The code base for this project was written primarily in the Octave programming language, but it is being ported to the R language and developed into a larger project for general genetic simulation called GenetSim . All of the source code that was used to generate the GAW 15 Problem 3 data is freely available for download at .Data for Problem 3 of the Genetic Analysis Workshop 15 were generated by computer simulation in an attempt to mimic some of the genetic and epidemiological features of rheumatoid arthritis (RA) such as its population prevalence, sex ratio, risk to siblings of affected individuals, association with cigarette smoking, the strong effect of genotype in the HLA region and other genetic effects. A complex genetic model including epistasis and genotype-by-environment interaction was applied to a population of 1.9 million nuclear families of size four from which we selected 1500 families with both offspring affected and 2000 unrelated, unaffected individuals all of whose first-degree relatives were unaffected. This process was repeated to produce 100 replicate data sets. In addition, we generated marker data for 22 autosomes consisting of a genome-wide set of 730 simulated STRP markers, 9187 SNP markers and an additional 17,820 SNP markers on chromosome 6. Appropriate linkage disequilibrium between markers and between trait loci and markers was modelled using HapMap Phase 1 data  HLA-DRB1 (OMIM: 142857) on chromosome 6 is extraordinarily strong and well established. In terms of environmental contributors to risk, we know that cigarette smoking is positively associated with RA. Two quantitative traits measured from serum, anti-cyclic citrullinated peptide (anti-CCP) and immunoglobulin M (IgM), are often elevated in RA. Much more is known about RA, but we focused our simulation on the features of the illness and its covariates listed here. Anything else that was known about RA genetics was ignored and we created a genetic model that we hoped would provide interesting data for Genetic Analysis Workshop participants.The plan for this data simulation was to mimic the epidemiology and familial pattern of rheumatoid arthritis (RA), a complex genetic disease with several loci contributing to susceptibility. We took into account the following facts about RA epidemiology when choosing parameters for the simulation. The lifetime morbid risk of RA is roughly 1%, but risk in women is about triple the risk in men. Severity of illness is variable in RA but age of onset is only weakly related to disease severity and mortality is only slightly increased in RA. The risk to siblings of affected people is about five to ten times the risk in the general population, which suggests some genetic influence, and we know that the contribution of variation at In the simulation of trait loci and genetic marker data for linkage studies, it is very difficult to provide an appropriate model of linkage disequilibrium (LD) between loci, including both markers and trait loci. In many earlier GAW simulations, interest was primarily in linkage analysis and it was acceptable for all loci to be in linkage equilibrium. Interest today has shifted much more to association analyses using large numbers of single-nucleotide polymorphism (SNP) markers. For simulated genetic data to be useful, the simulation must include an appropriate LD model. Our approach was not to model LD explicitly but to use real SNP haplotype data from the HapMap project to provide appropriate local LD patterns. By recombining HapMap haplotypes in a realistic way, it is possible to produce large numbers of different chromosome-long haplotypes that retain the LD pattern of the original HapMap data over short intervals  but show much more haplotype diversity over longer intervals  than is observed in HapMap because of HapMap's limited sample size (120 haplotypes per ethnic group). In our simulation, every allele, whether marker allele or trait-locus allele, has an ancestral origin on one of the 120 CEPH European (CEU) HapMap haplotypes and this ancestry is what determines local LD patterns. so that the simulation process can be studied in detail by any interested reader. None of the software used in this project is proprietary or unavailable.After GAW15 participant manuscripts had been submitted for publication we discovered that there were several small errors in the Problem 3 simulation, none of which were noticed by participants. These errors were mostly trivial mistakes in the positions of some markers and trait loci and in the heterozygosities of the STRP markers. We present the simulation parameters below as they were presented to the GAW participants, but we note with asterisks any values that turned out to be incorrect and we then present the correct values. The most important error was in the positioning of Locus D relative to Locus DR/C: We intended for there to be only a 5 cM distance between those two loci on the sex-averaged map, but due to an error in the code for generating recombination in that region, the interval was roughly doubled to about 10 cM. This error should have almost no effect on association analyses because LD patterns were not affected. Marker order was always presented correctly. Another way to conceptualize the problem is that some of the map locations were presented incorrectly but the data were otherwise correct. All of our source code and other information about the Problem3 data is freely available at We used a two-stage simulation process in which the first stage consisted of generating a large population of families with affection status, and the second stage consisted of generating full data for a much smaller number of families, selected based on affection status. Both stages were repeated 100 times to produce 100 replicate data sets.We generated a large population of 1.8 million nuclear families, each consisting of two parents and two offspring, with RA affection status determined by the complex genetic/environmental model described below. At this stage of the analysis we generated for every family only the variables that were needed to determine affection status. These variables included age, sex, smoking status, IgM, and the trait loci described below. We did not determine patterns of recombination at this stage except in the regions between pairs of trait loci that were on the same chromosomes nor did we generate any marker data. For trait loci, we determined both the alleles and the HapMap haplotypes from which those alleles were derived. It was necessary to retain that haplotype data so that we could generate markers in LD with the trait loci in the second stage of the simulation process.From the large population of families generated in Stage 1, we retained a random sample of 1500 families with an affected sibling pair (ASP) and we retained a random sample of 2000 control families in which none of the four members were affected. We then generated for the selected families all data, including marker data, that had not been generated in the first stage of the simulation. Use of this tactic required that the second stage of simulation was conditional on the results of the first stage. All 22 human autosomes were simulated. Information about the marker data is given below.We present data on phenotypes and marker genotypes for all members of the 1500 ASP families and on one randomly selected offspring from each of the 2000 unaffected control families . Those data were shared with all GAW15 participants who requested Problem3 data, and for those participants who requested the answers, we also made available all trait-locus genotypes and latent traits that were used to generate observed quantitative traits.Table The model uses a constant hazard function to determine risk of RA. We planned at first to determine age at onset according to this exponential survival model, but it turned out that age of onset was then too strongly linked to some loci. We then retained the hazard approach but gave every individual the same risk period and the same "base hazard" (exponentiated intercept term). Therefore, multiplying hazard by some value is equivalent to multiplying risk by that value and the terms "risk" and "hazard" are used somewhat interchangeably below. Once hazard was known for a subject, we used the hazard to determine the mean of an exponential random variable. If this variable was less than a fixed threshold value , the subject was affected. The values of the base hazard and threshold are arbitrary, but they jointly determine population prevalence. Also see the section "RA affection status" under "Modeling phenotypes" below.We imitated the HLA-DRB1 locus and its effects somewhat but not in great detail. We will refer to our simulated locus as "DR". Our model includes three DR alleles. DR is in strong LD  and complete linkage (0 recombination fraction) with Locus C. DR effects are independent of locus C effects, but DR effects are epistatically controlled by Locus A. In females only, each C allele increases risk by a factor of 2.1 . Females with no C alleles (cc) have no increased risk. The allele frequency for C is 0.5. DR/C haplotypes are shown in Table Locus A affects the impact of HLA-DR types in a dominant fashion. Individuals with Aa or AA genotypes have their hazard multiplied by a value that is determined by their DR type according to the "Risk Multipliers" Table . A valueIn smokers only, Bb or BB genotype multiplies RA risk by 1.5. This has the effect that smokers have no directly increased risk if their genotype is bb, but they still have some indirectly increased risk through the effect of smoking on IgM. The allele frequency for allele B is 0.35.Locus D has a direct effect on RA risk but a low allele frequency. Each D allele multiplies hazard by 5. The D allele frequency is only 0.0083 .This locus has a strong direct effect on RA hazard, multiplying by 2.2 for each E allele (2.2 for Ee and 4.84 for EE). Locus E also affects anti-CCP by controlling which DR genotypes place a subject in the "high-mean" anti-CCP group . For DR4 homozygotes only, having one or more E alleles puts them in the group with a high mean anti-CCP level. Thus, the high-mean group for anti-CCP consists entirely of DR4 homozygotes with either Ee or EE genotypes. The frequency of the E allele is 0.25.An additive effect of locus F causes 30% of