Obsessive Compulsive Disorder (OCD) is a neuropsychiatric disorder observed both in humans and animals. Examples of Canine Compulsive Disorder (CD) include excessive tail chasing (TC), light/shadow chasing and flank sucking. We performed a questionnaire survey to investigate the characteristics of compulsive (TC) and its possible associations with environmental correlates and personality in a pet population of 368 dogs from four dog breeds. We observed an early onset of TC at 3–6 months of age and a large variation in TC frequency in all breeds, with an overrepresentation of milder cases. Almost half of the TC dogs showed lowered responsiveness during bouts and displayed also other types of compulsions more often than the controls. Interestingly, dogs that received dietary supplements, especially vitamins and minerals, expressed less TC compared to dogs that did not receive any supplements. Neutered females had less TC, suggesting an influence of ovarian hormones on TC. Tail chasers were shyer and had separated earlier from their mothers than the controls. Finally, our genetic study did not find an association between TC and CDH2, a locus previously associated with the canine flank sucking compulsion. In conclusion, the early-onset and the variable nature of the repetitive behaviour, which is affected by environmental factors such as micronutrients, neutering and maternal care, share several similar components between canine and human compulsions and supports canine TC as a model for human OCD. Obsessive compulsive disorder (OCD) in humans is characterized by recurrent intrusive thoughts (obsessions) and mental rituals and repetitive behaviours (compulsions), such as ordering, cleaning or checking, which interfere with daily functioning and/or are highly distressing Exaggerated, inappropriate and repetitive behaviours in animals are referred to as stereotypic or compulsive behaviours. These are often compared to symptoms of human OCD, although the existence of obsessive thoughts in animals remains controversial Spontaneous compulsive behaviours occur in many dog breeds and can take several forms including repetitive pacing, tail chasing, sucking (i.e.fabric or flank sucking), licking, chasing “invisible flies” or shadows/lights, freezing, and staring Tail chasing (TC) is a classic compulsive behaviour in dogs. A variant of TC is “spinning”, in which the affected dog spins rapidly in tight circles without apparent interest in the tail. TC often occurs in bouts and might include episodes in which the dog stares at its tail quietly for a while before resuming chasing. TC is suggested to have a genetic predisposition as it is more common in certain breeds, such as Bull Terriers, German Shepherds Our aim was to study the phenotypic and genetic characteristics of compulsive TC, including possible environmental and personality correlates. Towards these aims, we have developed detailed behavioural questionnaires for dog owners and collected data from a population sample of 368 dogs from four different breeds, including Bull Terriers (Standard BT and Miniature MBT), Staffordshire Bull Terriers (SBT) and German Shepherds (GS). Furthermore, DNA samples were collected from 181 dogs and a candidate gene approach was used to test the association of TC with the CDH2 locus.Attachment S1) yielded data for a total of 368 dogs from four breeds. This dataset indicated the typical onset of TC at 3–6 months of age in BT and GS and 6–24 months in MBT and SBT . In relation to the number of returned questionnaires per breed, the least TC (index = 1TC–12) dogs were reported in GS (54/180), and the most in BT (83/122) . GS had also lower mean indexTC compared with SBT and BT . These results may reflect the actual breed differences in tail chasing, but may also be the result of a difference in sampling methods between breeds, and activity of breed clubs in sharing information from the study to the dog owners.The frequency of TC behaviour showed a large variation in our study populations. Some of the dogs had only few episodes during their lifetime, while the most severe cases were engaged in TC several times a day Fig. 2. 2χ1,367 = 2.92, p = 0.095). Males and females did not differ in the severity defined by the indexTC, however, we found that neutered individuals had lower indexTC compared to non-neutered individuals in the pooled data TC, the effect of the neutering was significant only among females , suggesting that neutering in females may have a controlling effect on TC behaviour. The total number of neutered females in our study was 60, whereas there were only 18 sterilized, males preventing us from drawing further conclusions on the effect of sterilization on TC in males. A within-breed analysis of the effect of neutering on TC showed a significant association only in SBT , nor were there any differences in TC between dogs neutered at younger age  and dogs neutered at an older age  .There were no differences in TC prevalence between males and females, although there were slightly more females in the control group TC. Differences in general responsiveness may exist between breeds regardless of TC, however, we do not have the data to investigate the general responsiveness among the controls. The more the dog chased its tail, the more difficult it was for the owner to stop the behaviour  and the less it reacted to the owners’ calls , indicating that the severity of the TC affects the dog’s awareness. Only one dog in our study  was reported to be on medication for TC (fluoxetine). The medication had markedly reduced TC, but the dog still suffers from occasional hallucinatory fly-catching compulsions.Although most owners (72%) reported that TC did not affect the dogs’ daily activities, the majority of them had tried to stop the behaviour 89%, Fig. 3c.22,x89 = 6.77, p = 0.034). In addition, we compared the demographic info, dog phenotype and dog personality of dogs whose owners had replied boredom or stress as triggers and those whose owners indicated some other trigger-option. ‘Bored’ dogs chased their tails significantly more  than dogs, whose owners had indicated some other option as the trigger for TC. The same applied for the ‘stressed’ dogs; they had also a significantly higher indexTC compared to the other trigger-options . ‘Bored’ dogs had also experienced better maternal care . ‘Stressed’ dogs were given less dietary nutrients  and their TC tended to start at a later age . No other differences were observed between the dogs that had different triggers for TC.We asked owners to describe the circumstances preceding the episodes in order to investigate whether there were any particular signs or behaviours which might precede or trigger TC. TC was most often attributed to the dog’s boredom or lack of activities (29%), stressful events (15%) or “something else” (18%) Fig. 4a.21,x308 = 4.42, p = 0.035), licking , repetitive pacing  and freezing or trance-like behaviour   and the controls . The latter comparison was included to investigate whether the most severe tail chasers were also affected by environmental factors. We found that gender, amount of exercise, amount of activities, time spent alone, age of arrival to the household, number of adults in the household, number of diagnosed diseases, type of food, or birth place were not associated with TC in any of the analyses in a pooled sample or a breed-specific analysis (data not shown), and these same factors were dropped from the final models (data not shown).The possible association of environmental factors with TC was investigated using two different models: one including all individuals (n = 368) and the only tail chasers: dogs that had received dietary nutrients had less TC compared to dogs receiving no dietary nutrients  Table 1.indexTC≥2, all breeds pooled N = 116) were receiving vitamins  and minerals . Also, individuals receiving vitamins  and minerals  chased their tails less than dogs that were not receiving these dietary nutrients. No difference was found between the case and control groups in receiving Omega-3, Omega-6 or a group labeled “something else” . We further focused on the micronutrients within the vitamin and mineral groups, and included only those vitamins (n = 12) and minerals (n = 10) into the analysis which had been given to more than 25 dogs. Among these micronutrients only Mg (p = 0.05), B5 (p = 0.037), B6 (p = 0.0003), B12 (p = 0.04) and vitamin-C (p = 0.04) differed between the cases and the controls, however after the Bonferroni correction for multiple testing, only vitamin B6 showed a statistical difference (p = 0.004) between the cases and the controls. Fewer tail chasers had received vitamin B6 compared to the controls. Furthermore, tail chasers that received vitamin B6  or vitamin-C  had significantly less tail chasing compared to those tail chasers not given any vitamin B6 or vitamin C.An analysis of the specific diet supplement groups Fig. 6 rThe number of other dogs in the household also affected TC. Dogs that lived with many conspecifics chased less compared with the dogs living alone or having fewer companions at home  and the controls. In this analysis, dietary supplements , the amount of conspecifics at home  and sterilization  were the only TC-associated factors .Finally, we performed the same analyses described above using the pooled data  including 2χ1, 74 = 5.64, p = 0.018, all breeds pooled) and were separated earlier from their mothers  compared to dogs with no tail chasing. TC dogs had been separated from their mothers on average at 7 weeks of age, whereas in the control group the average age of separation was 8 weeks. There were no differences between females or males or between breeds (data not shown). When only the most severe cases  were compared with the controls, the only notable difference was a trend towards decreased maternal care between severely affected TC cases and controls (n = 32) .The effect of maternal care and age of separation (from the mother) on TC was also evaluated using a generalized linear model with a binomial distribution. Tail chasers had experienced lower quality care (Attachment S2) of dogs with a index = TC0 or indexTC≥2. We received a total of 129 Dog Personality questionnaires . Four factors were derived from the Dog Personality questionnaire using factor analysis. These factors were named Shyness/Boldness, Sociability/Dogs (sociability towards dogs), Amicability/Humans (friendliness towards humans), and Aggressiveness/Humans (aggressiveness towards humans) based on the highest loading questions in each factor  and less aggressive towards humans  than non-tail chasers (n = 51)  and less aggressive  compared to the control males, although females (n = 25) also had the same non-significant trend  or Amicability/Humans  personality factors between tail chasers and non-chasers. When breeds were analysed separately, we found statistically significant personality differences only in BT, where tail chasers (n = 31) were shyer  compared to the controls (n = 19), and the male dogs were less aggressive towards humans  than the female dogs.The pooled analysis including all breeds indicated that tail chasers (n = 59) are generally shyer  compared to the controls and the same non-significant trend was also observed in SBT . Tail chasers in BT (but not in other breeds) remembered frightening situations longer than the controls . The cases and the controls in none of the breeds differed in the amount of separation anxiety (results not shown).We analysed questions that were left out of the factor analysis  due to low communality values and (Q8) binomial distribution, separately. Pooled analysis of the breeds showed differences between the breeds in these questions and we therefore analysed each breed separately. Both BT and GS tail chasers had more noise phobia (Q7)  and possibly live prey  . No differences were found in playfulness  or activity  compared to the control dogs. Analysing SBT and BT breeds separately did not yielded any significant associations, probably due to the low sample number.We also found that tail chasers from SBT and BT (pooled data) were more keen on chasing moving objects  (indexTC 5–12) and the controls. We found similar results: tail chasers  (N = 24) were shyer , and less aggressive towards humans  compared to the controls (n = 51). Tail chasers (n = 24) in SBT and BT breeds also tended to be more interested in chasing moving objects  than the controls (n = 51).Finally, we performed the analysis in the group including only the most severe cases . The first locus for a canine compulsive behaviour was recently mapped to CFA7 for flank sucking behaviour We established large pedigrees for each breed to evaluate the mode of inheritance of TC. The pedigrees indicate several affected individuals in many litters and suggest a strong genetic component, although it is unlikely to be a simple Mendelian disorder in any of the breeds  represented only 23% of the cases in our study. This is in contrast to a recent TC study in BTs where a majority of the cases were recruited through a veterinary clinic resulting in a study population with of 74% severe cases with daily TC activities We found a large variation in the frequency of tail chasing in each of the studied breeds, from zero to several times per day. Unlike the previous studies consisting mostly of clinical samples with more severe cases We found an early onset of TC across breeds, varying from 3–6 months of age, thus preceding sexual maturity, as observed before in other canine compulsions Almost half of our cases showed partially impaired responsiveness to owners’ calls during TC bouts, and this was clearly associated with the severity of