Recent technological advances in DNA sequencing and genotyping have led to the accumulation of a remarkable quantity of data on genetic polymorphisms. However, the development of new statistical and computational tools for effective processing of these data has not been equally as fast. In particular, Machine Learning literature is limited to relatively few papers which are focused on the development and application of data mining methods for the analysis of genetic variability. On the other hand, these papers apply to genetic data procedures which had been developed for a different kind of analysis and do not take into account the peculiarities of population genetics. The aim of our study was to define a new similarity measure, specifically conceived for measuring the similarity between the genetic profiles of two groups of subjects  taking into account that genetic profiles are usually distributed in a population group according to the Hardy Weinberg equilibrium.We set up a new kernel function consisting of a similarity measure between groups of subjects genotyped for numerous genetic loci. This measure weighs different genetic profiles according to the estimates of gene frequencies at Hardy-Weinberg equilibrium in the population. We named this function the "Hardy-Weinberg kernel".The effectiveness of the Hardy-Weinberg kernel was compared to the performance of the well established linear kernel. We found that the Hardy-Weinberg kernel significantly outperformed the linear kernel in a number of experiments where we used either simulated data or real data.The "Hardy-Weinberg kernel" reported here represents one of the first attempts at incorporating genetic knowledge into the definition of a kernel function designed for the analysis of genetic data. We show that the best performance of the "Hardy-Weinberg kernel" is observed when rare genotypes have different frequencies in cases and controls. The ability to capture the effect of rare genotypes on phenotypic traits might be a very important and useful feature, as most of the current statistical tools loose most of their statistical power when rare genotypes are involved in the susceptibility to the trait under study. Recent advances in DNA technology have led to the accumulation of a remarkable quantity of data on genetic polymorphisms. Consequently, there has been a growing interest in the possibility of carrying out studies for a variety of human complex traits, that is traits due to the variability of many genes, each contributing a minor or very small effect. For instance, many studies have been devoted to the analysis of the genetic components of cancer, cardiovascular diseases, dementias, and aging. In particular, the availability of ultra-high-volume genotyping platforms at a manageable cost has permitted genome-wide association studies where genetic profiles observed in groups of affected subjects (cases) are compared to groups of healthy subjects (controls) in order to identify multiple low-penetrance variants involved in complex phenotypes -5. In faRecently, kernel-based methods have attracted the attention of many researchers in the broad field of Knowledge Discovery and Machine Learning methodologies. The main aim of a kernel-based method is to devise a suitable kernel function to encode a similarity among the entities of the data set. In this framework many kernel-based methods have been developed, e.g. kernel principal component analysis , kernel SVM represent a set of data mining methods that, taking advantage of a kernel function, are used to analyze large datasets in order to perform classification, clustering, and regression analysis . For insvice versa. Thus, we named this kernel the "Hardy-Weinberg kernel" (HWk). This kernel, estimates the similarity between different genetic profiles based on the frequency of each genotype in the general population. Consequently, once embedded in a SVM classifier, HWk allows to estimate the influence of each genotype on the probability of it being part of a given group of subjects (for instance a group of subjects with a given phenotype or disease).The aim of our study was to define a new similarity measure specifically conceived for incorporating the knowledge of population genetics into the study of genetic datasets obtained from high throughput analysis for association studies. The main feature of such measure is that the similarity between groups of subjects typed for their genetic profiles is weighed according to the estimates of gene frequencies at Hardy-Weinberg equilibrium in the population. The Hardy-Weinberg equilibrium represents the main principle regulating population genetics. It states that allele and genotype frequencies in a population are constant – that is, they are in equilibrium- from generation to generation unless specific disturbing influences are introduced. This allows the estimation of the expected frequency of a genotype on the basis of allele frequencies and dataset is a table composed of n rows, namely X1, X2,..., Xn, where Xi represents the genetic profile of a single subject. The subjects typed for their genetic profiles are subdivided into two different classes, i.e. class +1 and -1, reflecting the presence or absence of one specific phenotype (i.e. subjects belonging to class +1 are the "cases" and -1 are the "controls"). Each row Xi is composed of m variables, SNP1, SNP2,..., SNPm, representing the set of Single Nucleotide Polymorphisms (SNPs) under study  of the generic alleles A1 and A2 (A1A2 ∈ A2A1).In the present study, a SNPjk , for each SNPj; in this way each binary variable represents one of the three possible genotypes of the relevant SNP. By encoding in numerical format, each row Xi of the dataset will contain 3· m binary variables  and a comparabale number of healthy subjects (controls). In all the cases, to avoid biased estimates due to the phenotypic selection, we estimated the allele frequencies from the control group (class -1) of each dataset.We assumed the existence of a generic population, where one percent (1%) of subjects is affected by a specific phenotype. The subjects with the phenotype under study are called cases, while the remaining subjects are controls. We further assumed that all subjects of the population were genotyped for 20 different SNPs. Among the 20 SNPs, 5 were assumed to be informative with respect to the phenotype, while the remaining were not influencing (they can be considered as noise).A1 with a frequency p-1 for the control subjects. Thus, the other allele A2 will be forced to have a frequency q-1 = 1 - p-1, while the genotype frequencies will be determined by the Hardy-Weinberg law Table For all the informative SNPs, we assigned allele A1 alleles of the informative SNPs had a frequency equal to p1 = r·p-1 where r is a real number greater than one. That is, the allele A1 of each informative SNPs is more common in the subset of the population affected by the phenotype than in the control subset. In this way we created a relationship between the informative SNPs and the phenotype itself.For the cases, the r:In order to vary the strength of the relationship between the informative SNPs and the phenotype, we adopted different rules for the generation of r values set to 1.5;1. r values set to 2;2. r values set to 2.5;3. r values set to 3;4. r values randomly chosen in the interval .5. In cases 1–4 the strength of the relationship grows, while the fifth case ensures there is a variable strength of relationship for each informative SNP.Regarding the 15 uninformative SNPs, we set that they are not related to the presence of phenotype, by simply forcing the genotypes frequencies at thirty three percent both for the cases and for the controls.p-1 frequency and the rule for the setting of the r values. In particular, the p-1 frequency ranged from 0.005 to 0.10 with a step of 0.005, and from 0.11 to 0.33 with a step of 0.01. It should be noted that the p-1 frequency is low, the informative SNPs have a rare allele that influence the presence of the phenotype, while when the p-1 frequency is high, the informative SNPs do not have any rare genotype. In such a way we can test the validity of our kernel either in situations where we expect a better performance , or in those situations where the HWk and the linear kernel should not show significant differences.At this point, we generated several populations by varying the r, we generated a total of 43 populations ; each population was composed by 30000 subjects, and then approximately 300 subjects were cases. From each population we extracted only one dataset by selecting all the cases and an equal number of randomly chosen controls.In synthesis, for each value of p-1 frequency that we used for the other populations, but only the fifth rule for the generation of r values.Finally, we generated a last set of populations, by introducing a different kind of noise. The new noising SNPs were characterized by having a rare allele, with the same frequency for both cases and control. We replaced 5 of the uninformative SNPs with 5 of the new noising SNPs. In this way we wanted to test whether the HWk performance is influenced by the presence of uninformative SNPs with rare alleles. For this last set of populations, we used the same values of To further test the function of our kernel function we used a dataset which included genotypic data collected in the context of a study aimed at investigating the role of genetic variability of candidate genes in the susceptibility to Sporadic Colorectal Cancer (SCC). A complete list of the genes and of the polymorphisms can be requested from VM.Genotyping was carried out by APEX technology  on a samX1 and X2 is computed using the well known linear kernel function KL:The proposed HWk was obtained by modelling Hardy-Weinberg law into a linear kernel function. In order to introduce the HWk, we will first describe how the similarity measure between two genetic profiles, j and k represent, respectively, the jth SNP with the kth genotype. It is clear that the similarity measure computed by the linear kernel merely consists in the sum of SNPs presenting the same genotypes in both genetic profiles X1 and X2.As we stated in the "Methods" section the indexes wjk for each variable SNPjk. The HWk KHW can now be defined as:In order to model the Hardy-Weinberg law into a linear kernel function, we introduced a weight wjk were defined in terms of genotypic frequencies fjk as:The weights fjk is defined according to the Hardy-Weinberg law by the frequencies of the alleles it is made of.where fjk and wjk; the term j with respect to its highest genotypic frequency. Consequently, wjk assumes the highest values for rare genotypes and the smallest values for common genotypes.The term The main objective of our experimentation protocol