Statistical analysis strategies for association studies involving rare variants

The effect of collapsing variants and testing their collective frequency differences on power can be substantial.

“The effect of collapsing variants and testing their collective frequency differences on power can be substantial, as depicted in Figure 1B.”

Many genetic and epigenetic factors, including multiple rare single nucleotide variants, copy number variations, and other structural variation, likely contribute to common complex diseases.

“It is now widely believed that many genetic and epigenetic factors are likely to contribute to common complex diseases, including multiple rare SNVs (defined by convention as those that have frequencies < 1%), copy number variations (CNVs), and other forms of structural variation. 3–12”

• cites [3] Pinto, D. et al. Functional impact of global rare copy number variation in autism spectrum disorders. Nature 466, 368–372 (2010). sourceNot checked yet

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• cites [4] Frazer, K. A., Murray, S. S., Schork, N. J. & Topol, E. J. Human genetic variation and its contribution to complex traits. Nature Rev. Genet. 10, 241–251 (2009). sourceNot checked yet

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• cites [5] Tycko, B. Mapping allele-specific DNA methylation: a new tool for maximizing information from GWAS. Am. J. Hum. Genet. 86, 109–112 (2010). sourceNot checked yet

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• cites [6] Kong, A. et al. Parental origin of sequence variants associated with complex diseases. Nature 462, 868–874 (2009). sourceNot checked yet

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• cites [7] Eichler, E. E. et al. Completing the map of human genetic variation. Nature 447, 161–165 (2007). sourceNot checked yet

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• cites [8] Hunter, D. J. Gene–environment interactions in human diseases. Nature Rev. Genet. 6, 287–298 (2005). sourceNot checked yet

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• cites [9] Cordell, H. J. Detecting gene–gene interactions that underlie human diseases. Nature Rev. Genet. 10, 392–404 (2009). sourceNot checked yet

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• cites [10] Bodmer, W. & Bonilla, C. Common and rare variants in multifactorial susceptibility to common diseases. Nature Genet. 40, 695–701 (2008). sourceNot checked yet

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• cites [11] Schork, N. J., Murray, S. S., Frazer, K. A. & Topol, E. J. Common vs. rare allele hypotheses for complex diseases. Curr. Opin. Genet. Dev. 19, 212–219 (2009). sourceNot checked yet

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• cites [12] Cirulli, E. T. et al. Common genetic variation and performance on standardized cognitive tests. Eur. J. Hum. Genet. 18, 815–820 (2010). sourceNot checked yet

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Sequencing studies focusing on specific genes have shown that collections of rare variants can associate with particular phenotypes.

“Fifth, importantly, sequencing studies focusing on specific genes have shown that collections of rare variants can indeed associate with particular phenotypes (Table 1).”

• cites Table 1Not checked yet

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Collapsing sets of rare variants into a single group and testing their collective frequency differences can overcome the power issues associated with testing rare variants individually.

“In order to overcome power issues associated with testing rare variants individually, one could ‘collapse’ sets of rare variants into a single group and test their collective frequency differences between cases and controls.28, 30”

• cites [28] Li, B. & Leal, S. M. Methods for detecting associations with rare variants for common diseases: application to analysis of sequence data. Am. J. Hum. Genet. 83, 311–321 (2008). One of the first papers to comprehensively evaluate statistical methods for testing collapsed sets of rare variants to a trait. The paper discussed both distance-based and regression approaches. sourceNot checked yet

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• cites [30] Morgenthaler, S. & Thilly, W. G. A strategy to discover genes that carry multi-allelic or mono-allelic risk for common diseases: a cohort allelic sums test (CAST). Mutat. Res. 615, 28–56 (2007). This paper introduced the notion of collapsing sets of variants into a single group whose collective frequency could be contrasted between groups. sourceNot checked yet

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Obtaining phase from sequence data alone is not trivial.