the variance in IgM. Mean values of IgM are proportional to number of F alleles. The frequency of the F allele is 0.5.These two diallelic loci have allele frequencies of 0.1 and 0.2, respectively, and each contributes an additive genetic effect that accounts for 25% of the variance of latent severity . These loci are about 2 cM apart on chromosome 9, but they are not in LD. Thresholds on latent severity are used to produce observed severity.Ages for pairs of siblings were drawn from a bivariate normal distribution having parameters similar to pairs of affected siblings in real RA data we were given , but pairs were retained only if both ages were between 18 and 87. The mother's age at the birth of the oldest sibling was uniformly distributed between 20 and 30 years and the father's age was equal to the mother's age plus a triangular random variable with a range from -1 to 5 and a mean of 2. This kept all ages reasonable and within acceptable ranges. The age reported for deceased individuals is the age they would have been at ascertainment of their oldest child, if they had lived. Age at death is also reported for deceased parents.The sex of offspring was determined by age from published census data on sex ratio by age.All offspring are living. The variable "dead" has value 1 for parents who were deceased at the time of ascertainment, and value 0 for parents who were living. A parent was determined to be dead based on 2002 Centers for Disease Control (CDC) mortality statistics for 10-year age classes. We applied a constant hazard within all but the oldest age group and started at the age of the parent when the youngest child was born. In the oldest age group (85 to 100 years), the density for age at death had a linear form with the mode at 85 and zero density at 100, limiting longevity to age 100. We present data for dead parents as if they were alive. Age at death is provided. RA has a small mortality effect. The age of death for affected parents is on average 2 years  earlier than expected.Affection was determined by taking a fixed threshold on an exponential random variable . The mean of the exponential random variable  was determined by multiplication of risk factors. More precisely, the log-hazard was modeled as a linear function of risk factors and the individual exponential mean was 1/exp(log-hazard). This is a proportional hazards model with constant hazard and fixed follow-up time. Mortality and age were ignored in determining affection status. Variables and parameters that determined hazard are described below.This was based on an age-dependent threshold model. A normal  random variable was generated for every subject such that variance was due to additive polygenic (50%), shared environmental (40%), and non-shared environmental (10%) influences. These numbers were based on results of a published twin study. Parents were genetically independent. Thresholds were determined by age according to CDC data so that individuals whose normal value exceeded a threshold were considered to be lifetime smokers at a probability appropriate for their age.We generated a latent IgM value from a normal mixture with means determined by Locus F. Variance in latent IgM is caused by smoking status (24%), additive effect of Locus F (30%), and a residual (46%), with the residual variance being divided between additive polygenic (60%), and non-shared environmental (40%) components. The IgM latent variable was transformed monotonically to fit the distribution of IgM in real RA data.Locus E and HLA-DR genotype jointly created 10.3% of the variance in anti-CCP as described in the "Locus E" section above. The remaining variance was caused by additive polygenic (60%), and non-shared environmental (40%) components. The anti-CCP latent variable was rank rescaled using the observed distribution of values in the RA reference data to create the final anti-CCP values.Severity was determined by two diallelic loci  with additive effects. Each of the loci accounts for 25% of the total variance. The remaining variance (50%) is due to an individual random environment effect. There are 5 severity classes, each containing 20% of the affected persons.The age of onset (for affected offspring) was created from an "onset" latent variable that equally weighed the hazard, latent severity, and an independent random variate. This variable was converted to ranks and used with real RA data to derive a "proportion of life affected," which multiplied by the ascertainment age, yielded the age of onset.There is a residual effect on the log-hazard for RA that is composed of shared environment effect (85% of variance) and a non-shared environment effect (15%). The shared environment effect is a constant multiple of a Bernoulli-distributed random variable and it is shared by all members of a family in 30% of families. The non-shared environment effect was normally distributed. The convolution (sum of the two variables) was a normal mixture with a standard deviation of 2.079.Smoking affects RA risk both directly with Locus B moderation and through its effect on IgM.Age affects RA risk through its affect on smoking and through its effect on the sex ratio. Age affects mortality, but only in the parents, and we report affection status regardless of mortality.Nearly all of the sex effect in RA risk comes from Locus C, but the sex ratio in the general population, which was based on CDC data, also has an effect in the offspring generation.We present markers on 22 autosomes that were designed to be like real human autosomes in terms of genetic and physical map lengths, but we did not generate data for sex chromosomes. The markers were presented in three sets:1. A set of 730 microsatellite markers, fairly evenly spaced on chromosomes with an average inter-marker distance of about 5 cM and with heterozygosities always exceeding 0.70 .2. A set of 9187 SNPs distributed on the genome to mimic an Affymetrix 10 K SNP chip set but without monomorphic SNPs. Because these SNPs were derived from 120 HapMap haplotypes, all SNP allele frequencies were integer multiples of 1/120 (0.0083) and the lowest frequency was precisely 1/120.3. A very dense map of 17,820 SNPs on chromosome 6 . The chromosome 6 dense map includes 210 of the markers from the 10 K SNP map (they are easily identifiable because they have the same names in both sets).Offspring haplotypes were generated by dropping genes from parental haplotypes in the usual Mendelian fashion and assuming a Haldane model (no interference). Parental haplotypes were derived by recombining the 120 HapMap CEU haplotypes under the assumption of Hardy-Weinberg conditions and assuming 30 generations of random mating from a large population where the 120 HapMap haplotypes initially had equal frequency. This was done by generating a Poisson-distributed random variable with a mean of 30 times the length of the chromosome in Morgans and then distributing uniformly along the chromosome the Poisson-distributed number of recombination points. To every interval between recombination points, one of the 120 HapMap haplotypes is then assigned at random. Any regions that held a trait locus had to be assigned in Stage 2 of the simulation whichever HapMap haplotype was assigned to the trait locus in Stage 1.We provided more information in the simulated data than one would ordinarily have in real data. These special features of the data include the following:Marker data are usually missing on some family members, especially those who died before the family was ascertained. We provide marker data on all family members. Researchers who would like their data to be more realistic can delete marker information from deceased individuals. By supplying data that would normally be missing, we provide more opportunity to test effects of missingness, etc.We did not model any errors in the data simulation. In real data there are typically some errors in genotyping and sometimes there are sample mixups. By not modeling any errors, we make it possible for the analyst to simulate his own errors and test the effect of genotyping error on other aspects of a genetic analysis. We also added no errors to phenotypes.The allele inherited from the father is always presented on the left side within every genotype. This allows researchers to determine haplotypes for all subjects and to determine their parental origin. In real data, it is usually not possible to know haplotypes or their origin, but new methods have made molecular haplotyping possible and it is currently being used. So, in real data we can sometimes know haplotypes, but the parental origins of those haplotypes still must be inferred.We analyzed the data from a randomly selected general population of 1.8 million families in our Stage 1 simulation to see that our epidemiological parameters had the correct values. The results for 1.8 million sibling pairs (3.6 million subjects) generated using the model we developed are shown in Table The sibling relative risk is the lifetime prevalence in siblings of affected individuals (proband-wise concordance) divided by the lifetime prevalence in our simulated general population. The numbers in Table .After generating the Problem 3 data we undertook a series of genetic analyses to check the data for flaws. We were satisfied, despite the very pronounced affect of the HLA locus on RA. This effect may be too large, but it does reflect the actual effect found in real RA data. The results of these analyses are available at The use of software developed in an interpreted language such as Octave  or R 2]2] can be about the Problem 3 data, including the full source code used to produce it, and we will continue to update that web page if more information becomes available about the data . Because we stored the seeds used to generate the Problem 3 data, it is theoretically possible to reproduce it in its entirety. We have done this but it does require a computer with considerable amounts of RAM (maybe 10 GB). We are adding code on our web page that will allow users to generate smaller data sets under the same model and thus circumvent the memory requirement.The data contained a few small errors, but these probably did not have important effects on GAW15 participant research. We provide information on our web page at The author(s) declare that they have no competing interests.


