimate type I error rate for each studied method (Table p and variance p(1 - p)FST. FST, the "fixation index", was also a scaled variance of the subpopulation allele frequencies [p of the 100 admixture SNPs is 0.3; the QTL variance are 0 and 0.005 for assessing type I error and power, respectively; the polygenic variance is 0.3; FST is 0.025; and the difference in phenotypic means is created by adding an offset value δ 0.25 to phenotypic value in one subpopulation. Power is evaluated separately for detecting SNPs in LD  with the QTL and the QTL SNP. The software Eigenstrat [In addition, to evaluate the robustness and power of the three-stage approach in the presence of population admixture, we simulated phenotype and genotype of 100 admixture SNPs. We first partitioned the FHS SHARe population into two similar-size subpopulations with different allele frequencies and phenotypic means. For these 100 admixture SNPs, the allele frequencies in the two subpopulations were produced by Balding and Nichols approach ,10 that quencies . The comLME analyses were conducted using the lmekin function in the R GWAF package  modifiedTable Table To study the relationship between FBAT and LME statistics under the null hypothesis of no association, we present in Table -6 genome-wide significance level (Bonferroni correction) using 100 replicates of Normal phenotypes without QTL (MAF 0.1) effect and real genotype data of 34,265 SNPs. The type I error rates are estimated by replicate. We use 0.01, 10-6, and 0.05/n as the p-value cut-offs for the first, the second and the third stage, respectively, where n is the number of SNPs entering the third stage. We choose 0.1 as the p-value cut-off at the first stage because it gives slightly more conservative type I error rate than 0.2 does, as shown in Tables Table r2 with rs1570092. The power and type I error rates of each LD group are estimated at 10-6 significance level by replicate. There is no inflated type I error (0 <r2 ≤ 0.01 group) for all compared methods except for LM. In general, the power increases as r2 increases as expected, except some fluctuations are observed in LM and FBAT, which may be due to the large number of SNPs in the 0 <r2 ≤ 0.01 group. When r2 > 0.3, LM, LME and the two-stage approach have 100% power to detect the association between the tested SNP and the simulated phenotype; while the three-stage approach and FBAT have about 99% and 39-51% power, respectively. The three-stage approach has shown to have similar power as LME and to be more powerful than FBAT.Table FST = 0.025 and δ = 0.25) in our simulations where the type I error and power estimates are assessed at 10-6 significance level by replicate (Table Even though the three-stage approach is slightly less powerful than LME and the two-stage approach as shown in Table -8), and all the loci have been replicated in two other independent cohorts, the Rotterdam Study and the ARIC Study [We applied the strategies to the GWA analyses of uric acid levels in FHS SHARe project. A genome-wide scan of Affymetrix 550K SNP GeneChip on about 9,000 subjects was performed. GWA analyses using LME have identified 3 loci SCL2A9, ABCG2 and SCL17A3 with genome-wide significance  identified by LME in FHS SHARe project.A potential modification of the three-stage approach to avoid power loss in FBAT is to include one more stage by applying quantitative trait linkage disequilibrium (QTLD ) to testi-th ranked SNP with the significance level wiα, where Σwi = 1, w1 > 0 and α is the genome-wide significance level. [FBAT is known for the robustness against admixture and the lack of power compared to population-based methods. To circumvent multiple testing and improve its power in GWA analyses, two-stage FBAT approaches were proposed ,17. In be level.  presentsEven though our main interest focuses on quantitative traits, similar strategies can be applied to dichotomous traits, where the first stage uses logistic regression, the second stage uses generalized estimating equations (GEE) , and theFor GWA analyses on quantitative traits with family data, our three-stage approach provides another appealing method robust to population admixture, in addition to using LME adjusting for PC.All authors contributed to the design of the overall strategy. MHC conducted all the analyses. QY and MHC drafted the manuscript. All authors read and approved the final manuscript.