TC. Previous studies on canine compulsive behaviours have reported a similar phenomenon Our TC dogs exhibited other stereotypic behaviours such as snapping at invisible flies or lights, trance-like freezing, licking and repetitive pacing. Similarly, tail chasing Bull Terriers were found to have more trance-like behaviour TC was associated with dietary supplements, neutering status and also the number of conspesifics in the household. Furthermore, these factors were also associated with TC when comparing only severe cases to the controls. Our study revealed that dogs receiving dietary supplements chased their tails less compared to dogs not receiving any nutrients. This may be a correlative indication that dietary supplements lead to reduced TC. In addition, the data set including only tail chasers showed lower TC activity for dogs receiving dietary nutrients (in BT and SBT), further supporting an effect of dietary nutrients on TC behaviour.Our rough categorization of the dietary supplements into five main groups, labelled vitamins, minerals, Omega 3, Omega 6 and ‘something else’ and comparison between cases and controls revealed that fewer tail chasers received vitamins and minerals, especially vitamin B6 compared to the control-dogs. Dogs receiving vitamins and minerals  also chased their tails less compared to the dogs not receiving these micronutrients. Interestingly, there are indications that vitamins and minerals have beneficial effect also in human OCD treatment. Two case studies report decreased anxiety and remission of OCD symptoms after treatment with EMPowerplus, which is a formula consisting of 14 vitamins, 16 minerals, 3 amino acids and 3 antioxidants The minimum requirement of vitamin-B6 and Mg that a dog should get via its daily food is internationally agreed upon and should be 0.04 and 5.91 mg/kg bodyweight raised to 0.75, respectively It is also possible that owners who give their dogs dietary supplements handle their pets differently in other respects that could also have a preventing effect on TC. However, our questionnaire covered a large spectrum of important issues of dog’s daily routines, which did not associate with either dietary supplements or TC. An earlier investigation about the role of dietary nutrients  on compulsive tail chasing in BT, however, did not find any association We found that sterilized individuals, especially females, had less TC compared to intact dogs in a pooled analysis of all breeds. When only the more severe TC dogs were compared to the controls, neutering was significantly associated with TC in only females. Findings were somewhat inconsistent when analyzing within breeds, perhaps reflecting the smaller sample sizes for these analyses. In contrast to our study, a previous OCD study A recent study suggests that tail chasing in dogs might, at least partly, result from lack of activities, exercise or stimulation We found four major personality factors to exist based on the personality questionnaires; Shyness/Boldness, Sociability/Dogs (sociability towards dogs), Amicability/Humans (friendliness towards humans), and Aggressiveness/Humans (aggressiveness towards humans). Shyness/Boldness, Sociability and Aggressiveness personality factors have been also found earlier in dogs using both behavioural testing and questionnaires Different personality types may confer differential susceptibility for compulsive behaviours, or alternatively compulsive behaviours may influence personality. We found that TC dogs were generally shyer (more fearful) and less aggressive towards humans , and this was also true when only the extreme cases and controls were included. Tail chasers also exhibited more noise phobia, especially towards fireworks. Although we could not find an earlier study assessing the personality of compulsive dogs, one earlier study suggested an association between fearfulness and compulsive disorder Early-life experiences may predispose to various types of anxiety. We found that TC dogs were separated earlier from their mothers and experienced lower quality care from their mothers (as assessed by their owners/breeders) compared to the control dogs. Our finding is in line with the hypothesis that early maternal separation increases the risk of stereotypic behaviours A recent study suggested that tail chasing may relate to autism TC is observed in some breeds more often than in others indicating that genetic factors play an important role. Although the definitive mode of inheritance is often difficult to estimate from pedigrees due to missing phenotypes, our pedigrees in all breeds suggest a strong genetic influence with multiple affected dogs across generations and even within several litters. No association was observed among the studied breeds between the TC and the CDH2 gene, which was previously found to associate with flank sucking in Dobermans In summary, we describe here the first large-scale questionnaire study of TC in a pet population sample including four different dog breeds. Our study reveals several similarities between canine tail chasing and human OCD, together with a novel finding of the effect of dietary nutrients on TC. Altogether our results add more evidence for shared etiology and mechanisms of OCD in dogs and humans Attachment S1 and S2). Questionnaires were sent to: 1) the owners who had already given blood samples to our Dog DNA bank, and 2) breed clubs . The owners were invited to participate in the survey and asked to fill out the questionnaire whether their dog was a non-chaser or chaser. The first questionnaire (Stereotypic Behaviour Q) consisted of a series of questions including dogs’ a general history, environmental factors, diet, tail chasing history and the presence of other possible compulsive behaviours (Attachment S1). Altogether 368 questionnaires were received from four breeds . We also received few questionnaires  from American Staffordshire Bull Terriers (AST), and because of the small number these were grouped together with SBT  and are interbred in Europe and also in Finland.Behavioural data from Finnish Bull Terriers (Standard BT & Miniature MBT), German Shepherds (GS) and Staffordshire Bull Terriers (SBT) was collected using two owner-completed web-based questionnaires  is a sum of numerical answers to the questions “Does your dog chase its tail?” from ‘never’ to ‘multiple times per day’ and “On average, how much time in a normal day does the dog spend chasing its tail?” from 0 min up to 5 hours or more (Attachment S1). Dogs with no history of tail chasing were considered as controls (index = 0)TC. In addition to using the variable indexTC in the data analysis as a response variable, we also used a binary case-control set up (control =  no history of TC and case  = TC observed from “few time during the dog’s life” to “multiple times per day” (indexTC≥1) in the analysis. Variables amount of socialisation  and amount of exercise  and “How many hours/minutes does your dog get exercise in a typical day?”  were derived from the owners’ answers combining two or more related questions.As a measure of the frequency and intensity of tail chasing we used a variable Attachment S2) was sent to those SBT, BT and GS owners that had returned Stereotypic Behaviour Questionnaires and whose dogs had either indexTC≥2 or indexTC = 0. This questionnaire aimed to provide a personality profile of the dogs, especially their potential fearful or aggressive reactions to everyday situations , interest in play, and activity. The noise phobia –section was derived from a questionnaire developed for assessing the genetic basis of noise phobia The second questionnaire, Dog’s Personality Q , commercial (supermarket) or something else. Since there was only one dog receiving homemade leftovers and nine dogs with commercial (supermarket), we regrouped the main categories by combining the original categories as follows: homemade, (both homemade categories) something else, commercial  and special raw food diet (Bone And Raw Food). Owners were also asked if dogs received any dietary supplements. From the 231 dogs receiving dietary supplements, detailed nutritional supplement information was specified for 139 dogs. The nutrient content of the supplements was divided into five main groups; vitamins, minerals, Omega-3, Omega-6 and “something else”. The group “something else” included mainly different herbs, glucosamine and other joint products, some amino acids, polysaccharides or lactobacilli.As part of the Stereotypic Behaviour Questionnaire owners were also asked to report the type of food dogs received in five different categories: indexTC was used as a response variable using a generalized linear model with either Poisson error or negative binomial structure in PROC GENMOD (SAS version 9.2) – in this analysis all individuals were included (indexTC 0–12). Second, a case-control setup was used to compare differences between the most severe tail chasers (indexTC5–12) and the controls (indexTC = 0) using a generalized linear model with a binomial distribution (logistic regression). The following explanatory variables were included in the analysis: gender, breed, age of arrival to a new home (in weeks), place of birth (at mother’s home/at breeder) amount of socialisation, number of children in the household, number of adults, number of dogs in the household, number of other diagnosed diseases, the time the dog has to spend alone during a normal day, amount of daily exercise, amount of activities done with the dog, dietary supplements, neutering status and type of food. For most of the questions in the Stereotypic Behaviour Q we had answers from 258–367 dogs, except for the question ‘time dog has to spend alone during normal day’ for which we received only 134 answers (question was added later to the Q). The Goodness of Fit value (describing how well the model fits into the distribution) was checked for each model and values close to 1.0 were considered a very good fit indexTC≥2).The data collected via two questionnaires was analysed in two ways: all breeds pooled together and each breed separately. The possible association of TC with environmental factors in the pooled data and for each breed was further analysed with two methods. First, Attachment S2). Questions 9, 10 and 11 were left out from factor analysis due to the low number of answers . Similarly, question 8 was left as it was in yes/no scale. Questions 9–11 were analysed in a separate analysis using a generalized linear model with a binomial error distribution. In factor analysis estimating the communalities we used squared multiple correlation (R2) (Option PRIORS = SMC). Two questions (7 and 6d) were excluded from the factor analysis due to low communality values, and these were also analysed separately using generalized linear model with binomial error distribution. Four factor models were chosen in both cases based on the inspection of the scree plot and residuals and partial correlations. The possible association of personality traits with TC behaviour was investigated using a generalized linear model with a binomial error distribution (PROC GENMOD) in SAS. In this model the status of the dog (case or control) was used as a binary response variable and the four personality factors as explanatory variables. In addition, explanatory variables included breed and gender and their interaction with other variables. The same statistical methods were also used in analysing the willingness to chase moving objects, chase living prey, playfulness and general activity. The possible association of personality with TC was analyzed for each breed separately as well as for all breeds together. Type 3 analysis statistics are presented, which means that the analysis is not dependent on the order in which the terms for the model are specified.Personality data from BT, GS and from SBT  was first analysed with factor analysis to assess latent variables and reveal possible inter-correlations between different variables in the questionnaire. All analysis was performed with SAS (version 9.2). Factor analysis (PROC FACTOR) was conducted using principal factor method with VARIMAX rotation. Questions from sections 1–7 were included in the factor analysis  , breed, gender as explanatory variables. As breed, gender and all the interaction terms were not statistically significant they were dropped out of the final model.The effects of the mother’s quality of care, possible complications in birth, and age in weeks when separated from the mother were estimated using a generalized linear model with a binomial error structure in PROC GENMOD (SAS version 9.2). In the preliminary model we included tail chasing status (case/control) as binary response variable, and indexTC≥2) and 66  controls were genotyped. The study cohort included 12 Standard BT cases and 12 controls from France, while the rest of the samples originated from Finland. The French samples were recruited through a veterinary clinic and all the cases exhibited severe tail chasing, for which they needed veterinary consultation. A pedigree analysis of both the Finnish and the French dogs was used to ensure that the cases and the controls were unrelated at least at parental level. The association was analyzed by comparing the allele frequencies in the cases and the controls using the Fisher’s exact t-test. Additionally, coding regions and splice sites were sequenced according to Ensembl’s CDH2 gene reference Q9GKK9_CANFA ENSCAFG00000018115 from 4 (2 unrelated cases and 2 controls) French BTs, and from 2 (one case and one control) French MBTs. Primers are available upon request. Pedigrees were established with the help of the Finnish Breeding Association Registry.In order to analyze the association of the Doberman flank sucking locus CDH2 we developed Taqman-based assays (Applied Biosystems) for two SNPs at positions 63.867.472 bp and 63.867.492 within the CDH2 gene, including the best associated SNP in the Doberman study  The blood sample collection from the privately-owned Finnish dogs was performed by trained professionals, with permission from the dog owners, and was conducted according to Finnish and international guidelines and laws. The French blood samples were collected in the veterinary clinic during veterinary consultation, with permission from the owners. We have a valid ethical license . Dog behavior was assessed via questionnaires, and no behavioral experiments were conducted.Figure S1Short examples of pedigrees of a) Bull Terrier b) Miniature Bull Terrier, c) German Shepherd d) Staffordshire Bull Terrier. Dogs with indeTCx>2 are marked with black squares, dogs with mild TC (indeTCx = 1) are marked with grey squares, and dogs marked with white squares are dogs with no TC or other stereotypy observed. Dogs inside a dotted line have some other stereotype than TC; (a) compulsive licking, d) compulsive drinking. The other dogs’ phenotype is unknown. Affected littermates had variation in indeTCx in every breed. This is illustrated in one d) SBT family where all the dogs in the litter were affected – the number below the dog is indeTCx.