The goal of this analysis is to compare different test strategies for genetic association in case-control studies using related individuals. The first test is the trend test that is corrected for related individuals on the basis of identity-by-descent information. The second approach is to use generalized estimating equations to adjust for the correlation between relatives, and the third is the multiple outputation method. We compare the power of these test strategies in a simulation study, and apply these methods to a candidate gene dataset of Genetic Analysis Workshop 15 from the North American Rheumatoid Arthritis Consortium. The case-control design is a widely used and powerful approach for genetic association studies ,2. GenotDifferent methods may be used to evaluate genetic associations of candidate genes in case-control studies when some individuals (cases or controls) are related. We briefly sketch three of these methods, the Cochran-Armitage trend test corrected for identity-by-descent (IBD) information, the generalized estimating equations method, and the multiple outputation method. Little is known about their relative efficiency and performance. We compare their power in a simulation study and apply these methods to the candidate gene data of Genetic Analysis Workshop 15 (GAW15) from the North American Rheumatoid Arthritis Consortium (NARAC), which contains affected sibs with rheumatoid arthritis and unrelated controls.N and M, where N is a normal allele and M is a risk allele or is in linkage disequilibrium with a risk allele. Denote genotypes as g0 = NN, g1 = NM, and g2 = MM. Let the genotype frequencies for cases and controls be pj and qj, j = 0, 1, 2, respectively. Hence, the null hypothesis of no association is pj = qj for each j.Consider data for a case-control study of genetic association as in Table Zx = U(x)/U(x) = x = T is a set of increasing scores (weights) assigned to the three genotypes  a priori based on the underlying genetic model. Under the null hypothesis, Zx asymptotically follows a standard normal distribution N.Given the data in Table ui = T be the genotype indicator vector for the ith case, where uij = 1 for the ith case with genotype gj and uij = 0 otherwise, i = 1,...,R. Similarly, we use vj for controls. Then φ = R/n. Then the above test statistic is U(x) = xT [(1 - φ)r - φs], and var[U(x)] = xT{var[(1 - φ)r - φs]}x = However, because cases and controls within the same family may be biologically related, Slager and Schaid  proposedHere the variance and covariance terms can be calculated based on the multinomial distributions and IBD-sharing probabilities for pairs of related individuals .ni related subjects, i = 1,...,m, where m is the total number of families. For a binary trait, yij = 1 for cases and 0 for controls. The logistic regression model can be considered for the case-control data in Table E(yij)/(1 - E(yij))] = β0 + β1xij + wij, where xij = x0, x1, or x2 is the score assigned to the genotype as above, and wij denotes other covariates. The test of genetic association is equivalent to the test of β1 = 0. Due to correlation of related family members, the conventional methods assuming independence are incorrect. The estimate and standard error for β =  and Vi = Vi denoting the "working" covariance matrix of yi. The estimate of β is asymptotically normally distributed and its variance is given by Vi and it has been shown that the GEE estimates are valid and consistent even if the working covariance matrix is misspecified. For family or affected sib-pair data, a simple and reasonable choice is the exchangeable correlation matrix with a common correlation θ for each pair of relatives [The GEE developed by Liang and Zeger  for the elatives .2. For example, the trend test statistic Zx above is a sensible choice, which estimates the weighted differences of the genetic frequencies. For case-control data sampled from families, a new sample can be obtained by randomly selecting an individual from each family, and then 2 can be computed based on this new sample. After repeating this multiple times, the estimate of association will be the average of the 2 minus the sample variance of the The MO method proposed by Hoffman et al.  and FollK, is 0.1, the marker allele frequency, p, is 0.3, and Hardy-Weinberg equilibrium holds. To facilitate the calculation, each case-control data set included 200 cases generated as 100 affected sib pairs drawn from 100 different families, and 200 unrelated controls. Let the genotype relative risks RR1 = f1/f0, and RR2 = f2/f0, where f0, f1 and f2 are the penetrances for genotypes g0, g1, and g2. Thus, equivalently, the null hypothesis can be written as RR1 = RR2 = 1. The alternative hypothesis can be specified by varying RR1 and RR2.To compare the performance of the three methods, we conducted a small simulation by generating case-control data sets and computing the empirical power for all the tests under three genetic models: recessive, additive, and dominant. The simulations were similar to those performed by Tian et al.  with 10,ZIBD-Tr), the tests based on the GEE estimate (ZGEE), and the MO estimate (ZMO). The relative risks RR1 and RR2 were chosen so that a particular trend test had about 85% power for each given model. The scores  =  for the additive model were used for the three tests in the simulations assuming the underlying model was unknown. Under the null hypothesis of no association, all three tests have the correct type I error, around 0.05. For all three genetic models, both the GEE and MO tests have relatively good power, ranging from 73% to 84%, compared with the IBD-corrected trend test.Table PTPN22 locus [The GAW15 NARAC candidate gene data consisted of affected sibs with rheumatoid arthritis from multiplex families and unrelated controls. The candidate gene data from the 22 locus  had 14 S22 locus .p-value less than 0.05 in any one of the tests are presented. All three test methods identified the same markers that were significantly associated with the susceptibility of rheumatoid arthritis. The unadjusted trend test that assumed independent cases overestimated the association and could result in a larger false-positive rate.Table We consider three methods that use completely different approaches to account for correlation among family members. The IBD-corrected trend test requires the genotype information from parents or other family members to obtain more accurate IBD calculation. Because the variance of the test is corrected for correlation among related cases using the genealogy and marker information, this test is expected to be more powerful than the tests using only family pedigree information. The GEE approach estimates the correlation among related cases through a working correlation matrix, and the MO accounts for the correlation through repeated sampling. In our simulation study, the GEE and MO approaches appear to have similar power. Note that Follmann et al.  showed tNote that these methods used in case-control studies are sensitive to population stratification. In genetic association studies, case-control and family-based designs are two fundamentally different approaches. While case-control designs study the contrast of allele/genotype frequencies between cases and controls to identify associations within populations, family-based designs use families to look for susceptibility alleles through transmission within families. Thus, when population stratification is suspected, family-based designs are preferred to case-control designs. For such designs, the well known transmission disequilibrium test (TDT) and its various extensions, such as the family-based association tests (FBATs), are commonly used ,12. Theyx =  indicating the numbers of risk alleles. Applying a trend test with one set of scores would result in a loss of power if the genetic model is misspecified. Hence, more robust tests can be considered to protect against model uncertainty [The test results from the three methods depend on the scores assigned to the genotypes based on the assumption of the underlying genetic models such as recessive, additive, and dominant. In practice, since the genetic model is unknown for most complex diseases, the additive model is usually assumed first, with ertainty .In summary, we compare three methods of testing genetic association for case-control studies with cases drawn from families and unrelated controls. Our results indicate that all three methods perform well, and their performance is comparable in the simulation and application to the GAW15 NARAC data. All three methods can be applied to more general situations where the controls or both cases and controls are also correlated.FBAT: Family-based association testGAW: Genetic Analysis WorkshopGEE: Generalized estimating equationIBD: Identical by descentMO: Multiple outputationNARAC: North American Rheumatoid Arthritis ConsortiumSNP: Single-nucleotide polymorphismTDT: Transmission-disequilibrium testThe author(s) declare that they have no competing interests.


Genet. Epidemiol. 34: 188–193, 2010. © 2009 Wiley-Liss, Inc.Genome-wide association (GWA) studies have proved to be extremely successful in identifying novel common polymorphisms contributing effects to the genetic component underlying complex traits. Nevertheless, one source of, as yet, undiscovered genetic determinants of complex traits are those mediated through the effects of rare variants. With the increasing availability of large-scale re-sequencing data for rare variant discovery, we have developed a novel statistical method for the detection of complex trait associations with these loci, based on searching for accumulations of minor alleles within the same functional unit. We have undertaken simulations to evaluate strategies for the identification of rare variant associations in population-based genetic studies when data are available from re-sequencing discovery efforts or from commercially available GWA chips. Our results demonstrate that methods based on accumulations of rare variants discovered through re-sequencing offer substantially greater power than conventional analysis of GWA data, and thus provide an exciting opportunity for future discovery of genetic determinants of complex traits.  ABCA1, APOA1 and LCAT have been demonstrated to contribute collectively to low plasma levels of high-density lipoprotein cholesterol [Recent advances in whole genome genotyping technologies, the availability of large, well-defined population-based disease cohorts, and a better understanding of common human sequence variation, coupled with the development of appropriate quality control and analysis pipelines, have led to the identification of many novel common genetic determinants of complex traits . Neverthlesterol .http://www.1000 genomes.org) soon reaching completion. Furthermore, large-scale deep re-sequencing technologies are becoming increasingly efficient and cost effective, and thus may soon be realistic for rare variant discovery in specific genes in large disease or population-based cohorts. We have developed a novel test of association with rare variants discovered through such re-sequencing efforts, based on the accumulation of minor alleles within the same functional unit, for example a gene-coding region extended up and downstream to incorporate additional functional elements and the regulatory region. We have then undertaken a simulation study to focus on two distinct, but timely, scenarios with the aim of addressing specific, as yet unanswered, methodological questions in each. First, when deep re-sequencing data are available to discover rare variants, do methods based on accumulations of minor alleles within the same functional unit offer greater power to detect association with complex traits than traditional analysis of SNPs on GWA chips? Second, when only GWA chip data are available, what is the most powerful strategy for identifying rare variant associations with complex traits?Currently, most studies of rare variants utilise data from commercially available GWA chips, which are far from ideal since they are designed for capturing common human genetic variation. However, the availability of data more appropriate for rare variant association analysis is just around the corner, with whole genome re-sequencing efforts, such as the 1,000 Genomes project , andConsider a sample of unrelated individuals, phenotyped for a normally distributed trait, and typed for rare variants in a gene or small genomic region. Let ix denotes a vector of covariate measurements for the ith individual, with corresponding regression coefficients β. The parameter λ is the expected increase in the phenotype for an individual carrying a full complement of minor alleles at rare variants compared to an individual carrying none. As an alternative, we can model the expected phenotype of the ith individual asIn this expression, i)I, is weighted by in to allow for differential call rates between samples. We denote the likelihood ratio test based on the proportion of rare variants at which an individual carries minor alleles by RVT1, and that based on the presence/absence of at least one minor allele at any rare variant by RVT2. Both RVT1 and RVT2 can be generalised to tests of association with a binary trait within a logistic regression-modelling framework.We thus construct likelihood ratio tests of association of an accumulation of rare variants with disease by comparing the maximised likelihoods of two models via analysis of deviance: (i) the null model where λ = 0; and (ii) the alternative model for which λ is unconstrained. The contribution of the any causal variant; and (ii) the mean trait value determined by the proportion of causal variants at which a minor allele is present. Trait association models were then parame-terised in terms of: (i) the maximum MAF of any individual causal variant; (ii) the total MAF of all causal variants; and (iii) their joint contribution to the phenotypic variance. Full details of the simulation process are described in the Appendix.In order to evaluate the relative merits of different analytical approaches to identify rare variant associations with a quantitative trait, we have performed simulations using simple models of population genetics to generate high-density haplotype data in a 50-kb genomic region used to represent a functional unit of interest. We considered a range of models for association of the trait with multiple causal variants in the same region, under two different assumptions: (i) the mean trait value is determined by the presence or absence of a minor allele at We began by simulating a population of 40,000 haplotypes, and selected causal variants according to our chosen model of association. We selected 10,000 haplotypes, paired together at random to form 5,000 individuals in our “analysis cohort”, and generated their phenotypes according to their genotypes at the causal variants. We then selected a further 2,000 haplotypes in our “discovery panel”, used here to represent the deep re-sequencing data we expect from the 1,000 Genomes project. Over all simulations, the mean number of rare variants with at least two copies of the minor allele in the discovery panel was 52.2. We assumed that each of these rare variants was taken forward for genotyping in the analysis cohort, and tested for association using both RVT1 and RVT2.Our next step was to select variants in the 50 kb region to have similar properties to the Affymetrix Human SNP Array 6.0 in terms of mean density and MAF profile in the population of 40,000 haplotypes. All SNPs on the GWA chip were analysed independently, using conventional trend tests of association, with Bonferroni correction for multiple testing, and jointly, using standard haplotype-based techniques. Over all simulations, the mean number of GWA chip SNPs in the region was 14.8, while the mean number of SNP haplotypes with population frequency greater than 1% was 18.0. We attempted to apply RVT1 and RVT2 to the GWA chip data, but the mean number of rare variants in the region was just 0.2, and provided minimal power to detect accumulations of minor alleles at these loci. As a result, we extended our analysis to include “low-frequency” SNPs (1%<MAF<5%), which are less scarce on the GWA chip (mean 1.6 variants in the region).Our results highlight a number of general conclusions. First, when rare variants are discovered through re-sequencing, RVT1, based on the proportion of rare variants at which an individual carries minor alleles, is always at least as powerful as RVT2, based on the presence/absence of minor alleles. The difference in power between the two tests is most noticeable when the trait mean is determined by the proportion of causal variants at which a minor allele is present, which is not surprising, since this model is assumed by RVT1 . However, at present, there is no unbiased evidence to suggest that causal variants are more likely to aggregate in such regions and current annotation of the genome is incomplete, making identification of potentially functional loci difficult.Experience with current genotyping technologies would suggest that rare variants are more difficult to type than SNPs, and thus stringent quality control procedures are required to avoid increased false-positive error rates as a result of genotype misspecification. To increase power, an obvious step would be to combine results of rare variant studies through meta-analysis. Although each study may genotype different loci, we can combine results on the level of the functional unit. This may reduce, or even eliminate, the need for imputation, which may be potentially prone to bias because the spectrum of rare variants is more diverse than that of SNPs, even between populations sharing relatively recent common ancestry, and therefore more difficult to predict . This hiThe field of complex trait genetics is moving rapidly towards an understanding that deep re-sequencing technologies will provide the necessary data to unearth novel-associated loci. It is anticipated that researchers will soon be faced with the challenge of selecting the appropriate analytical strategy for these data sets, which will be of unprecedented scale and depth. In this study, we have developed and evaluated targeted rare variant analysis methods and have provided insights into their relative merits. The methodology we have developed here for detecting rare variant associations is extremely simplistic, and as technologies probing human genome sequence variation move rapidly forward, the development and testing of analytical strategies that maximise output from these investments will continue to be of critical importance.


