SLC24A5 and SLC45A2 are strongly associated with melanin levels in the sample.We carried out an admixture analysis of a sample comprising 1,019 individuals from all the provinces of Cuba. We used a panel of 128 autosomal Ancestry Informative Markers (AIMs) to estimate the admixture proportions. We also characterized a number of haplogroup diagnostic markers in the mtDNA and Y-chromosome in order to evaluate admixture using uniparental markers. Finally, we analyzed the association of 16 single nucleotide polymorphisms (SNPs) with quantitative estimates of skin pigmentation. In the total sample, the average European, African and Native American contributions as estimated from autosomal AIMs were 72%, 20% and 8%, respectively. The Eastern provinces of Cuba showed relatively higher African and Native American contributions than the Western provinces. In particular, the highest proportion of African ancestry was observed in the provinces of Guantánamo (40%) and Santiago de Cuba (39%), and the highest proportion of Native American ancestry in Granma (15%), Holguín (12%) and Las Tunas (12%). We found evidence of substantial population stratification in the current Cuban population, emphasizing the need to control for the effects of population stratification in association studies including individuals from Cuba. The results of the analyses of uniparental markers were concordant with those observed in the autosomes. These geographic patterns in admixture proportions are fully consistent with historical and archaeological information. Additionally, we identified a sex-biased pattern in the process of gene flow, with a substantially higher European contribution from the paternal side, and higher Native American and African contributions from the maternal side. This sex-biased contribution was particularly evident for Native American ancestry. Finally, we observed that SNPs located in the genes  SLC24A5 and SLC45A2 show a strong association with skin pigmentation in the sample.Cuba is the largest island of the Greater Antilles and its most populous country. The post-Columbian history of the Caribbean has been marked by the encounter of people from different continents. Here, we present an admixture analysis of 1,019 individuals from all the provinces of Cuba, using autosomal, mtDNA and Y-chromosome markers. We also analyzed the association of 16 single nucleotide polymorphisms (SNPs) with quantitative estimates of skin pigmentation (melanin index). The highest proportions of African ancestry were observed in the Southeastern provinces of Santiago de Cuba and Guantánamo, and the highest proportions of Native American ancestry were found in the Eastern provinces of Granma, Holguín and Las Tunas. Similar geographic patterns were observed in the analyses of the uniparental markers. Additionally, by comparing the autosomal and uniparental admixture proportions, we identified a clear sex-biased pattern in the process of gene flow, with a substantially higher European contribution from the paternal side than the maternal side, and conversely higher Native American and African contributions from the maternal side than the paternal side. Finally, we observed that SNPs located in the genes  The post-Columbian history of the Caribbean has been marked by the encounter of people from different continents. This is reflected in the gene pool of the present inhabitants of the Caribbean archipelago, as shown in recent studies using autosomal, mtDNA and Y-chromosome markers th century. Historical records indicate that most of the immigrants from Spain were male (60–85%), and that mixing between European males and indigenous and African females occurred since the early stages of the colonization of the island Evidence of human habitation in Cuba goes back to approximately 7,000 years BP Here, we present an admixture analysis of a large sample comprising 1,019 individuals from the 16 provinces of Cuba. We used a panel of 128 Ancestry Informative Markers (AIMs) to estimate the admixture proportions. In addition to the AIMs, we also characterized a number of haplogroup diagnostic SNPs in the mtDNA and Y-chromosome in order to evaluate admixture using uniparental markers. Finally, we also evaluated the association of 16 single nucleotide polymorphisms (SNPs) with skin pigmentation.SLC24A5 and SLC45A2 are strongly associated with melanin levels in the sample.This study is relevant from different points of view. Understanding the distribution of admixture proportions throughout Cuba is important from an anthropological perspective, and this is the most extensive effort carried out to date in terms of the size and representativeness of the sample. Additionally, the study of uniparental markers provides interesting evidence regarding the directionality of gene flow. The elucidation of admixture proportions is also of interest for future application of admixture mapping studies or genome-wide association studies in Cuba. Finally, we show that SNPs located in the genes The average age of the participants was 49.35 years  and 58% were female. The participants came from all the provinces of Cuba, primarily from urban areas . In terms of the self-reported census classification, 55% of the participants indicated to be “blanco”, 33% “mestizo” and 12% “negro” .F = 11.54, P<0.001; Native American F = 13.06, P<0.001). Post-hoc tests indicate that, in terms of African proportions, the differences are driven by the higher African proportions in the provinces of Santiago de Cuba (39%) and Guantánamo (40%), with respect to the other provinces (11% to 24%). With respect to the Native American contributions, a clear pattern is also present, with higher average contributions in the Eastern provinces, particularly Granma (15%), Las Tunas (12%) and Holguín (12%) than in the Western provinces.Estimates of admixture proportions were obtained with the program ADMIXMAP, using data from 128 AIMs. In the total sample, the average European, African and Native American contributions were 72% (range 4.3% to 98.2%), 20% (range 0.8% to 95.2%) and 8% (range 0.4% to 34%), respectively . By provkappa = 0.8873 kappa = 0.9091 kappa = 0.9345 As indicated above, 55% of the participants self-reported to be “blanco”, 33% “mestizo” and 12% “negro”. These proportions are similar to those based on the report of an external observer; there were discrepancies for only 65 out of the 1019 individuals. Several measures of concordance indicated excellent agreement between both classifications (Cohen's P = 0.015). The average melanin index of the total sample was 39.8, but there was a broad distribution of values, from 23.4 to 85.9. In individuals who self-reported to be “blanco”, the average melanin index was 34.06±3.70 (mean ± SD), in those who self-reported to be “mestizo” 41.69±6.29 and in those who self-reported to be “negro” 60.59±8.87 .Age did not have a significant effect on melanin levels (M), measured quantitatively with the reflectometer (melanin index) .59±8.87 . The difF = 1048.04, P<0.001; African: F = 1138.97, P<0.001; Native American: F = 34.19, P<0.001).The average European, African and Native American ancestry in those self-reporting to be “blanco” were 86%, 6.7% and 7.8%, in those self-reporting to be “mestizo” 63.8%, 25.5% and 10.7%, and in those self-reporting to be “negro” 29%, 65.5%, 5.5% . , and European ancestry was inversely correlated with melanin index . No significant correlation was observed between Native American ancestry and melanin index .The levels of pigmentation show a strong correlation with the estimates of individual ancestry proportions obtained with the panel of AIMs. African ancestry was positively correlated with the melanin index  and Santiago de Cuba (SC) have significantly higher melanin index values  .2 = 0.69, P = 7×10−5, and r2 = 0.63, P = 0.63, P = 2×10−4, see also 2 = 0.43, P = 6×10−3). In addition to the relationship of ancestry and census proportions by province, we also explored to which extent there are differences in admixture proportions within each census category  between provinces  African admixture proportions are higher in Guantánamo and Santiago de Cuba because these provinces have higher proportions of individuals self-reporting to be “negro” or “mestizo”, who on average have higher African contributions than individuals reporting to be “blanco”, or (ii). There are no differences in the proportion of individuals self-reporting to be “blanco”, “mestizo” or “negro” between Guantánamo and Santiago de Cuba and the other provinces, but the average African admixture contributions in at least some of the census categories are higher in Guantánamo and Santiago de Cuba than in the other provinces. In order to evaluate these two scenarios, we explored the relationships between African admixture proportions and the proportion of individuals in each province reporting to be “negro”, “mestizo”, or “blanco”. We observed a strong positive relationship between average African ancestry in each province and the proportion of individuals reporting to be “negro” or “mestizo” (rrovinces . The preP = 0.003), and conversely, the Native American ancestry proportions were significantly higher in rural than urban areas (P = 2×10−6)  . A plot A total of 943 mtDNA haplotypes could be allocated to a specific branch of the mtDNA phylogeny resolved by the mtSNPs genotyped in the present study  P<0.0031): rs1426654 located on the SLC24A5 gene (P = 1.2×10−25), rs16891982 and rs35395 located on the SLC45A2 (MATP) gene , and rs12913832 located on the HERC2 gene, linked to OCA2 (P = 0.0018). In order to evaluate if there was evidence of residual stratification unaccounted for in the analysis based on the three-parental model, we used the P-values obtained for 86 AIMs located more than 5 cM apart from the 16 pigmentation markers to estimate the lambda inflation factor. We observed evidence of residual stratification (lambda = 1.38). Therefore, we implemented genome control (GC) SLC24A5 rs1426654 (P = 5.1×10−19), SLC45A2 rs16891982 (P = 2.9×10−15) and SLC45A2 rs35395 (P = 1.5×10−8) remained significant after Bonferroni correction. However, the P-value for HERC2 rs12913832 (P = 0.0078) slightly exceeded the Bonferroni-corrected threshold. P-values for all the pigmentation markers. Assuming an additive model, we estimated that each copy of rs1426654 allele A and rs16891982 allele G decrease the melanin index by 5.04 and 3.40 units, respectively. The HERC2 SNP rs12913832 has a substantially smaller effect, with each copy of the G allele, which has been associated with blue iris color in previous studies P-value observed for rs35395 at the SLC45A2 locus was no longer significant, indicating that the significant result for this marker is primarily due to its linkage with rs16891982, which is located approximately 3 kb apart from rs35395 on chromosome 5. None of the other 12 SNPs surveyed had significant effects on melanin levels after conditioning for the rs1426654, rs16891982 and rs12913832 polymorphisms.Sixteen genetic markers located within or nearby genes that previously have demonstrated association with skin pigmentation , 20%  and 8% , respectively. However, the amount of European ancestry tends to be higher in the Western provinces of Cuba than in the Eastern provinces. In contrast, the highest African proportions are observed in the eastern provinces of Santiago de