Hybrids represent a cornerstone in the success story of breeding programs. The fundamental principle underlying this success is the phenomenon of hybrid vigour, or heterosis. It describes an advantage of the offspring as compared to the two parental lines with respect to parameters such as growth and resistance against abiotic or biotic stress. Dominance, overdominance or epistasis based models are commonly used explanations.The heterosis level is clearly a function of the combination of the parents used for offspring production. This results in a major challenge for plant breeders, as usually several thousand combinations of parents have to be tested for identifying the best combinations. Thus, any approach to reliably predict heterosis levels based on properties of the parental lines would be highly beneficial for plant breeding.Recently, genetic data have been used to predict heterosis. Here we show that a combination of parental genetic and metabolic markers, identified via feature selection and minimum-description-length based regression methods, significantly improves the prediction of biomass heterosis in resulting offspring. These findings will help furthering our understanding of the molecular basis of heterosis, revealing, for instance, the presence of nonlinear genotype-phenotype relationships. In addition, we describe a possible approach for accelerated selection in plant breeding. The introduction of the concept of hybrids probably represents the most important single innovation in plant breeding. Central to the concept of hybrid breeding is the phenomenon of heterosis or hybrid vigour Despite its central importance for the hybrid breeding concept, the molecular basis responsible for the heterosis effects is far from being understood. From a genetics perspective, dominance, overdominance or epistasis based models are commonly used as explanations for heterosis One central observation in hybrid breeding programs is that the extent of heterosis is strongly dependent on the two parental lines. Thus, with respect to yield, for instance, heterosis can vary strongly depending upon the specific combination. In addition to its puzzling biological complexity, this represents a severe challenge to plant breeding, as usually the best combination of two parental lines can only be determined by trial and error. Therefore many thousands of testcrosses are required in order to find the optimal parental combination for the trait of interest. Numerous attempts have been followed with the goal to reduce the level of uncertainty concerning suitable parental combinations and to achieve some level of predictability. Not surprisingly mostly genetic markers of the two parents were used in these approaches Despite the fact that genetic markers have proven to be highly useful in plant breeding for marker-assisted selection of simple traits that are difficult to assay Arabidopsis thaliana. The reason for choosing these predictors is that metabolite levels are the result of more genes than those represented by genetic markers, and as a rule they are also influenced by several genes and/or their products.We set out to test whether heterosis prediction can be improved by using more complex parameters of the parental line than genetic markers. To this end, we decided to investigate parental metabolic markers, i.e. relative levels of particular metabolic compounds, with regard to their predictive power for biomass heterosis in the plant model organism As shown in the Results section, the predictive power of genetic data for heterosis is significantly improved by combining it with metabolic measurements of one parent, suggesting complex mechanisms underlying heterosis. Finally, when analyzing the minimal set of metabolic and genetic markers needed for heterosis prediction in the two different testcross populations used, three classes can be identified. Firstly, there are markers highly predictive in both kinds of testcross combinations, secondly, we find markers specifically predictive for one kind of testcross combination, and there are also markers negligible in any of our prediction models.Arabidopsis thaliana accessions C24 and Col-0 As described in the Introduction, heterosis levels are a function of the two parental lines used to produce the offspring. Classical heterosis experiments are performed between two completely different parental lines, which have been inbred to a high degree and are essentially homozygous, resulting in a highly heterozygous F1 offspring. We here deliberately chose a different and genetically simpler experimental set-up as a first step towards investigation of the information carried by metabolic markers in comparison to, or in combination with, molecular genetic markers. To this end, a recombinant inbred line (RIL) population consisting of 359 lines derived from a cross between the two The analysis of a full or half diallele involves crosses among numerous lines with different degrees of relatedness, and in each cross only a subset of the genetic factors responsible for heterosis might be shared with any other cross. In contrast to that, in our much simpler experimental design one parent was kept constant  approach In a first approach we compared the whole set of available genetic versus metabolic markers according to their suitability for heterosis prediction. Applying PLS-modelling on all 110 genetic markers, the Pearson correlation between observed and in cross-validation predicted heterosis was 0.39 for the C24 crosses and 0.35 for the Col-0 crosses. Using, on the other hand, all available 181 metabolic markers as predictor set, the corresponding numbers were 0.27 for C24 crosses and 0.24 for Col-0 testcrosses.These results show that some prediction has been achieved. But the level of predictive power is very low, above all in the case of the 181 metabolic markers. We believe this to be a problem of overfitting, indicated by the fact that the larger predictor set yields the smaller prediction success in cross-validation.In order to rank the available variables according to their contribution to the response, we utilized the variable importance in the projection (VIP), which calculates the contribution of each predictor variable to the response in the respective PLS-model Applying this feature selection approach to our four PLS models (i.e. heterosis according to the Col-0 or C24 parent using either metabolic or genetic markers) led to improvements of the predictive power to values of about 0.40 cf. , irrespeWe wanted to answer the question of whether a combination of genetic and metabolic markers improves the predictability of heterosis as compared to the use of genetic markers alone. Since our variable selection algorithm allowed to overcome the problem of overfitting when dealing with a high number of predictors, we were now in a position to apply this algorithm on the combined