A consistent debate is ongoing on genome-wide association studies (GWAs). A key point is the capability to identify low-penetrance variations across the human genome. Among the phenomena reducing the power of these analyses, phenocopy level (PE) hampers very seriously the investigation of complex diseases, as well known in neurological disorders, cancer, and likely of primary importance in human ageing. PE seems to be the norm, rather than the exception, especially when considering the role of epigenetics and environmental factors towards phenotype. Despite some attempts, no recognized solution has been proposed, particularly to estimate the effects of phenocopies on the study planning or its analysis design. We present a simulation, where we attempt to define more precisely how phenocopy impacts on different analytical methods under different scenarios. With our approach the critical role of phenocopy emerges, and the more the PE level increases the more the initial difficulty in detecting gene-gene interactions is amplified. In particular, our results show that strong main effects are not hampered by the presence of an increasing amount of phenocopy in the study sample, despite progressively reducing the significance of the association, if the study is sufficiently powered. On the opposite, when purely epistatic effects are simulated, the capability of identifying the association depends on several parameters, such as the strength of the interaction between the polymorphic variants, the penetrance of the polymorphism and the alleles (minor or major) which produce the combined effect and their frequency in the population. We conclude that the neglect of the possible presence of phenocopies in complex traits heavily affects the analysis of their genetic data. Highthroughput genetic analysis represents the present and the future in catching the genetic determinants of complex diseasesThe most widely used statistical tests are single point statistics  along the genome; these tests can be integrated with haplotype (or multi-marker) analysis once the linkage disequilibrium (LD) structure is drawn and thus haplotype blocks have been identified.All these tests can be performed under different assumptions and with slightly different approaches, and multivariate analyses are generally performed.Two main obstacles can be envisaged as:the false positive rates, and consequently the efficacy of the corrections adopted;the capability to identify low-penetrance variations across the human genome.As for false positives, many different approaches have been proposed and, provided the sample collection to be large enough, a multi-stage design has been shown to be very effective in detecting key leads in the genome, often replicated in other populations. It's not the purpose of this paper to address this areaAs for the identification of low-penetrance polymorphisms, the area is of a major consideration when disentangling the picture of any complex trait. Indeed, it's quite realistic for complex phenotypes to be determined by a combination of many different polymorphic loci each of them accounting for a minor part of the total varianceDespite this issue being of a key importance, most of the papers reporting GWA studies applied single point statistics, multi-marker analysis and haplotypes analyses, performed LD mapping, adopted different false-positive rate correctionsAmong the phenomena reducing the power of these analysis, phenocopy hampers very seriously the investigation of complex diseases, a well known issue in neurological disorders Considering the scenario we are dealing with, additional terminology needs to be clarified. As previously mentioned, one of the hot topics geneticists are currently debating is whether the so called “missing heritability” issue would find an answer in very rare and highly penetrant mutations , three markers  6 different case-control datasets with increasing phenocopy level generated with the method implemented within the software (PM1); b) 6 different case-control datasets with increasing phenocopy level generated with an alternative method (PM2) develop in our lab, as described in As far as the model ME is concerned, the results show that strong main effects are not hampered by higher levels of PE, despite an inflation of the significance .In the case-control dataset with PM1 method, RL0-855 was highly significant at each phenocopy level until 45%, displayed a −log10(p) = 62.54 at 0%PE and a −log10(p) = 25.84 at 45%. The analysis of the datasets obtained with the PM2 phenocopy algorithm produced similar results  = 40 at 0%PE and −log10(p) = 8.63, see Supplementary Among the other markers where only an interaction was simulated, only the marker RL0-245 appeared among the top ten significant at 0%PE (−log10(p) = 11.47) but it was no more on the top 10 when the phenocopy level reached 10%. The same happened on the TDT analysis.When we analyzed the EPI model on the case control dataset, none of the three markers ranked among the top list of significant markers. Moreover if we had to correct for multiple testing, none of the markers would reach a 0.05 level of significance neither at 0% PE level, nor at 45%.Despite some fluctuations on the data, mainly due to sampling and data extraction, a positive but no significant trend in the number of falsely significant markers could be observed according to the increase of phenocopy error percentage . The samWhen applying PM2 we observed the appearence of a single progressively significant marker (RL0-255), which was borderline for the Hardy-Weinberg equilibrium in the main dataset and therefore was unbalanced when affected individuals from different dataset suffering the same simulation phenomenon were added. This SNP can be considered a false positive, as it was not simulated in association of the disease in none of the additional datasets.A similar behaviour of the markers with a purely epistatic effect was observable in the pedigree dataset with a TDT analysis: again none of them ranked as significant (Supplementary −21) and at a 45% PE (p = 4.17*10−6).In order to check for the correctness of the model we generated, we performed a logistic regression on the interaction term between the three markers we simulated to be associated with a purely epistatic effect. The p value of the logistic regression was highly significant both at a 0% PE  combinations of the original predictors. By applying this methodology the analysis was capable to identify in most cases two of the three interacting SNPs among the top ranking interactions .The more the phenocopy error was increasing and the more these interactions ranked lower, even if in any case at least one of the three markers (RL0-153) was always present among the top five.As a purely epistatic model is a challenge for the analysis in itself, we adopted a further analysis method, i.e. the multifactor dimensionality reduction (MDR)Comparably with the logic regression analysis, the MDR method perfomed with random non exhaustive explorations, was unable to catch efficiently all the interactions, and this became more evident with increasing PE levels , then future analysis methods have to take into account this scenario and model not only interactions, but also phenocopy within their statistical model.In our simulation we decided to verify the impact of phenocopy level by testing two methods for the generation of phenocopies: the PM2 method we developed, specifically produces phenocopies by introducing affected individuals in which different genetic determinants have been simulated. The PM2 method thus allowed us to test a scenario where different combinations of loci could produce the same phenotype.Our results show that strong main effects are not hampered by the presence of an increasing amount of phenocopy in the study sample, despite progressively reducing the significance of the association, if the study is sufficiently powered.On the opposite, when purely epistatic effects are simulated, the capability of identifying the association depends on several parameters, such as the strength of the interaction between the polymorphic variants, the penetrance of the polymorphism, the alleles (minor or major) which produce the combined effect and their frequency in the population. The influence of these parameters has been partially discussed in 0% PE datasets in the literature. In our simulation the critical role of phenocopy emerges, and the more the PE level increases the more the initial difficulty in detecting these gene-gene interactions is amplified, even with methodologies more suitable to the discovery of epistatic models.Classical analytical methodologies are very sensible to this error, and new statistical methods have to be developed, addressing in a less computing-intensive way SNP-SNP interactions as well as accounting or adjusting their results on estimates of the phenocopy error.Since the presence of phenocopy can be a characteristic intrinsic to the phenotyping of complex traits, we conclude that the neglect of the possible presence of phenocopies in these scenarios heavily affects the analysis of their genetic data.We performed simulations by using the software genomeSIMLAWe generated two different disease models.In the first one  a single SNP RL0-855,  was simuIn the second model , we performed a simulation on a smaller chromosome (401 markers), where no main effect was present and three SNPs  were affecting disease with only a purely epistatic disease model, generated by using SIMPEN In both simulations the SNP chosen to be associated with the disease had a MAF>0.30, in order to allow us to simulate the condition so called “common variant common disease”For each of the two models case-control data and pedigree data were generated. On each case six different large pooled datasets were extracted, with an increasing level of phenocopy error . In order to avoid biases due to data extraction and fluctuation, each dataset has been obtained by sampling and then pooling 50 different datasets on each PE level.The case/control simulation included datasets of 200 cases and 200 controls each, i.e. finally 20.000 individuals each PE level dataset.Each family simulation included 25 families with 1 affected sib and 2 unaffected, 25 families with 3 affected and 1 unaffected, 25 families with 2 affected, 2 unaffected sibs and 3 random extra sibs: the total number of individuals for each dataset of different PE level was 25.000 samples. Supplementary The genomeSIMLA software version used (1.0.7w32), currently implements a method for generating the phenocopy designed as follows.The software generates cases and controls using the penetrance function and the marker specified by the user. Then, in case-control datasets, it removes a percentage (user specified) of cases and replace them with individuals sampled from the control individuals in the full population and assign them the affected status. In family datasets, the software determines the total number of affected to modify as phenocopies, identifies the pedigrees to be modified and redraw the family according to the new requirements. Pedigrees with the required number of affected and unaffected are selected and then the unaffected phenocopies are marked as affected, according to the initial design specified by the user .This method has been referred as “phenocopy method one” (PM1).In order to verify the correspondence of such phenocopy generation method with what we defined as “phenocopy” see , we alsowww.r-project.org) and PLINK. In particular whole-chromosome case-control analysis and TDT analysis were performed with PLINK and visualized with R. The calculation of genetic contrasts and the logistic regression on single markers, markers' interaction analysis with logistic regression where performed according to Clayton as developed in the “DGCgenetics” package. Interaction analysis by using a logic regression approach was performed by using the R package “logicFS” by Schwender, according to the developer's specifications.The analysis were conducted using the R software (www.epistasis.org)The MDR analysis has been conducted by using the MDR java package (Model S1Model Configuration files.