was to demonstrate that the incorporation of previous data derived from the Hardy-Weinberg law in a kernel function provides sensible advantages.In order to achieve this objective, we compared the performance obtained using the HWk embedded in SVM models to results obtainable using the well known linear kernel.We chose to compare the HWk with the linear kernel because the first can be considered as an extension of the latter. Thus, we attempted to measure the advantage of employing the genotype frequencies calculated according to Hardy-Weinberg equilibrium. Moreover, we had to choose a class of classification function in order to test our similarity measure, since kernel functions are exclusively used embedded in classification/regression algorithms. SVM models seemed to be the most suitable choice, given their wide applicability.C. This parameter can be thought as a lever for regulating the training phase of SVM models: high C values force the SVM training algorithm to be more sensitive to the presence of outliers, while lower C values make SVM models more robust but can fail in detecting the real shape of the data. Machine Learning practitioners usually adopt the cross-validation technique in order to determine the optimal values of C. Cross-validation consists in splitting the dataset in n folds and repetitevily hold out one fold while the remaining ones are used to fit the model. The n models are then tested on the respective hold – out fold. In this way it is possible to obtain an almost unbiased estimation of SVM model performances. However, cross-validation performance estimation strongly depends on the dataset splitting. Thus, we adopted a repeated cross-validation technique, by repeating the whole cross-validation procedure multiple times and then averaging the results. Schematically, our experimentation protocol can be described as follows:A drawback of SVM algorithms is that SVM require the choice of a regularization parameter, called n times:1. Repeat k different folds.a. Split the dataset D in C value:b. For each k different folds.i. Perform a whole cross-validation on the C value, average the n performance values.2. For each C.3. Select the best values of n cross-validated performances for each values of C, and then we selected the best C value. Therefore our choice is far away more robust than using a single cross-validation. The whole experimental protocol was repeated once for each kernel function.Please note that we average A key point of each model evaluation procedure is the choice of an appropriate metric; for our experimentation protocol we adopted the Area Under the Curve (AUC) measure. AUC metric is a widely used performance metric in the field of Machine Learning , since Aχ2 test. Only the variables with p-values lower than a threshold T were selected. We used three significance thresholds, namely 0.1, 0.15 and 0.2, and thus we constructed three reduced datasets from the original one. The elimination of uncorrelated features was necessary in order to eliminate possible noise. Actually, a far more sophisticated feature selection procedure could be employed, but we decided to use the simple univariate selection procedure in order to maintain the focus of our experimentation on the differences between the linear and the HWk.The protocol was applied to both the simulated and the SCC datasets. However, the SCC dataset was treated with some additional pre-processing steps. In fact, we preliminarly eliminated the SNPs that did not comply to Hardy-Weinberg equilibrium. Then, we further reduced the number of variables of the real dataset, by applying an univariate feature selection protocol. In particular, we selected all the variables that were significatively correlated to the class attribute from a  or upon request from the corresponding author.The experiments were run using a computer program implemented in MATLAB; the script was interfaced with the software package LIBSVM  for the r parameter; the horizontal axis reports the p-1 frequency, while the vertical axis reports the best cross-validated AUC values obtained with HW and linear kernels.Figure r; also the datasets generated with a different type of noisy SNPs follow the same behaviour of the other datasets.Figure p-1 increases. We can explain this trend by looking at the odds ratio (OR) between cases and controls with respect to a single informative SNP. This OR can be formulated in terms of p-1, p1 and r:We observed an evident linear trend in each figure: the performances of both HW and linear kernels tend to growth as p-1 increases, the numerator decreases, but the denominator diminishes faster, since r is greater than one. Then the OR grows with p-1, and the SNP becomes more informative.In (3), as C parameter of the SVM classifier. In fact, we observed that the best AUC values were always obtained with small C values, while for higher C values the performances of the HW and linear kernels tended to the same value.Lastly, we noted that the performances of the HWk kernel follow a characteristic trend also with respect to the T for the univariate feature selection procedure of respectively 0.2, 0.15 and 0.10. The results for each repetition of the cross-validation procedure are reported in Additional file C values.The results using the SCC dataset confirm the characteristics of the HWk already pointed out with the experiments on simulated datasets. Figures C values. This characteristic can be explained by noting that the HWk essentially multiplies the variables corresponding to rare genotypes for positive factors. In fact, by multiplying a relevant dimension (i.e. a dimension that gives a strong contribution to the separation of the two classes) it is possible to obtain SVM models which are more robust, because of a larger separation margin. A wide separation margin ensures better generalization capabilities, that is a higher probability of correctly classifying new instances [We set up a new kernel, the HWk, which is specific for handling genetic profiles data and that performs better than the linear kernel. It is worth noting that, the HWk described here represents one of the first attempts aimed at inserting specific-domain knowledge into the definition of a kernel function specifically devised for the analysis of SNPs in complex phenotypes. The results obtained from the simulated data, as well as the results on the SCC dataset, pointed out that the HWk always obtains better performance than the linear kernel, especially with small nstances . On the In other words, the performance of HWk is always favourable with respect to linear kernel, but such a difference in performance is maximum when relatively rare genotypes (about 10%) are crucial for distinguishing between cases and controls, that is to say they have a role in the susceptibility to the trait analyzed. This is a very important and useful feature, as most of the current statistical tools loose most of their statistical power when rare genotypes are involved in the susceptibility to the trait under study. Thus, HWk may represent a valuable tool for the case-control studies carried out with high-throughput genotyping. Finally, it might be worth noting that in most of the human complex traits, the genetic component account for 10–50% of the individual risk. That is, in most cases the possibility to estimate the individual risk on the basis of genetic factors is quite low . Thus, tSVM: Support Vector Machine; SNP: Single Nucleotide Polymorphism; DNA: Deoxyribonucleic Acid; PCR: Polymerase Chain Reaction; APEX: Arrayed Primer Extension; SCC: Sporadic Colorectal Cancer; HWk: Hardy-Weinberg kernel; AUC: Area Under the Curve.The authors declare that they have no competing interests.VL and AM carried out all the computational experiments. FDC, SL, VM provided the molecular data of the samples included in the dataset. DC, GR and GP conceived the study, and participated in its design and coordination. The Ms was initially drafted by GP and then finalized with VL, AM, FDC and GR. All the authors read and approved the final manuscript.The results for each repetition of the cross-validation procedure.Click here for file


When the number of phenotypes in a genetic study is on the scale of thousands, such as in studies concerning thousands of gene expression levels, the single-trait analysis is computationally intensive, and heavy adjustment of multiple comparisons is required. Traditional multivariate genetic linkage analysis for quantitative traits focuses on mapping only a few phenotypes and is not feasible for a large number of traits. To cope with high-dimensional phenotype data, clustering analysis and principal-component analysis (PCA) are proposed to reduce the data dimensionality and to map shared genetic contributions for multiple traits. However, standard clustering analysis and PCA are applicable for independent observations. In most genetic studies, where family data are collected, these standard analyses can only be applied to founders and can lead to the loss of information. Here, we proposed a clustering method that can exploit family structure information and applied the method to 29 gene expression levels mapped to a reported hot spot on chromosome 14. We then used a PCA approach based on heritability applicable to small number of traits to combine phenotypes in the clusters. Lastly, we used a penalized PCA approach based on heritability applicable to arbitrary number of traits to combine 150 gene expression levels with the highest heritability. Genome-wide multipoint linkage analysis was carried out on the individual traits and on the combined traits. Two previously reported peaks on chromosomes 14 and 20 were identified. Linkage evidence was stronger for traits derived from methods that incorporate family structure information. Gene expression levels, treated as complex quantitative traits, have been found to show familial aggregation . MicroarHere, we proposed a clustering approach that takes into account of the family structure information. We then used a principal-components approach based on heritability proposed by Ott and Rabinowitz  to combiAll analyses were performed on the GAW15 Problem 1 human gene expression data. Clustering analysis was applied to the 29 gene expression phenotypes found to have significant linkage results on chromosome 14  was appli index families and j index subjects. Let ni be the number of members in the ith family. Then the distance between trait x and trait y is defined asHere we proposed a clustering method that uses all subjects in the data set and incorporates family structure information by defining a distance measure that reflects similarity of traits among family members. This distance measure is a sum of weighted family-specific mean trait differences. The weights are