Cuba and Guantánamo and the highest Native American contributions in the Eastern provinces of Las Tunas, Granma and Holguín. Importantly, the results based on analyses of the mtDNA and Y-chromosome SNPs are fully consistent with this picture. The highest Eurasian proportions observed for both the mtDNA and the Y chromosome are found in the Western provinces, particularly Matanzas and Pinar del Río, and the highest African contributions are present in Santiago de Cuba. Regarding the Native American contribution, the mtDNA analysis also indicates that the highest Native American proportions are present in the provinces of Holguín and Las Tunas. We only observed two Native American Q-M3 haplogroups in the male sample, corresponding to individuals from the provinces of Camagüey  and Santiago de Cuba (in the East).Our analyses indicate that the geographic trends observed in ancestry proportions are due, at least to some extent, to differences in the relative proportions of individuals reporting to be “blanco”, “mestizo” or “negro” across provinces. The provinces of Guantánamo and Santiago de Cuba, which show the highest average African ancestry and melanin index levels, also have the highest proportion of individuals self-reporting to be “mestizo” and “negro”. However, this does not seem to be the only reason behind these differences. We also observe that there are some differences in average admixture proportions within each census group between provinces. For example, the average African ancestry of individuals self-reporting to be “blanco” tends to be higher in Guantánamo, Santiago de Cuba and Granma than in other provinces. In general, our study highlights the subjectivity involved in the categories “blanco”, “mestizo” and “negro”. Although there are significant differences in melanin index between the three categories, there is some overlap in melanin values between these groups. This means that two individuals with the same melanin index values may report different census categories (e.g. “blanco” or “mestizo”). In addition to the analyses by province, we also evaluated the distribution of ancestry proportions in urban vs. rural areas. We observed that the African ancestry proportions were significantly higher in urban than rural areas, and conversely, the Native American ancestry proportions were significantly higher in rural than urban areas.th century The geographic patterns observed in the distribution of admixture proportions are in agreement with historical and archaeological data. It is known that at the arrival of the Spaniards to Cuba, the Taino primarily inhabited the eastern regions of Cuba. Estimates of the population distribution in the year 1510 indicate that more than 50% of the indigenous Cuban population lived in the eastern region (from Las Tunas to Guantánamo), less than 40% lived in Camagüey and Las Villas , and less than 10% inhabited the western region of the island. Within the eastern region, Holguín was the most populated area, followed by the region of Bayamo (currently the province of Granma) The comparison of the relative autosomal, paternal and maternal admixture proportions clearly show that the process of admixture in Cuba has been sex-biased, with a relatively higher European contribution observed for the paternal lineages, and a higher African and Native American contribution in the maternal lineages. This sex-biased contribution is particularly evident for the Native American ancestry. We estimated the average maternal Native American proportion to be 34.5% in the sample, in sharp contrast to the autosomal (8%) and paternal (0.5%) proportions. The African maternal, autosomal and paternal proportions were estimated to be 39%, 20% and 18%, respectively. Overall, our results are very similar to those obtained in an independent study that analyzed mtDNA and Y-chromosome variation in a Cuban sample comprising 245 individuals P = 5.8×10−4). In contrast, none of the AIMs surpass this threshold when the analysis is carried out conditioning on individual ancestry. This implies that in case-control studies in which there are differences in ancestry proportions between the case and control group, or association analysis of quantitative traits that have different distributions in the parental populations, such as pigmentation, there would be a dramatic inflation in the number of false positives. We observed that even after conditioning for individual ancestry there was evidence of residual stratification in the Cuban sample, although of relatively small magnitude (lambda 1.38). Consequently, the P-values observed for the pigmentation markers were corrected using Genome Control (GC) strategies.We explored the relationship between admixture estimates based on genetic markers, melanin levels measured with a reflectometer, and self-reported census categories . We observed strong relationships between admixture proportions and melanin levels, admixture proportions and census categories, and melanin levels and census categories see  section.SLC24A5 gene (P = 5.1×10−19) and rs16891982, located within the SLC45A2 (MATP) gene (P = 2.9×10−15) with skin pigmentation. These two markers have the strongest effects on melanin levels described in human populations, and in our study we estimated that each copy of rs1426654 allele A and rs16891982 allele G decrease the melanin index by 5.04 and 3.40 units, respectively. The marker rs12913832, which is located within the HERC2 gene and is known to affect the transcription of the OCA2 gene, showed a significant effect in the initial ADMIXMAP association tests (P = 0.0018), but it did not surpass the Bonferroni-corrected threshold (P<0.0033) after GC-correction (P = 0.0077). This marker is strongly associated with blue eye color in European populations Finally, we also evaluated the association of 16 SNPs located within or nearby pigmentation genes with melanin levels (e.g. melanin index). These polymorphisms have been associated with pigmentary phenotypes in previous studies 2 values for European, African and Native American ancestry were 0.72, 0.72 and 0.27, respectively. For 194 AIMs, the r2 values for European, African and Native American ancestry were 0.85, 0.89 and 0.43. The lower r2 values observed for Native American ancestry are primarily due to the low overall Native American proportions observed in the Puerto Rican sample . Therefore, based on the Puerto Rican data, we can infer that our panel of AIMs should provide reasonable estimates of European and African contributions at the individual level (r2 with estimates based on genome-wide data close to 0.8), although the precision for the Native American ancestral component is probably substantially lower (r2<0.4). These r2 values give an indication of the average precision of the individual ancestry in the full sample, but there will be some variation in the level of concordance between the genome-wide and the AIMs estimates for each individual. With respect to the estimates of maternal and paternal contributions, the number of markers characterized in the sample is enough to obtain adequate estimates of ancestral contributions at the continental level, but given the relatively low number of diagnostic sites the resolution of the haplogroups is phylogenetically low; therefore a much more extensive analysis would be necessary in order to obtain a more precise picture of the mtDNA and Y-specific lineages present in the Cuban population. We hope that future studies of this sample using microarray platforms, and a much more extensive characterization of the mtDNA (e.g. sequencing the whole molecule) and Y-chromosome will make it possible to obtain a more complete perspective of the complex history of the Cuban population, expanding the current level of resolution from the continental to the intra-continental level . A recent paper by Moreno-Estrada et al. One of the limitations of this study is the relatively small number of genetic markers used to characterize admixture proportions. We employed 128 autosomal AIMs to identify ancestral contributions, and this panel should be sufficient to obtain precise admixture estimates for the overall sample and the provinces. However, the precision of the individual admixture estimates is not comparable with the precision that can be achieved with dense microarrays. Unfortunately, we do not have genome-wide data to evaluate the precision of our individual admixture estimates. An indirect estimate can be obtained through comparison with a sample from Puerto Rico SLC24A5and SLC45A2 are significantly associated with skin pigmentation in the sample, in accordance with what has been reported in other admixed populations.By genotyping a panel of autosomal AIMs in combination with mtDNA and Y-chromosome markers in a large sample representative of all Cuban provinces, we were able to identify very clear patterns in the distribution of admixture proportions throughout Cuba. The analysis using AIMs indicated that the average European, African and Native American contributions were 72%, 20% and 8%, respectively. However, the African and Native American contributions were relatively higher, and the European contributions lower, in the Eastern provinces than in the Western provinces. In particular, the Southeastern provinces, such as Santiago de Cuba and Guantánamo, showed the highest African proportions, and the highest Native American proportions were found in the Eastern provinces of Granma, Holguín and Las Tunas. Similar geographic patterns were observed in the analyses of the uniparental markers. Additionally, by comparing the autosomal and uniparental admixture proportions, we identified a clear sex-biased pattern in the process of gene flow, with a substantially higher European contribution from the paternal side than the maternal side, and conversely higher Native American and African contributions from the maternal side than the paternal side. The geographic patterns observed for the admixture proportions are consistent with historical and archaeological evidence. The identification of sex-biased gene flow is also in agreement with historical information indicating that most of the European immigrants throughout Cuban history were male and that the process of admixture took place primarily between European males and Native American and African females. Finally, we observed that SNPs located in the genes The study was approved by the Research Ethics Committee of the National Centre of Medical Genetics of Cuba. Each individual in this study gave written informed consent prior to the interview, physical examination and blood sample collection.The final sample comprised 1,019 individuals representing all the provinces of Cuba. The selection of the individuals was made in collaboration with the National Statistics Office from Cuba. The individuals were selected based on the demographic characteristics of the Cuban population in terms of population density, age, gender and census category . Individuals were recruited from 1,229 households, located in 137 of the 168 Cuban municipalities. Selection of individuals from each household was based on the Kish grid, in order to ensure that all the members of the household had the same probability of being selected for the study. The final sample represents quite well the current distribution of the Cuban population in terms of