set of metabolic and genetic markers  and test their suitability for heterosis prediction using PLS regression cf. .As shown in One advantage of the experimental design used here is the identification of variables that are important for heterosis prediction in both testcross populations as compared to variables that are strongly relevant in the prediction models for only one kind of combination, i.e. either with C24 or with Col-0. However, in order to perform this analysis, the number of variables in the respective models had to be reduced further to a minimal set of variables whose predictive power does not differ significantly from the optimal predictive power. To achieve this goal we developed a MDL based strategy cf.  section.When comparing the relative importance of the 110 genetic markers as judged by their contribution to heterosis prediction with the genetic analysis of heterotic biomass QTL, a substantial overlap is observed cf. . In partper seet al. (2008 submitted). The same is true for the two highly predictive markers at chromosome 3. The remaining one important marker at bottom of chromosome 1 also coincides with one heterotic QTL  derived from both parents, suggesting that complete genetic information should be sufficient for predicting heterosis. The genetic markers used here and in most other studies however are far from representing a complete coverage of the entire genome. On the other hand, in our study, individual genetic markers contain much information on the neighbouring regions, since we investigated a RIL population. Each line carries on average 1.86 recombinations per chromosome, and the average length of segments of a certain parental origin is 32.06 cM ArabidopsisIn our analysis, metabolic markers turned out to carry information on heterosis that is complementary to the genetic markers' information. Therefore, one should assume that epistatic gene effects are actually involved in heterosis. This is consistent with recent analyses which indicate a strong role for epistasis in the manifestation of heterosis in Concerning an effective genetic heterosis prediction model, the complex trait thus would require to be modelled via complex nonlinear interactions of the different genetic markers. Since we know little concerning gene-gene interactions in relation to their influence on the trait of our interest, too many possibilities exist for modelling such a nonlinear phenomenon. Thus, nonlinear gene interactions should be integrated indirectly by using metabolic markers. This is very simple to model, since this approach essentially follows a linear combination of genetic and metabolic markers cf. . NeverthBiomass is an integrated variable reflecting the action (and thus presence) of many, if not all, genes of the respective genotype. We therefore expected, following the argument used for metabolic markers, that the RILs' biomass as additional predictor is even more valuable.Actually, just like metabolic markers cf. , the RILThe combination of the RILs' metabolic markers and the biomass variable as predictors yields a predictive power of 0.51 and 0.47 for C24- and for Col-heterosis respectively. These numbers correspond approximately to the predictive power of the combined metabolite-genetic models cf. . FurtherOn the other hand, we added the genetic markers as predictors to the pure biomass model. In that way, the predictive power has been increased in both testcross populations to an almost equal amount, from 0.44 and 0.35 up to 0.60 and 0.50 respectively, for the C24 and the Col-0 testcrosses, independently of the presence or absence of metabolic markers as predictors. In both testcross populations, these numbers represent a significant improvement, as compared to all considered models cf. . But becSome of the predictors, such as parental biomass, are significantly correlated to the heterosis effect in at least one of the testcross populations. Accordingly, their contribution in the respective multivariate models is high. Such variables show an interesting difference in their influence on heterosis prediction in the two testcross populations.In contrast to the biomass variable, which correlates stronger with C24-heterosis (Pearson correlation: −0.45) than with Col-heterosis (Pearson correlation: −0.36), the remaining highly predictive markers are more important for Col- than for C24-heterosis. The most important single effect is that of the first genetic marker at top of chromosome 4. Its correlation with Col-heterosis is 0.40, as compared to 0.17 with C24-heterosis. The four subsequent markers on top of chromosome 4 also have a higher single effect on Col-heterosis (correlations between 0.31 and 0.35) than any marker has on C24-heterosis, where the strongest correlation (apart from the biomass variable) is −0.20 with a specific marker in the middle of chromosome 3.Since the most important single effects are stronger on Col-heterosis than on C24-heterosis, the contribution of the corresponding markers in the multivariate genetic model is also higher in the case of Col-heterosis cf. . Here a Naturally, this affects also the combined genetic-metabolic models cf. , not onlet al. 2008 submitted).These observations about the substantial influence of top of chromosome 4 for Col-heterosis  in connection with its minor influence on C24-heterosis  can be explained in the following way. It is crucial for strong Col-heterosis that the respective testcross is heterozygous at top of chromosome 4, i.e. that the corresponding parental RIL carries C24 alleles at this locus, indicated by a positive coefficient of the marker in the model . Indicated by the negative sign of the coefficient, the respective RIL parent is required to carry Col-0 alleles at this locus to yield high heterosis in C24 testcrosses, whereas it does not matter for Col-0 testcrosses whether they are homozygous or heterozygous at this locus. Consequently Col-0 is assumed to be dominant at the middle of chromosome 3. The same rational is applicable for some other accession-specific markers at other loci. Nevertheless, as mentioned above, we have to take into account also epistatic effects, in consequence of which the single dominance effects are often not as clearly revealed.Concerning the metabolic markers important for C24- and Col-heterosis prediction, there are some of them, whose model coefficients are positive in the Col-0 model while negative in the corresponding C24-model (e.g. glycine) and vice versa. This means, for instance in the case of glycine, that high levels in the parental RIL are associated with high Col-heterosis but with low heterosis in the C24 testcross. On the other hand, we find in the Col-0 parent a low level of glycine, whereas it is high in the C24 parent (and moderate in the F1 progeny). Consequently, the fact that a Col-0 testcross shows stronger heterosis when the corresponding RIL parent