calculated from within-family trait sum-of-squares. When the trait values for subjects within a family are more similar, leading to a smaller within-family sum-of-squares, the differences in their trait means is more important and thus is weighted larger. To be specific, let F statistic in the ANOVA test. The proposed clustering using all subjects was compared to the standard hierarchical clustering using founders.where B is the family-specific variation and W is the subject-specific variation. Note that this maximization criterion is equivalent to maximizing the heritability  of a score. Here we use between-family sum-of-squares to estimate B, and use within-family sum-of-squares to estimate W. The first three PCHs are computed in each of the clusters found in the previous section.The principal-components approach based on heritability proposed by Ott and Rabinowitz  exploiteW) could be singular and cannot be inverted. Although generalized inverse can be used, the results will be highly unstable. In order to screen large number of traits, we used a penalized principal components of heritability [Without knowing which expression levels are regulated by a common gene, it may be desirable to apply the principal components of heritability approach on a large number of traits and evaluate which traits have significantly large loadings at linkage peaks. However, the method of Ott and Rabinowitz  is not atability  defined λ is the tuning parameter. When λ is zero, the penalized PCH is reduced to the PCH in Ott and Rabinowitz [λ approaches infinity, the penalized PCH approaches the score that maximizes the family-specific variation. In the latter case, the penalized PCH is close to the regular principal component applying to the founders. The λ is chosen by maximizing a cross-validated heritability [to stabilize the PCH. Here, binowitz ; when λ tability . We applt statistics and p-values.Prior to linkage analysis, genotype consistency was checked by PEDCHECK. SNPs with Mendelian genotyping errors were set to missing. Multipoint linkage analyses were performed by SIBPAL in S.A.G.E. The weighting method used for different sibling pairs was 'W4' . The RutStandard hierarchical clustering computed from 56 founders is summarized in Figure Principal components of heritability were computed for traits in Clusters A through D. Results were presented in Table t value for the peaks reached 7.25, which corresponded to a p-value of 1.22 × 10-12 and a genome-wide p-value of 3.53 × 10-9 [t value for the component A.2 using the standard method was 3.01, while the peak t value for the component D.1, which shared several members with cluster A, was 4.61. Two components in Cluster B and one component in Cluster C mapped to the hot spot on chromosome 14 had t values 4.31, 4.82, and 5.35, respectively. The component C.2 showed a new peak on chromosome 6 with t value 4.99  and 5.25 (4.8 cM), respectively. The peak on chromosome 20 was also identified by Morley et al. [We applied the penalized PCH  to the 1p = 7.35 × 10-8) than the ones computed from the standard clustering (p = 1.00 × 10-3). The penalized PCH approach applied to 150 traits with highest heritability identified a previously reported peak on chromosome 20 [We proposed a clustering method applicable to correlated family data. The distance measure used for clustering takes into account the trait similarity among family members. Unlike the standard hierarchical clustering, which only includes independent individuals, all the subjects in the data set contribute to the proposed method and can potentially recover some of the information lost in restricting analysis to founders. The clustering followed by PCH and multipoint linkage analysis identified the peak on chromosome 14 reported by Morley et al. . The linLinkage analysis on the combined trait may give less significant results than on the individual trait after adjusting for multiple comparisons. This could be because the combined trait involves a linear combination of all traits, which is subjected to more noise. However, when the marginal effect of a gene on each trait is moderate but the combined effect is large, investigating single trait separately may not identify the gene, while a multivariate method could reveal the joint effect of such a gene. Another possible reason for less significant results of PCH might be that here we used within-family sum-of-squares to estimate subject-specific component variation and relatives' kinship relationship was not exploited. Such information can be added by incorporating kinship coefficients into a variance components model .The clustering analysis and the principal-components analysis based on family structure are useful to exploit available familial information in the gene expression family data. The linkage evidence is stronger using these methods than using the standard ones that ignores the family information. The penalized PCH approach can be applied to large number of traits. The cross-validation procedure can be used to select the optimal value of the penalty parameter.The author(s) declare that they have no competing interests.


Such models are commonly used to mitigate the tendency for population structure, or cryptic relatedness, to inflate the false-positive rate of test statistics. They also allow for explicit modeling of varying degrees of relatedness in samples in which some individuals are related by (possibly unknown) pedigree, whereas others are not. Furthermore, the implementation of the method we describe here is quick enough to be used effectively on genome-wide data. We present an analysis of the data for Genetic Analysis Workshop 15, Problem 3, in which we show that these methods can effectively find signals in this data. Somewhat disappointingly, the false-positive rate does not appear to be reduced, but this is largely because the method used to simulate the data appears not to have encompassed effects, such as population stratification, that might have led to inflation of  A major issue when analyzing genome-wide data is that of false-positive signals. In part, this is caused by the large number of loci that are typically analyzed in such studies. It is often also caused by the effects of population stratification ,2 or cryLCT that is totally unrelated to height showed strong association with height in a study in a European American population.Although the confounding effect of population structure can be minimized by careful matching design in case/control studies, there is still some evidence of confounding even in well designed studies . Even whArabidopsis thaliana in which correlation between phenotypic distribution and population structure is high, and saw that the mixed-model approach greatly reduced the effects of population structure on false-positive rates [Two approaches that are commonly used to reduce the false-positive rate in the presence of population structure are genomic control  and struve rates .The novelty in this paper is two-fold. First, we apply the method in a situation where the number of markers is much greater than in existing applications. Second, we apply the method in a context in which the degree of relatedness is known for some pairs of individuals  and unknown for others .We use a generalized linear mixed-model, which is an extension of Yu et al. . We writη is the vector of linear predictors, which is related to the binary phenotype, affection status, through the inverse link function; α is a vector of fixed effects, corresponding to the SNP effects we are testing; υ is a vector of random effects reflecting the polygenic background; and X, Z are known incidence matrices relating the observations to fixed and random effects, respectively.where The mean and the variance of the model are assumed to be:y to denote phenotype, the inverse link function for the probability of an individual being affected is the logit function:where K is the relationship matrix reflecting the genetic background correlations between individuals. (This is the term that reflects known or unknown relatedness information.) Using K is calculated in the model. First, because pedigree information is available, and controls are taken from different families and are assumed to be unrelated, we can use the known kinship to calculate K directly from the pedigree information. Second, in order to investigate how accurately kinship can be estimated when pedigree information is unknown, we can estimate the relative kinship [Zυ in Eq. (1).We vary the way in which  kinship  from genA combined SNP data set with both of the 1500 ASP families and the 2000 unrelated control subjects is analyzed for each replicate. Because methods such as ours are widely used on SNP data, we analyze the SNP data only (9187 SNPs). Due to computational constraints, we only test the mixed model with estimated kinship (below) using a random subset of 50 ASP families and 200 controls. The Matvec package  was usedp-value of 1 × 10-4, chosen because an examination of chromosomes with no functional loci rarely contained p-values below this number (see discussion of significance below). The results from models using estimated kinship give the same pattern.In Figure p-values across all null SNPs , for Replicate 1. This is similar to the idea in Papanicolaou et al. [p-values are distributed close to the expected way. In fact they lie slightly below the diagonal, indicating under-dispersion. Rather than correcting the under-dispersion of the p-values, the mixed-model seems to exaggerate that tendency.These plots suggest that cryptic relatedness is not a problem for these data. To further examine this, in Figure u et al. . Compareu et al. ), here tp-value distributions. Positive correlation between loci  can lead to under- or over-dispersion of p-values. We tested this possibility by thinning the data by choosing 1/10 of the SNPs. Now, the SNPs are no longer correlated . The dispersion pattern remains the same. Thus, correlation between loci is not the cause. The apparent tendency of a mixed-model analysis to exaggerate the under-dispersion has, to our knowledge, not been documented previously, and deserves further investigation to discover whether it is a consequence of the particular simulation scheme used for this data. Nonetheless, it is reassuring that signals are found on Loci C, D, E, and F despite this. Indeed, while mixed models are known to help when cryptic relatedness is present, our results indicate that they do not hurt a great deal when it is not.All replicates show the same pattern for the p < 10-4. One scheme is to proceed via a permutation-based test in which replicate data sets are created, their phenotypes permuted, and the distribution of smallest p-value is observed. Computational requirements prohibit the use of such a scheme