sex, age, census category , provincial population density and rural/urban residence. A detailed comparison of the relative proportions of each category in the study sample and the Cuban census is provided as supplementary information see . Researcvia questionnaire and physical examination. Information about census category was obtained in two ways: self-reported by the participants and independently classified by one trained researcher (EFS) for all the individuals included in the study.The concordance between the two classifications was evaluated using Cohen's kappa coefficient kappa coefficients.Information about individual, parent and grandparents place of birth, demographics, education level, physical health, mental disorders, non-communicable disease risk factors and anthropometry was collected Melanin content of the skin was measured with a narrow band reflectometer  In order to estimate genomic ancestry, 128 AIMs were genotyped using the SequenomMassARRAY Genotyping platform   were genotyped. MtSNPs were selected from a wider mtSNP panel published by Álvarez-Iglesias et al. http://www.isogg.org/wiki/Y_Chromosome_Consortium).We analyzed 12 Y-SNPs, namely, M22, 92R7, SRY1532, M70, M173, Tat, M213, M9, M269, M173, M242, M3. These SNPs were selected from a wider panel of SNPs described in Brión et al. Average admixture proportions, the sum of intensities parameter  and the individual ancestry proportions were estimated using the software ADMIXMAP v3.8 for Windows. This is a general purpose program for modeling population admixture with genotype and phenotype data, based on a combination of Bayesian and classical methods. If information for a quantitative trait (such as skin pigmentation) is provided, ADMIXMAP fits a linear regression model of the trait conditioning upon individual admixture. Covariates such as sex and age can be included in this model. Detailed information about this program can be found in Hoggart et al. rho test. A two-way ANOVA was conducted in order to evaluate the relationship between melanin index and skin color using sex as a covariate. Finally, potential differences in the distributions of mtDNA and Y-chromosome haplogroups among provinces were evaluated using exact tests. The above described statistical analyses were performed in Statistic 7.0 and SPSS 20.0.Differences between provinces and between sexes for the melanin index and the ancestral genetic proportions were assessed using one-way ANOVA. The relationship between age and skin pigmentation was assessed by the parametric Pearson correlation test and also the non-parametric Spearman's Figure S1Relationships between admixture proportions estimated with AIMs and census categories:”negro”, “mestizo”, “blanco”.(TIF)Click here for additional data file.Figure S2Plot of admixture proportions estimated with AIMs and census category: “negro”,“mestizo” and “blanco”, by province.(TIF)Click here for additional data file.Figure S3Plot of admixture proportions: African, Native American, European, estimated with AIMs in urban and rural areas.(TIF)Click here for additional data file.Figure S4Plot of admixture proportions: African, Native American, European estimated with AIMs in urban/rural areas by province.(TIF)Click here for additional data file.Figure S5mtDNA phylogeny.(TIF)Click here for additional data file.Figure S6Y-chromosome phylogeny.(TIF)Click here for additional data file.Table S1Comparison of demographic characteristics in the study sample and the Cuban census from 2002.(DOCX)Click here for additional data file.Table S2Autosomal AIMs genotyped in the study.(DOCX)Click here for additional data file.Table S3SNPs on pigmentation genes.(DOCX)Click here for additional data file.Table S4Primers designs of the mtSNPs genotyped in the present study.(XLSX)Click here for additional data file.Table S5Haplogroup assignations based on 18 mtDNA markers.(DOCX)Click here for additional data file.Table S6Contingency table analysis for mtDNA.(DOCX)Click here for additional data file.Table S7Haplogroup assignations based on Y-chromosome markers.(DOCX)Click here for additional data file.Table S8Contingency table analysis for Y-chromosome.(DOCX)Click here for additional data file.


In this work, I present a decision theory for the use of family-wise corrections for multiplicity and a generalization of the Dunn-Šidàk correction that relaxes the assumption of uniformly-distributed null p-values. The independence assumption is also relaxed and handled through calculating the effective number of independent tests. I also explicitly show the relationship between order statistics and family-wise correction procedures. This generalization may be applicable to multiplicity problems outside of genomics.The most important decision faced by large-scale studies, such as those presently encountered in human genetics, is to distinguish between those tests that are true positives from those that are not. In the context of genetics, this entails the determination of genetic markers that actually underlie medically-relevant phenotypes from a vast number of makers typically interrogated in genome-wide studies. A critical part of these decisions relies on the appropriate statistical assessment of data obtained from tests across numerous markers. Several methods have been developed to aid with such analyses, with family-wise approaches, such as the Bonferroni and Dunn-Šidàk corrections, being popular. Conditions that motivate the use of family-wise corrections are explored. Although simple to implement, one major limitation of these approaches is that they assume that p-values are i.i.d. uniformly distributed under the null hypothesis. However, several factors may violate this assumption in genome-wide studies including effects from confounding by population stratification, the presence of related individuals, the correlational structure among genetic markers, and the use of limiting distributions for test statistics. Even after adjustment for such effects, the distribution of  A recurring question in large-scale studies concerns the proper statistical treatment of findings when numerous tests are performed. Using nominal significance levels as a threshold for reporting findings is prone to false positives. Historically, this is particularly problematic in genetic epidemiology studies focused on disease association within sets of candidate genes. It is well-known that the rate of replicating results from such studies was exceedingly low, suggesting ubiquitous type I errors ,2. SeverIn some instances—but not all—it is useful to think of interpretation of reported results as being dependent on the total number of tests performed as part of a study. Numerous methods have been devised to address this multiplicity problem and most provide a fairly reasonable tradeoff between false positive and false negative error rates across many applications. These methods include family-wise corrections e.g., –9), fals, fals9])p-values under the null. Integration of this null generates the generalized Dunn-Šidàk experiment-wise p-value. As technological artifacts, cryptic relatedness, and population stratification produce departures from the uniform distribution of p-values under the null, this simple method may be particularly useful for genomic studies. Lastly, one can incorporate an effective number of tests procedure, such as the Cheverud-Nyholt method, into the generalized experiment-wise p-value calculation to treat the correlation between tests. Hence, the full approach enables the relaxation of both the uniform-distribution and independence assumptions in an experiment-wise correction.In this work, I present a decision theory based on an exchangeability principle to determine if adjusting for multiple tests is a necessary component of the statistical analysis or not. If the exchangeability principle is satisfied and an experiment-wise correction is employed, then, through relating properties of order statistics that reveal the null density of the top-ranked test, I develop a generalization of the Dunn-Šidàk correction which relaxes the assumption of uniformly-distributed nominal p-value from the Armitage trend test or a Bayes factor. Now suppose that another SNP, rs2, is subsequently interrogated to again test for disease association with the same samples. Assume that the two SNPs are independent and independent conditioned on disease status. Should the evidence that rs1 is truly associated with the disease change after we have evaluated rs2? Stated this way, the common sense answer is no. By extension, the same reasoning applies to an arbitrary number of markers—the weight of evidence for rs1 being involved in the disease remains unaffected. Hence, if the hypothesis evaluated is specific to rs1, the probability of a significant disease association result for rs1 is independent of genetic information at other markers:prs1 is the p-value testing the null hypothesis of independence between genotypes at rs1 and disease status, α is a pre-specified significance level, and n indicates an arbitrary number of genetic markers. Therefore, when the hypothesis tested is framed with regard to rs1, the determination of disease association should be independent of the total number of markers evaluated—free from a standard family-wise type I adjustment procedure. Similarly, the statistical evaluation of rs1 should also not depend on the unit of how the result is reported: study-by-study. As biology cares not about how results are reported, much of human genetics work might fall under this statistical umbrella. Rather, for the unit of analysis when the hypotheses tested are specific to a marker, should be on a marker-by-marker basis. That said, on both theoretical . Given data at a particular SNP, say ‘rs1’, there are many methods to quantify the evidence that rs1 is indeed associated with the disease studied, including the calculation of a l  and empl , α = 0.frequent . This isfrequent .A natural extension of the marker-specific analysis paradigm would be the creation of informatics repositories of data at every marker evaluated in each study. Then  evidence for or against each marker being involved in a particular phenotype can be amassed and compared against a stationary, objective significance level.a priori, the result from any marker may be reported as being significant. Under this scenario, the hypotheses tested need to be a priori exchangeable. Adjustment for multiplicity is therefore appropriate to account for the selection of top results from a larger set of tests. Under this framework, the top ranked test result is often of considerable interest. And since (i) the top-ranking could, a priori, be occupied by any marker and, (ii) if thought of successive tests within a study, there is clearly a non-zero probability that successive test results could occupy the top-ranked position, adjusting for the number of tests performed is appropriate.Now consider the situation where a large-scale genetic study, testing hypotheses that are not specific to particular markers—that is, Assuming the exchangeability principle between markers as described above holds, warranting an accounting for multiplicity, the following uses order statistics to develop an experiment-wise statistical procedure which generalizes the Dunn-Šidàk method. This generalized method enables treatment of a broader set of empirically-defined