has a high glycine level, and a C24 testcross performs better when the corresponding RIL parent has a low glycine level, suggests that heterosis is dependent on an optimally balanced level of certain metabolites.That is in agreement with the established metabolic balance concept of heterosis, which requires the coordination of all reactions and systems for efficient growth under a given environment This idea is also supported by some of our specific metabolic markers cf. , whose VAs described in the Results section, combined genetic-metabolic models yield a correlation of approximately 0.5 between observed and in LOOV predicted response cf. . AlthougHowever, an enrichment of crosses displaying a higher likelihood for strong heterosis would probably be helpful. To evaluate whether this approach might be feasible, we trained a linear discriminant model for C24-heterosis. This model discriminates the 359 RILs into lines with high and low heterotic potential using our minimal genetic-metabolic predictor set. In LOOV 233 RILs  were classified correctly by that model. Incorporating all 181 metabolic markers and all 110 genetic markers resulted in a discriminant model that classified only 49% of the RILs correctly, which corresponds to a random classifier. Thus the two-step approach described here, i.e. identifying in a quantitative model the most important set of genetic and metabolic markers and subsequently applying those in a qualitative model, might be an interesting path also with respect to practical applications In addition to the incorporation of gene interactions by metabolic markers, as shown in this study, we will also consider nonlinear relationships of the most important metabolic markers identified in this work. This seems to be a promising step, since on the one hand, the highly predictive metabolic markers show distributions deviating from normal ones. On the other hand, for linear models normal distributions of the predictors are required. Consequently, the consideration of some nonlinear terms in the discrimination model, which account for the special distributions of the highly predictive markers, will probably improve the classification success.Arabidopsis thaliana heterosis experiments that included the accessions C24 and Col-0 Data was derived from a RIL population We investigated two sets of predictor variables, both, independently and in combination. The first set was the metabolic profile of the RILs consisting of 181 metabolic markers. Their levels were measured via gas-chromatography/mass-spectrometry at 15 days after sowing, and the data was normalized as described elsewhere Our response variables of interest were C24-heterosis and Col-heterosis. These were determined by the shoot biomass of the particular RIL, the shoot biomass of the corresponding testcross C24 x RIL (or Col-0 x RIL) and that of the background line C24 (or Col-0). Shoot biomass was measured as dry weight at 15 days after sowing. The determination of the shoot biomass values cf.  via mixeThe absolute mid-parent heterosis is defined as the difference between the hybrid's shoot biomass and the mean shoot biomass of its parents. Dividing the absolute mid-parent heterosis by the mean shoot biomass of the parents, results in the relative mid-parent heterosis, which we focus on in this analysis cf. . In our R for statistical computing and graphics R package plsOur computations were conducted on the free software environment R function within the pls package is called plsrR by setting the parameter validation of the function plsr to “LOO”. The correlation, achieved with the optimal number of latent variables, is referred to, in this work, as the predictive power of the considered set of predictors for the response of interest. The R function to accomplish these computations is called plsr.For training the particular prediction models, we used the PLS approach The rational of using PLS instead of ordinary least squares regression is the potential existence of latent variables, on which the particular response depends, but which are not available, because they cannot be measured. Fortunately, one latent variable often regulates not only the response of interest but also several other variables, which are in fact measured in experiments. Since they are all influenced by the one latent variable, many of them correlate strongly. Therefore we can down-weight some of the measured variables. The remaining variables could be considered as biomarkers for the particular response. That means there is not necessarily a causal dependence, but the biomarkers act as an indicator for the response. Since we consider very complex response effects, such as heterosis, probably several latent variables are involved. Thus, it is possible that two different latent variables influence the same measurable variable. For example, one of them up- and the other one down-regulates the measurable variable. Then, knowing only the value of the measured variable, it is not possible to reconstruct both latent variables correctly. We therefore have to weight the measured variables and to select the optimal number of latent variables. We use the PLS-algorithm for this purpose. Low weights in important latent variables give a hint for measured variables that do not improve the prediction.The PLS-approach is able to handle a high number of measured predictor variables relative to the number of samples. But certain response effects are very sensitive with regard to overfitting. Down-weighting the measured variables with a low contribution to the response, is not enough in this case. We therefore go one step further and suppress variables that contribute the least to the response of interest in the PLS-model.The contribution of a predictor variable to the response is measured by the VIP suggested previously The computational costs of optimizing the number of latent variables increase with the number of original variables in the model. We therefore do not undertake those efforts for every possible number of original variables. The increment of our outer loop is ten, as a start, to get a general idea cf.  