here. In any case, the use of large numbers of genome-wide SNPs to get the null distribution and then derive an empirical p-value cut-off (10-4 above), is probably sufficient. All 100 replicates have p-value less than 10-4 at the SNP nearest to the functional Loci C, D, E, and F for the mixed-model analysis.To examine overall power, we analyzed all 100 replicates for the cases discussed above. We find that our method consistently finds the functional Loci C, D, E, and F in these regions. A formal power study would require a less heuristic method of assessing significance than an arbitrary  definition of Finally, we assess the accuracy with which kinship is estimated using a pool of genome-wide markers. We find that results are good for the GAW15 simulated data. For kinship values within families that are supposed to be 0.25, estimates vary from 0.2 to 0.35. For values supposed to be 0, estimates vary from 0 to 0.05. Unfortunately, the simulated scheme appears not to have included any ancestry relationships between control individuals, or across case families. In reality, all individuals are related to some degree, although the significance of that relatedness will vary with individuals and with the analysis being performed. While our results show that kinship can be estimated in this study, a more comprehensive exploration of this issue, involving data with a more complex relatedness structure, would be of some interest.These results show that a mixed-model scheme can be used successfully to analyze genome-wide SNP data. Unfortunately, the simulation scheme used for GAW15 has resulted in data with a range of relatedness that is not particularly rich. Thus, the data does not provide an ideal environment for assessing the performance of our method. This caveat is further strengthened by the fact that relatively simple methods, such as the logistic regression analysis we show here, also find the functional loci in the regions we have considered. Thus, while there is a growing body of evidence that mixed models provide an effective way of mitigating the negative effects of genome-wide correlation between genotypes (induced by factors such as population structure), the data here does not provide an ideal test for the method. In particular, the population of controls have been simulated in a way that results in little relatedness between them.An obvious extension for future work is the detection of interactions. While there are a variety of problems associated with such analyses , the inWe explored the feasibility of genome-wide association studies for binary traits using mixed models. In the simulated data we found no confounding due to population structure. Mixed models are flexible enough to be used in a context in which some individuals are related through known pedigree and others are not. While the results here provide an imperfect example of such an implementation, they provide cause for optimism in future studies.ASP: affected sib pairGAW: Genetic Analysis WorkshopSNP: single-nucleotide polymorphismThe author(s) declare that they have no competing interests.


Modern approaches to identifying new genes associated with disease allow very fine analysis of associaton and can be performed in population based case-control studies. However, the sibpair design is still valuable because it requires few assumptions other than acceptably high penetrance to identify genetic loci.We conducted simulation studies to assess the impact of design factors on relative efficiency for a linkage study of colorectal cancer. We considered two test statistics, one comparing the mean IBD probability in affected pairs to its null value of 0.5, and one comparing the mean IBD probabilities between affected and discordant pairs. We varied numbers of parents available, numbers of affected and unaffected siblings, reconstructing the genotype of an unavailable affected sibling by a spouse and offspring, and elimination of sibships where the proband carries a mutation at another locus.Power and efficiency were most affected by the number of affected sibs, the number of sib pairs genotyped, and the risk attributable to linked and unlinked loci. Genotyping unaffected siblings added little power for low penetrance models, but improved validity of tests when there was genetic heterogeneity and for multipoint testing. The efficiency of the concordant-only test was nearly always better than the concordant-discordant test. Replacement of an unavailable affected sibling by a spouse and offspring recovered some linkage information, particularly if several offspring were available. In multipoint analysis, the concordant-only test was showed a small anticonservative bias at 5 cM, while the multipoint concordant-discordant test was generally the most powerful test, and was not biased away from the null at 5 cM.Genotyping parents and unaffected siblings is useful for detecting genotyping errors and if allele frequencies are uncertain. If adequate allele frequency data are available, we suggest a single-point affecteds-only analysis for an initial scan, followed by a multipoint analysis of affected and unaffected members of all available sibships with additional markers around initial hits. The sib pair design has been widely used in human studies for mapping genes that affect both quantitative and dichotomous traits. The objective of sibling studies is to determine whether the siblings (or other close relatives) tend to express the same disease phenotype  when they share a commonly inherited genomic segment measured by genetic markers. Because two loci located close together on the same chromosome tend to be inherited together, sibs who have inherited an allele predisposing them to disease will also inherit a variety of other genetic characteristics located in the same genomic segment as the gene responsible for disease susceptibility. By examining, in a set of pairs of affected sibs, the degree of sharing of genetic marker alleles located throughout the genome, researchers can identify regions that are shared more often than would be expected by chance. This excess allele sharing constitutes the statistical evidence for linkage between the shared markers and putative disease susceptibility loci.The popularity of the sib-pair and related small-family study designs reflects several attractive characteristics. For highly penetrant alleles, extended families can often be recruited and so provide a powerful source of information for disease localization and fine mapping. However, for complex diseases that result from interactions among loci or that result from both genetic and environmental effects, large pedigrees that include multiple affected individuals may be rare and may not reflect a single etiologically-related genetic factor. Since the pioneering work of Haseman and Elston  on quantThe modern approaches to identifying new genes associated with disease allow very fine analysis of associaton and can be performed in population based case-control studies. However, the sibpair design is still valuable because it requires few assumptions other than acceptably high penetrance to identify genetic loci. There remains skepticism about relying solely on genome-wide-association studies , and sibSibships and small families are relatively easy to identify and recruit (compared with designs that make use of large multiplex families). Moreover, a number of familial disease registries and high-risk clinics have been established and have enrolled substantial numbers of sib pairs and other groupings of affected relatives, so that in many cases recruitment has already occurred. In practice, however, the design of an effective small-family linkage study requires more care than is immediately apparent, particularly for complex diseases such as cancer, in which late onset, incomplete penetrance, large numbers of phenocopies, gene-environment interaction, and locus heterogeneity must be anticipated. The purpose of this paper is to evaluate the impact of choices of family sampling strategies in selecting the design of a study aimed at identifying novel genetic factors that predispose individuals to colon cancer. The study is a collaborative effort by two National Cancer Institute-sponsored consortia investigating the genetics of cancer: the Cancer Genetics Network (CGN) and Cooperative Family Registry for Colon Cancer Studies (CFRCCS).All population based studies of colon cancer have documented its strong familiality -24. HistThe choice of sampling schemes for a colon sibpair study requires evaluation, as several different options exist simultaneously for the sampling plan (how many families and which relatives to sample), disease model , and statistical test of linkage. These aspects, in addition to the method of generating the data sets for the simulations comprise the methods of determining an optimal design strategy for a colon sibpair study. In our analysis of design issues we have pursued a deterministic simulation approach. The first step was to check that the tests we considered had appropriate size, using extensive simulations. For those tests that were valid, we then performed a moderate number of simulations of a large number of families, to obtain the noncentrality parameters describing the behavior of each design configuration and test. We were then able to compare the attributes of these studies across the different design configurations genetic models and tests by fitting regression models, as further described below.BRCA2, was mapped by Wooster et al. [BRCA1 linkage was excluded. Genetic syndromes such as juvenile polyposis, Peutz-Jeghers syndrome and familial adenomatous polyposis can be readily eliminated prior to sample collection on the basis of phenotypic characteristics. However, mutations in mismatch repair (MMR) loci such as hMSH2 or hMLH1 cannot be excluded without performing molecular studies.  