null models using the distribution of p-values across a large-scale genetic study.n markers. For the development of the methods here, I will assume that all markers are in linkage equilibrium and independent conditioned on disease status. Let the null model (H0) consist of independence between disease status and genetics. Further assume that the proportion of tests that truly depart from the null is small relative to the proportion consistent with the null. For each marker, a nominal p-value is calculated testing the null hypothesis of independence with disease status, denoted by p. Provided large sample sizes, the absence of confounding, unrelated individuals, the condition that the number of null markers dramatically exceeds the number of true disease markers, and the appropriate nominal statistical methods, the density of the p-values is uniform on the unit interval. That is, P(p ≤ α|H0) = α. Let U = −loge(p). Under the null model described above, the density of U is simply the exponential: f(u) = exp(−u). Applying subscripts to indicate ranking with regard to calculated p-values yielding the ordering set:{u1, u2,…,un}, such that un is the largest value in the set of transformed p-values in the study, corresponding to the most significant marker. Hence, ui indicates the ith –ranked result from the set of n results. The general form for the density of the ranked ui isF(u) is the distribution function of U. This is a well-studied result from order statistics [Suppose one has collected data from a large disease genetics study of atistics . Hence, Under these assumptions, the probability density function (pdf) of the least significant test is the exponentialAnd the pdf of the most significant test isp-value, pE,n, for the nominal result for the most-significant −logep. Let x denote this most significant result, negative log-transformed p-value.p-value:Taking the result from p-value in a standard manner assuming a uniform density for the p-values. For an arbitrary ranked result, the p-value accounting for rank isThis makes sense as we have derived the density of the top-ranked result under the null and calculated the rank-adjusted p-values. This carries broad utility as many studies have systematic biases or employ overly conservative or anti-conservative statistical techniques. For example, genome-wide association studies in human genetics can suffer from both problems: population stratification can generate systematic shifts in the p-value distribution through confounding, uncorrected effects from the inclusion of related individuals also generates departures from uniformly-distributed p-values under the null, and relying on limiting distributions for the calculation of p-values often changes the p-value distribution under the null. These systematic departures in the null p-value distribution from a uniform are problematic in the appropriate application of experiment-wise corrections. As shown above, the Dunn-Šidàk correction relies on strictly uniformly-distributed p-values under the null for an appropriate calculation of the top-ranked p-value accounting for multiplicity. By using an empirical approach assuming that the vast majority of markers are indeed consistent with the null model of no disease association, we can model these types of systematic departures in the null p-value distribution and incorporate these effects into a more general and realistic null model that focuses on the disease association. A similar approach was used for the calculation of Bayes factors in genome-wide association studies [U is a gamma density, of which exponentials are a special case:The above derivation provides a useful framework for relaxing the original assumption of a uniform density for the nominal  studies . A naturb and c are the scale and shape parameters, respectively. Setting c = 1 restores the exponential distribution and setting both b = 1 and c = 1 yields the unit exponential variate analyzed above . Applying the gamma distribution to p-value under a more general null model. Focusing on the top-ranked result, the general ordered statistics result  is the incomplete gamma function equal to p-value for the top-ranked test,Substituting the gamma distribution,b and c can be estimated using the entire set of individual test −logep values from the experiment or the subset of those values that is estimated to be consistent with the null hypothesis. Concurrent estimation of the gamma parameters is the subject of much work and both frequentist  and sample variance (σ2) of {u1, u2,…,un}:The parameters t  and Bayt  have bep-values, modeling a more general null, excluding the most significant test results from a large-scale study is a reasonable idea. More sophisticated approaches may be to concurrently model null and alternative densities as is often done with FDR procedures .p-values can be used in a number of scenarios. For example, one may want to model the p-value distribution as a Beta variate in which case the most significant finding, q, from n independent tests would have the null density ofp-values from the experiment. Another example would be to use the commonly-generated Chi-Squared test statistics from a large-scale experiment, modeled as either a Chi-Squared distribution or a Rayleigh-Rice distribution, and calculate the top-ranked density  may have error that stems from the level of fit to observed data. That error would then propagate to the calculation of the experiment-wise p-values. Intuitively, the fit of the model to the tail of the distribution is highly critical to obtain accurate experiment-wise p-values through the methods promoted here.Importantly, depending on the specifics of the application, the distribution selected to model the statistical measure  procedure. The proportion of top-ranked (most significant) tests that exceed a predefined significance level (α) are reported using both procedures. The Dunn-Šidàk corrected α is calculated according to p-value distribution in the Monte Carlo with a Beta variate having shape parameters ν = 0.9 and ω = 1.1, and simulate an experiment with 10,000 independent tests, we would calculate a generalized, Gamma-model significance level of 1.36E-06, corresponding to an experiment-wise αG = 0.05. Whereas, one would calculate a Dunn-Šidàk level to be at a less conservative value of αDS = 5.13E-06. The result of this difference in multiple test-adjusted significance levels is that, over 5,000 replications of this experiment, 17% of the top-ranked tests under the null exceed the αDS, but the Gamma model retains an appropriate significance level to control false positives with 5.2% of the top-ranked tests exceeding αG. To explore the effect of a variety of different p-values from a model that was adjusted for principal components to correct for population stratification effects. The top-ranked SNP exhibited a p = 9.30E-33 (x = 73.7553) testing the association with extreme BMI. Not surprisingly, this SNP, rs11075990, is located within the well-established fat mass and obesity-associated gene, FTO on chr 16q12.2. To refine the list of p-values for the purpose of modeling a generalized null hypothesis, I removed 228 SNPs that exceeded the standard threshold for genome-wide significance (5.0E-08) and proceeded to estimate the parameters for the gamma distribution for the negative log-transformed p-values with the remaining 1,984,585 SNPs. Using matching moment estimators, p-values, both parameters should be unity. p-values from this study following the removal of the 228 SNPs. p-value, yields pE,n = 2.601×10−23 for rs11075990 –highly significant by virtually any measure following adjustment for multiplicity. However, this is over a 1000-fold larger (less significant) than the Dunn-Šidàk corrected p-value of 1.85×10−26.To illustrate the use of this generalized family-wise approach to multiplicity, data from a genome-wide association study of extreme BMI was analyzed . In thisp-values), and we have measured 1,000,000 SNPs in a GWAS, then we would expect 10 positive findings under the null hypothesis. However, if the true null was defined by the Gamma model estimated above (Model2), then we would expect to see 26.6 false positive findings if we ignore this revised null in the determination of the significance level. Stated another way, if the real null distribution of p-values took on a Gamma model that was observed in the extreme BMI GWAS, then not adjusting for the effects of such a model (and implicitly using a uniform density for the Dunn-Šidàk correction) would produce an elevated number of false positives because the tail of the null distribution was inflated over that expected under a uniform distirbution. Such an increase in the number of false positive findings can greatly impact subsequent studies designed to replicate initial findings through genetic association or functional studies to investigate biological effects of variants in an associated region. Interestingly, analyzing a second GWAS, extreme height, from the same study [Comparing the fold increase in the rate of positive findings between the Gamma model (Model1) and the Gamma model (Model2) as a function of α, we observe a substantial departure between the two models . For exame study , larger p-values. Individual genotype data is not readily available from the Berndt et al study, so I will approximate the total number of independent tests using work from Gao X, et al. 2008 and Gao X, 2011 [p-value is revised to 4.70×10−27. Similarly, revising the experiment-wise p-value gives pE,n = 6.61×10−24, still with the same fold-increase (>1000-fold) in the p-value as with the previous calculation.Treating the correlation among the tests will also change these experiment-wise  X, 2011 ,35. Gao  X, 2011  shows thp-value, and (iv) a more general framework for calculating an experiment-wise p-value when the assumptions of a strict null model may be mildly violated. The generalized experiment-wise multiplicity correction proposed uses the empirical data from large-scale experiments to account for departures from the uniform distribution of null p-values which are often generated through imperfect experimental designs, technological issues, sampling biases, and inaccurate statistical procedures.Several multiplicity ideas are presented here including (i) the importance of marker-specific hypotheses in large-scale genetic studies with the level of statistical significance sufficient for a positive result being free from the number of tests performed, (ii) the notion of exchangeability between tests as a criterion for use of multiple testing procedures, (iii) the connection between order statistics and the Dunn-Šidàk experiment-wise corrected