A. AfterTo exclude the possibility that the predictive power is insignificant (which means that the in LOOV predicted response does not correlate significantly with the observed response), we perform a randomisation test. We build 1000 random permutations of the true response. Then the Pearson correlation between the in LOOV predicted response and each permutation is calculated. The 1000 random correlations are compared to the predictive power, i.e. the correlation between the predicted response and the real response.To judge the difference in predictive power between two distinct predictor sets, confidence intervals for the predictive power of optimized models are estimated using jackknife resampling. Given a predictor set and a response variable, we randomly select 358 out of our 359 samples and recompute the predictive power of the optimal variable selection on the resampled jackknife data. The resampling and the recomputation of predictive power are repeated 200 times. This results in a specific range of values for the predictive power of the regarded optimal variable selection for the particular response. We consider the central 99% of those 200 values as an estimation for the confidence interval. It stretches from the mean of the two smallest values to the mean of the two largest ones. If the estimated confidence intervals for different predictor sets or for different response variables are disjoint, we consider the discrepancy of the corresponding predictive powers significant.In addition, the estimation of a confidence interval for the optimal predictive power enables us to follow Occam's razor The predictor variables, which are always contained in the minimal variable selection, can be considered as biomarkers. Comparing the biomarkers for the two different testcross settings, we learn about common and specific effects, We refer to a certain metabolic marker as specific for heterosis prediction in one testcross population, if and only if it is contained in both, the minimal metabolic variable selection and the minimal variable selection of the combined genetic-metabolic approach for one testcross setting, but in none of the corresponding minimal variable selections for the other testcross setting. On the other hand, we consider a certain metabolic marker as highly predictive for heterosis in both testcross populations, if it is contained in the minimal metabolic and also in the minimal metabolic-genetic variable selection for both testcross settings cf. . AnalogoIf we want to consider the order of importance of the biomarkers cf.  and S5, Figure S1Additional histograms of metabolic markers over the 359 RILs, in comparison to a random generation. The panels A-F show the six metabolic markers most important according to their VIP in the minimal metabolic and in the minimal combined genetic-metabolic models. Their deviation from a single normal distribution seems to abate with decreasing importance. Panels G-K show the 5 metabolic markers with the lowest mean VIP in the complete metabolic and the complete combined genetic-metabolic model for C24- and Col-heterosis, in comparison to a random generation of 359 numbers following a normal distribution with expectation zero and a standard deviation of one third (L).(0.05 MB PDF)Click here for additional data file.Figure S2VIP of genetic markers in the complete (A) and in the minimal (B) genetic models. The figure shows the contribution of the 110 genetic markers, which have been arranged horizontally, to the respective response in the different models. The darker the bar, the higher the VIP of the corresponding marker in the particular model. Panel A shows that, when training on the whole set of markers, the contribution to C24-heterosis prediction is more diffused on many different markers, whereas it is strongly concentrated on top of chromosome 4 in the case of Col-heterosis. Panel B shows the VIP when trained on those selected genetic markers, which turned out to be essential predictors in the respective models. Each of the five chromosomes is represented by at least one marker in both minimal models, which overlap on the chromosome 1, 3 and 4. The two markers at the bottom of chromosome 3 only selected as predictors in the minimal Col-heterosis model were confirmed to be Col-heterosis specific markers by the combined genetic-metabolic model cf. . This ho(0.11 MB TIF)Click here for additional data file.Figure S3Histograms of allele frequencies. The figure shows how the allele frequencies are distributed in the RIL population. The panels A and B deal with the frequency of C24 alleles and Col-0 alleles, respectively. For each RIL there are 110 genetic markers featuring C24, Col-0 or heterozygosity. The x-axis represents the number of the corresponding alleles per RIL. The y-axis presents how many of the 359 RILs show the corresponding allele frequency. The mean frequency of C24 alleles and Col-0 alleles per RIL is 48% and 50%, respectively. In average, 2% of the markers are heterozygous. The minimal frequencies for C24 and Col-0 alleles are 11% and 10%, respectively, while the maximal frequencies are 89% and 85%. The standard deviation was about 15.4 and 15.1, respectively. Using a Mantel test (P<0.001) to estimate association between marker matrices, we did not find significant differences in marker distribution between the two sub-populations (0.00 MB PDF)Click here for additional data file.Figure S4Feature selection process in metabolite model for C24-heterosis. Panel A shows the crude optimization of predictive power according to the number of predictors in the model with increment 10. It determines the breakpoint for the refined version (panel B) to reduce the computational costs (cf. (0.03 MB PDF)Click here for additional data file.Table S1Estimated confidence intervals of the optimal predictive power in leave-one-out validation.(0.03 MB DOC)Click here for additional data file.Table S2Number of variables in the optimal and minimal predictor sets, in comparison to the number of all available predictors in the corresponding set. Abbreviations: Het, heterosis; Gen, genetic marker set; Met, metabolic marker set; Bio, biomass marker; Gen-Met, combined genetic-metabolic marker set etc.(0.04 MB DOC)Click here for additional data file.Table S3List of metabolic markers that turned out to be relevant neither for C24- nor for Col-heterosis prediction in our analysis, i.e. omission of those markers did not significantly deplete the predictive power in the metabolic models or in the combined genetic-metabolic models.(0.03 MB DOC)Click here for additional data file.Table S4List of the 40 metabolic markers highly ranked in C24-heterosis prediction, sorted according to the sum of their VIP in the minimal metabolic (met) and in the minimal combined genetic-metabolic (gen-met) model. Interestingly, the three highest ranked metabolic markers are distinct from those most important for biomass per se prediction (0.02 MB XLS)Click here for additional data file.Table S5List of the 40 metabolic markers highly ranked in Col-heterosis prediction, sorted according to the sum of their VIP in the minimal metabolic (met) and in the minimal combined genetic-metabolic (gen-met) model. Interestingly, again the three highest ranked metabolic markers are distinct from those most important for biomass per se prediction (0.03 MB XLS)Click here for additional data file.Table S6Dry weight (DW) and rMPH values for the 359 investigated RILs and the corresponding testcrosses (TC-C24 and TC-Col), including the standard deviation (sd) and the arithmetic mean (mean) for each column.(0.10 MB XLS)Click here for additional data file.