(TIF)Click here for additional data file.Table S1Demographic parameters of our study populations.(DOCX)Click here for additional data file.Movie S1Tail chasing in Bull Terrier puppy. This female puppy is four months at the time of video shooting, and indexTC is 9 (index varies between 0–12). Dog performs TC multiple times per day, and no clear reason for the behavior can be seen. Dog started the TC behavior at the age of 9 weeks.(WMV)Click here for additional data file.Movie S2Tail chasing in German Shepherd male. This is a four year old male at the time of video shooting and has indexTC 9. Dog chases its tail multiple times per day and usually in situations where the dog has to wait for food or when owner talks to other people.(WMV)Click here for additional data file.Movie S3Tail chasing in Staffordshire Bull Terrier male. This dog is ten months of age, and all his sisters and brothers and a father (litter size 7) chase tails, while the mother does not have any stereotypic behavior. Dog has a indexTC 7, and the owner reports that the dog may start TC when nobody pays attention to the dog. This dog also displays a trance-like behavior.(WMV)Click here for additional data file.Attachment S1Stereotypic Behavior Questionnaire.(DOCX)Click here for additional data file.Attachment S2Dog Personality Questionnaire.(DOCX)Click here for additional data file.


After an association between genetic variants and a phenotype has been established, further study goals comprise the classification of patients according to disease risk or the estimation of disease probability. To accomplish this, different statistical methods are required, and specifically machine-learning approaches may offer advantages over classical techniques. In this paper, we describe methods for the construction and evaluation of classification and probability estimation rules. We review the use of machine-learning approaches in this context and explain some of the machine-learning algorithms in detail. Finally, we illustrate the methodology through application to a genome-wide association analysis on rheumatoid arthritis.The online version of this article (doi:10.1007/s00439-012-1194-y) contains supplementary material, which is available to authorized users. Unraveling the genetic background of human diseases serves a number of goals. One aim is to identify genes that modify the susceptibility to disease. In this context, we ask questions like: “Is this genetic variant more frequent in patients with the disease of interest than in unaffected controls?” or “Is the mean phenotype higher in carriers of this genetic variant than in non-carriers?” From the answers, we possibly learn about the pathogenesis of the disease, and we can identify possible targets for therapeutic interventions. Looking back at the past decade, it can be summarized that genome-wide association (GWA) studies have been useful in this endeavor , and for classification on the other hand, such as sensitivity (sens) and specificity (spec), there is a simple relationship between them with In the following, we will focus on classification and probability estimation based on GWA data. For this, we will describe in the next section how to construct and evaluate classification and probability estimation rules. In recent years, approaches from the machine-learning community have received more attention for this. Therefore, we will present a systematic literature review on the use of machine-learning methods. Some of these methods will then be described in more detail before we finally show examples of construction and evaluation of classification and probability estimation rules using a number of different methods on data from a GWA study on rheumatoid arthritis.The overall process of rule construction and evaluation is shown in Fig. p values from association analyses of single marker analyses. In the simplest of all cases, the rule uses only the genotype of one SNP, and subjects are assigned a higher risk if they carry one (or two) susceptibility variant(s). Usually, however, a number of SNPs fulfilling some criterion are combined to a score. For the construction of the rule from the selected SNPs, a score is often used that simply counts the number of predisposing variants a single subject carries. This assumes that all variants contribute equally to the risk, and a more sophisticated rule weights the variants depending on their respective genetic effect  as well as in chapter 14 of Ziegler and König nalytic validity evaluates how well the test is able to measure the respective genotypes. (C)linical validity is a criterion for how consistently and accurately the test detects and predicts the respective disease. (C)linical utility focuses on the influence of the test on outcome improvement for the patient, and (E)LSI comprises (E)thical, (L)egal and (S)ocial (I)mplications of the genetic test. Our aim here is the statistical evaluation of the classification and probability estimation rule, which is why we will focus on the clinical validity of the test.For this, we firstly require established associations with the disease of interest. These are rendered from candidate gene association studies or from classical GWA studies and they need to be extensively validated König .Secondly, as indicated above, the predictive value of the test needs to be established that indicates how well the test is able to differentiate between cases and controls and/or how good the probability estimates are. Specifically, the test needs to show calibration and discrimination. For a good calibration, the predicted probabilities agree well with the actual observed risk, i.e., the average predicted risk matches the proportion of subjects who actually develop the disease. Ideally, this should hold both for the overall study population and for all important subgroups. Reasonable measures for discrimination depend on the scale of the rule result. This might be dichotomous, because it is based on a single SNP only, or because the algorithm used for constructing the rule renders a binary classification. Alternatively, it might be (quasi-) continuous, as is the case if a score has been constructed, or if the algorithm renders risk probabilities. The respective measures are shown in Fig.  c-statistic have often been criticized. For example, the c-statistic is not clinically meaningful, and a marginal increase in the AUC can still represent a substantial improvement of prediction at a specific important threshold  andTo evaluate predicted probabilities the Brier score (BS), which is given by the average over all squared differences between an observation and its predicted probability, is preferably used. The Brier score is a so-called proper score , where π1 and π0 are the sampling proportions of cases and controls, respectively, from the general population. Thus, if the sampling proportions are known, probabilities can be estimated as if the data came from a prospective study.The final question is whether consistent probability estimates can be obtained under any sampling scheme. The simple answer to this question is no. In fact, prospective sampling, not case–control or cross-sectional sampling, is required to guarantee unbiased probability estimates. This has been considered in detail for the logistic regression model by Prentice and Pyke  and by AA similar function for relating prospective and retrospective study designs is unknown for machine-learning approaches. Thus, the interpretation of probability estimates from machine-learning approaches based on retrospective data is not necessarily consistent.To illustrate some of the methods described so far, we applied them to a data set from a GWA study on rheumatoid arthritis. This data set had been provided for the Genetic Analysis Workshop 16  and a test data set (231 cases and 251 controls).−8, 183 SNPs were associated with disease status. Analyzed in the test data set, 65 SNPs of these were again genome-wide significant.In the training data set, we performed single SNP analyses using a trend test resulting in associations shown in Supplementary Fig. 1. Based on a genome-wide significance threshold of 5 × 10“allele count”: count the number of risk alleles over all included SNPs for every person,“logOR”: weight SNPs using respective log odds ratio from single SNP analysis,“lasso”: least absolute shrinkage and selection operator (lasso) combining shrinkage of variable parameter estimates with simultaneous variable selection by shrinking some of the coefficients of the full model to zero  simultaneously,“RJ-Reg”: RFs in the regression mode using Random Jungle  and 63,334 (12.5 %), where the last set was only used for the logOR and the RJ-Reg method.For a binary classification, we selected the threshold that maximized the Youden index in the training data for the scores based on allele count, logOR, logReg and lasso. For RFs, Random Jungle was utilized in the classification mode, again using default parameters but without pruning. The resulting classification is termed “RJ-Class”.Every score applied to the training and test data was evaluated in the test data by plotting ROC curves Fig. . We compWithin the allele count method, we found that smaller SNP sets yielded higher AUCs. The pattern was more irregular for the logOR method; here, AUC was lowest for the 0.025 and 0.049 % as well as for the 12.5 % SNP set. No differences in AUC were observed for the lasso method. Finally, for RJ-Reg, AUC was highest for medium SNP sets with 0.049 to 0.782 % of the total number of SNPs.On comparing the methods within one SNP set, we found that overall, RJ-Reg led to higher AUCs than any of the other methods in any SNP set. Furthermore, the allele count method rendered a higher AUC than the logOR method in the 0.025 % and the 0.049 % SNP sets, but was worse than the lasso or the logOR method within the 0.782 % SNP set.We estimated the Brier score that is based on the squared differences between observed and predicted probabilities. As this requires estimated probabilities, we could only use this for the methods lasso and RJ-Reg, and the results are shown in Fig. For a binary classification, for every score, we selected the threshold that maximized the Youden index in the training data. Then, sensitivity and specificity were calculated with 95 % CIs according to Wilson  and are The detailed results in Supplementary Table 1 show that these analyses mostly mirror the results from comparing the AUCs. The only remarkable difference was that for RJ-Class, smaller SNP sets led to a better classification, although for RJ-Reg, medium SNP sets had shown the best AUC.In summary, the prediction accuracy based on continuous scores or probabilities was usually better when using RJ-Reg as compared to the other methods. The number of SNPs for an optimal prediction was dependent on the method, whereas it played no role when using the lasso. Smaller SNP sets were better for the allele count method, but a medium number of SNPs was optimal for the RJ-Reg.Although based on one small data set, our analysis of a GWA study on rheumatoid arthritis showed two things. Firstly, when different SNP sets were compared, our results did not substantiate previous results that using more SNPs yielded better results; instead, our results indicated that the best SNP set may depend on the actual method used for rule construction. Secondly, in this data set, there was a consistent advantage of using Random Jungle over other methods.In contrast, our literature review showed that machine-learning algorithms have so far been underutilized. Moreover, when applied, their specific value with regard to classification and probability estimation has usually not been exhausted.In line with this, we make a plea for clearer definitions of the terms and study aims. Specifically, association, classification and probability estimation can be different aims of studies, require different methods, and result in different interpretations.p values from single SNP trend tests of association with rheumatoid arthritisSupplementary material 1 (PPTX 57 kb) Manhattan plot showing −log Supplementary material 2 (XLSX 23 kb) Comparison of the area under the curves (AUCs) and percentage of correct classifications across methods and SNP setsBelow is the link to the electronic supplementary material.