Although penalized regression methods have shown many advantages in variable selection and outcome prediction over other approaches for high-dimensional data, there is a relative paucity of the literature on their applications to hypothesis testing, e.g., in genetic association analysis. In this study, we apply several new penalized regression methods with a novel penalty, called Truncated  Genome-wide association studies (GWAS) have uncovered many common variants (CVs) associated with complex diseases, but the proportion of variance explained by the identified CVs is often low Maher, . With thF-test in linear regression. For example, in simple regression, a trait Y is regressed on each of multiple variants sequentially. However, because of the extremely low minor allele frequency (MAF) of a RV, a test to detect the association between a trait and a single RV might be low powered. Also, this approach may be too conservative due to a stringent control for multiple testing, e.g., by the Bonferroni correction to control the family-wise error rate. In addition, ultimately, complex diseases are expected to be affected by a combination of multiple genetic variants. Thus an analysis in which a group of variants are tested simultaneously for their joint effects on the trait may be more powerful. In multiple regression, to assess any association between a trait and k RVs, all k RVs are added to a regression model. However, as k increases, the statistical power might decrease due to the cost of large degrees of freedom (DF), k. To avoid the large DF and to aggregate information across multiple RVs, one common strategy is to pool or collapse multiple RVs in a region or gene   βj′|, where either r = 1  or r is the sign of the correlation between the two variants j and j′ . There are two main differences between our proposed TLP-SG and gflasso. First, TLP-SG shrinks the absolute values of the two parameters toward each other by penalizing j| and |βj′| toward each other only if their difference is relatively small (as compared to a tuning parameter to be decided), thus, for example, avoiding severely biasing the estimate of the effect size of an associated variant toward 0 by shrinking it toward the null effect of a null variant. We note that, although penalized regression methods have been widely used and studied, their applications to the current context with RVs are much more limited; in particular, we are not aware of any applications of TLP-S, TLP-SG and gflasso to association testing of RVs.On the other hand, to deal with high-dimensional genetic and genomic data, penalized regression methods have received much attention, especially those based on the Lasso penalty  sequence data , i = 1, …, n, with Yi as a quantitative trait and a vector Xi =  as genotypes of k variants for subject i, we would like to test for any possible association between the trait and genotypes. We use the dosage coding for Xij: Xij = 0, 1, or 2, representing the count number of one of the two alleles present in variant j of subject i. A multi-locus association analysis is based on fitting a linear model,i are assumed to be independently drawn from N, a Normal distribution with mean 0 and variance σ2. A global test of any possible association between the trait and k variants can be formulated as testing on the multiple parameters βjs for j = 1, …, k with null hypothesis H0: β = ′ = 0 by an F-test, which is based on the OLS estimates that minimize the residual sum of squares. A potential problem with the test is the power loss due to the large variance of j since the MAFs of RVs are small.We briefly review some existing global tests based on the ordinary least squares (OLS) estimates. Given U and its covariance matrix V under H0:2 under H0. The corresponding four test statistics areUj is the jth element of U and vj is the th diagonal element of V. Under H0, asymptotically TScore has a χ2k distribution, each of TSSU and TSSUw has a mixture of chi-squared distributions , its weighted version SSUw Pan, , and theons Pan, , and thec, as in the following model:Next, we extend the Sum test Pan,  and its Y on a new covariate, the sum of the genotypes over the multiple variants. To address the question of whether any association between the disease and the variants exists, one simply needs to test H0 : βc = 0, without the need for multiple testing adjustment. The main advantage of the Sum test is that, because it tests on only one parameter βc, there will be no power loss due to the large DF. The common association parameter βc is a weighted average of the individual βM, 1, …, βM, k in the marginal models Yi = βM, 0 + ijXβM, j + ϵij for j = 1, …, k . If the signs are not the same, the test may have a quite small c and thus low power. To overcome the limitation of the Sum test, Han and Pan  Fit the model (Equation 2) with the new coding X*. To test H0 in the aSum test, we use a permutation-based log-likelihood ratio test (LRT), which is asymptotically equivalent to the score test. For the choice of α0, we use the same value as recommended by Han and Pan (0 is used.Fitting (Equation 2) is equivalent to conducting a simple regression of , k Pan, . On the  and Pan  proposed and Pan , 0.1, toF-test is based on OLS estimates, in next section we apply some penalized regression methods, the Lasso, gflasso and a recently developed TLP for either only variable selection (TLP-S) or both variable selection and parameter grouping (TLP-SG). In short, both the Lasso and TLP-S consider only variable selection, while the gflasso and TLP-SG pursue parameter grouping along with variable selection to improve power by striking a better balance between goodness-of-fit and reduced DF in the joint model (Equation 1).While the Y = ′ and a design matrix for k variants X = , the Lasso estimate of β is obtained from the penalized least squares function:L1)-penalty (TLP) +, tends to the L0-loss, I(|x| ≠ 0). The degree of approximation by TLP is controlled by a tuning parameter, τ. See Figure j|'s less than a threshold τ are penalized, hence realizing variable selection (if some are shrunken to 0) while avoiding penalizing larger |βj|'s and thus leading to their almost unbiased estimates.Given a vector of traits n et al.  proposedY = Y, …, Yn′ r is the sign of the correlation between two variants Xj· and Xj′·, which is used to approximate the target |βj| ≈ |βj′|; this method is denoted gflassor = cor. On the other hand, if r = 1 is used, the penalty targets βj ≈ βj′.While both the Lasso and TLP-S consider only variable selection, an alternative way to reduce model complexity is grouping pursuit  are selected to balance between the model complexity and model goodness-of-fit, which presumably may contribute to enhanced power. As a comparison, in the Sum test all parameters (or variants) are forced to belong to the same single group even if the variants' associations with the trait are quite different both in effect sizes and directions; the TLP-SG method attempts to conduct a more precise grouping over all variants in a data-adaptive way.The TLP-SG estimate of β comes fromTo compute β in Lasso, gflasso, TLP-S and TLP-SG, we used the Feature Grouping and Selection Over an Undirected Graph (FGSG) package of Yang et al. , which iH0 : β = 0 in Equation (1), we conduct a permutation-based test, in which the p-value is calculated by comparing a test statistic T applied to the original dataset to the ones Tb)}, we solve a penalized regression problem to obtain Step 1. With the original data {Yi, Xi)} for b = 1, …, B. For each permuted data set, {((b)Yi, Xi)}, we repeat the Steps 1 and 2, obtaining the null statistics T(b)0.Step 3. By repeatedly permuting the observed p-value is Step 4. The final To test the null hypothesis F-statistic (1-df) to test the association between Y and XH′0 : α = 0. This 1-df test uses variable selection and possibly parameter grouping result from the corresponding penalized method, while allowing testing with only 1 DF. Second, for TLP-SG, we also apply the corresponding SSU and SSUw tests, where the test statistics TSSU and TSSUw are both based on the selected variables from the corresponding penalized estimates. Specifically,U* is a sub-component vector of the score vector U corresponding to |j| ≠ 0, and |j| > 0.001 is considered as non-zero. Similarly, V* is the corresponding sub-matrix of the covariance matrix V. Note that the grouping information is not used.We apply each of several test statistics in Step 2. First, across all penalized methods, we use a 1-df L = (−nlog(2) − n − p − 1)/2 is the log-likelihood with the penalized estimate plugged-into model (Equation 1), and p, in AIC is computed as the number of non-zero |j|'s for Lasso and TLP-S, as the number of non-zero unique j's for gflassor = 1, and as the number of non-zero unique |j|'s for gflassor = cor and TLP-SG, respectively. For λ in Lasso, the one resulting in the smallest AIC out of 50 equally spaced points in  is selected. Similarly, the values of each of λ1, λ2 and τ in other methods are searched over five equally spaced grid points of , , and , respectively. For each permuted dataset {(Y(b)i, Xi)} for b = 1, …, B, we also estimate its own (λ(b)1, λ(b)2, τ(b)) to properly control the type I error.To select the suitable tuning parameters, we apply a grid-search with Akaike's information criterion (AIC) Akaike, :AIC=−2ln = 400 in each replicate. The permutation size is set as B = 100. For each replicate, to generate k variants including six causal ones in linkage disequilibrium (LD), as in Wang and Elston (R) are simulated, where R has a first order auto regressive (AR1) structure; the association between any two elements of the latent vector decreases by ρ = 0.8 times as 1 lag increases. Then, the vector is dichotomized to yield a haplotype with the minor allele frequency (MAF) of each variant randomly chosen between 0.005 and 0.01. The genotype data Xi = ′ for sample i is obtained by adding two haplotypes together. Finally, Yi is generated from the randomly located six causal variants with σ2 = 2 in model (Equation 1), where the intercept β0 is set as 0.3 throughout the simulations. The considered three cases are:We consider two simulation schemes. In the first scheme, we generate only RVs with a total of 200 replicates and d Elston , two latk-6 from 0 to 24 so that the total number of RVs, k, ranges from 6 to 30. The Type I error is computed from the Y under H0 : β = ′.In each case, we vary the number of non-causal RVs j is scaled down to βj/10 in the following cases to prevent its dominating association with the outcome. The considered three cases for mixed RVs and CVs are:In the second scheme, multiple RVs and two CVs are generated to mimic the GAW17 data we use later. The frequency of one allele for each CV is randomly distributed between 0.2 and 0.7, and CVs may or may not be chosen as a causal variant in each replicate. When a CV is randomly selected as a causal variant, its effect size βj| over a tuning parameter given other(s), where two horizontal lines at 1.2 and 0 give the true parameter values for Case 2 set-up with only RVs. In contrast to piece-wise linear solution paths of the Lasso estimates, the TLP solution paths are like step functions as expected from an L0-penalty .Figure F-test regardless of the number of non-causal RVs included. There seems to be no gain with grouping in TLP-SG as compared to no grouping in TLP-S, and the 1df-test of TLP-SG works better than gflassor = cor unless the number of non-causal RVs is large at 24. Overall, penalized regression methods do not significantly outperform the power over the Sum and aSum tests. In Cases 2 and 3, where the causal effect directions are mixed, the Sum test works poorly as expected, while the aSum test has higher power. Overall, either the SSU or SSUw test is the winner. In particular, the TLP-S- and TLP-SG-based tests do not significantly improve over the SSU and SSUw tests, though they may perform better than those based on the Lasso and gflasso. Again, a comparison between TLP-S and