(0.01 MB ZIP)Click here for additional data file.Box S1R code used to generate the alternative phenocopy method datasets.(0.03 MB DOC)Click here for additional data file.References S1References cited in the Supplementary Information.(0.03 MB DOC)Click here for additional data file.Table S1The table summarizes the 10 best models for each phenocopy level identified during the MDR analysis. It has to be stressed that the MDR analysis has been conducted by performing 5.000 evaluations of possible interactions. An exhaustive analysis as implemented in the software would be computationally very intensive, as pointed out by the authors in a recent paper Click here for additional data file.Figure S1For the case-control dataset generated with the main effect disease model (see SF6), an alternative method of producing phenocopies has been applied (see SF8). The method displays the same performance of the internally implemented one, with the only exception of few markers which progressely fall outside the equilibrium of Hardy-Weinberg, thus resulting in a false-positive association (indicated by the arrow). The red circle indicates the marker associated with the disease in the main dataset.(1.29 MB EPS)Click here for additional data file.Figure S2The figure summarizes the significance level for each marker in the pedigree datasets simulated with a main effect disease model at each phenocopy level. The red circle indicates the marker associated with a main effect to the disease in the model. The PM1 phenocopy generation method was applied.(1.31 MB EPS)Click here for additional data file.Figure S3For the case-control dataset generated with the purely epistatic disease model (see SF6), an alternative method of producing phenocopies has been applied (see SF8). The method displays the same performance of the internally implemented one, with the only exception of one marker which progressively falls outside the equilibrium of Hardy-Weinberg, thus resulting in a false-positive association (indicated by the arrow).(1.22 MB EPS)Click here for additional data file.Figure S4The figure summarizes the significance level of the markers in pedigree datasets, at each phenocopy level. The red circles indicate the position of the markers associated in the model, which is the same in the other plots.(1.54 MB EPS)Click here for additional data file.Figure S5MDR attribute construction. The figures illustrates the distribution of cases (left bars) and controls (right bars) when the three associated SNPs are considered jointly.(2.07 MB EPS)Click here for additional data file.Figure S6Two disease models have been applied. In the first model a single SNP displays a main effect (target OR = 2.225) and three additional SNPs do not have a main effect and interact with each other with a modest effect; this model is implemented as part of the SIMLA logistic function(1.07 MB EPS)Click here for additional data file.Figure S7For each disease model, two groups of datasets have been generated: a case-control dataset and a family based dataset. In order to reduce the fluctuations due to the sampling, in each case 50 different smaller datasets have been independently sampled from the population and then merged together in order to obtain a large pooled dataset. The figure explains the process step by step.(1.37 MB EPS)Click here for additional data file.Figure S8The method has been developed by using the R software (code provided) in order to perform a random sampling from five additional datasets where different SNPs have been associated in the disease model with the affected individuals. A uniform and random sampling, followed by a random substitution of the individuals in the original dataset produced different levels of phenocopies in the sample, thus generating six dataset with increasing phenocopy percentage. This method ensures the effective substitution of individuals generated as affected but with completely different causative markers. The method has been developed as a further analysis of possible effect generated by the “phenocopying” method implemented in the genomeSIMLA software.(1.67 MB EPS)Click here for additional data file.


Significant alterations of T-cell function, along with activation of the inflammatory response system, appear to be linked not only to treatment-resistant schizophrenia, but also to functional psychoses and mood disorders. Because there is a relatively high comorbidity between rheumatoid arthritis (RA), schizophrenia and major depression, the question arises whether there is a common, genetically modulated inflammatory process involved in these disorders. On the basis of three family studies from the U.S. and Europe which were ascertained through an index case suffering from RA , we aimed to predict the inter-individual variation of autoantibody IgM levels, as an unspecific indicator of inflammatory processes, through molecular-genetic factors. In a three-stage strategy, we first used nonparametric linkage (NPL) analysis to construct an initial configuration of genomic loci showing a sufficiently high NPL score in all three populations. This initial configuration was then modified by iteratively adding or removing genomic loci such that genotype-phenotype correlations were improved. Finally, neural network analysis (NNA) was applied to derive classifiers that predicted the phenotype from the multidimensional genotype. Our analysis led to an activation model that predicted individual IgM levels from the subjects' multidimensional genotypes very reliably. This allowed us to use the activation model for an analysis of the DNA of an existing sample of 1003 psychiatric patients in order to test, in a first approach, whether a deviant, genetically modulated inflammatory process is involved in the pathogenesis of major psychiatric disorders. While the ultimate goal of molecular-genetic research is the detection of causality, clinicians are also interested in reliable classification and prediction through objective laboratory methods. Classification and prediction do not require full understanding of causality but can, nonetheless, contribute to significantly improved treatments. This is particularly true for rheumatoid arthritis (RA), where autoantibody formation develops years before the first symptoms of RA occur. From the psychiatric point of view, it is most intriguing that active immune processes may be involved in the pathogenesis of major psychiatric disorders, as suggested by evidence from recent studies. Specifically, significant alterations of T-cell function, along with activation of the inflammatory response system, appear to be linked to treatment-resistant schizophrenia . SimilarNNA provides powerful tools for modeling pre-specified responses to complex, multidimensional input stimuli. It is the specific advantage of NNA that no causal relationship between stimuli and response is required. NNA connects the "neurons" of input and output layers via one or more "hidden" layers. All outputs are computed using sigmoid thresholding of the scalar product of the corresponding weight and input vectors. All outputs at stage "s" are connected to each input of stage "s + 1". The most popular learning strategy, the back-propagation algorithm, looks for the minimum of the error function in the weight space (goodness of fit) using the method of gradient descent. The basic algorithm is:yi observed   (i) output:   j = 1, 2,...,Nj)(j) hidden layer:   sk = xk   xk observed   (k) input:   ν = 1, 2,..,p)   improvements:   xk denotes observed stimuli, yi denotes observed responses, σ denotes the activation function of sigmoid-type: R → , α denotes the learning rate, and p is the number of probes (genotyped subjects). This algorithm can easily be adapted to genetic models.where k-fold cross-validation, the data are split into k roughly equal parts, and k - 1 partitions are used for training, while one partition is used for testing. The process is repeated until each partition has served as a testing set, so that k estimates of prediction error are generated. The choice of k is crucial in this approach, because the resulting prediction error is approximately unbiased for the "true" error only for sufficiently large k .Results derived through the standard NNA approach, which uses 80% of samples for training and the remaining 20% for testing, tend to be over optimistic, in particular if genotype errors and missing data are present. Therefore, in the n-dimensional genotype patterns at n loci, the Housholder-Torgerson formulaOnce a function is defined that quantifies the genetic distance between any two subjects with djk a matrix (bjk) of scalar products between points with origin at the centroid of all of the points. The matrix is then factored by any of the usual factoring procedures to obtain the projections of the points onto r orthogonal axes of a vector space. In this metric vector space, individuals are characterized as distinct "points" in such a way that individuals with similar genotype patterns form compact clouds, while genetically dissimilar individuals are located in more distant regions. Accordingly, one expects the groupings associated with different IgM classes to be well separated in a "genetic" vector space constructed from those genomic loci that influence IgM levels.gives a routine method for computing directly from the inter-individual genetic distances Although the detection of causal genotype-phenotype relationships (in the strict sense) was not the primary goal of our analysis, we have taken special precautions to ensure that a biologically meaningful solution was established. Specifically, we used a three-stage strategy: 1) nonparametric linkage (NPL) analysis across three independently ascertained family samples was applied for initial signal detection; 2) the initial configuration was then modified by iteratively adding or removing genomic loci to increase genotype-phenotype correlations; 3) subsequent NNA was used to weight genomic loci and their interactions optimally. Nonetheless, all of these steps do not necessarily establish biological meaningfulness, but merely identify genomic regions likely to harbor functional DNA polymorphisms that are causally related to the trait of interest. Accordingly, our approach to establishing biological significance also involves a large-scale SNP analysis using 5728 selected SNPs. Because there are complex patterns of linkage disequilibrium and haplotype block structure across the whole genome with strong nonlinearities, special techniques are necessary to narrow in on candidate regions successfully . ResultsOur sample comprised 599 nuclear families  with 1868 genotyped subjects (718 + 717 + 433) who were genotyped for either 396 (NARAC) or 1083 microsatellites (France). An integrated genetic map was constructed on the basis of deCODE and NCBI-36 data, so that the three