Autism spectrum disorders (ASD) are early onset neurodevelopmental syndromes typified by impairments in reciprocal social interaction and communication, accompanied by restricted and repetitive behaviors. While rare and especially de novo genetic variation are known to affect liability, whether common genetic polymorphism plays a substantial role is an open question and the relative contribution of genes and environment is contentious. It is probable that the relative contributions of rare and common variation, as well as environment, differs between ASD families having only a single affected individual (simplex) versus multiplex families who have two or more affected individuals.By using quantitative genetics techniques and the contrast of ASD subjects to controls, we estimate what portion of liability can be explained by additive genetic effects, known as narrow-sense heritability. We evaluate relatives of ASD subjects using the same methods to evaluate the assumptions of the additive model and partition families by simplex/multiplex status to determine how heritability changes with status.By analyzing common variation throughout the genome, we show that common genetic polymorphism exerts substantial additive genetic effects on ASD liability and that simplex/multiplex family status has an impact on the identified composition of that risk. As a fraction of the total variation in liability, the estimated narrow-sense heritability exceeds 60% for ASD individuals from multiplex families and is approximately 40% for simplex families. By analyzing parents, unaffected siblings and alleles not transmitted from parents to their affected children, we conclude that the data for simplex ASD families follow the expectation for additive models closely. The data from multiplex families deviate somewhat from an additive model, possibly due to parental assortative mating.Our results, when viewed in the context of results from genome-wide association studies, demonstrate that a myriad of common variants of very small effect impacts ASD liability. Most authors recruited families, produced or evaluated data and commented on the manuscript. All authors read and approve the final manuscript.Figure S1. Ancestry projects for principal component 1 (PC.1) versus principal component 2 (PC.2) for the samples used in the analysis of heritability. Red dots represent subjects with an ASD diagnosis and blue are controls. HealthABC=HABC.Click here for fileTable S1. Heritability estimates and their standard errors (se) using 391,425 SNP when AGP and SSC simplex family data are combined or only multiplex AGP families are analyzed. Analyses include all HealthABC and NGRC control samples.Click here for fileTable S2. Heritability estimates and their standard errors (se) obtained when contrasting AGP and SSC samples of the same relationship type, as well as contrasting HealthABC versus NGRC controls.Click here for fileFigure S2. Heritability for ASD probands as a function of estimated “genomic coverage” for varying levels of r2. Coverage is estimated as the fraction of all known SNPs identified by 1000 Genomes with minor allele frequency > 0.1 tagged by the set of SNPs used to estimate heritability for probands; see Methods for more details. From the left points map onto 12.5%, 25%, 50%, and 100% of the SNPs used to estimate heritability. Top line is for probands from multiplex families, bottom for probands from simplex families.Click here for file


APOC3 gene that lowers fasting triglyceride levels in HAPI Heart study participants.Owing to recent advances in DNA sequencing, it is now technically feasible to evaluate the contribution of rare variation to complex traits and diseases. However, it is still cost prohibitive to sequence the whole genome (or exome) of all individuals in each study. For quantitative traits, one strategy to reduce cost is to sequence individuals in the tails of the trait distribution. However, the next challenge becomes how to prioritize traits and individuals for sequencing since individuals are often characterized for dozens of medically relevant traits. In this article, we describe a new method, the Rare Variant Kinship Test (RVKT), which leverages relationship information in family-based studies to identify quantitative traits that are likely influenced by rare variants. Conditional on nuclear families and extended pedigrees, we evaluate the power of the RVKT via simulation. Not unexpectedly, the power of our method depends strongly on effect size, and to a lesser extent, on the frequency of the rare variant and the number and type of relationships in the sample. As an illustration, we also apply our method to data from two genetic studies in the Old Order Amish, a founder population with extensive genealogical records. Remarkably, we implicate the presence of a rare variant that lowers fasting triglyceride levels in the Heredity and Phenotype Intervention (HAPI) Heart study (p = 0.044), consistent with the presence of a previously identified null mutation in the  The genetic architecture of most complex traits and diseases is poorly understood. Indeed, genome-wide association studies (GWAS’s) have identified hundreds of loci with relatively weak effects on complex traits and diseases, leaving much of their heritability unaccounted for Recent advances in DNA sequencing technology have dramatically increased the capacity to discover rare variants. However, it is still cost prohibitive to sequence whole genomes (or even whole exomes) on the scale of a GWAS, e.g., by sequencing all study participants. For studies of quantitative traits, one strategy to reduce cost is to sequence individuals with extreme phenotypes. Simulation studies The power of extreme-trait sequencing or selective genotyping, originally introduced by Lander and Botstein Briefly, the RVKT leverages the relatedness of individuals in family-based studies to identify quantitative traits that are most likely to be influenced by rare variants. The premise of our test is that rare variants with at least modest effects will be enriched in the tails of the trait distribution and preferentially carried by closely related individuals. Unlike complex segregation analysis, which attempts to identify a particular mode of inheritance, our approach makes few assumptions about the trait architecture. We assess the power of our test via simulation and apply it to dozens of quantitative traits from two of our studies in the Old Order Amish population.All human subject research was previously reviewed and approved by the Institutional Review Boards at the University of Michigan and the University of Maryland. Written informed consent was obtained from all study participants.Here we describe the RVKT, simulations to assess power, and applications to two family-based studies. The RVKT requires a sample of families with pedigree and phenotype data and assumes that each of the quantitative traits to be tested has a narrow-sense heritability that is significantly different from zero. The null hypothesis of the RVKT is that a given trait is purely polygenic, meaning influenced by multiple additive, independent loci of small effect. Under the null hypothesis, individuals in the tail of the trait distribution carry trait-influencing alleles at many loci. The alternative hypothesis of the RVKT is that at least one locus of modest to large effect influences the trait, and accordingly, that the trait-associated allele(s) is necessarily rare (the rare variant). Under the alternative hypothesis, individuals in the tail of the trait distribution should preferentially carry the rare variant and thus may be more closely related when measured against the null hypothesis.For each trait, we define and calculate the RVKT statistic as the mean of the pair-wise kinship coefficients between individuals in the tail of the quantitative trait distribution. Tail membership is determined by ordering individual trait values. Conditional on the pedigrees in the sample, the kinship coefficient between two individuals is the probability that a randomly chosen allele from one individual and a randomly chosen allele from the other individual at an autosomal locus are inherited identical by descent from a recent, common ancestor. We calculate pair-wise kinship coefficients using the matrix method described by Lange min).To assess statistical significance, we compare the observed RVKT statistic for each trait to its expected distribution under a purely polygenic model (the null hypothesis) (described below). Under the alternative hypothesis, the observed RVKT statistic may exceed its expected value, meaning individuals in the tail of the trait distribution may be more closely related than expected under the null hypothesis. Thus, we use a one-sided test. Because the genetic architecture of each trait is unknown, we conduct the RVKT for both tails of the trait distribution (upper and lower) and multiple tail sizes. Tail size is the proportion of individuals in the tail of the trait distribution. We then select the RVKT statistic with the minimum p-value in each tail .The expected distribution of the RVKT statistic depends on the actual pedigrees and the narrow-sense heritability of the trait. Thus, we use simulation to generate an empirical null distribution for each trait. Specifically, using MORGAN version 3.0 [th percentile of the empirical null distribution, i.e., using a significance level of 0.05. We generated a single null distribution (as described above) for narrow-sense heritabilities of 40, 60, and 80% and repeatedly compared each replicate under the alternative hypothesis to this distribution.To evaluate the power of our test, we conducted gene dropping simulations conditional on our Amish pedigrees (described below), and for comparison, four-person nuclear families (two parents and two offspring) with sample sizes corresponding to our Amish studies. Specifically, we simulated a single additive, bi-allelic locus with a trait-influencing allele frequency of 0.5, 1, 2, 3, or 4% (the rare variant) that accounted for 2, 5, 10, 20, or 30% of the