TLP-SG reveals that parameter grouping does not seem to contribute much to increased power.Table The results of the mixed RVs and CVs set-ups are listed in Table n, small k, and more importantly with RVs. In Table j| > 0.001 is counted as a positive . As expected, the OLS estimates  cannot conduct variable selection with the mean TP and mean FP close to their maximum possible values. Among the penalized methods, a method tends to be either more conservative (fewer FP and fewer TP at the same time) or more liberal (higher FP and higher TP). If we look at the ratio of FP over TP, it seems that the Lasso and TLP-SG are best with the highest ratio, especially for a larger number of non-causal RVs.An advantage of penalized methods over global tests is the formers' ability for variable selection, narrowing down possible causal variants. We note that causal variant selection is an under-studied problem in genetics, which will become more important when we transition from association studies to causal inference. On the other hand, variable selection via penalized methods or any other methods has yet been fully investigated in the current context with large c), Lasso and gflasso shrink it more toward 0, while TLP-S and TLP-SG give much less biased estimates.We compare the performance of the parameter estimates in Table We apply the methods to the mini-exome sequence data from the GAW17  in each gene affecting Q2, and some summary statistics of their MAFs and pairwise correlations (COR) are listed in Table In this study, we test on each of all causal genes  except GCKR, which contains just one SNP. The number of causal variants (F-test is the winner for the genes VLDLR, VNN3, PDGFD, and LPL; however, for the genes VLDLR, BCHE, VNN1, and VWF, the SSU or SSUw test is the best. The two gflasso-based tests work quite similarly over all genes. The TLP based tests perform best for the genes SREBF1, RARAB, VNN1, and INSIG1. After removing a few CVs in each gene (Table F-test based on the OLS estimates perform best for genes VNN3, SREBF1, and PDGFD. For gene VNN1, the TLP-SG with the SSU statistic has the highest power.In Table ne Table , the SSUA potential advantage of penalized regression is variable selection, which is missing from existing global tests. Table i or |βi|, in a data-adaptive way, which can be considered as a generalization of the Sum and other genotype pooling/collapsing-based burden tests. In particular, our proposed TLP-SG overcomes several limitations of the Sum and other burden tests. First, by variable selection, the result of TLP-SG is presumably less influenced by the presence of many non-associated variants to be tested. Second, rather than pooling all the variants into a single group or two groups, TLP-SG automatically determines the number of groups to be formed based on the given data. Furthermore, since TLP-SG shrinks the effects sizes |βi|, not βi, toward each other, it is robust to varying association directions of the causal variants. However, based on our studies on both simulated and real sequence data, we found that TLP-SG and other penalized methods sometimes might be more powerful than some existing global tests, though they do not always outperform the SSU or SSUw test. The discovery of no uniform gain of penalized methods over existing global tests is interesting and even surprising, and can be due to non-optimal implementation of the penalized methods in several aspects. First, the selection of the tuning parameters based on the model selection criterion AIC may not be optimal. As an example, in a simulated dataset, when we set the tuning parameters to properly group the variants, the estimates were quite close to the true values, but the corresponding AIC was less desirable, leading to choosing other low performing tuning parameters. Importantly, there is no theory yet to justify the applicability of AIC for the gflasso- and TLP-based methods; in particular, it is unclear how to count the effective number of parameters in the AIC. Alternatively, one may want to try a more popular model selection method, multi-fold cross-validation. However, for RVs as considered here, if we divide the data into multiple folds, the training data may contain several monomorphic variants, causing non-identifiability of their corresponding effect sizes. Second, due to the repeated model-fitting with many permuted datasets, to save computing time, we only searched relatively few grid points for the tuning parameters, which might not have covered some suitable tuning parameter values. These are all issues to be addressed in the future.In this study we have conducted hypothesis testing to detect the association between a quantitative trait and multiple RVs based on some new penalized regression methods. In addition to the traditional use of penalized regression for variant selection, we have also considered several state-of-the-art grouping pursuit methods that smooth the effect sizes of the variants, either βL1 penalty. Although SCAD can be equally applied and compared here, we chose the TLP as a representative of non-convex penalties for its good properties: as shown by Shen et al. (L0 regularization is optimal in variable selection, and its computational surrogate, TLP, shares the same property for sufficiently small tau; furthermore, the variable selection consistency of TLP regularization also led to enhanced parameter estimation and prediction in numerical studies with finite sample sizes. Nevertheless, we note that, penalized regression methods have been intensively studied for high-dimensional data, but not for the type of data considered here, which are low dimensional but with RVs as sparse predictors.Another non-convex penalty is SCAD (Fan and Li, n et al. , L0 reguIn summary, the established benefit of penalized regression for variable selection and risk prediction for high-dimensional data (Kooperberg et al., The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


This includes the challenges of (i) assembling a large genetic database for the evaluation of the genetic architecture with high statistical power; (ii) exploring the role of gene-environment interactions including the effects of epigenetic phenomena; (iii) employing endophenotype-based approaches to understand the shared etiology between GTS, OCD, and ADHD; (iv) establishing a developmental animal model for GTS; (v) gaining new insights into the neurobiological mechanisms of GTS via cross-sectional and longitudinal neuroimaging studies; and (vi) partaking in outreach activities including the dissemination of scientific knowledge about GTS to the public. Fifteen partners from academia and industry and 12 PhD candidates pursue the project. Here, we aim to share the design of an interdisciplinary project, showcasing the potential of large-scale collaborative efforts in the field of GTS. Our ultimate aims are to elucidate the complex etiology and neurobiological underpinnings of GTS, translate research findings into clinical applications, and establish Pan-European infrastructure for the study of GTS and associated disorders.Gilles de la Tourette Syndrome (GTS) is characterized by the presence of multiple motor and phonic tics with a fluctuating course of intensity, frequency, and severity. Up to 90% of patients with GTS present with comorbid conditions, most commonly attention-deficit/hyperactivity disorder (ADHD), and obsessive-compulsive disorder (OCD), thus providing an excellent model for the exploration of shared etiology across disorders. TS-EUROTRAIN  is a Marie Curie Initial Training Network ( The network spans 13 academic and two industrial partners as well as two patient groups. Twelve individual, yet complementary, PhD projects interact to form a comprehensive study of GTS and comorbidities from genetics, and epigenetics through to physiology, brain anatomy, and function. These projects are all currently underway and can roughly be divided into three groups by their main approach; genetic (and epigenetic), animal models, and human neuroimaging, respectively. Research into the neurobiology of GTS stands at the precipice of discovery thanks to collaborative efforts  is a frequent disorder  to investigate the role of single nucleotide polymorphisms (SNPs) in GTS did not manage to identify SNPs that meet the genome-wide significance level for association to GTS, however, four additional GWAS for GTS are currently underway  and the future meta-analysis of these datasets is expected to provide important insights into the etiology of the disorder Figure . FurtherThis project makes use of the extensive Icelandic population genotyping done by deCODE genetics. Approximately one third of the population  has been genotyped into which 20,000,000 SNPs from the Icelandic sequencing project have been imputed. Tasks include (i) a genome-wide search for genetic variants conferring risk of GTS. This consists of a search for common and rare variants in more than 500 chip typed subjects diagnosed with GTS, (ii) a genome wide search for CNVs associated with GTS, (iii) a test for association of identified variants with phenotypic measures as well as performance on neuropsychological tests, (iv) an investigation of how implicated variants may lead to alteration of gene-expression pathways through analysis of already generated expression cohorts.AADAC gene as a susceptibility factor for GTS when deleted  as well as gene expression data on 200 GTS patients that are followed up for tic exacerbation and remission in an attempt to correlate with environmental factors. Gene-expression and correlation with environmental triggers is also investigated in a cohort of first degree relatives of patients with GTS that develop tic symptomatology within a 3-year follow-up period. Furthermore, the first ever epigenome-wide association study for tics, analysing data from the NTR, has been carried out [55]. This study comprised the largest epigenetic data collection so far undertaken . Although no site reached genomewide significance, the top hits include several genes, and regions previously associated with neurological disorders and warrant further investigation  screening of cell lines and GTS animal models treated with dopaminergic and glutamatergic modulating compounds for epigenetic regulatory markers, (iii) investigation of brain tissue samples from treated and untreated animal models developed within the TS-EUROTRAIN consortium to determine DNA methylation profiles and histone modification changes, and (iv) investigation of blood samples from patients with GTS for whole genome DNA methylation profiling  the study of candidate miRNAs which are predicted to be in the control of tissue-specific gene expression by The aim of this project is to determine the extent of “genetic overlap” in terms of shared underlying gene pathways and molecular signaling cascades between GTS and OCD and to provide further insights into how aberrant processes underlie these genetically related, clinically overlapping but still distinct neurodevelopmental disorders. Combining literature search approaches with diverse bioinformatics analytic tools , top candidate genes emerging from GWASs of GTS , including a range of phenotypic data from questionnaires and genetic data. Structure equation model fitting procedures are used to model the phenotypic resemblance between family members and the