populations could be compared through NPL analyses. On the phenotype level, the quantitative clinical measure rheumatoid factor IgM was available for the NARAC screens, whereas the French data included only a dichotomous affected/unaffected measure. For the NPL analyses, which were carried out independently for the three populations under investigation, we relied on the dichotomous measures under the assumption of a sufficiently close association between RA and the measured antibody IgM, while the optimization procedures  evaluated the quantitative measures of NARAC screens 1 and 2 for which we defined three subject classes using IgM levels: 1) normal: 0 ≤ IgM < 13.5, 2) low: 13.5 ≤ IgM < 50, and 3) elevated: 50 ≤ IgM. Due to incomplete data, only 926 subjects could be included.sjk between any two subjects j, k; 2) from these sjk we constructed a genetic vector space; 3) linear discriminant analysis of the three IgM classes then yielded an estimate of the underlying genotype-phenotype correlation; and 4) genotype-phenotype correlations were improved by iteratively adding or removing genomic loci and repeating steps 1 to 3. Results suggested a configuration of 16 polymorphisms on chromosomes 1, 2, 5, 6, 11, and 22 which allowed a fairly powerful classification of subjects by means of linear discriminant analysis, offering an overall performance of 73.8% across NARAC screens 1 and 2. The overlap between the subgroups, as seen in Figure NPL analyses carried out separately for the three populations under investigation revealed several candidate regions that showed significant NPL scores in all three samples Figure . Twenty k-fold cross-validation (k = 10) revealed reduced overall performances in the range of 78.2% (± 3.9) which, nonetheless, mean slight improvement compared to 73.8% derived through discriminant analysis.Subsequent NNA , under the constraint of reproducibility across NARAC screens 1 and 2, yielded weights that enabled re-classification of subjects through genotype-based classifiers at a sensitivity and specificity of >90%  and responses (output). Epiphenomena that are only indirectly related, or may even be physiologically unrelated, to the inflammatory response system are likely to explain the observed genotype-based, reproducible classification of patient IgM levels. Even though our current activation model with its overall performance of 78.2% does not yet meet the clinical requirements of diagnostic tools, its performance is high enough to justify an analysis of the DNA of our existing sample of 1003 psychiatric patients so that the hypothesis of whether deviant, genetically modulated inflammatory processes are involved in the pathogenesis of major psychiatric disorders can be tested in a first approach.The author(s) declare that they have no competing interests.


We attempted to replicate these findings and to conduct a candidate gene and locus evaluation of genetic involvement in common forms of myopia.A previous study has reported evidence of a strong linkage, but no association, between FGF2, BDNF, COL2A1, COL18A1, and PAX6).Samples were collected from 517 individuals in 123 families with a myopic child participating in the Orinda Longitudinal Study of Myopia or the Contact Lens and Myopia Progression Study. Myopia in the proband children was defined as -0.75 D or more and as being present in both meridians on cycloplegic autorefraction (1% tropicamide). Affected status in parents and siblings was determined by survey. After DNA was extracted from buccal mucosal cells and genotyped using assays for microsatellite markers and single nucleotide polymorphisms (SNPs), DNA was analyzed for linkage disequilibrium. Markers on chromosomes 12 and 18 were selected as regions previously associated with pathological myopia. SNPs were also analyzed in genes where their expression pattern or their association with syndromes conveys myopia as part of the phenotype . No SNP for FGF2, BDNF, COL18A1, or PAX6 showed significant over-transmission to affected individuals after correction for multiple comparisons. Markers on chromosome 12 and 18 previously associated with pathological myopia also showed no significant associations with the more common form of myopia in this study.The SNP rs1635529 for PAX6 showed no association with myopia. Associations in the current analysis are suggestive of involvement of COL2A1. Future studies should focus on replication in other samples and in genome-wide approaches.As reported previously by others,  Myopia is a common, complex trait most often acquired in childhood where the axial length of the eye exceeds its focal length, resulting in reduced distance visual acuity. The costs of providing clear distance vision through spectacles, contact lenses, or refractive surgery are considerable . Myopia Evidence points to a substantial role for genetic factors in the etiology of myopia. Myopic parents tend to have myopic children -12. HeriYet, differences in the prevalence between groups with supposedly similar genetic makeup but separated geographically and in near work demands suggests that near work may influence refractive error . ResearcPAX6 gene located in that region, there was no evidence for association with myopia [In addition to enhancing our understanding of the underlying biology of myopia, a better understanding of genetic factors in myopia might lead to improvements in prediction of the onset, treatment, and, perhaps, prevention. Identification of the genetic factors involved in complex traits is complicated by the involvement of a multiplicity of genes, genetic epistasis, and population heterogeneity. Despite these issues, several research groups have made strides in the last eight years toward identifications of genetic regions of interest with respect to myopia. Typically, the studies have been of families with histories of pathological, more severe degrees of myopia. These regions include 18p11.31 in eight American  and 15 Ch myopia . Therefobrain-derived neurotrophic factor (BDNF) is of interest as a potential genetic marker for myopia. Two clinical conditions have severe myopia in common: Knobloch and Stickler syndromes. Each has been associated with one or more mutations in collagen genes. Among these are collagen, type XVIII, alpha 1 (COL18A1) for Knobloch [collagen, type II, alpha 1 (COL2A1) for Stickler syndrome [COL2A1 locus in several other studies [In this study, we examined the role of candidate genes and loci in myopia. We either evaluated loci cited in the above reports from other investigators (except for the most recent) or evaluated based on the possible biological relevance of a candidate gene to myopia. Basic fibroblast growth factor (FGF-2) has been shown to inhibit form deprivation myopia in the chick . Brain-dKnobloch  and collsyndrome . Familie studies ,37,39,41We used an association approach and a large sample that has been well characterized phenotypically in conjunction with detailed candidate genetic analysis.Myopic children enrolled in the Orinda Longitudinal Study of Myopia (OLSM) through 2000  and in tTo be classified as affected, probands and siblings in OLSM or CLAMP had to have at least -0.75 D or more myopia in each principal meridian according to the most recent annual measurement of refractive error in the right eye by cycloplegic autorefraction (1% tropicamide). Other non-study siblings and parents were classified as affected according to their responses to survey questions .DNA was extracted from buccal mucosa cells using described protocols . AdditioPAGE assays were processed through polymerase chain reactions using Biolase reagents  then run out for size comparison on acrylamide gels as described previously by Lidral et al. . SSCP asfibroblast growth factor 2  on chromosome 4, five for PAX6 and one for BDNF on chromosome 11, four for COL2A1 on chromosome 12, and three for COL18A1 on chromosome 18. The PAX6 TaqMan assays listed in Markers and SNPs used in this study are shown in Myopia was considered to follow an autosomal dominant model with penetrance of 95% by 14 years of age . Two anaFor linkage analysis, we used both parametric and non-parametric approaches. We calculated model-based two-point LOD scores between myopia and each of the markers or SNPs using the Elston-Stewart algorithm  and emplCOL2A1 SNP rs1635529 was found  along with weak evidence for linkage (parametric LOD of 1.11). Assuming the presence of linkage with the empirical calculation of the test statistic, repeating the TDT analysis resulted in a p-value of 0.0008, which is above the Bonferroni level of 0.0004 but still of interest. The reverse TDT analysis was insignificant . In analyzing only the 101 Caucasian families, this COL2A1 SNP rs1635529 was significant at the p=0.0005 level with 33 informative families, again above the Bonferroni level of 0.0004 but still of interest. Reverse TDT on this Caucasian sample was also insignificant . The haplotype TDT analysis for the COL2A1 SNP group was not significant (p=0.78). Other TDT results following correction for multiple comparisons were not significant for microsatellite markers D12S2076 (GATA30F04), D12S1051 (GATA2401), and D12S1059 (GATA47G01) in the biallelic analysis.On chromosome 12, strong evidence of association between myopia and the common allele of the FGF2 group showed significant findings from the different analysis methods after correction for multiple comparisons. There was some evidence of association in the TDT analysis between myopia and over-transmission of the common allele of the FGF2 SNP rs1048201 (p=0.01). In the two-point dominant model linkage analysis, the FGF2 SNP rs308447 had a LOD score of 0.95. The haplotype TDT analysis for this FGF2 SNP group was not significant (p=0.59) and the non-parametric linkage was not significant for any SNP in this group. Within the PAX6 group, no SNP demonstrated statistical significance in any of the analyses. Lack of informative families for two of the PAX6 SNPs made the association between myopia and these SNPs unknown. Elsewhere on chromosome 11, weak evidence for linkage was found with the BDNF SNP rs6265 (LOD=1.19).None of the three SNPs within the COL18A1 SNPs had sufficient number of informative families yet, none had significant results from any of the analyses.On chromosome 18, all analyses for the microsatellite markers were performed on a sufficient number of informative families yet, there were no significant findings . On chromosome 21, all of the collagen COL2A1 and Stickler Syndrome [COL18A1 and Knobloch Syndrome [FGF2 [BDNF [PAX6 [We used a large sample size and a range of genetic models and test strategies to search for genetic causes of myopia using candidate genes and loci. Myopia is a complex trait where analyses are complicated by the likely involvement of multiple genes, gene-gene interactive effects, and the need for large sample sizes to detect effects. A candidate gene approach as opposed to a genome-wide approach is obviously limited by gene and SNP choice. However, SNP coverage could not be complete given the availability of assays at the time of the study, the associated costs, and the limited amount of genetic material available from our buccal swabs. Coverage was intended to be at a density of at least three markers per gene. The recent publication of a genome-wide, dense-haplotype map makes it practical to consider genome-wide association approaches . One sucSyndrome , COL18A1Syndrome ). Othersme [FGF2 ,74, BDNFF2 [BDNF , and PAXNF [PAX6 ). Other NF [PAX6 -36.COL2A1 with a p-value