We present a new method for testing association when data from both case-parents trios and unrelated controls are available. Our method combines test statistics for case-parents trio and unrelated case-control studies by adjusting for the correlation that arises when the same set of cases is used for both tests. We further consider several analytical approaches for two-stage studies on a large number of markers, including methods based on the joint analysis. The performance of the proposed approaches is examined by analyzing the simulated data provided by the Genetic Analysis Workshop 15. Genetic association studies are a popular method to detect genetic markers associated with a complex human disease. Two common designs in genetic association studies are family-based designs using case-parents trios and population-based designs using unrelated cases and controls. The transmission disequilibrium test (TDT) is frequently used to analyze the case-parents trio data . The TDTData that contain both case-parents trios and unrelated cases and controls on the same set of markers are increasingly available. Nagelkerke et al.  providedIn this paper, we study several approaches for testing genome-wide association in such situations. Based on the design, either a TDT-type statistic or a linear trend test will be used in the first stage to select a proportion of markers that will be tested in the second stage. The other test will then be applied in the second stage while controlling the genome-wide false positive rates by adjusting for the correlation with the first stage. Following a recently proposed method by Skol et al. , we alsop, and N is a normal allele with frequency q = 1 - p. Penetrances are defined as the probabilities of disease conditional on the genotypes, that is, f0 = Pr(disease|NN), f1 = Pr(disease|NM), and f2 = Pr(disease|MM). No association implies f0 = f1 = f2, whereas f0 ≤ f1 ≤ f2 with at least one strict inequality implies there is an association between the marker and a disease. Using f0 as a baseline penetrance, the genotype relative risks are defined as ψi = fi/f0 for i = 1, 2. A genetic model is recessive, additive, or dominant when f0 = f1 , f1 = (f0 + f2)/2 , or f1 = f2 (or ψ1 = ψ2 = ψ).Consider a marker with two alleles, M and N, where M itself is a risk allele or is in linkage disequilibrium with a risk allele with frequency nij can then be obtained and is presented in the fourth column. The last column contains the probabilities of a case genotype given parental mating type  MM × MM, 2) MM × NM, 3) MM × NN, 4) NM × NM, 5) NM × NN, and 6) NN × NN. These six mating types are given in the first column of Table ψ), then the score test for H0: ψ = 1 can be obtained by ∂logL(ψ)/∂ψ/{-∂2logL(ψ)/∂ψ2}1/2|ψ = 1.Schaid and Sommer  suggester0, r1, r2) in cases and  in controls that follow multinomial distributions mul and mul. Then the null hypothesis of no association implies pi = qi for each i.For the unrelated case-control design, denote the genotype counts of three genotypes NN, MN and MM as  =  and N = R+S. Under the null hypothesis, ZCC asymptotically follows the standard normal distribution.Sasieni  proposed2, and 1 ,7 and thZTDT and ZCC overlap, results from the two tests are correlated, and this correlation, ρ, must be considered when obtaining a combined test. By noting that both tests are functions of a multinomial random variable n with dimension 10 for the 10 nij categories from Table ZTDT and ZCC can be obtained given a specific genetic model (Appendix). The probability of each category can be consistently estimated by the observed counts and ρ can be consistently estimated by the sample correlation between ZTDT and ZCC.Because the cases used in w1 = w2 = 1 [We propose the weighted average, = w2 = 1 ,9 for siK markers in a two-stage analysis, we consider four strategies that use either ZTDT or ZCC in the first stage based on the intended design, and in each situation, the other test or the joint test is applied in the second stage. As in Skol et al. [C1 and C2 (or Cjoint) for two stages in each strategy by controlling the genome-wide significance level at α. C1 can be obtained as C1 = Φ-1(1 - π1/2), where π1 is the proportion of markers selected in the first stage. On the other hand, Cjoint and C2 need to be calculated iteratively so that they satisfyTo test l et al. , we obtaorZi 1and Zi 2denote the tests used in the first and the second stage for the ith SNP . We need the subscript i because the correlations between two tests for different SNPs are generally not the same. Under HWE, however, we can show this correlation is a constant (Appendix), and these equations can then be simplified to P = α/K and P = α/K.when the joint analysis is used or when the other test is used. Here, The Genetic Analysis Workshop 15 provided simulated rheumatoid arthritis data that contain 1500 families with affected sib pairs and their parents, and 2000 unrelated controls on 9187 SNPs distributed throughout the genome. We used the first simulated data set and we randomly selected one from the affected sib pairs for data analysis. The minor allele frequencies of all 9187 SNPs were greater than 1%.π1 = 0.1 (C1 = 1.6449) and Eq. (1) and (2). Therefore, we control the genome-wide false-positive rate at 0.05, and we define a "significant" SNP as one with test statistic greater than the threshold in both stages. As expected, a slightly larger threshold for the second stage is required for the joint analysis to control the same genome-wide false-positive rate (C2 = 4.5121 vs. Cjoint = 4.5470) [p-value from the second stage is listed. We noticed that even with a larger threshold required, the joint analysis in the second stage found more significant SNPs near the major genes. Also, we noticed that when the joint analysis was used in the second stage, the same set of significant SNPs was found regardless of the choice of the test statistic in the first stage. However, different results were obtained when either ZTDT or ZCC was used in the first stage followed by the other test in the second stage. Specifically, the joint analysis using either ZTDT or ZCC in the first stage found 18 significant SNPs among which 9 and 14 were located within 1 Mb (bold) and 5 Mb  of the major genes. When ZTDT in the first stage was followed by ZCC in the second stage, we found 17 significant SNPs, and 8 of these were located within 1 Mb of the causal genes, and 13 were located within 5 Mb. These methods found SNPs near the major genes on chromosome 6, 11, and 18. On the other hand, when we used ZCC in the first stage followed by ZTDT in the second