total trait variance. In each simulation, we assumed that multiple additive, independent genetic factors, including the rare variant, accounted for 40, 60, or 80% of the trait variance (the narrow-sense heritability). For each set of parameters, we simulated 1,000 replicates using MORGAN version 3.0 and tested tail sizes of 1, 2, 4, 6, and 8%. For each tail size, power was calculated as the proportion of replicates for which the RVKT statistic equaled or exceeded the 95A subset of the simulations above were conducted on pedigree structures connecting 1,481 women from our genetic study of mammographic density We applied the RVKT to dozens of quantitative traits from the two genetic studies described above, with the goal of prioritizing traits and individuals for extreme-trait sequencing. Specifically, we applied the RVKT to 35 quantitative traits from our study of mammographic density , including absolute measures of the dense and non-dense area of the breast, percent breast density, total breast size, measures of body size, reproductive and menstrual traits, and several serum hormones and growth factors see . These tWe also applied the RVKT to 37 quantitative traits from the HAPI Heart study (n = 868), including measures of body size, fasting lipid levels, and measures of vascular health and arterial stiffness see . These tmin) in the upper and lower tail of each trait distribution. To control for multiple testing of traits, some of which may be correlated, we calculated the effective number of tests using the method described by Li and Ji min, denoted pmin, corrected.As in our simulations, we tested tail sizes of 1, 2, 4, 6, and 8%, corresponding to 15, 30, 59, 89, and 118 subjects from our study of mammographic density and 9, 17, 34, 51, and 68 subjects from the HAPI Heart study. We then selected the RVKT statistic with the minimum p-value  of the test. As expected, the cumulative distribution function (CDF) was discrete. However, it became increasingly discrete as the number and types of relative pairs in the tail or sample decreased. For example, q denotes the frequency of the rare variant, power was greatest for a tail size of 2(1−q)q+q2. Thus, we report results below for tail sizes that maximized power.Under the alternative hypothesis, power was generally maximized when the tail size matched the expected carrier frequency of the rare variant (data not shown). In other words, if As expected, power of the RVKT increased as the effect size increased, meaning as the rare variant accounted for an increasing proportion of the trait variance. For example, using the trimmed pedigrees from our study of mammographic density  and assuPower degraded substantially as pedigree complexity increased, meaning as the number and types of distantly related pairs in a sample increased. For example, consider a sample of 1,481 individuals, a narrow-sense heritability of 40%, and a rare variant with frequency 2% and effect size 20%. Under these parameters, power decreased from 64% for the trimmed Amish pedigrees to 26% for the complete 13-generation pedigree (grey versus black bars in min) from our study of mammographic density and the HAPI Heart study, respectively. The RVKT statistic was nominally significant for 8 of the 35 traits in the density study (pmin≤0.05). After correcting for multiple testing (26 effective tests), the RVKT remained significant for 3 of the 8 traits, including free estradiol and prolactin in pre-menopausal women and estradiol in post-menopausal women . Similarly, in the HAPI Heart study, the RVKT was nominally significant for 14 of the 37 traits, one of which, namely, fasting triglyceride levels, remained significant after correcting for 22 effective tests .After evaluating the power of the RVKT via simulation, we applied our test to dozens of quantitative traits from our two Amish studies. min). For example, in pre-menopausal women from our study of mammographic density, pmin, which corresponded to a tail size of 2% (14 of 728 women), was 0.0004 for prolactin. These 14 women had the lowest batch-standardized and age-adjusted levels of prolactin and a mean pair-wise kinship coefficient of 0.080 compared to an expected value of 0.068 under a purely polygenic model . For each of the other 3 traits, the RVKT statistic was also significant when testing the lower but not upper tail of the trait distribution.In total, after multiple test correction, the RVKT statistic was significant for 4 of 72 quantitative traits across our two genetic studies. The advantage of using the RVKT to prioritize traits and individuals for sequencing in family-based studies is best illustrated by results from the HAPI Heart study. In testing 37 quantitative traits, many of which are established risk factors for cardiovascular disease, we found significant evidence of excess relatedness between individuals in the lower tail of the distribution for fasting triglycerides. For tail sizes of 1 to 8%, the mean pair-wise kinship coefficient ranged from 0.114 to 0.020, respectively, and was significantly different from the kinship coefficient expected under a purely polygenic model of trait architecture (p≤0.05). Although differences between significance levels were not pronounced for different tail sizes, the significance of the RVKT was minimized for the 17 individuals with the lowest age- and sex-adjusted triglyceride levels, or equivalently, for a tail size of approximately 2%.et al.APOC3 gene (R19X) (rs76353203) with a frequency of 0.024 that lowers fasting triglyceride levels in HAPI Heart study participants. This mutation was discovered because it was tagged by another SNP (rs10892151) (MAF = 0.028) in the context of a GWAS . Had we sequenced the 17 individuals in the lower tail of the age- and sex-adjusted triglyceride distribution, we would have discovered APOC3 R19X since 7 of these individuals were mutation carriers, an 8-fold enrichment compared to the ∼5% of individuals who were carriers in the overall sample. Notably, none of the 17 individuals in the upper tail of the distribution carried the mutation.Remarkably, Pollin APOC3 R19X on fasting triglycerides in the HAPI Heart study was less than 25%. As such, it cannot be used to exclude the presence of rare trait-associated alleles, unless these alleles account for a large proportion of the phenotypic variance. However, when multiple medically relevant quantitative traits are available, the RVKT may be a valuable starting point for prioritizing traits and individuals for sequencing. For example, even though APOC3 R19X carriers in the HAPI Heart study had cardio-protective profiles for several lipids, including higher HDL and lower LDL cholesterol and lower triglyceride levels, Pollin et al. As expected, the power of the RVKT was low for small to modest effect sizes. In fact, the power of our test to implicate the presence and influence of The power of the RVKT is heavily influenced by the number and types of relationships in a sample. Specifically, the power of the RVKT increases as the number of closely related pairs increases. In contrast, power is lost as the number of distantly related pairs multiplies. For instance, in our simulations –4, powerAlthough trimming increases power, the RVKT may actually be conservative when pedigrees are too simple. In fact, it may be impossible to choose a rejection region from the empirical null distribution of the RVKT statistic such that the size of the test does not exceed the significance level. For example, consider a single pair of siblings from each of 741 families . To obtain the null distribution, we simulated 1,000 replicates of a purely polygenic trait with a narrow-sense heritability of 40%. However, when we tested a 1% tail size, we obtained only three values of the RVKT statistic (data not shown). The largest value occurred 17 times; therefore, the smallest possible test size was 0.017. In other words, it would have been impossible to conduct a 0.01 level test. This problem was especially pronounced for modest sample sizes and small tail sizes due to discontinuities in the empirical null distribution of the mean pair-wise kinship coefficient (data not shown).An implicit assumption of the RVKT is that – within each family – a specific allele at the same locus has an effect on the trait of interest. In other words, the power of the test depends on the extent of allelic and locus homogeneity within each family but does not require homogeneity between families. For example, if multiple rare variants influence a trait, then phenotypically extreme individuals from the same family are more likely to share the same trait-influencing alleles than phenotypically extreme individuals from different families. Thus, the RVKT statistic may still exceed its expected value since individuals in the tail of the trait distribution may be more closely related than expected under the null hypothesis. From this perspective, isolates like the Amish are an ideal population in which to apply the RVKT and carry out extreme-trait sequencing since many copies of the same rare trait-associated allele are likely to be segregating within a family due to a combination of founder effect and genetic drift.In our simulations, we considered rare variant frequencies ranging from 0.5 to 4%. We did so for two reasons. First, the Old Order Amish population of Lancaster County, PA derives from a small number of European ancestors (∼300) who immigrated nearly 250 years ago and has since increased in size to approximately 45,000 individuals (census size) min for the RVKT was 0.018 and 0.031 for the lower and upper tails, respectively  for quantitative traits from our study of mammographic density stratified by menopausal status.RVKT p-values ; gray bars, not significant. Before applying the RVKT, traits were transformed to approximate normality, when necessary, and adjusted for age.(TIF)Click here for additional data file.Table S1Trait descriptions from our study of mammographic density.(PDF)Click here for additional data file.Table S2Trait descriptions from the HAPI Heart study.(PDF)Click here for additional data file.