relative contribution of genetic and environmental factors to variation and covariation among traits. Also, genome-wide association methodologies are being used to disentangle the genetic architecture underlying the etiology of GTS traits by estimating SNP heritability and polygenic risk scores for example.This study uses data that has been gathered by the NTR over the last 25 years, on twins, and family members . For example, using meta-analysis data comprised of 1285 GTS cases, and 4964 controls ancestry-matched to the GTS sample from the first GWAS  circuitry and in particular the role of the glutamatergic system are being investigated. Furthermore, the effect of older and newer psychotropic compounds  are tested and novel targets identified. Similarly to the genetics and human neuroimaging projects a wide field of investigation is taken to include common comorbidities. Furthermore, samples from these projects undergo epigenetic testing as mentioned in project 4.The unilaterally lesioned 6-hydroxidopamine (6-OHDA) adult rat is a well-established model used in Levodopa-induced Dyskinesia research. In this model a rapid degeneration of nigrostriatal neurons is chemically induced by the intrastriatal or intranigral administration of 6-OHDA, which selectively targets monoaminergic neurons. Chronic application of L-dopa to 6-OHDA lesioned rats leads to the development of repetitive involuntary movements, mainly involving the forepaw, neck, and mouth  neuroimaging projects are highly complementary with similar techniques used across all sites so as to allow for the cross-comparison of findings with limited methodological confounding factors. Projects 11 and 12 even pool data for certain comparisons. Each project utilizes MRS to evaluate the role of the glutamatergic system; T1-weighted structural magnetic resonance imaging (MRI) to examine structural brain differences; functional MRI  data to interrogate the functional coupling between cognitive, limbic, and sensory-motor CSTC networks; and diffusion-weighted MRI (dMRI) data to inspect the structural connectivity. Each project does, however, differ in the populations under investigation and aims to address different unknown areas regarding GTS neurobiology. Together these works, along with the animal MRI study, may have implications on future glutamatergic modulatory therapies for tic suppression and could potentially extend the current pathophysiological model of GTS and related circuits beyond CSTC circuitry . The participants with OCD as well as the controls have been chosen from a previous local OCD study while those with GTS are newly recruited. Genetic data is collected to contribute to genetic analysis within other projects of the network and to perform imaging-genetic analyses.The neural correlates of GTS and OCD have scarcely been compared and contrasted despite the high rate of co-occurrence  techniques to investigate whether patients exhibit an altered distribution of iron concentrations within basal ganglia nuclei in comparison to 40 healthy controls. At the neurochemical level, we investigate the role of the glutamatergic system within cortico-striatal regions using MRS at baseline and following treatment. At the network level, we use resting-state fMRI to investigate the interaction between large scale networks and their relationship to clinical status.TS-EUROTRAIN is a showcase of the potential impact of large-scale interdisciplinary and collaborative efforts aiming to understand GTS. Our basic science research combined with clinical neuroimaging studies will greatly increase our knowledge of the biological underpinnings of GTS and related disorders and allow a suitable biological model for these disorders to be established. The benefits of our research will include the potential identification of novel treatment targets and the availability of a suitable animal model on which to test newly developed pharmacotherapies targeting these newly identified biological pathways. This will ultimately lead to improved treatments and consequently increased quality of life for those suffering from GTS and their families. Despite being common, GTS is still considered a rare, unusual disease by the public, and has been associated with symptoms and signs causing social misunderstanding and stigmatization , Grant Agr.No.316978); we further acknowledge support by the European Union Seventh Framework Programmes . CB was supported by the Merit-prize scholarship of Semmelweis University and the János Bolyai Research Scholarship of the Hungarian Academy of Sciences BO/00987/16/5.JB has been in the past 3 years a consultant to / member of advisory board of / and/or speaker for Janssen Cilag BV, Eli Lilly, Medice, Shire, Lundbeck, Roche and Servier. He is neither an employee of any of these companies nor a stock shareholder of any of these companies. He has no other financial or material support, including expert testimony, patents, or royalties. PH has been in the past three years consultant to / member of advisory board of Shire. OV received speakers' honorarium from Lundbeck and received research funding from PhotoPharmics. The other authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Mega- or meta-analytic studies (e.g. genome-wide association studies) are increasingly used in behavior genetics. An issue in such studies is that phenotypes are often measured by different instruments across study cohorts, requiring harmonization of measures so that more powerful fixed effect meta-analyses can be employed. Within the Genetics of Personality Consortium, we demonstrate for two clinically relevant personality traits, Neuroticism and Extraversion, how Item-Response Theory (IRT) can be applied to map item data from different inventories to the same underlying constructs. Personality item data were analyzed in >160,000 individuals from 23 cohorts across Europe, USA and Australia in which Neuroticism and Extraversion were assessed by nine different personality inventories. Results showed that harmonization was very successful for most personality inventories and moderately successful for some. Neuroticism and Extraversion inventories were largely measurement invariant across cohorts, in particular when comparing cohorts from countries where the same language is spoken. The IRT-based scores for Neuroticism and Extraversion were heritable  with a significant part of the heritability due to non-additive genetic factors. For Extraversion, these genetic factors qualitatively differ across sexes. We showed that our IRT method can lead to a large increase in sample size and therefore statistical power. The IRT approach may be applied to any mega- or meta-analytic study in which item-based behavioral measures need to be harmonized.The online version of this article (doi:10.1007/s10519-014-9654-x) contains supplementary material, which is available to authorized users. Mega- or meta-analytic studies (e.g. genome-wide association (GWA) studies) are increasingly used in behavior genetics. Because phenotypes have not always been assessed similarly across cohorts (and sometimes not even within cohorts), measures need to be harmonized, that is, phenotypic scores need to be made comparable such that data from individuals who were assessed by different inventories can be compared meaningfully. Such harmonization then enables fixed effect meta-analytic analyses  test linking can be applied to map item data from different inventories to a common metric. We conduct such an analysis for Neuroticism and Extraversion personality traits, based on data from the Genetics of Personality Consortium (GPC). If different inventories indeed measure the same phenotype, the only requirement for this approach is that multiple inventories have been administered in at least a subset of individuals. That is, in order to be able to harmonize across different inventories, some participants must have filled in multiple inventories so that they can function as a “bridge” between inventories. This can be done if we assume that the true phenotype  does not change between the multiple assessments. If this can be assumed, then for all individuals in the different (sub-)cohorts, a score on the latent construct can be estimated based on all available item data for that person. The IRT-based score estimates for Neuroticism and Extraversion can subsequently be meta-analyzed to assess heritability, or can be used as phenotypes in GWA or brain-imaging studies.This IRT approach has multiple advantages. First, within each cohort there is increased measurement reliability, because when multiple inventories have been administered to the same individual, scores can be estimated using the items from all relevant inventories. In addition, items can be differentially and optimally weighted if necessary, and items that do not fit the measurement model can be identified and omitted, thereby increasing power. Subgroups of individuals that were assessed with only a subset of items can now also be included in the study. Moreover, the IRT approach can statistically evaluate the extent to which different inventories actually measure the same construct. Lastly, IRT enables researchers to determine the extent of measurement invariance across cohorts: can scores across cohorts be quantitatively compared and therefore pooled and meaningfully used in a meta-analysis?Applying the IRT method to Neuroticism and Extraversion is especially relevant for the field of behavior genetics, as these personality traits are correlated with numerous other traits and disorders, not only phenotypically but also genetically  . Seventeen cohorts originated from Europe, 4 cohorts were from the USA and 2 cohorts from Australia. Most cohorts are large epidemiological studies. Some of the cohorts focused on specific birth cohorts and/or recruited individuals of specific regions in the country , or targeted twins and their family members . Three cohorts were designed to include cases and controls for Nicotine dependence, Alcoholism or Mood and Anxiety disorders . The data collection in some of the cohorts is longitudinal in nature.Supplementary Table 1 and Supplementary Fig. 3 give an overview of the personality inventories administered in each cohort. The Supplementary Materials Online describes these inventories in detail. For the Neuroticism analysis, we included all Neuroticism items from the NEO, the International Personality Item Pool (IPIP) and Eysenck  inventories, the Harm Avoidance (HA) items from the Temperament and Character Inventory (TCI), and the Negative Emotionality (NEM) items (excluding the aggression items) from the Multidimensional Personality Questionnaire (MPQ). The Neuroticism scales of the NEO, IPIP and Eysenck inventories consist of different items, but there is strong overlap in item content and the sum scores correlate highly across inventories  items from the TCI, and the Positive Emotionality (PEM) items from the MPQ. Extraversion sum scores derived from the NEO, IPIP and Eysenck inventories correlate highly across inventories , and unidimensionality. For every cohort and every inventory separately, item parameters were estimated based on data from individuals without missing data. Such a set of parameter values for a particular sample of items assessed in a particular sample is termed a calibration. Calibrations were also obtained for