of 0.00007. This is somewhat surprising since, typically, myopia is regarded as a condition of excessive axial, scleral growth, yet, human sclera is predominantly comprised of type I collagen with little to no evidence for the presence of type II collagen [COL2A1 is due to a shared linkage disequilibrium pattern with a causative variant in a nearby gene, but the two known adjacent genes, vitamin D receptor (VDR) and SUMO1/sentrin specific peptidase 1 (SENP1) are not obvious candidates. However, there is some evidence that variations in type II collagen might affect the development of the eye. Comparisons between normal and transgenic mice with deletions or mutations for type II collagen show that expression of type II collagen mRNA is widespread throughout the eye during development with the transgenic mice showing reduced filament density in vitreous, anterior displacement of iris and lens, shallow anterior chamber, and disorganized structure to cornea and lens [The most significant association for myopia seen in the current study was for collagen . Type IIcollagen , althougand lens . Common and lens  but haveand lens . These sand lens ,79. Seveand lens ,37,39,41and lens .The failure to find additional, positive results with the association-based approach does not exclude any particular gene from involvement considering the sample size and the presence of an unknown level of heterogeneity. Linkage can find signals for etiologic genes when there is allelic heterogeneity, but the current study had only modest power to detect linkage. Ethnic diversity in the sample may be a weakness because it may add to heterogeneity. However, we believe there is value in evaluating candidates that are represented across ethnic backgrounds. Subject numbers for individual ethnic groups seem insufficient for analyses of association on a group-by-group basis. However it is worth noting that the allele frequencies calculated from all parents in this ethnically diverse sample are similar to those from the predominantly Caucasian data taken from CEPH . AnotherPAX6. Using the same five SNPs used by Hammond et al. [Unlike Hammond et al. , we wered et al. , we wered et al. . ClearlyFGF2 in myopia in our sample.Expression of FGF-2 is altered in animal deprivation studies but has not been evaluated previously in human studies. In the tree shrew, the experimental induction of myopia did not result in differences in the level of scleral FGF-2 compared to control eyes, but there was upregulation of FGF receptor mRNA in experimental myopia . The speThree markers on chromosome 12  continued to show no significant associations with myopia in this larger sample, consistent with a previous analysis of a subset of the samples used in the current study . A previCOL2A1. There was no significant evidence for involvement by FGF2, BDNF, or COL18A1. No significant associations were found for markers on chromosomes 12 and 18 (previously linked with high myopia) and the more common forms of myopia in the present study. Consistent with a report by others, we were unable to demonstrate an association between PAX6 and myopia.In summary, the primary findings from the current study suggest involvement in common forms of myopia by


We investigated efficient case-control association analysis using family data. The outcome of interest was coronary heart disease. We employed existing and new methods that take into account the correlations among related individuals to obtain the proper type I error rates. The methods considered for autosomal single-nucleotide polymorphisms were: 1) generalized estimating equations-based methods, 2) variance-modified Cochran-Armitage (MCA) trend test incorporating kinship coefficients, and 3) genotypic modified quasi-likelihood score test. Additionally, for X-linked single-nucleotide polymorphisms we proposed a two-degrees-of-freedom test. Performance of these methods was tested using Framingham Heart Study 500 k array data. Several single-gene variants associated with coronary heart disease (CHD) using Framingham Heart Study (FHS) 100 k array data were reported previously  as well QLS) test [QLS test to the corresponding genotypic test (gMQLS), assuming a multiplicative model [Our aim is to use family information efficiently. In this paper we study an association between CHD and candidate genes using the binary outcome of CHD directly. The following methods were investigated: 1) a logistic regression model taking into account familial dependence of the observations using GEE, 2) Cochran-Armitage (CA) trend test taking into account the correlations among related individuals when computing the variance, and 3) the extensions of modified quasi-likelihood score (MLS) test . The lasve model .QLS test.Unil now, little has been reported on performance of such test statistics for association on the X chromosome ,7. Becau® Human Mapping 500 k Array Set provided by the FHS SHARe  project. The large pedigrees (n = 841) were broken up into nuclear family units . The data consist of 2,878 subjects in the Offspring Cohort  and their parents in the Original Cohort (n = 323). A binary outcome variable was created as any event of hard CHD (n = 225). The details of data sets created and used are described in Table We analyzed Problem 2 of Genetic Analysis Workshop 16 data, using GeneChipp ≥ 0.001. For chromosome 8, by ignoring relatedness between subjects, we conducted allelic tests for the preprocessed 22,207 SNPs  using PLINK. Then, 121 SNPs were selected using a threshold of allelic p-values < 0.005. For chromosome X, 8,020 SNPs  were tested, and using the same threshold 35 SNPs were selected.We checked inheritance error. PLINK version 1.02  was usedOne merit of using pedigrees in a case-control study is that cases with affected relatives might have higher expected frequency of associated alleles than cases without affected relatives. For GEE, an exchangeable working correlation matrix was used to account for correlation within each sibship and each family. However, this correlation is prone to misspecification, and subsequent loss of efficiency may be substantial .U is a sum of weighted differences of genotype counts between cases and controls. When subjects are biologically related, we need to account for their correlations by computing the variance of U. Slager and Schaid [Under the null hypothesis of no association between genotype and disease, CA trend test is d Schaid  proposedQLS test proposed by Thornton and McPeek [Alternatively, we considered Md McPeek , which in + m sampled individuals with phenotypic information. Let Y =  denote genotype data of n individuals with non-missing genotype, so that m individuals have missing genotype. Let Φ be the kinship matrix of the non-missing genotype individuals, and ΦN, M between missing and non-missing genotype individuals. The entries of the matrix are 1 on the diagonal and 2ϕij kinship coefficient between the ith and jth individual off the diagonal. AN and AM are the column of the phenotype of the respectively non-missing and missing genotype individuals. The entry in A for the ith individual from the jth family isSuppose we have k < 1 specified to be the population prevalence of the trait. Then, the statistic is given bywith 0 <α = AN + Φ-1 ΦN, M AM, Γ = αT- (1T α)2 (1TΦ-11T)-1,where, QLS test to the corresponding genotypic test, gMQLS, assuming multiplicative model using genotypic mean We extended the allelic MQLS test. To combine the results we combined the two chi-squared tests to obtain a two-degrees-of-freedom test (xMQLS).For the X-linked SNPs, a simple allele-based test can be constructed by counting alleles, with males contributing a single allele and females two alleles. Because the assumption that the allele frequency does not vary with sex could not be met, we stratified the analysis by sex, and used the allelic MThe analyses using new methods have been conducted using functions written by the authors in R .k in Eq. (1) - was set as 5%. To compare type 1 error rates, the quantile-quantile plots of 0.5-percentiles (the percentage of SNPs selected) are depicted in Figure We compared the following methods: CA, MCA, GEE, and gMQLS. These tests were performed 1) using Offspring Cohort and 2) using the Original and Offspring Cohorts as described in Table p-value decreased from 9.80 × 10-5 to 1.05 × 10-5 for RS17094201. None of the SNPs tested were found to have genome-wide significance .In Table p-value = 6.05 × 10-7).We performed analysis using GEE adjusted for sex and the two-degrees-of-freedom test, xMQLS. The results of the top ten ranking SNPs using xMQLS are reported in Table The fact that the behavior of the GEE-based methods sometimes deviates from other methods may be explained by the fact that the working correlation matrix has not been specified correctly, especially for nuclear families . This caWe did not perform simulation studies regarding type 1 error rates of the new methods. However, a good performance of the allelic variants has been reported ,12, and QLS tests can be used for different types of families, and also to incorporate phenotypic information of ungenotyped relatives. Therefore, a better performance can be expected by increasing the number of cases. For this, selecting families with many cases might be more efficient.The extended MThe use of an allelic test for X-linked SNPs leads to criticism that males have only half the impact on the analysis as females. Instead, Clayton  proposedQLS methods are promising. However, these may not be computationally feasible for family-based genome-wide association study. We recommend these tests to be used in a two-stage approach.The extended MAnalyzing family data using all information available in a case-control association study may improve efficiency. Two different subsets of data were considered: one consists of the Offspring Cohort, and the second with nuclear families . To account for relatedness among individuals, we considered first the GEE-based methods. As an alternative, we proposed new methods by extending CA trend test.To gain efficiency, we also considered the extensions of MQLS test. The last methods utilize most of family information, and therefore might be more efficient than others. Using these methods, we analyzed the real FHS data. The new methods performed well compared with the GEE-based methods.n = 323) was added, the proportion of cases added (20%) was relatively large compared with that in the sibling-only data (6%). And, the gMQLS test might be more efficient because it incorporates all phenotypic information available - even CHD cases of un-genotyped parents.Adding family information seemed to improve the results. Although only a small number (For X-linked SNPs, equivalent results were obtained: the xMQLS test outperform the GEE-based methods using these specific data. Further work should be done to evaluate the new methods.QLS: Modified quasi-likelihood score; SNP: Single-nucleotide polymorphism; xMQLS: Two-degrees-of-freedom MQLS.CA: Cochran-Armitage; CHD: Coronary heart disease; FHS: Framingham Heart Study; GEE: Generalized estimating equations; gMQLS: Genotypic test corresponding to the modified quasi-likelihood score; MCA: Modified Cochran-Armitage; MThe authors declare that they have no competing interests.H-WU performed the analyses and wrote the manuscript. H-WU and JJH-D participated in the development of the methods, and interpreted the results of the analysis. HJvdW participated in data preprocessing. All authors read and approved the final manuscript.