Estimating the proportion of affected families that might be excluded from analysis because they carry MMR mutations is difficult. Population-based estimates of the prevalence of germ-line MMR mutations among subjects diagnosed with colorectal cancer vary widely even within populations of European descent [The genetic basis of many complex human diseases, including some common cancers, is known to include mutations in loci that confer a high penetrance to carriers. In order to minimize the impact that such genetic heterogeneity may have on the statistical efficiency to identify novel loci, gene-hunting studies are often restricted to those cases that have been determined not to be related to any known susceptibility locus. For example, the second susceptibility locus for breast cancer, r et al.  based on descent -41, and  descent ,43. More descent  found thhMSH2/hMLH1 for HNPCC in the case of colon cancer), unlinked to the search region for new loci and a more common but less penetrant gene being sought by the linkage analysis. We also evaluated the effect of experimental elimination of a previously-known predisposition syndrome such as HNPCC. We investigated both the power and the relative efficiency of different designs under a range of assumptions about the contribution of an additional unlinked locus. The single unlinked locus with varying allele frequency and penetrance that we simulated could also approximate the effects of a few unlinked noninteracting alleles. Although our efforts focused on a study of colorectal cancer, the general issues identified above are similar to considerations encountered in the design of genetic studies of other common conditions such as other cancers, diabetes, hypertension and many other chronic diseases that arise from both environmental and genetic causes.The basic assumption for our studies was thus a two-locus non-interacting model, with a rare high-penetrance gene  indicates a dominant coding of the genotype, i.e. presence of one or two copies of the deleterious allele identically increases the risk of the disease. We also simulated some situations in which only one autosomal dominant predisposition syndrome was present in the population.where Dom(q1 = 0.003 and a log relative risk of β1 = 3 (relative risk = 20.1), q2 = 0.001 and β2 = 4.6 (relative risk = 99.5), the resulting penetrances are 0.018 for carriers of neither mutation, 0.268 for carriers of a mutation in the linked gene, 0.646 for carriers of a mutation in the unlinked gene, and 0.973 for carriers of both mutations. The linked locus accounts for approximately 7.2% of colorectal cancers and the unlinked locus accounts for approximately 6.0% of colorectal cancers. Table In the U.S. population, lifetime risks for colorectal cancer are approximately 2.5–5 percent . In the The primary concern in the design of CFRCCS-CGN colon cancer study is to maximize the relative efficiency per genotype, i.e., to find the combination of family structures and numbers of families that will produce the greatest power for a given number of genotypings. While the number of ASPs available for study will affect the power of the study, at the time when we were designing the study, approximately 425 ASPs (plus about 400 other relative pairs) were already available from the combined CFRCCS resources, and samples were already available from many of the potential subjects. An additional 500+ sib pairs were anticipated from the CGN sites. Thus, the primary constraint was the total cost of genotyping in a full genome scan, not the number of families. We therefore chose to concentrate on four main questions of efficiency: 1) whether (and how many) unaffected sibs should be genotyped, 2) how critical the absence of parental genotypes is to the efficiency of the analysis; 3) the relative loss in efficiency of genotyping spouses and offspring of a deceased affected sib, and 4) how different strategies for addressing genetic heterogeneity might affect these efficiency comparisons.Although our primary interest was in the relative efficiency per genotype, we also wished to observe the effects on overall power and sample size requirements. We were particularly interested in the question of whether the total number of families that might be available for study in this large collaborative project would be adequate for the detection of linkage given a set of realistic assumptions concerning the genetics of colorectal cancer susceptibility.identical by descent  between pairs of relatives with given phenotypes with that expected simply on the basis of their relationships. However, IBD status can only be determined unambiguously when both parents are different heterozygotes. Since late-onset diseases such as colon cancer severely restrict the availability of parental genotypes, the first step is to estimate the IBD probabilities from the marker data on all available pedigree members, using statistical approaches such as those as implemented in such software as GENEHUNTER [GENIBD [Simwalk 2 [Merlin [Model-free linkage analysis is usually based on a comparison of the observed number of alleles at a marker locus shared NEHUNTER , GENIBD  [GENIBD , Simwalkimwalk 2 , or Merl [Merlin . The fampfjki denote the estimated probability that sib pair  in family f = 1,. . .,F shares i = 0,1,2 alleles IBD, we first computed the mean pcf of (pfjk1/2 + pfjk2) in all affected pairs in family f and the corresponding mean pdf in discordant pairs in the same family. We then computed the means pc and pd and standard deviations sc and sd of these quantities across families, and conducted a standard one-sample t-test comparing pc to 1/2 and a two-sample t-test comparing pc to pd, where F is the total number of families in the sample:For the simulation studies reported here, we compared the power and efficiency of two tests: the classic "means test" for linkage , which cZd does not take account of the correlation in IBD status between the two types of pairs within a sibship, so we used a paired t-test to allow for this, i.e.,both of which are tested against a standard Normal distribution. Note sw denotes the empirical standard deviation of pcf - pdf across families.where G at the two disease loci by sampling from their respective population distributions . We then retained the simulated genotype vector with probability Pr(Y|G), where Y =  denotes the phenotype vector of the sibship under the design being considered (with D affected (Yi = 1) and U unaffected (Yi = 0) members). This process was continued until the total sample size of F families was ascertained. For each family structure, marker data were then simulated conditional on the genotypes at the linked locus. We assumed each marker locus had four alleles and that it was linked to the disease locus with two different recombination values of 5 and 10 centiMorgans between the disease and marker loci.For a given family structure and choice of parameters (described below), we simulated phenotype and marker data as follows. First, we generated genotypes l - 1 with probability 1 - θl, or the opposite chromosome with probability θl, for marker loci l = 1 ... L, l = 0 at the disease locus, where θl is the probability of recombination between loci l - 1 and l. All marker alleles were independent of the second (unlinked) disease locus, if one was employed in a given simulation.Regardless of the number of markers, marker alleles were simulated by dropping, for each parent, the parental allele corresponding to the chromosome of origin of the allele inherited at marker pfjki of each of these configurations into an array [We computed IBD probabilities for each marker locus by enumerating all possible alleles for each untyped founder and all possible segregation indicators for all nonfounders that are consistent with the observed marker data. We then accumulated the probabilities an array . These pan array . We did an array  and are F = 100 families under the null hypothesis of no linkage between the marker and either disease locus. For these analyses, we simulated families of two affected sibs, both genotyped, and two unaffected sibs, both genotyped.In order to compare the test size of each linkage test we employed, we carried out 10,000 replicate simulations of Zc and Zp statistics under the null. To calculate these, we initially simulated six markers with four alleles each spaced at 10 cM intervals, and obtained multipoint estimates of pairwise IBD sharing at 20 cM from the origin using the program Merlin [Zmc and Zmp using the formulas given above. The disease genes were unlinked to the six markers. We then repeated the simulations after reducing the marker distance by half. We did not go below 5 cM.We also considered the behavior of multipoint variants of the m Merlin , then caF = 500 families each. As a measure of cost efficiency per genotype, we divided the average Zc2 (or Zp2) scores across the 20 replicates by the number of genotypes required, and reported the ratio (times 100) of this value to that based on Zc2 for families consisting only of two sampled affected sibs. We call this the asymptotic relative efficiency (ARE). We chose to generate 20 replicate observations for any given combination of parameter values because we wished to simulate a wide variety of non-null conditions, while producing an adequate number of replicate observations to obtain reliable estimates of noncentrality parameters.For each non-null simulation, we generated 20 replicate simulations of F required for a desired level of power sample was calculated in the standard way [The number of families dard way  by solviF, where Zα and Zβ 1-are the quantiles of the standard normal distribution for selected values of α and β, and Zsim is the sample mean of the Z-scores (Zc or Zp) based on the sample size Fsim of the simulation run.for Zsim/ZsimR2) ranged from 70–75%. The open source statistical package R [The relative efficiency and absolute power comparisons were evaluated over a range of assumptions about disease allele frequency, penetrance, and heterogeneity. Summaries are provided for the relative efficiency from the non-null simulations of each combination of parameters and sample sizes required to attain 80% power. Our simulations involved the manipulation of 16 parameters, with over 725,000 possible combinations arising just among the limited set of settings we chose for each parameter. In practice, we were able to simulate 20 replicates for 332 actual parameter combinations. In order to assess the impact of each variable parameter setting on the power and efficiency of each study design, and to facilitate generalization of our results to other similar situations that we did not specifically simulate, we constructed linear regression models of the square root of the per-family contribution to the noncentrality parameter  were collapsed into "attributable risks" (AR) for the linked and unlinked loci respectively. The attributable risk is the proportion of the total disease risk attributable to variation at each genetic locus. The fit of linear regression models employing the two AR values is as good as those employing the five original terms to fit the data, using the Akaike Information Criterion .Zc, and the paired test, Zp, most closely matched the nominal test size. Both the mean and standard deviation of Zc were close to theoretical expectations. The standard deviation of Zp was only slightly larger, and the mean was slightly less than zero (0.05 > p > 0.01). The standard deviation of Zd was about 9% larger than expected, so the significance of tests based on this statistic will be overstated unless adjustments are made. We therefore omit Zd from further consideration.In Tables Zmc. Zmp