MetS traits included body-mass index (BMI), waist-to-hip ratio (WHR), systolic blood pressure (SBP), fasting glucose (GLU), fasting insulin (INS), fasting trigylcerides (TG), and fasting high-density lipoprotein (HDL). We found the percentage of 2h accounted for by common SNPs to be 58% of 2h for height, 41% for BMI, 46% for WHR, 30% for GLU, 39% for INS, 34% for TG, 25% for HDL, and 80% for SBP. We confirmed prior reports for height and BMI using the ARIC population and independently in the Framingham Heart Study (FHS) population. We demonstrated that the multivariate model supported large genetic correlations between BMI and WHR and between TG and HDL. We also showed that the genetic correlations between the MetS traits are directly proportional to the phenotypic correlations.We used a bivariate (multivariate) linear mixed-effects model to estimate the narrow-sense heritability  survey a large set of genetic markers common to the population. They have identified several single markers that are associated with traits and diseases. However, these markers do not seem to account for all of the known narrow-sense heritability. Here we used a recently developed model to quantify the genetic information contained in GWAS for single traits and shared between traits. We specifically investigated metabolic syndrome traits that are associated with type 2 diabetes and heart disease, and we found that for the majority of these traits much of the previously unaccounted for heritability is contained within common markers surveyed in GWAS. We also computed the genetic correlation between traits, which is a measure of the genetic components shared by traits. We found that the genetic correlation between these traits could be predicted from their phenotypic correlation. To reduce the chance of false positives, a stringent p-value criterion has been adopted . It has been suggested that this selection criterion is too conservative The main approach of GWAS has been to identify significant single-nucleotide polymorphisms (SNPs) by examining each SNP individually for significance. The g2h, may be estimated by adapting a linear mixed-effects model 2h. This model decomposes the phenotypic variance into genetic and residual variance components. Usually, the model is applied to related individuals where the genetic relationships are estimated by using family pedigree or genetic markers g2h could be estimated using genetic relationships obtained from the common SNPs for unrelated individuals. The main assumed difference between g2h and 2h is due to the difference in linkage disequilibrium (LD) between the common SNP markers and the rest of the genome, with the assumption that closely related individuals would be in greater LD than unrelated individuals. Thus, heritability estimated with the genetic relationships of unrelated individuals is attributed to the common variants while that estimated with genetic relationships of related individuals is attributed to the entire genome. While the method does not identify single variants, it provides the maximum expected variance expected by the set of markers or the relative complement of the set . Recently, it has been shown that a large proportion of 2h is explained by the common single-nucleotide polymorphisms (SNPs) for several traits using this model Alternatively, the narrow sense heritability explained by the common SNPs, 2h and g2h for height and body-mass index (BMI) in the Framingham Heart Study population (FHS), and height and seven metabolic syndrome traits (MetS) traits: BMI, waist-to-hip ratio (WHR), systolic blood pressure (SBP), fasting glucose (GLU), fasting insulin (INS), fasting triglycerides (TG), and fasting high-density lipoprotein (HDL) in the Atherosclerosis Risk in Communities population (ARIC)  for height and 0.39 (s.e. 0.04) for BMI in FHS, and 0.88 (s.e. 0.09) for height and 0.34 (s.e. 0.12) for BMI in ARIC. The estimated 2h were consistent with values obtained using phenotypic regression (data not shown) and previous results We first estimated g2h for unrelated individuals with relationships less than 0.025  for height and 0.10 (s.e. 0.18) for BMI in FHS, and 0.46 (s.e. 0.05) for height and 0.14 (s.e. 0.05) for BMI in ARIC. These values are consistent with previously estimated values 2h for height and 33% for BMI. To assess whether including more common SNPs would explain more of the 2h, we examined how g2h depended on the number of SNPs. As shown in g2h estimate for height in the ARIC population appeared to stabilize after approximately 300,000 SNPs.We then compared these values to estimates for 2h and g2h for the MetS traits in the ARIC population using the same subjects as above . The median 2h was 0.33, the minimum was 0.23 (INS), and the maximum was 0.48 (HDL). The median g2h was 0.13, the minimum was 0.09 (INS), and maximum was 0.24 (SBP). Comparing the medians suggested that g2h explains ∼39% of the 2h for these MetS traits. We found that the common SNPs explained large proportions of the 2h: 41% of 2h for BMI, 46% for WHR, 30% for GLU, 39% for INS, 34% for TG, 25% for HDL, and 80% for SBP.We then estimated bove see . We valit-distribution p-value with 20 d.f. = 8.2*10−3). The phenotypic correlations between traits were similar for related and unrelated individuals and are shown in We next estimated the genetic correlations between MetS traits using a bivariate (multivariate) model see  with a pWe validated our genetic correlation estimates using bivariate models for each pair of traits by analyzing all 7 MetS traits simultaneously for the unrelated individuals in a single multivariate model. This 7 trait multivariate model was much more expensive computationally so we used a less stringent convergence rule. The results were similar to the bivariate model see  and S6 apr were proportional to the genetic correlations gr with a proportionality constant of 1.2 . For unrelated individuals, we found that the phenotypic correlations were proportional to the genetic correlations with a proportionality constant of 0.85 . The direct proportionality between pr and gr implies that the ratio g/rpr is approximately constant for the MetS traits.We then examined the relationship between the genetic and phenotypic correlations see . For rel2h and g2h. We computed both in the same population. However, differences between estimates of 2h and g2h may also arise due to differences in environmental influences and non-additive genetic effects that may bias the estimates. Provided that these biases are small then the ratio of g2h to 2h provides an estimate of the proportion of narrow sense heritability captured by the common SNPs.We used a recently developed approach to analyzing GWAS data and provided new estimates for the total amount of additive genetic information contained in the common SNPs for MetS traits. The approach uses a linear mixed-effects model to estimate the additive genetic variances and correlations between traits. The model relies on knowing the genetic relationships between the individuals analyzed. Previously, this had been obtained from family pedigrees. Visscher et al. 2h is explained by the common SNPs. Our g2h estimates for height and BMI in two independent analyses (i.e. ARIC and FHS) were consistent with previously reported values 2h estimates for BMI, GLU, INS, TG, HDL, and SBP were similar to the findings of the large family National Heart, Lung, and Blood Institute (NHLBI) Family Heart Study g2h explained a large proportion of 2h across the MetS traits, and g2h explained approximately 39% of the 2h for these traits. We estimated that the common SNPs explain 58% of 2h for height, 41% for BMI, 46% for WHR, 30% for GLU, 39% for INS, 34% for TG, 25% for HDL, and 80% for SBP. Our g2h findings are striking compared to traditional GWAS approaches where significant common SNPs have been shown to explain only 4% of 2h for BMI with 32 SNPs, 11% for GLU with 14 SNPs, 20% for TG with 48 SNPs, 25% for HDL with 60 SNPs, 3% for SBP with 10 SNPs, and 12% for height with 180 SNPs g2h, which was consistent with having a large 2h. Surprisingly, SBP had the largest proportion of 2h explained by the common SNPs while only a few percent of this has been uncovered by traditional GWAS. However, the standard error of g2h for SBP was large and reducing this error will be important for further investigation. Conversely, our analysis suggested that the SNP markers already identified for TG and HDL may contain the maximum heritability expected from the common SNPs.We confirmed previous findings that a large proportion of g2h against the number of SNPs suggested that the mean and standard error of g2h for height is well estimated by approximately 300,000 markers and that including more markers would have little effect for this trait and perhaps others. The standard error of g2h also increased with SNP number. This may seem paradoxical but can be explained by recalling that the estimate for g2h is proportional to the regression coefficient of the square of the phenotype differences versus the genetic relationship (i.e. Haseman-Elston regression) g2h is thus inversely proportional to the variance of the genetic relationship. Since the latter is estimated from the common SNPs, this variance is expected to decrease as the number of SNPs increases thereby increasing the standard error Our analysis of Using the bivariate (multivariate) model We found that the genetic correlation was directly proportional to the phenotypic correlation, which was an unexpected, empirical finding. Previously, a linear relationship between the correlations was hypothesized by Cheverud for sets of traits with common functions, and shown empirically for a number of traits In summary, we provided evidence that the common SNPs explain large proportions of the variance for several MetS traits in agreement with previous findings for some of these traits Our main study population was the Atherosclerosis Risk In Communities (ARIC) population. The ARIC population consists of a large sample of unrelated individuals and some families across North America. The population was recruited from four centers across the United States: Forsyth County, North Carolina; Jackson, Mississippi; Minneapolis, Minnesota; and Washington County, Maryland. For this study, we restricted our analysis to the European-American group. The population was recruited in 1987 from the general population consisting of subjects aged 45 to 64 years. The ARIC population consisted of 8,451 subjects.−6) and minor allele frequency >0.05. Subjects with missingness >0.05 were removed. This resulted in 436,126 retained markers.Quality control and genotype calls for common SNPs were evaluated previously for ARIC using the Affymetrix Human SNP Array 6.0. We selected bilallelic autosomal markers based on the following criteria: missingness <0.05, Hardy-Weinberg equilibrium  indicate significant population stratification between self-identified white (European-ancestory kind group) and black populations when projected onto HapMap components. Furthermore, principal-components analysis of the European-ancestory group by dbGAP showed that no component explained more than 0.1% of the population variance. For this study we only analyzed the European-ancestory group and treated it as a single population.ARIC phenotypes were adjusted for age, sex, and study center. Only single measurements from visit 1 were used for these subjects. We only used subjects with negative diabetes status and with genotype and phenotype information for all traits. This resulted in 8,451 subjects. We standardized all the traits. We first log-transformed BMI, glucose, insulin, triglycerides, HDL, and systolic blood pressure. All laboratory measurements are under fasting conditions. Population trait statistics are in 2h and g2h for height and BMI in the Framingham Heart Study population (FHS). The FHS population is a large multi-generational dataset that started in 1948 in Framingham, Massachusetts in the United States. It consists of a number of ethnicities predominantly from the United Kingdom, Ireland, Italy, and Western Europe We estimated 2h using the linear mixed-effects model (see derivation below) and related individuals defined as genomic relatedness between 0.35 and 0.65. We assume that the common SNPs are in greater linkage disequilbrium among related individuals and, as such, can be used to estimate the total additive-genetic variance across the allele spectrum as suggested by Visscher et al., 2006 We determined 2h was estimated with 2h = gvar/(gvar+evar), where gvar and evar are the genetic and residual variance components estimated by the REML model using related individuals. The error was estimated from the inverse Fisher Information (see linear mixed-effects model below) and propagated using a first-order Taylor expansion.g2h). Unrelated individuals were defined as subjects with maximum genomic correlation of <0.025. The genomic relationship matrix was then produced as above based on this cutoff. The cutoff was taken from Yang et al. 2010 nd cousins. For these estimates we used the same group of 5,647 unrelated individuals for all estimates in ARIC and 1,489 individuals in FHS. g2h was estimated as g2h = gvar/(gvar+evar), where gvar and evar are the genetic and residual variance components estimated by the REML model using unrelated individuals. The standard error was estimated as above. The height hg2 versus SNP number analyses were performed over allele frequency range of 0.05 to 0.5 in order of increasing and decreasing frequency.We used the linear mixed-effects model and only unrelated individuals to estimate the additive-genetic variance attributable to the common SNPs (gr) is defined as g(it)) is the additive genetic variance of trait i and covariance ) is the additive genetic covariance between the traits. The variances and covariances are estimated directly in the multivariate linear mixed-effects model. The error was computed from the estimated errors of the variances and covariance using a first-order Taylor expansion. The residual and phenotypic correlations were analogously defined. Phenotype correlations and error were estimated by linear regression of the standardized phenotypes.The genetic correlation  assuming that the error around the mean parameter estimate was normally distributed and that the parameters were independent. We then fit a linear function with the y-intercept fixed at 0 (after first confirming that it was not significantly different from zero).r) using the standardized Fisher transformed estimate of r: arctan(r)/arctan(s.e.