Genome-wide association studies have been successful in finding common variants influencing common traits. However, these associations only account for a fraction of trait heritability. There has been a shift in the field towards studying low frequency and rare variants, which are now widely recognised as putative complex trait determinants. Despite this increasing focus on examining the role of low frequency and rare variants in complex disease susceptibility, there is a lack of user-friendly analytical packages implementing powerful association tests for the analysis of rare variants.We have developed two software tools, CCRaVAT  and QuTie (Quantitative Trait), which enable efficient large-scale analysis of low frequency and rare variants. Both programs implement a collapsing method examining the accumulation of low frequency and rare variants across a locus of interest that has more power than single variant analysis. CCRaVAT carries out case-control analyses whereas QuTie has been developed for continuous trait analysis.CCRaVAT and QuTie are easy to use software tools that allow users to perform genome-wide association analysis on low frequency and rare variants for both binary and quantitative traits. The software is freely available and provides the genetics community with a resource to perform association analysis on rarer genetic variants. Recent advances in high-throughput genotyping have made large-scale genetic association studies possible. Genome-wide association studies (GWAS) for complex disease have met with unprecedented success in identifying common susceptibility variants. However, the discovered common-frequency single nucleotide polymorphism (SNP) associations do not account for a large proportion of the genetic component of disease. The field is now focusing on the analysis of low frequency and rare variants  ≤0.05) to investigate if they will help explain the missing heritability in complex trait etiology ,2. WhileCCRaVAT and QuTie are Linux command-line based utilities written in Perl. The scripts utilize the GetOpt, POSIX, and GD Perl modules. The GD module is necessary to produce the graphical output, and the POSIX module is used to calculate the logarithm base 10 of the p values. The tools have been tested on a variety of GWAS datasets and the system requirements depend mainly on the size of the study . The software requires that the data be separated by chromosome for efficiency. For a genome-wide dataset separated by chromosome consisting of 450,000 SNPs typed in 5,000 individuals, CCRaVAT requires ~200 Mb of RAM. The software development and testing of the applications were performed on machines with dual-core Athlon processors. The scripts can take a variable amount of time to run depending on the options used. The run time for a typical gene-centric genome-wide analysis, using approximately 450,000 SNPs and 5,000 individuals separated by chromosome, is less than 24 hours. Permutation testing can add considerably to the computing time depending on the number of regions analyzed and the numbers of permutations run.The statistical properties of the low frequency/rare variant collapsing (super-locus) association test that we have implemented have been described previously ,4. AlthoFigure CCRaVAT and QuTie require two input files per chromosome: a map file and a pedigree file. The map file contains information about the markers analyzed and their position along the chromosome. CCRaVAT and QuTie allow both a 3 column and a 4 column formatted map file, as seen in Table CCRaVAT and QuTie provide users with 25 command-line options, all detailed in the users manual, allowing the analysis to be tailored to specific interests. The options belong to three broad categories: altering the definitions of a region, low frequency/rare variant; altering significance levels and defining statistical analysis method, and altering the appearance of the graphical output.Fundamental to the collapsing method is the definition of the region within which the accumulation of low frequency/rare variants will be examined. CCRaVAT and QuTie provide the user with two options for defining the locus of interest, either through defining regions based on known gene coordinates or by employing a sliding window approach. If the analysis is based on sliding windows, the user defines how large the analysis windows should be. If a gene-based analysis is undertaken the user can also define how further upstream and downstream from the transcription start and stop sites to extend the analysis. The user can adjust the MAF cut-off that determines which markers are considered to be low frequency/rare variants and therefore included in the analysis.Unlike association tests of common variants, there is no well-defined significance threshold for the analysis of multiple low frequency/rare variants. The programs allow the user to define a significance threshold that produces separate files for significant regions, allowing the researcher to focus on top hits without having to troll through all the data. The researcher can also set significance thresholds to select regions for follow-up by undergoing permutation analysis. The number of permutations can also be preset. As chi-squared test results can be unreliable with low cell counts, CCRaVAT provides an option for the user to set a minimum number of cell counts; the Fisher's exact test is then implemented for any region that falls below this value. The standard analysis of QuTie is a linear regression, but QuTie provides an option to additionally carry out a two-sample t-test.To assist researchers in interpreting the results, CCRaVAT and QuTie produce visual output summaries. The programs allow the user to define a significance threshold to highlight loci in the Manhattan plot on the basis of their p value, as well as to manipulate graphical parameters such as the height, width, and size of data points of the figures. The programs also provide an option to (re)produce figures based on previously run analyses.CCRaVAT and QuTie produce text-based summaries and graphical summaries of the analysis results. The format of the CCRaVAT output file that provides summary statistics for all genes/windows that achieved a user-specified level of significance is displayed in Table Performing the collapsing analysis based on low frequency and rare variants (particularly those typed as part of GWAS) requires special attention to quality control. Genotype calling algorithms for GWAS chips perform well for common variants, but are known to be error-prone for loci with low MAF. Therefore, we recommend users that have performed the analysis based on GWAS chip data to check the cluster plots for all variants contributing to interesting signals, exclude any poorly clustering variants and rerunning the analysis for the specific regions of interest to ensure the association is robust to these exclusions. Quality control is also an important consideration when analyzing sequencing data. Major considerations are the effects of small insertions-deletions leading to false positive SNPs, read depth at variant sites, mapping quality score, and SNP quality score.In this paper we have described two novel analysis tools, CCRaVAT and QuTie, for investigating low frequency/rare variant associations in GWAS and resequencing data. Both programs employ a simple collapsing method to increase power over single point analysis. CCRaVAT analyzes case/control data and investigates significance using Pearson's chi-squared and Fisher's exact tests. QuTie analyzes quantitative trait data and implements a linear regression and Student's t-test. Both CCRaVAT and QuTie are easy-to-use Linux command line tools that use standard files typically employed in common variant GWAS analysis. CCRaVAT and QuTie can be used as a complement to existing common disease GWAS by analyzing low frequency/rare variant associations or in analyzing sequence-based low frequency/rare variant genotype calls in regions of interest or genome-wide. These tools are important first steps in the analysis of rare variants. We are currently developing more powerful natural extensions to the current methods as well as novel approaches that incorporate weights based on quality metrics.Project name: CCRaVAT and QuTieProject homepage: http://www.sanger.ac.uk/resources/software/rarevariant/Operating system: Linux/UnixProgramming Language: PerlLicense: GNU GPLCCRaVAT: case control rare variant analysis tool; QuTie: quantitative trait; QT: quantitative trait; GWAS: genome-wide association study; SNP: single nucleotide polymorphism; MAF: minor allele frequency; bp: base-pair; CHR: chromosome; POS: position; GEN: genetic; AFF STAT: affection status; RV: rare variant; Cont: control; ChiSq: Chi-square statistic; FisherEX: Fisher's exact test; Wind: window; Coef: coefficient; StEr: standard error; CI: confidence interval; Av: average; RegPval: regression p-value.RL wrote the code for CCRaVAT and QuTie. ADW wrote the documentation, developed the homepage, and drafted the manuscript. KSE compiled and created the gene files for the gene-centric analysis. APM supervised the development of CCRaVAT and QuTie. EZ supervised the development of CCRaVAT and QuTie and drafted the manuscript. All authors have read and approved this manuscript.