is also conservatively biased, but much less so, because the statistic compares estimated sharing between concordant pairs with estimated sharing between discordant pairs, which is also estimated to be significantly less than 0.5 by the multipoint algorithm. Schork and Greenwood, Cordell, and others [Zmc with increasing marker intervals is not surprising.The mean multipoint estimate of allele sharing was significantly below 0.5 for concordant pairs in these null simulations, leading to a conservative bias in d others ,63 recenZc and Zp behaved differently depending on the heterogeneity model we simulated. Although Zp was conservatively biased when disease allele frequencies differed between populations, regardless of whether marker allele frequencies differed, its small conservative bias was not significantly different from that observed in the homogeneous population of Table Zc exhibited an anticonservative bias when marker allele frequencies differed between populations, regardless of whether disease allele frequencies differed.When we ran null simulations in the presence of heterogeneity of marker alleles, disease alleles, or both, we observed that A subset of results from alternative model simulations in which there were linkages are given in Table Zc/Zp/Zc/Table In general, the effects on power of changes to the genetic and design parameters were very similar for the discordant test. Increasing the number of unaffected sibs typed did yield a small increase in power, but increasing the number of affected sibs, parents or offspring proxies increased power by a larger amount, even with the discordant pair test.The effect of experimental screening for the unlinked syndrome varied substantially depending on the relative magnitude of the effects of the unlinked syndrome: if the unlinked syndrome had an attributable risk greater than or equal to that of the linked syndrome, experimental screening resulted in a large increase in power. Otherwise, the effect of experimental screening was negligible.F and test size α with a specified combination of design and genetic parameters can be derived from the regression models in Table Z/β in the equation below:Power for a given sample size β is the probability of Type II error (hence power is 1-β) and Φ(z) is the cumulative standard normal distribution. A script for computing the predicted power for any particular combination of these parameters, using the statistical languages S-plus or R is also available from the website [where  website .Zc test for varying sample sizes given several values of AR for the linked and unlinked loci, recombination fraction (θ), number of parents genotyped, and number of offspring proxies. Except as noted, the power estimates are based on the following settings of the genetic and design parameters: two total affected sibs, both sampled, two unaffected sibs (not sampled), no parents or offspring proxies, AR1 (linked locus) = 0.1, AR2 (unlinked locus) = 0.05, θ = 0.05, and no screening to exclude unlinked families.Figures ARE for the discordant test was larger than that for the concordant test in 13% of the replications. We used a logistic regression model with the same parameters as those in Tables Zp would outperform Zc in terms of relative efficiency (not shown). Only under circumstances that would result in very low power, such as attributable risks for the unlinked locus more than twice as large as attributable risks for the linked locus, or recombination fractions > 0.1, was Zp predicted to outperform Zc in our simulated sample of 500 families.Because the power of the discordant test was rarely much greater than that of the concordant test, and the concordant test requires genotyping of only the affected sibs, the ARE of the concordant test was always greater on average than that of the discordant test. Nevertheless, we were interested in specific combinations of design and genetic parameters that might have resulted in better relative efficiency for the discordant test. Overall, the Zc and Zp for a selected set of simulations with multipoint Zm scores for the same families as calculated by the computer program Merlin [Zc and Zp. The conservative bias of Zmc noted in Tables Zmc decreases consistently  as marker intervals contract, becoming significantly anti-conservative at 5 cM.In principle, including genotype data from unaffected siblings can improve the ability to estimate haplotypes and thereby improve power when multipoint data are studied. Table m Merlin . In thesReplacement of a missing affected individual by a spouse and offspring is not generally as efficient per genotype as if that individual had been available, although the efficiency improves with each additional offspring included. Figure Zmc is conservatively biased, while exhibiting an anticonservative bias in Table Zmp outperforms with markers spaced at 10 and 20 cM. At 5 cM, Zmc becomes anticonservatively biased, as noted above. It may be useful to perform simulations to assess the characteristics of the tests when the marker spacing decreases, as would be possible with the newer SNP array-based platforms. Further, since genome-wide-association studies do not utilize the full power of the sibpair design, future research should be aimed at assessing the optimal setting for relying on the sibpair design, as it is premature to move completely away from this study design [In studying a disease like colon cancer with both incomplete penetrance and a high incidence of sporadics, prior studies have shown that to be efficient, families must include two or more individuals with the same disease from whom samples can be obtained. The practical experience of many investigators suggests that once an initial entree is gained into a family, the chances of enrolling other members are quite high. Close relatives are often very motivated to participate in research into a disease that has afflicted their family, especially when the commitment is minimal, involving only a blood specimen and a signed consent, which are all that are required for a linkage study of diseases that have an easily established phenotype, like cancer. In our simulations, we considered inclusion of unaffected sibs and the use of spouse and offspring to replace missing affected sibs. Including unaffected siblings in the design of a study can improve the power to detect linkage for highly-penetrant diseases ,66. Howey design .If a secondary goal of a study is to estimate the penetrance, then unaffected relatives should be included in the design of the study; also unaffected siblings could help in evaluating the impact of environmental factors upon disease risk. Genotyping errors for microsatellites scans are currently very low but are hard to assess without the availability of parents or siblings. Our findings parallel those of Holmans et al. , who sugUnaffected siblings can be used for studies that take advantage of linkage disequilibrium to identify associations. Colorectal cancer and other late onset diseases with incompletely penetrant susceptibility alleles complicate the identification of unaffected individuals for association studies, because the probability that a person who does not currently exhibit the disease will become affected sometime in the future can be relatively large. In association studies using families, the oldest unaffected sibling is the most informative because s/he is more likely to have attained the age at which all the cases in the family were diagnosed  study  show thaThe family structures that could be studied are not necessarily restricted to the sibs of a proband ascertained through a registry or clinic. Consideration should also be given to collecting the extended family members of the affected sibs. Familial cancer registries such as the CFRCCS and CGN routinely collect family history from all their participants. Recent reports indicate that study subjects are capable of accurately reporting cancer status among their close relatives, with accuracy varying by cancer site and degree of relationship . PedigreFor rare autosomal dominant traits, Risch  showed tWe estimated the numbers of families required to study colorectal cancer and similar diseases with reasonable power, if our assumptions about disease allele frequencies, mode of inheritance, and heterogeneity are not too far from the truth. Our simulation studies show that at least 500–1000 families are required to provide reasonable assurance of adequate power across a range of genetic models that are consistent with the observed familiality and population prevalence of colorectal cancer. Colon cancer risk is strongly associated with certain environmental factors, some of which might interact with the gene(s) being sought. Although 1000 pairs will most likely provide adequate power to identify genetic risk factors, the further delineation of gene-environment interactions may yet require larger sample sizes . Our simBecause the costs of drawing blood and extracting DNA are far smaller than those of genotyping the 400–1000 markers needed for a genome scan, and because the unaffected and affected siblings can contribute different information, we suggest collecting all available members of each sibship, but only genotyping affected sibs, parents, and any spouse/offspring proxies for an initial genome scan. DNA from the unaffected sibs may still be useful for fine mapping and association studies and for estimating the penetrance. The CFRCCS and DARCC databases indicate that about 90% of the living ASPs have at least one unaffected sib alive, with a mean of about 2.5. Since the optimal number of unaffected sibs to sample per sibship if more than one were available has not been resolved, an ad-hoc plan may be to obtain the blood specimens from all those who consent. If the genotyping resources were constrained (e.g. to at most two unaffecteds per sibship), an efficient protocol is to start with the oldest first-degree relative and to proceed downwards, i.e. include both parents if available, otherwise one parent and the oldest unaffected sib, etc.Population heterogeneity and allele frequencies have an important impact on the study design. In the absence of parents, the marker allele frequencies in the study population have to be estimated as the basis for estimating the IBD probabilities, which requires an assumption of homogeneity of marker allele frequencies. Population heterogeneity arises when the allele frequencies vary across subgroups, because of demographic, geographical, or other factors. Table t-test, like Zp, a more sophisticated GEE-2 approach is possible, modeling the entire vector of phenotypes in each family in relation to its IBD matrix [Zp or multipoint approaches under the simulated conditions of population admixture, although the anti-conservative bias in Zc