(r)). We estimated the two-tailed p-value from a normal distribution and significance was determined by p<0.05 and Bonferroni corrected for 21 hypotheses.We assessed significance for correlation coefficients (Significance for regression coefficient (http://pngu.mgh.harvard.edu/purcell/plink/) and MATLAB . REML optimization was executed using software written in MATLAB.Preprocessing of SNPs and phenotypes was done using PLINK m individuals, n loci and t traits yi is a m×1 vector of trait i for m individuals, Xi is an m×s fixed effects matrix for trait i, vi is a s×1 vector of fixed effects parameters for trait i, Z is an m×n matrix of standardized genotypes, ui is an n×1 vector of random effects for trait i satisfying ui∼N and ei is an m×1 vector of residual effects satisfying ei∼N, with matrix blocks Gij = covgijIn and Rij = coveijIm and Il is the l×l identity matrix. This model can be used for single or multiple traits. For two traits, it is called a bivariate model. The model is identical to that used by We considered the following multivariate linear mixed-effects model for i have frequency pi. We assign a value of 2 for genotype qq, 1 for genotype qQ and 0 for genotype QQ. The Hardy-Weinberg mean frequency for the genotype at locus i is 2pi and the variance is 2ip(1−ip). The standardized genotype entries have values of (2−2pi)/(2pi(1−2pi))1/2 for qq, (1−2pi)/(2pi(1−2pi))1/2 for qQ, and −2pi/(2pi(1−2pi))1/2 for the QQ genotype.We considered only bi-allelic SNPs in Hardy-Weinberg equilibrium. Denote the minor allele by q and the major allele by Q. Let the minor allele frequency at locus m×m blocks V−1ij and A is the genetic relationship matrix. Following Yang et al. A, A are computed using the formulaIij is a tm×tm dimensional matrix with zero entries except for a m×m identity matrix at block location i, j, The log of the likelihood function is given byk+1 in terms of iteration k. We iterated until the rate of change of the log likelihood function was less than about 10−4. We also checked that the rate of change of the square of the covariance predictions was less than 10−8. We checked our results against the software developed by Yang et al. (GCTA) We solved the REML equations using an EM algorithm zj be the set of phenotypes for individual j. We used the canonical transformation Q can be computed from the formula S is the matrix of left eigenvectors of GR−1). The transformed genetic covariances are given by It. Each step consisted of taking a single step with the univariate EM algorithm for the transformed additive genetic and residual variance followed by a transformation back to the original coordinates. We iterated until the maximum of the magnitudes of the components of the gradient of the log likelihood function was less than approximately For the multivariate model, we transformed to a coordinate system where the covariance matrices were diagonal In our computations, we used both the direct EM algorithm and the canonically transformed algorithm because even though the transformed algorithm was in principle faster, it sometimes had poor convergence properties if the initial guess was not sufficiently close to the maximum likelihood value. We ensured that both give the same results. For computational efficiency, the results shown are computed from the bivariate model for the different trait pairs. We confirmed our results with a multivariate model that included all traits.F, which we computed by evaluating the Hessian of the log likelihood at the maximum likelihood predictions. F is a t(t+1)×t(t+1) dimensional matrix with rows corresponding to the genetic and residual variances and covariances  and with block elements  given byOur error estimates were given by the inverse of the Fisher information matrix Figure S1hg2 versus number of SNPs by sampling the allele frequency from 0.05 to 0.5 . A) hg2 estimates for height relative to the number of SNPs (mean and s.e.). B) Standard error versus number of SNPs.Height (TIF)Click here for additional data file.Figure S2Genetic correlation coefficient for unrelated individuals versus the genetic correlation coefficients for related individuals. Shown are the mean and standard errors. Dashed line is the least squares fit with the y-intercept fixed at 0 estimated using a Monte Carlo method (slope = 0.44).(TIF)Click here for additional data file.Figure S3A) Genetic correlation coefficients versus the phenotypic correlation coefficients for related individuals. Shown are the mean and standard errors. Dashed line is the least squares fit with the y-intercept fixed at 0 estimated using a Monte Carlo method (slope = 1.2). B) Genetic correlation coefficients versus the phenotype correlation coefficients for unrelated individuals. Shown are the mean and standard errors. Dashed line is the least squares fit with the y-intercept fixed at 0 estimated using a Monte Carlo method (slope = 0.85).(TIF)Click here for additional data file.Table S1Atherosclerosis Risk in Communities Study (ARIC) population statistics by sex; mean . BMI = body-mass index, WC = waist circumference, WHR = waist-to-hip ratio, GLU = fasting glucose, INS = fasting insulin, TG = fasting triglycerides, HDL = fasting high-density lipoprotein, SBP = systolic blood pressure.(DOCX)Click here for additional data file.Table S2Framingham Heart Study (FHS) population statistics.(DOCX)Click here for additional data file.Table S3Genetic and residual covariance estimates for the ARIC population among related individuals. Mean and standard error of genetic (upper triangle) and residual (lower triangle) covariance estimates from the univariate  and bivariate  REML model.(DOCX)Click here for additional data file.Table S4Genetic and residual covariance estimates for the ARIC population among unrelated individuals. Mean and standard error of genetic (upper triangle) and residual (lower triangle) covariance estimates from the univariate  and bivariate  REML model.(DOCX)Click here for additional data file.Table S5Genetic (upper triangle) and residual (lower triangle) correlations among unrelated individuals in the ARIC population based on simultaneous analysis of all MetS traits. Mean and standard error of the Pearson correlation coefficient for genetic correlations (upper triangle) and residual correlations (lower triangle). An asterisk indicates significance with p<0.05 adjusted for 21 hypotheses using the two-tailed hypothesis test and normal distribution of the Fisher transformed correlation coefficient.(DOCX)Click here for additional data file.Table S6Genetic (upper triangle) and residual (lower triangle) covariances among unrelated individuals in the ARIC population based on simultaneous analysis of all MetS traits. Mean and standard error.(DOCX)Click here for additional data file.


Phenotypic misclassification (between cases) has been shown to reduce the power to detect association in genetic studies. However, it is conceivable that complex traits are heterogeneous with respect to individual genetic susceptibility and disease pathophysiology, and that the effect of heterogeneity has a larger magnitude than the effect of phenotyping errors. Although an intuitively clear concept, the effect of heterogeneity on genetic studies of common diseases has received little attention. Here we investigate the impact of phenotypic and genetic heterogeneity on the statistical power of genome wide association studies (GWAS). We first performed a study of simulated genotypic and phenotypic data. Next, we analyzed the Wellcome Trust Case-Control Consortium (WTCCC) data for diabetes mellitus (DM) type 1 (T1D) and type 2 (T2D), using varying proportions of each type of diabetes in order to examine the impact of heterogeneity on the strength and statistical significance of association previously found in the WTCCC data. In both simulated and real data, heterogeneity (presence of “non-cases”) reduced the statistical power to detect genetic association and greatly decreased the estimates of risk attributed to genetic variation. This finding was also supported by the analysis of loci validated in subsequent large-scale meta-analyses. For example, heterogeneity of 50% increases the required sample size by approximately three times. These results suggest that accurate phenotype delineation may be more important for detecting true genetic associations than increase in sample size. Phenotypic misclassification reduces substantially the power to detect association, particularly in case-control studies It is also possible that heterogeneity contributes to the discrepancy between the heritability estimates of complex diseases and the proportion of phenotypic variance explained by the identified loci in genome-wide association studies (GWAS). Indeed, the estimated effect sizes of genetic associations in GWAS of complex traits are significantly reduced by imprecise phenotyping st century.Little attention has been given so far to the extent of the effect of heterogeneity on genetic association findings in common complex diseases. Testing the impact of heterogeneity on GWAS findings requires extensive knowledge of the pathophysiology and genetic architecture of the common trait under study. This assumption makes psychiatric disorders unsuitable for such analysis. On the other hand, another common disease such as diabetes mellitus (DM) is suitable for testing the impact of heterogeneity. The two types of DM were distinguished only in the late 1930s Here we investigate the impact of heterogeneity on the statistical power of GWAS. To do so, we first performed a computer simulation study. Next, we analyzed the Wellcome Trust Case-Control Consortium (WTCCC) data for DM T1D and T2D. We combined varying proportions of individual data from each of the diabetes subtypes to examine the impact of heterogeneity on the strength and statistical significance of association and compared these results with those previously found in the WTCCC study. Heterogeneity reduced the statistical power to detect genetic association and greatly decreased the estimates of risk attributed to genetic variation.−8. The sample size obtained at each iteration of the simulation was specified according to a binary search that terminated once 90% power  was achieved, or when the sample size limit of 1,000,000 was reached. In the second set of simulations, we studied the impact of β on the statistical power to detect association at p<5×10−8. To this end we generated 10,000 cases and controls, replicated 1,000 times, for each combination of parameters. For each genetic model (dominant and multiplicative) we obtained case-control frequency tables. Using χ2 and the Cochran-Armitage-Trend-Test (CATT) module implemented in R we calculated p-values and odds ratios (ORs) for increasing levels of β.To study the impact of heterogeneity on GWAS findings, we simulated case-control data assuming increasing (from 10% to 90% in 10% steps) phenotypic admixture. Admixture (indicated as β) was the proportion of “non-cases” (i.e. controls) in the case group. Specific genetic models of disease prevalence were used in order to simulate genotypes for case and control populations. We used two basic single-locus genetic models: dominant We accessed and downloaded all of the genotypic data available for the two control populations (the 1958 Birth Cohort (58C) and the UK National Study (NBS)) and for the T1D and T2D cohorts from the WTCCC website.