“Thus, leveraging phase information in an association study of rare variants may be crucial, but obtaining phase from sequence data alone is not trivial.24, 91–93”

• cites [24] Roach, J. C. et al. Analysis of genetic inheritance in a family quartet by whole-genome sequencing. Science 328, 636–639 (2010). sourceNot checked yet

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• cites [91] Andres, A. M. et al. Understanding the accuracy of statistical haplotype inference with sequence data of known phase. Genet. Epidemiol. 31, 659–671 (2007). sourceNot checked yet

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• cites [92] Kim, J. H., Waterman, M. S. & Li, L. M. Accuracy assessment of diploid consensus sequences. IEEE/ACM Trans. Comput. Biol. Bioinform. 4, 88–97 (2007). sourceNot checked yet

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• cites [93] Levy, S. et al. The diploid genome sequence of an individual human. PLoS Biol. 5, e254 (2007). sourceNot checked yet

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The discovery of rare independent somatic mutations within and across genes contributing to tumorigenesis may parallel the functional effects of inherited variants contributing to congenital disease.

“Second, the discovery of rare independent somatic mutations within and across genes contributing to tumorigenesis may parallel the functional effects of inherited variants contributing to congenital disease.11, 16, 17”

• cites [11] Schork, N. J., Murray, S. S., Frazer, K. A. & Topol, E. J. Common vs. rare allele hypotheses for complex diseases. Curr. Opin. Genet. Dev. 19, 212–219 (2009). sourceNot checked yet

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• cites [16] Wood, L. D. et al. The genomic landscapes of human breast and colorectal cancers. Science 318, 1108–1113 (2007). This study suggests that many different mutations in key genes are likely to drive tumorigenesis so that, although patients might have unique mutations, these mutations are likely to be in genes that harbour mutations across many patients. This rare variant heterogeneity may also contribute to the inherited basis of many common chronic diseases. sourceNot checked yet

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• cites [17] Lahiry, P., Torkamani, A., Schork, N. J. & Hegele, R. A. Kinase mutations in human disease: interpreting genotype-phenotype relationships. Nature Rev. Genet. 11, 60–74 (2010). sourceNot checked yet

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The identification of multiple functional variants within the same gene and their association with in vitro and clinical phenotypes indicates that multiple rare variants could influence general clinical phenotypic expression.

“Fourth, the identification of multiple functional variants within the same gene and the association of these variants with both in vitro and clinical phenotypes indicates that multiple rare variants could influence general clinical phenotypic expression20.”

• cites [20] Schork, N. J., Wessel, J. & Malo, N. DNA sequence-based phenotypic association analysis. Adv. Genet. 60, 195–217 (2008). sourceNot checked yet

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Differential genotyping error rate can have a substantial impact on common-variant based genome-wide association studies.

“It has been shown that differential genotyping error rate can have substantial impact on common-variant based GWA studies.89”

• cites [89] Moskvina, V., Craddock, N., Holmans, P., Owen, M. J. & O'Donovan, M. C. Effects of differential genotyping error rate on the type I error probability of case-control studies. Hum. Hered. 61, 55–64 (2006). sourceNot checked yet

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Pre-specified Bonferroni-like corrections on association p-values are not likely to be appropriate given possible correlations between defined groups of rare variants and/or overlapping windows to be tested.

“Pre-specified Bonferroni-like corrections on association p-values are not likely to be appropriate given possible correlations between defined groups of rare variants and/or overlapping windows to be tested.”

• cites [99] Efron, B. Correlation and large-sclae simultaneous significance testing J. Am. Stat. Asso. 102, 92–103 (2007). sourceNot checked yet

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Simulation studies and permutation testing that consider the entire set of tests performed are the most appropriate way to obtain a global false positive rate.

“Simulation studies and permutation testing that consider the entire set of tests performed (e.g., all windows and groups of variants across all genomic regions considered) to a get a global false positive rate are the most appropriate given their flexibility and sound theoretical bases, but will likely be very computationally intensive.75”

• cites [75] Hoggart, C. J., Whittaker, J. C., De Iorio, M. & Balding, D. J. Simultaneous analysis of all SNPs in genome-wide and re-sequencing association studies. PLoS Genet. 4, e1000130 (2008). Refs 74 and 75 introduced regularized regression techniques for accommodating a large number of predictors in a genetic association study and to separate causally associated from non-causally associated variants. sourceNot checked yet

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Testing rare variants individually with standard contingency table and regression methods is highly problematic because such tests have poor power to detect small rare variant frequency differences between groups.