under heterogeneity of marker allele frequencies may partially obscure a real power difference between the concordant and discordant tests. Population admixture presents a particularly insidious threat to the validity of tests for linkage if parents or unaffected siblings are not available. However, it might be possible to detect population substructure by checking for the departure from disequilibrium that it engenders.We observed moderate to substantial losses of power to detect linkage in the limited number of simulations we performed with population heterogeneity of this sort :195–203.) or estimate haplotype frequencies :754–67. Epub 2005 Sep 20.) If the parents are available, even though we have shown that genotyping them is inefficient, an argument can be made for genotyping them because their inclusion ameliorates any potential effect of population admixture, greatly facilitates the identification of any genotyping errors and reduces the dependence upon correct specification of haplotype frequencies when multipoint analyses are conducted :1106-12. Epub 2004 Oct 18.). The choice of whether or not to genotype unaffected individuals also would depend upon the feasibility and cost of cherry-picking for regional genotyping of regions showing evidence for linkage, but we have not studied either of these issues in this paper. Admixture is more likely to be of concern when studying populations that are known to have been founded by different ethnic groups or races such as Hispanics and African-Americans.We have also observed that, if genetic testing is available for previously-identified syndromes, and if those syndromes are thought to account for a larger portion of the disease burden than the syndrome of interest, prior exclusion of families linked to the known syndrome can meaningfully increase the power of the study.Finally we note that the colon sibpair study, for which this paper was written, was completed after accruing less than 100 families. In fact, most of the colon sibpair studies that have been published include fewer than 100 families, because recruitment is a major challenge. Although the results discussed here suggest numbers that may be challenging to accrue, the published literature has reported positive studies, suggesting that the assumptions used in our calculations may have been too conservative. In addition, linkage studies are meant to be performed in an iterative fashion so that the results from ongoing studies can be combined. Since our conclusions and recommendations arising from the simulations describe relative advantage of various designs, our results are of value in future study design.The authors declare that they have no competing interests.RAK took the lead in developing the results (performed simulations) and in writing the manuscript; CIA was a major participant in developing the results and preparing the manuscript; BYY drafted the manuscript and participated in manuscript preparation discussions, DMF coordinated the draft and development of the manuscript and participated in manuscript preparation discussions, DCT was a major participant in developing the results and preparing the manuscript. All authors read the final manuscript.The pre-publication history for this paper can be accessed here:


PTPN22 gene and rheumatoid arthritis across multiple resources containing both family-based and independent individuals. Our findings are generally consistent with previous reports for a panel of 14 single-nucleotide polymorphism (SNP) markers, including functional coding SNP R620W, in which the minor allele conferred a significant two-fold increased risk. More power to detect associations was achieved in certain analyses by using extra family-based samples, rather than restricting analyses to single cases randomly selected from each pedigree.PedGenie beta version 2.1 is a unique, flexible, and easily implemented analysis software tool that is enhanced significantly by incorporation of meta-statistics to allow valid combined analysis of multiple studies, including mixtures of family-based and independent resources, in the detection of genetic association with common disease. Genetic Analysis Workshop 15 Problem 2 data, provided by the North American Rheumatoid Arthritis Consortium, were used to demonstrate PedGenie 2.1 meta-association testing of variants in the  PTPN22 candidate gene  and consensus criteria rheumatoid arthritis (RA) phenotype and sub-phenotypes in combined family-based and independent individuals using PedGenie 2.1. RA, a common systemic autoimmune disease, affects about 1% of adults worldwide and has an estimated heritability of 50 to 60% [PTPN22 , has been previously suggested [In the study of common diseases and genes with modest effects, large consortium and multicenter efforts hold the promise of increased power to detect associations, but also present analytical challenges. Candidate gene study populations differ geographically and ethnically, and considerable differences in case-control ascertainment and pedigree structures between resources are likely. Currently, no software package exists that allows valid meta-genetic association testing in mixtures of independent and family-based resources (including pedigrees of arbitrary length and configuration) between or within studies. PedGenie 2.1 (beta version) extends the functionality currently available in PedGenie (version 1.2) [0 to 60% ,4. The auggested .PTPN22. The genotypes and phenotypes were collected from Caucasian individuals in NARAC affected sibling-pair families (1393 cases) and 1519 matched, independent non-diseased controls from New York City (NYC), reported in Carlton et al. [Data provided by the North American Rheumatoid Arthritis Consortium (NARAC) were obtained for 14 SNPs in n et al. . In addin et al.  RF titerPTPN22 SNP and phenotype data were separated into two study files, designated NARAC 1 and NARAC 2  which represents combinations of levels of several variables  . Meta stPTPN22 SNP associations with RA for each demonstration study and the combined study PedGenie 2.1 meta-analysis results are shown in Table r2 > 0.4) with each other. SNPs rs12730735 and rs12760457 were in complete LD. SNP ss38346943, which has a rare, protective minor allele, was not in LD with any other marker.The study characteristics and RA phenotypes used to demonstrate PedGenie 2.1 meta-association analysis are described in Table PTPN22 markers for an additive model (Armitage test for trend [Table or trend ) that weor trend . The oddPTPN22 R620W genotypes containing the variant allele were strongly associated with RF+ but not RF- disease [Previous studies reported that susceptible  disease ,6. Our mPedGenie 2.1 can correct for all relationships in family-based resources, therefore all family members with phenotype and genotype data are available can be included. If only one affected sibling was chosen from each pedigree, the sample size here would have reduced from 1285 cases and 1621 controls to 665 and 1518, respectively. For example, in NARAC 1, a family with five affected and five unaffected genotyped siblings and parents with known RA status (one genotyped) were included in PedGenie analyses, whereas only one affected sib was randomly selected from this family for the study performed by Carlton et al. [CMH statistics for ordered genotypes have been used to assess association in multiple case-control studies in which cases are independent, either probands or randomly selected affecteds . A combiPTPN22 gene is associated with RA. However, our results do not indicate that anti-CCP antibody status significantly discriminates for disease in the functional R620W SNP.In conclusion, our method is a more comprehensive way of using all data available in meta-association testing, with more power to detect associations by using extra family-based samples rather than restricting to randomly selected cases from each pedigree. Our findings generally corroborate those previously reported. We support previous findings that the The author(s) declare that they have no competing interests.


Rheumatoid arthritis  is a common and complex inflammatory disorder. The North American Rheumatoid Arthritis Consortium (NARAC) data, as part of the Genetic Analysis Workshop 15 data, consists of both genome scan and candidate gene studies on RA patients.PTPN22 and SUMO4. Based on significant association evidence, we built an association network among the loci of PTPN22, PADI4, DLG5, SLC22A4, SUMO4, and CARD15. To control for false positives, we used permutation tests to constrain the family-wise type I error rate to 1%.We applied the backward genotype-trait association (BGTA) algorithm to capture marginal and gene × gene interaction effects of multiple susceptibility loci on RA disease status. A two-stage screening approach was used for the genome scan, whereas a comprehensive study of all possible subsets was conducted for the candidate genes. For the genome scan, we constructed an association network among 39 genetic loci that demonstrated strong signals, 19 of which have been reported in the RA literature. For the candidate genes, we found strong signals for Using the BGTA algorithm, we identified genetic loci and candidate genes that were associated with RA susceptibility and association networks among them. For the first time, we report possible interactions between single-nucleotide polymorphisms/genes, which may be useful for biological interpretation. CTLA4) and 11p12 in a genome scan. Plenge et al. )For subsets identified with more than one SNP, we constructed a graphical network using the graph exploration system GUESS  Figures and 4. APADI4), 2q33.3 (CTLA4), 5p15.33, 8q24.23, 14q11.2, 14q12, and 18p11.21), which have a large number of interaction edges with other loci. The literature suggests that seven out of these eight loci have previously been found to be associated with susceptibility to RA. All 39 marker loci in the association network of Figure PTPN22, was not among these 39 loci, but its signal was right below our selection threshold.From the two-stage screening of the Illumina data, clusters of SNPs with high GTD scores were returned as important. Based on 50 permutations, we estimated the FDR as described by Storey and Tibshirani  at diffePTPN22), and rs237025 and rs577001 (both at the locus of SUMO4). The significantly associated subsets with two or more SNPs represent possible interactions between these candidate genes in affecting the risk of developing RA. In Figure For the candidate gene data, we studied all possible subsets of SNPs and identified eight significant BGTA-irreducible subsets on seven SNPs after controlling for family-wise type I error. The marginally significant (one-marker subset) SNPs are rs2476601  declare that they have no competing interests.