stage, a total of 10 significant SNPs were found: 7 of them were located within 1 Mb of a major gene only on chromosome 6 and 11, and 10 were located within 5 Mb. A SNP near the major gene on chromosome 18 was not found by this method.To apply the two-stage analysis, we first obtained the threshold for each strategy using 1 C1 = 1.449 and E (1) and . TherefoZCC, ZTDT, Zjoint) to a single-stage analysis, these tests found the same set of SNPs identified in a two-stage analysis with the corresponding test at the second stage. That is, ZCC, ZTDT, Zjointi in a single-stage found 17, 10, and 18 SNPs in columns 4, 5, and 6 of Table When we applied these three tests (ZTDT and not for ZCC. By adjusting for the correlation between the two test statistics (ZTDT and ZCC), we proposed a combined test statistic for analyzing such data.In this paper, we presented a new method for testing association when both case-parents trios and unrelated controls are available. Because parents are selected for having an affected child, we consider the characteristics of non-affected parents to be different from those of unrelated controls in case-control studies. Thus, the genotype information of parents was used only for For data with a large number of markers in a two-stage analysis, we considered several analytical approaches following the method by Skol et al. . Even wiZTDT. In this situation, the correlation between ZTDT and ZCC will decrease, and therefore, the advantage of the joint analysis could be accentuated. Complete justification, however, requires further study.Our method can be generalized to data with missing genotypes by either imputing the missing genotypes based on partially available data ,10, or bWe presented a new method for testing association when data from both case-parents trios and unrelated controls are available. By deriving the correlation of test statistics for these two designs, we proposed a combined test as a joint analysis. In a two-stage analysis for testing a large number of markers, we found that the joint analysis detects more SNPs near the major genes than other methods that do not use the combined test in the second stage. This approach is also robust against the choice of the first stage test.ZTDT, n1 = n12, n2 = , n3 = n31, n4 = , n5 = , and n6 = n60 are independent random variables conditional on parental mating types (m) where n2 and n5 follow a binomial distribution and n4 follows a trinomial distribution with probabilities given in column 5 of Table H0: ψ = 1 is then written as UT(n) = n22+n42, n22+n42+0.5(n21+n41+n51) and n42+n41+n51 for the recessive, additive, and dominant models. By applying the variance decomposition formula, we obtain the correlation between ZTDT and ZCC as When the conditional likelihood is used for η < 1 such that ZTDT and ZCC is reduced to Under HWE, we can show that the correlation for three models can be simplified to The author(s) declare that they have no competing interests.


Most studies on the effect of life events (LEs) have been carried out in convenience samples which cannot be considered representative of the general population. In addition, recent studies have observed that gender differences in the health related quality of life (HRQoL) impact of LEs might be lower than believed. We assessed the relationship between LEs and HRQoL in a representative sample of Spanish adolescents/youths, focusing on gender differences.Participants (n = 840) completed the KIDSCREEN-27 to measure HRQoL at baseline and again after 3 years (n = 454). Follow-up assessment included the Coddington Life Events Scales (CLES) to measure LEs experiences in the previous 12 months. Respondents were categorized according to the amount of stress suffered. We calculated both the number of LEs and the Life Change Unit (LCU) score, a summary of the amount of stress inherent to the event and the time elapsed since occurrence. LEs were classified as desirable or undesirable, and family-related or extra-family. Effect sizes were calculated to evaluate changes in HRQoL. To assess the impact of LEs typologies, multiple linear regression models were constructed to evaluate their effect on HRQoL.Girls reported a mean 5.7 LEs corresponding to 141 LCUs, and boys 5.3 and 129, respectively. The largest impact of LEs on HRQoL was observed in the group of boys that reported to have lived more stress (third tertil of LCUs distribution). The linear association between LEs and HRQoL tended to be stronger among boys than girls, but the difference was not statistically significant. The effect on HRQoL was deemed important when undesirable events had been experienced. To have an important impact on HRQoL, 200 LCUs due to undesirable events were necessary in boys. In girls, slightly higher scores were necessary for a similar impact.A moderate association was found between recent LEs and HRQoL, mainly among those who experienced several undesirable events that correspond to at least 200 LCUs. No gender differences were found in this association. Results may be useful for identifying adolescents with particular health risks, regardless of gender. Adolescence and youth are considered periods of development when individuals construct their own identity. These pMost studies on the effect of LEs have been carried out in convenience samples which cannot be considered representative of the general population-16, limiGender differences in exposure and reactions to LEs have been widely discussed,15,19,20The aim of the present study was to investigate the impact of LEs on HRQoL using data collected with a longitudinal design, in a general population sample. Additionally, we investigated whether there were gender-based differences in the association between LEs and HRQoL ; and wheThe Spanish KIDSCREEN baseline sample was recruited between May and November 2003 as part of the European KIDSCREEN fieldwork . The tarBetween May and November 2006, follow-up questionnaires were posted by mail to all adolescents and youths and their parents who had previously agreed to participate in the Spanish KIDSCREEN follow-up study . Data collection at follow-up took place 3 years after baseline, a period which was considered a sufficient interval to allow for substantive changes in participants' health status. The fieldwork followed the same methodology applied at baseline. Postal reminders were sent four and eight weeks after the first mailing to those who had not returned their completed questionnaires. A third reminder was sent after twenty weeks and any remaining non-respondents were contacted by phone.Stressful LEs were measured using the Coddington