“This strategy is highly problematic given, for example, the poor power that such statistical tests have to detect small rare variant frequency differences between diagnostic or phenotypic groups (figures 1A and 1B).14, 28, 29”

• cites [14] Gorlov, I. P., Gorlova, O. Y., Sunyaev, S. R., Spitz, M. R. & Amos, C. I. Shifting paradigm of association studies: value of rare single-nucleotide polymorphisms. Am. J. Hum. Genet. 82, 100–112 (2008). sourceNot checked yet

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• cites [28] Li, B. & Leal, S. M. Methods for detecting associations with rare variants for common diseases: application to analysis of sequence data. Am. J. Hum. Genet. 83, 311–321 (2008). One of the first papers to comprehensively evaluate statistical methods for testing collapsed sets of rare variants to a trait. The paper discussed both distance-based and regression approaches. sourceNot checked yet

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• cites [29] Altshuler, D., Daly, M. J. & Lander, E. S. Genetic mapping in human disease. Science 322, 881–888 (2008). sourceNot checked yet

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Including other factors in a regression model, such as covariate effects, previously identified common variants, or other collapsed sets of rare variants, could substantially increase power to detect an association involving rare variants.

“In addition, if one included other factors in a regression model - such as covariate effects, the effects of previously identified common variants, or other collapsed sets of rare variants - then the power to detect the association involving rare variants could increase substantially (Figure 1C).”

Comparing allele frequencies in a group of individuals with historical or publicly available control sets in rare variant studies is highly problematic because of stratification and sampling variation effects.

“The practice of identifying and quantifying allele frequencies in a group of individuals and comparing them with historical or publicly available ‘control’ sets in studies involving rare variants is highly problematic due to the potential for stratification and sampling variation effects.96”

• cites [96] Li, B. & Leal, S. M. Discovery of rare variants via sequencing: implications for the design of complex trait association studies. PLoS Genet. 5, e1000481 (2009). sourceNot checked yet

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The identification of multiple rare variants within the same gene in largely monogenic disorders suggests that rare variants might also influence common complex traits and diseases.

“Third, the identification of multiple rare variants within the same gene contributing to largely monogenic disorders such as Cystic Fibrosis and BRCA1 and BRCA2-associated breast cancer18, 19 suggests that rare variants might also influence common complex traits and diseases.”

• cites [18] Bobadilla, J. L., Macek, M. Jr, Fine, J. P. & Farrell, P. M. Cystic fibrosis: a worldwide analysis of CFTR mutations — correlation with incidence data and application to screening. Hum. Mutat. 19, 575–606 (2002). sourceNot checked yet

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• cites [19] Easton, D. F. et al. A systematic genetic assessment of 1,433 sequence variants of unknown clinical significance in the BRCA1 and BRCA2 breast cancer-predisposition genes. Am. J. Hum. Genet. 81, 873–883 (2007). sourceNot checked yet

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Interaction effects involving genetic or environmental factors are likely to be important in association studies involving rare variants.

“In addition, just as interaction effects involving either genetic or environmental factors must be considered in standard GWA studies9, they are also likely to be important in association studies involving rare variants.”

• cites [9] Cordell, H. J. Detecting gene–gene interactions that underlie human diseases. Nature Rev. Genet. 10, 392–404 (2009). sourceNot checked yet

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Regression-based collapsed variant and conditional tests can greatly enhance association studies involving rare variants.

“Regression-based collapsed variant and conditional tests can greatly enhance association studies involving rare variants.”

Rare variants likely influence phenotypic expression together with common variants or beyond the effects of common variants.

“Irrespective of how one might define ‘rare variant’ (which, although we have adopted the convention <1% frequency, might range from <0.1% to <0.01% depending on the context13) it is essential to recognize that such variants likely contribute to phenotypic expression in conjunction with, or over-and-above, common variants.”

• Also stated in: § The nature of the effect of rare variants · hedged

  “As noted, rare variants are likely to influence a trait along with common variants.4, 14”

• cites [4] Frazer, K. A., Murray, S. S., Schork, N. J. & Topol, E. J. Human genetic variation and its contribution to complex traits. Nature Rev. Genet. 10, 241–251 (2009). sourceNot checked yet

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• cites [14] Gorlov, I. P., Gorlova, O. Y., Sunyaev, S. R., Spitz, M. R. & Amos, C. I. Shifting paradigm of association studies: value of rare single-nucleotide polymorphisms. Am. J. Hum. Genet. 82, 100–112 (2008). sourceNot checked yet

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The potential for false positive associations due to population stratification is large in rare variant studies because specific rare variants are more likely to be unique to a particular geoethnic group.