BMC Proceedings contains the proceedings of Genetic Analysis Workshop (GAW) 16, which was held September 17-20, 2008, in St. Louis, Missouri, USA. Initiated in 1982, the GAWs are now held in even-numbered years with the purpose of evaluating strategies for detecting genetic effects of complex diseases, thought to be the result of the joint effects of environmental and genetic factors. Each GAW meeting begins with the distribution of datasets that those who attend the Workshop use for the purpose of developing and/or evaluating statistical methods. These datasets are jointly chosen for the next Workshop through a discussion of those attending the meeting and the GAW Advisory Committee. At most Workshops, GAW has included a set of simulated datasets, so that researchers can examine the behavior of statistical methods when knowing the answer. A primary goal of the Workshops is to focus discussion on specific topics of interest and areas of methodological concern. The datasets are generally available to any researcher who requests them. Each person who desires to attend the Workshops must participate in the evaluation of at least one of the distributed datasets, investigating novel approaches or comparing emerging and existing methods. Participants also include those who have provided the data or participate in the Workshop organization. More information about GAW, including details of upcoming Workshops, may be found at http://www.gaworkshop.org.This supplement to Genetic Analysis Workshop 16 focused its efforts on the evaluation of genome-wide association studies of large genomic chip datasets containing hundreds of thousands genotypes from single-nucleotide polymorphisms (SNPs). There were three problem datasets, two consisting of data from ongoing studies and one simulated. All three datasets consisted of phenotypic and genome-wide SNP scan data. Problem 1 data came from studies of rheumatoid arthritis (RA), Problem 2 included genotypic and phenotypic data from the Framingham Heart Study (FHS), and Problem 3 consisted of simulated phenotypic data using the pedigrees and genotypic data provided to GAW16 by the Framingham Heart Study. Each of these datasets is described in more detail in Amos et al. , which pDRB1 alleles, which were classified according to the RA shared epitope, levels of anti-cyclic citrullinated peptide, and levels of rheumatoid factor IgM.Data for Problem 1 was derived from a genome-wide study of RA. SNP genotype data were provided for 868 cases and 1,194 controls that had been assayed using an Illumina 550 k platform. The cases were independent individuals who had met the American College of Rheumatology criteria for RA. Four hundred forty-five cases came from a single member of sibling sets that were studied as a part of the North American Rheumatoid Arthritic Consortium (NARAC) because they had at least one additional sibling with rheumatoid arthritis; an additional 423 independent cases were included and were not selected for family history. The cases were recruited from across the United States and are predominantly of Northern European origin. The controls, derived from the New York Cancer Project, were enrolled in the New York metropolitan area and are somewhat enriched for individuals of Southern European or Ashkenazi Jewish ancestry compared with cases. Phenotypic data were also provided for Data for Problem 2 derived from a genome-wide scan conducted in Framingham Heart Study participants through the SNP Health Association Resource (SHARe). More detail describing this effort is included at the dbGaP . GenotypPhenotypic data for Problem 3 were simulated, using the pedigrees and genotypes from Problem 2. The simulated data were derived from a model emulating lipid traits and their relationships to cardiovascular disease. Two hundred simulated replicates were provided for GAW16. For each replicate there were 6,476 subjects in families from the FHS, with their actual genotypes for Affymetrix 550 k SNPs and simulated phenotypes. The total number of subjects and pedigree structures differed from those in Problem 2, because between the times that simulation began and data were made available, additional FHS participants provided consent for use of their data. Simulated phenotypes at three visits, 10 years apart, were generated for Problem 3. Up to six "major" genes influencing variation in high- and low-density lipoprotein cholesterol , and triglycerides (TG), and 1,000 "polygenes" were simulated for each trait. All polygenes act independently and have additive effects. A group of 39 polygenes influencing HDL were clustered on chromosome 11; otherwise, the polygenes for each trait were randomly distributed throughout the genome. At each simulated visit, individuals in the upper tail of the LDL distribution were designated as medicated. The proportion of subjects that are medicated increased across visits at 2%, 5%, and 15%. Coronary artery calcification (CAC) was simulated using age, lipid levels, and CAC-specific polymorphisms. The risk of myocardial infarction before each visit was determined by CAC and its interactions with smoking and two genetic loci. Smoking was simulated to be commensurate with rates reported by the Centers for Disease Control. The full model for these simulated data is included in Kraja et al. [Individuals on the GAW mailing list of nearly 2,600 were notified through e-mail in Spring 2008 that data for the three Problems were available. A total of 183 groups requested GAW16 data: 124 for Problem 1 data and 59 for Problems 2 and 3 data, which needed to be accessed through dbGaP. In Summer 2008, 168 contributed papers were received describing analyses of these data sets. A book and CD containing these contributions plus descriptions of the data sets were distributed to GAW16 participants before the meeting in September.Genetic Epidemiology [The GAW16 participants included 240 individuals from all over the world, including Austria, Brazil, Canada, France, Germany, India, Korea, the Netherlands, Singapore, Spain, Taiwan, the United Kingdom, and the United States. The 168 contributions submitted to GAW16 were organized into 17 presentation groups of 7 to 18 papers each. These presentation groups were organized around the following themes: genome-wide association (GWA) for discrete traits; GWA for quantitative traits; multi-stage GWA strategies; haplotype-based analyses; controlling false-positive rates; multi-phenotype analyses; phenotype definition and development; quality control in GWA studies; machine learning; gene-gene interaction; gene-environment interaction; using gene expression, function, and pathways in GWA; combining information from linkage and association analyses; population and evolutionary genetics, including linkage disequilibrium patterns and population stratification; GWA analysis of longitudinal data; family-based GWA analyses; and gene- or region-based association analyses. Each presentation group was led by a person with previous GAW experience who facilitated group discussion, organized the group's oral presentation for the general GAW meeting, and took a lead in writing the group summary paper, which are published simultaneously with these proceedings in Members of presentation groups began interacting by e-mail and/or conference calls before GAW16, comparing and contrasting their approaches and results. Each presentation group met a full day at the Workshop, a first for GAW. During these meetings, they continued their discussions and finalized a group presentation, which was delivered to the full GAW16 audience during the general sessions on the subsequent two days. The group meetings were attended mostly by group participants, but were open to all GAW16 attendees. Seventy-two participants also contributed to poster sessions held during the general sessions. There also was a special general session on Novel Methods. Four papers submitted to GAW16 were selected before the meeting for presentation in this session because they had used or developed novel analytical approaches.BMC Proceedings are a subset of the 168 contributions presented at GAW16. All contributions were peer-reviewed and selected on the basis of scientific merit.The 131 GAW contributions included in this issue of Genetic Epidemiology, published simultaneously with these Proceedings, a paper by each presentation group summarizes the contributions to that group and the lessons learned, comparing and contrasting contributions and describing their main themes and results. Overall, GAW16 generated many interesting discussions and some conclusions concerning appropriate approaches to the analysis of genome-wide association data. These discussions also highlighted areas in which further methodological development is needed.The first three papers of these Proceedings describe the datasets. These are followed by the 131 individual GAW16 contributions organized by presentation group, and alphabetically by first author within each group. Additionally, in a supplement to the journal The authors declare that they have no competing interests.