Life Events Scales (CLES),4,27, whLife events were classified according to two different typologies: desirable (e.g. "Graduating from high school) vs. undesirable events (e.g. "Divorce of parents) and family-related (e.g. "Loss of a job of your father or mother") vs. extra-family events (e.g. "Going on the first date") -5,27,31.HRQoL was measured using the KIDSCREEN-27, which wThe KIDSCREEN items use 5-point Likert-type scales to assess either frequency  or intensity . Rasch scores are computed for each dimension and for the overall score and are transformed into T-values with a mean of 50 and standard deviation (SD) of 10. The T scores refer to the mean values and SD from a representative sample of the European general population so that scores over (or under) 50 indicate better (or worse) HRQoL than the general EU population. The Spanish version of the questionnaire has demonstrated acceptable validity and reliability ,34. In tPubertal development was measured in order to adjust for possible differences between boys and girls in terms of pubertal status and becaOther variables collected in the present study to characterize the sample were family socio-economic status and parental level of education. Socio-economic status was measured using the Family Affluence Scale, which iDifferences between boys and girls in relation to LEs and HRQoL were tested using independent two-sample t-tests for continuous variables and chi-square tests for categorical variables. P-values were adjusted with the Hochberg method in order to address the multiple testing problem. The decision rule is to reject the null hypothesis when the adjusted p-value is less than α = 0.05.To investigate the first aim of the study, bivariate analyses of the effects of LEs on HRQoL dimensions for boys and girls were performed. We calculated the effect sizes of changes in HRQoL (difference between follow-up and baseline scores divided by baseline standard deviation) in three different groups of increasing LEs impact. The three categories were defined based on tertiles of LCU distribution (i.e. 0-67 LCU (low), 68-160 LCU (medium), and 161 LCU or more (high)). Two way ANOVA was used to determine whether gender differences were statistically significant.2 test to assess non-linearity between LCUs and HRQoL was not significant, and LCUs were therefore introduced as a linear variable in the model. Models were fitted to estimate the relationship between LEs and HRQoL controlling by baseline HRQoL, pubertal development, and age and stratified by gender. P-values were adjusted with the Hochberg method in order to account for the analysis of multiple end-points. We tested gender differences in the association between LEs on HRQoL by running similar models where the gender and the interaction between gender and LCU scores were included and evaluating the significance of the interaction effect with a two-sided significance test at α = 0.05.Multiple linear regression models wCoefficients in the multiple linear regression indicate the units of change in the dependent variable which is associated with 1 LCU suffered by respondents. To give more interpretable results, we selected four examples to illustrate the magnitude of the effect of the coefficients. To do so, the regression coefficients were multiplied by different LCUs values that correspond to selected amounts of LCUs  to assess the direct effect on KIDSCREEN. In addition, to determine minimally important differences and moderate important differences between respondents . This trWe did not attempt to evaluate age groups differences due to insufficient sample size after distributing participants by LE typology and gender.At follow-up, 454 families were re-assessed (response rate: 54%). A total of 423 adolescents/youths with complete data were included in the analysis. Mean age was 15.4 (SD 2.84) years and 51.8% were girls (Table Boys reported a mean of 5.3 LEs in the previous 12 months compared to 5.7 for girls (P = 0.98) . Our results do confirm the importance of undesirable LEs in HRQoL and suggest that it is not differential by gender, which put forward the importance of a longitudinal design of the study and changes in the traditional gender differences.These results should be interpreted taking into account several study limitations. First, the response rate at follow-up was 54%. This figure is quite standard for postal surveys ,42-44 anOur study has several strengths. Findings regarding the effect of LEs on HRQoL have almost always been presented from clinical samples ,45,46, aThere were HRQoL decreases at follow-up in both gender groups. Girls had lower scores at follow-up, but theThe differences we had hypothesized about the effect of the different LEs based on typologies were only partially confirmed. Undesirable events had the most important effect on HRQoL, but contrary to our hypothesis, family events did not affect any of the dimensions, when Hochberg method for multiple testing was applied. Our results are consistent with the literature  suggestiOne important undesirable event is sufficient to be part of the risk group. In the case of the first LEs combination exposed at Table Further studies in larger samples would help to confirm or refute our results. Especially, in order to confirm the role of undesirable LEs and the tendency of change of gender differences. Moreover, it should be useful to have different measures of LEs in order to take into account also their effect in previous HRQoL.The experience of LEs did impact the HRQoL of adolescents and youths in this sample, although the effect was moderate. Contrary to most previous studies, we didn't find that girls are more in risk than boys in the association between LEs and HRQoL. The occurrence of desirable life events did not produce a corresponding increase or decrease in HRQoL. In our sample, it is necessary to have lived LEs with at least a final sum score of 200 LCUs associated with undesirable events to have a moderate impact. This value may be useful as a cut-point to detect risk profiles in general population which may involve a considerable decrement in perceived health.LEs: Life events; HRQoL: Health related quality of life; LCU: Life change unitThe authors declare that they have no competing interests.JMV, LR, and JA participated in the conception and design of the study. EVO, SRF, GV and JAPV analyzed the data. EVO, JMV, MH, MF, LR and JA participated in the drafting of the article. All authors contributed to a critical revision of the manuscript and made a substantial contribution to its content, and read and approved the final manuscript.