combinations of item sets from various inventories, if there was a subsample of individuals that was assessed with those inventories. Based on these calibrations, , latent scores can be estimated for those individuals for which one has either complete data or data with some missing values, assuming these are missing at random. In order to investigate local independence, latent scores for a particular item set  were estimated and compared based on different calibrations: one based on the calibration of several inventories combined  and one based on only one inventory (NEO-PI-R items). The resulting scores were then correlated. A correlation of 1 indicates that the estimated scores are completely independent of what inventory was used for assessment .We assessed whether the IRT Neuroticism and Extraversion scores in the 23 cohorts were truly independent of the specific inventory used. First, the appropriateness of linking tests Unidimensionality was assessed by plotting the test information curves (TICs) Lord  for inveThe choice for the above approach to assessing model fit, which is a bit unconventional, was motivated by the fact that the personality inventories are well-developed and validated instruments. Also, from previous research we know that two-parameter models generally are more appropriate for personality data than one- and three-parameter models , the same test items might have different parameters across cohorts. Ignoring these differences results in systematic bias when comparing individual sum scores from different cohorts. The assumption of equal item parameters across groups is usually termed measurement invariance . In addition, to identify the variance of the scale the product of the discrimination parameters was fixed at 1. Allowing for such random fluctuations in difficulty and discrimination across cohorts is also referred to as the assumption of approximate measurement invariance. This Bayesian method was only applied to NEO-FFI and EPQ-R test items, as for those tests, the numbers of cohorts were sufficiently large. We randomly selected 1,000 individuals from each cohort  and determined which items showed considerable DIF across cohorts by computing Bayes factors , the Finnish HBCS calibration were used? If measurement invariance holds perfectly, the correlation between the different score estimates should be very close to 1. These correlations were computed for NEO-FFI, NEO-PI-R and EPQ inventories in the appropriate cohorts.In each of the 6 cohorts with twin data separately, twin correlations for the IRT latent trait scores were estimated using the structural equation modeling package OpenMx within the statistical software program R  and non-additive (d2) genetic effects: r(MZ) = h2 + d2. The expected DZ twin correlation is a different function of these two types of effects: r(DZ) = ½h2 + ¼d2. IRT-score-based twin correlations  thus were constrained to be the same across cohorts. First it was tested whether the correlation in opposite-sex twins could be equated to the expectation above . Next, it was tested whether the relative sizes of the genetic components could be equated across sexes, that is, whether hm2 = hf2 and dm2 = df2. Lastly, it was tested whether non-additive genetic effects were present, by comparing the fit of the model with a model in which d2 = 0.Under the classical twin model assumptions, the expected MZ twin correlation is a function of the proportions of variance in a trait explained by additive  and 160,713 individuals (Extraversion). Correlations between estimated latent scores and sum scores were high for Neuroticism  and moderately high for Extraversion  . Only for TCI Neuroticism in the HBCS cohort, was the correlation lower (r = 0.87). Thus, the latent scores are largely independent of the inventories included. TICs for these cohorts are presented in Supplementary Figs. 4–27. Supplementary Figs. 11, 14, 18, and 20 thru 23 show that combining tests always leads to higher information content, and therefore more measurement precision for those individuals with multiple-inventory data. However, the TICs of the combined tests are not a simple sum of the TICs of the individual tests, showing that the personality inventories largely, but not completely, measure the same phenotypes.across cohorts, latent scores in each cohort were estimated several times based on different values for the item parameters coming from different cohorts . That is, a certain pattern of item responses was used to estimate the latent trait based on the item parameters as calibrated in one cohort, and this was repeated but then using item parameters as calibrated in another cohort. The correlations (see Supplementary Tables 4 and 5) are generally very high . Thus, ranking is not much affected by the particular cohort that individuals were in.To assess whether personality scores could be compared Figures Allowing for these significant deviations from measurement invariance across cohorts by applying the Bayesian model, Tables p value <0.01) were found in the MCTFR, Finnish Twin and STR cohorts, but not in the NTR and two QIMR cohorts. The NTR and QIMR cohorts included opposite-sex twins. Table MZ twin correlations for the estimated Neuroticism and Extraversion scores ranged between 0.39 and 0.54 Table . DZ corrhm, hf, dm, df, and one for allowing the opposite-sex twin correlation to differ from its expectation under the hypothesis of no qualitative sex differences) did not show a better fit than one where the opposite-sex twin correlation was equated to its expected value . The base model χ2 was 88.33, and the restricted model χ2 was 88.89, a non-significant change with 1 degree of freedom. Next, this restricted model with qualitatively the same additive and non-additive genetic effects for males and females was compared with a model that specified that the proportions additive and non-additive genetic variance were equal across sexes. This model had a χ2 statistic of 91.63, a non-significant increase of the χ2 statistic by 2.74 for 2 degrees of freedom. Next, it was tested whether the non-additive genetic effects could be dropped from the model. The χ2 statistic increased to 170.39, which is highly significant. Thus, for Neuroticism, both additive and non-additive genetic effects seem to be operating, which seem to be the same in males and females, and of equal importance in males and females. Proportions of additive and non-additive genetic variance were estimated at 27 and 21 %, respectively.In the meta-analysis of the 27 twin correlations in Table 2 of 97.15. Restricting the opposite-sex twin correlation led to a χ2 of 104.67, a difference of 7.54, which is significant at one degree of freedom. We therefore allowed for qualitative sex difference when testing for quantitative sex differences . This restriction led to a χ2 of 101.20, a non-significant change of 4.06 at 2 degrees of freedom, p = 0.13. Thus, there seem to be only qualitative differences in genetic variance components. Dropping non-additive genetic variance from the model resulted in a significantly higher χ2 statistic, of 194.60, a difference of 93.40.For Extraversion , the base model had a χ2 statistic for these qualitative sex differences was relatively small given the large sample size, but nevertheless, the opposite sex twin correlation was a factor 0.76 smaller than expected under no qualitative differences .Thus, for Extraversion, there are qualitative sex differences in the additive and non-additive genetic effects, but the additive and non-additive genetic effects are of equal magnitude in males and females: 24 % and 25 %, respectively. The χFor the NTR cohort, the statistical power to detect a SNP at the genome-wide significance level that explains 0.1 % of the true phenotypic variance (latent trait) with an allele frequency of 0.5 when using only the 12 NEO-FFI items was 18 %  and increased to 44 % when using IRT scores based on both NEO-FFI and ABV data . In the QIMR-adult sample, the power with only 12 NEO-FFI items was 0 % . Using all available data from all inventories and analyzing IRT scores yielded a power of 30 % . Thus, the power in GWAS substantially increases if item data from multiple inventories are included, if available.This study examined for Neuroticism and Extraversion personality traits whether measures from different inventories could be harmonized using IRT test linking. The IRT analyses showed that the linked scores for Neuroticism and Extraversion that were estimated in >160,000 individuals from 23 cohorts were largely independent of the particular inventory. The success of this approach is demonstrated by the power study that showed a clear increase in statistical power to find a genetic variant associated with personality that is mainly the result of an increase in sample size.The NEO, Eysenck and IPIP inventories were especially conducive to being linked. Linking was slightly less successful for TCI and MPQ with the NEO, Eysenck and IPIP inventories. The mapping of Harm Avoidance onto Neuroticism, despite theoretical differences between the concepts, was found to be relatively good. However, the mapping of Reward Dependence to Extraversion was less feasible, as was suspected. Such imperfect linking results in bias when individuals are ranked, which is very important in for example educational settings . However, when scientific interest is in population effects, like a correlation in twins or between the phenotype and a SNP, results are highly satisfactory. When dealing with non-identical but correlated traits, an alternative could be the use of multidimensional IRT models , but these imperfections have little effect on results for population effects, because the correlation of two scores based on different calibrations was generally very high. Overall, the conclusion is that data pooling within cohorts and subsequently pooling results across cohorts in a meta-analysis is meaningful for Neuroticism and Extraversion and these inventories. As the power study showed, such pooling of data within cohorts can lead to a potentially large increase in statistical power. Such increase in power is largely due to the increase in sample size, but also of using more phenotypic information per individual.possible: the only requirement is that there is either overlap in individuals that were administered several inventories, or overlap in items, when some items are present in multiple inventories. It remains however to be determined whether the linking leads to psychometrically sound re-scaled phenotypes in order to for the test linking to be meaningful and successful.Note that IRT test linking is always and IRT score estimates are skewed as well, see . There was clear evidence of non-additive genetic variance for both traits. Although this finding could be partly due to a scale effect . The harmonized phenotypes can now also be confidently correlated with brain measures or used in a GWA study. The IRT analysis is not only useful for harmonizing phenotypes, it is also informative regarding the power to find significant genetic variants of various allele frequencies. The TICs show where in the distribution of Neuroticism and Extraversion scores there is most phenotypic information. Relating these TICs to the power a phenotypic test might give in a GWAS Below is the link to the electronic supplementary material.