−7  A number of quality control (QC) steps were performed on this data in the original WTCCC GWAS study Since the QC analysis in the original study was performed across ∼14,000 subjects , we also applied exclusion lists supplied in the WTCCC data in addition to in-house QC. The scripts used for QC are available online.2) to confirm the validity of the QC steps using PLINK Two recoded phenotype files were created each containing 2,938 control individuals  and the 1,963 T1D or the 1,924 T2D cases, respectively. Next, we performed the WTCCC standard case-control association analysis  and are both associated with T2D. Further, we studied 21 and 16 polymorphisms found associated in subsequent large-scale meta-analyses for T1D −6 in at least one meta-analysis study. We created alternate phenotype files in order to simulate heterogeneity. Let N1 and N2 denote the respective totals of T1D and T2D cases. At each 10% increment of β, we removed N1*β subjects randomly selected from the T1D population and replaced them with N1*β subjects randomly chosen from the T2D population. Similarly, we analyzed T2D data, replacing N2*β T2D with T1D cases. For each of T1D and T2D, 100 alternate samples were created at each 10% increment of β. Association analyses were then run using the χ2 test in PLINK http://web.cs.dal.ca/~cullis/heterogeneity/.To investigate the effect of heterogeneity, we examined the 20 SNPs most significantly associated with T1D or T2D, respectively. These SNPs are independent and in linkage equilibrium to each other, with the exception of rs9939609 and rs7193144 within the FTO gene which are in strong linkage disequilibrium  reduced both the statistical power as well as the observed risks attributed to susceptibility alleles or genotypes. These findings were supported by the analysis of both simulated case-control and GWAS data from WTCCC T1D and T2D cohorts Several findings deserve comment. First, irrespective of the various parameters and genetic models tested, the absence of heterogeneity in samples allows for a power to detect association that would require a far larger sample size if a medium or high level of heterogeneity were present. A recent study examining the impact of diagnostic misclassification in genetic studies by Wray et al. In the absence of more reliable measures (for instance diagnostic tests) in more heterogeneous complex traits – including many psychiatric and neurological diseases – researchers have obtained promising results by selecting more homogeneous subgroups of patients such as responders to lithium treatment in BD We have also shown that the presence of heterogeneity strongly influences the estimates of the effect sizes. This result suggests that the effect sizes of marginally significant variants identified in GWAS might be larger if they were instead examined in more homogeneous samples. This is in agreement with previous studies pointing to the importance of accurate and stringent phenotypic definition in GWAS data Here we observed that as the degree of heterogeneity increased, so did the minimum sample size required to achieve sufficient statistical power. This effect was particularly evident for genotypic relative risk values on the order of 1.2 and 1.5 and for common variants (MAF>0.05). Interestingly, for a complex trait such as BD, most of the reported genetic risk variants have an associated effect size of approximately 1.5 or below In conclusion, we demonstrated that heterogeneity can have a major impact on GWAS findings. The extent of its effect is of large magnitude and, unexpectedly, affects significantly even loci robustly associated with the trait under study. We showed that even a relatively low proportion of “non cases” (20%) can dilute the observed genetic effect size for common variants (with MAF>0.05) targeted in the current GWAS analyses. The partial failure of GWAS to detect a substantial proportion of the heritability of genetic complex diseases could be a consequence of the presence of a high degree of heterogeneity.Figure S1Impact of the admixture of diabetes type 1 (T1D) and type 2 (T2D) on Wellcome Trust Case-Control Consortium (WTCCC) T1D findings confirmed in large scale meta-analyses [−log]. SNP = single nucleotide polymorphism; β = admixture; nr = not reported.(TIF)Click here for additional data file.Figure S2Impact of the admixture of diabetes type 1 (T1D) and type 2 (T2D) on Wellcome Trust Case-Control Consortium (WTCCC) T2D findings confirmed in large scale meta-analysis [−log]. SNP = single nucleotide polymorphism; β = admixture; nr = not reported. *p-value reported in the Zeggini et al. (TIF)Click here for additional data file.Table S1−8 with increasing levels of admixture (β). Results are presented for dominant and multiplicative genetic models with the following parameters: population prevalence for the disorder , minor allele frequency (MAF) , and the relative risk of the disorder for the minor allele .Results of case-control simulation to determine the minimum sample size needed to detect an association in 90% of trials at a significance level set at p<5×10(XLS)Click here for additional data file.Table S2−8. Results are presented for dominant and multiplicative genetic models with the following parameters: population prevalence for the disorder , minor allele frequency (MAF) , and the relative risk of the disorder for the minor allele .Case-control simulation results of the impact of increasing level of admixture (β) on the statistical power to detect association at p<5×10(XLS)Click here for additional data file.


Regional-based association analysis instead of individual testing of each SNP was introduced in genome-wide association studies to increase the power of gene mapping, especially for rare genetic variants. For regional association tests, the kernel machine-based regression approach was recently proposed as a more powerful alternative to collapsing-based methods. However, the vast majority of existing algorithms and software for the kernel machine-based regression are applicable only to unrelated samples. In this paper, we present a new method for the kernel machine-based regression association analysis of quantitative traits in samples of related individuals. The method is based on the GRAMMAR+ transformation of phenotypes of related individuals, followed by use of existing kernel machine-based regression software for unrelated samples. We compared the performance of kernel-based association analysis on the material of the Genetic Analysis Workshop 17 family sample and real human data by using our transformation, the original untransformed trait, and environmental residuals. We demonstrated that only the GRAMMAR+ transformation produced type I errors close to the nominal value and that this method had the highest empirical power. The new method can be applied to analysis of related samples by using existing software for kernel-based association analysis developed for unrelated samples. Genome-wide association studies (GWAS) identified a large number of loci involved in the control of complex traits. However, the results of these studies can explain only a small proportion of trait heritability Usually, region-based tests use different methods of collapsing rare variants within a region of interest. In this case, a set of rare variants in the region is replaced by a single genetic variable which can then be tested for association with the help of conventional GWAS methods A new kernel machine regression-based method was recently proposed for conducting regional association analysis Here, we describe a new kernel-based association analysis method for genetically related samples, which is based on a transformation of trait values. This method analyzes related samples by using existing software developed for unrelated samples.y be described by the linear regression mixed modelμ is the trait's mean; gβ is the impact of marker genotype g on quantitative trait; u is polygenic component and е is a random environmental effects.Let inheritance of a quantitative trait R is a pairwise relationship matrix. Relationship coefficients are defined by a pedigree structure of the sample, or are estimated from the genomic data We assume that the quantitative trait follows multivariate normal distribution with vector of meansM SNP markers, the kernel-based score test statistic Q is defined as a weighted sum of the individual score statistics mw is a weight of thm individual marker.In the analysis of the genomic region including a set of m is defined as:N is a size of the sample, The score statistic for testing association between trait and genotypes of given marker Here we introduce such transformation of phenotype values, To obtain mγ is scalar introduced asThe formulas (4) are expressed through two vectors Since M) of the genetic loci of small effect, the values of mγ for different markers do not differ significantly one from another and may be approximated by averaged value ash2, total variance σ2, and the relationship matrix RRecently we demonstrated that when a trait of interest is controlled by a large number (The vector http://www.genabel.org/ for the GenABEL project web-site).Thus the proposed phenotype transformation allows us to perform the association analysis of genetically related samples using simple linear regression applied in analysis of unrelated samples. GRAMMAR+ transformed traits can be calculated in the ‘polygenic’ procedure in the GenABEL package v 1.7–2 or later  study, which is embedded in a young genetically isolated Dutch population P values not exceeding a given threshold.SNP markers were analyzed as 23,384 regions obtained with a sliding window of 20 markers shifting by 10 markers. The kernel-based analysis and the trait transformations applied were the same as for the GAW17 data. Genomic kinship was used to run polygenic model and to construct the principal components. The type I error was calculated as a proportion of Type I errors for the analysis of the original traits, GRAMMAR+ trait transformation, and environmental residuals are shown in When phenotypes were analyzed without PCs as covariates, the type I errors deviated further from the nominal level. The analysis of original traits and GRAMMAR+ trait transformations became more liberal and that of the environmental residuals became even more conservative .t-test P values<0.001 and 0.01 for Q1 and Q2, respectively).The estimates of empirical power for Q1 and Q2 are shown in We compared the empirical  and nominal  power for the original data, GRAMMAR+ transformations, and environmental residuals . NominalP value is estimated by using two approaches, one based on non-central chi-square distribution and other based on bootstrap resampling. We compared P values obtained by these two approaches by using the first simulation of Q1 trait and demonstrated that they produce very close estimates for all variants of the trait presentation . This method was proposed to correct the population structure under the kernel-based association analysis Therefore, none of the known approaches can correct the distribution of the test statistic under the null hypothesis when original traits or environmental residuals are analyzed by using kernel-based methods developed for samples of unrelated individuals. A special method for kernel-based association analysis of related samples was recently proposed by Schifano et al. Figure S1Nominal versus resampling P value for different trait variants.(PDF)Click here for additional data file.Table S1Type I errors for three GAW17 traits analyzed with SKAT.(PDF)Click here for additional data file.Table S2Empirical power at causal genes for various trait presentations of Q1 analyzed with SKAT.(PDF)Click here for additional data file.Table S3Empirical power at causal genes for various trait presentations of Q2 analyzed with SKAT.(PDF)Click here for additional data file.Table S4Type I errors for human height, body mass index (BMI), high- and low-density lipoprotein cholesterol , total cholesterol (TC) and triglyceride (TG) levels analyzed with SKAT.(PDF)Click here for additional data file.