“The potential for false positive associations due to population stratification is large in studies involving rare variants since specific rare variants are more likely to be unique to a particular geoethnic group.”

Imputation methods are highly problematic for de novo or even moderately rare variants with frequencies below 1%.

“Although highly problematic in situations involving de novo or even moderately rare variants (<1%), imputation methods involving rare variants have begun to receive attention and could be extremely useful in future association studies.98”

• cites [97] Li, Y., Willer, C., Sanna, S. & Abecasis, G. Genotype imputation. Annu. Rev. Genomics Hum. Genet. 10, 387–406 (2009). sourceNot checked yet

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Multiple rare variants, both within the same gene and across different genes, collectively influence the expression and prevalence of traits and diseases in the population.

“There are many reasons to believe that multiple rare variants, both within the same gene and across different genes, collectively influence the expression and prevalence of traits and diseases in the population at large.”

• cites [14] Gorlov, I. P., Gorlova, O. Y., Sunyaev, S. R., Spitz, M. R. & Amos, C. I. Shifting paradigm of association studies: value of rare single-nucleotide polymorphisms. Am. J. Hum. Genet. 82, 100–112 (2008). sourceNot checked yet

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• cites [15] Pritchard, J. K. Are rare variants responsible for susceptibility to complex diseases? Am. J. Hum. Genet. 69, 124–137 (2001). sourceNot checked yet

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• cites [20] Schork, N. J., Wessel, J. & Malo, N. DNA sequence-based phenotypic association analysis. Adv. Genet. 60, 195–217 (2008). sourceNot checked yet

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Recent human population expansion likely produced many segregating, functionally relevant rare variants that mediate phenotypic variation.

“First, it has been argued that population phenomena, such as the recent expansion of the human population, are likely to have resulted in a large number of segregating, functionally-relevant, rare variants that mediate phenotypic variation.14, 15”

• cites [14] Gorlov, I. P., Gorlova, O. Y., Sunyaev, S. R., Spitz, M. R. & Amos, C. I. Shifting paradigm of association studies: value of rare single-nucleotide polymorphisms. Am. J. Hum. Genet. 82, 100–112 (2008). sourceNot checked yet

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• cites [15] Pritchard, J. K. Are rare variants responsible for susceptibility to complex diseases? Am. J. Hum. Genet. 69, 124–137 (2001). sourceNot checked yet

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The power to detect an association between a single rare variant is low even in very large samples.

“Association analyses involving rare variants are not as straightforward as analyses involving common variations since the power to detect an association between a single rare variant is low in even very large samples (Figure 1).14, 28, 29”

• cites [14] Gorlov, I. P., Gorlova, O. Y., Sunyaev, S. R., Spitz, M. R. & Amos, C. I. Shifting paradigm of association studies: value of rare single-nucleotide polymorphisms. Am. J. Hum. Genet. 82, 100–112 (2008). sourceNot checked yet

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• cites [28] Li, B. & Leal, S. M. Methods for detecting associations with rare variants for common diseases: application to analysis of sequence data. Am. J. Hum. Genet. 83, 311–321 (2008). One of the first papers to comprehensively evaluate statistical methods for testing collapsed sets of rare variants to a trait. The paper discussed both distance-based and regression approaches. sourceNot checked yet

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• cites [29] Altshuler, D., Daly, M. J. & Lander, E. S. Genetic mapping in human disease. Science 322, 881–888 (2008). sourceNot checked yet

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If the frequency of rare variants in a collapsed set is large enough or if there are many such variants, the percentage of individuals possessing any one of them could reach 100%.

“Second, if one collapses variants by counting individuals possessing rare variants, then if either the frequency of those variants is large enough or if there are many of them, the percentage of individuals possessing any one of them could reach 100%.”

Newer regression techniques using regularization and shrinkage can overcome collinearity and overfitting problems.

“Newer regression techniques that make use of regularization and shrinkage parameters to control for collinearity and overfitting can be used to overcome these problems.”

• cites [74] Malo, N., Libiger, O. & Schork, N. J. Accommodating linkage disequilibrium in genetic-association analyses via ridge regression. Am. J. Hum. Genet. 82, 375–385 (2008). sourceNot checked yet

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• cites [75] Hoggart, C. J., Whittaker, J. C., De Iorio, M. & Balding, D. J. Simultaneous analysis of all SNPs in genome-wide and re-sequencing association studies. PLoS Genet. 4, e1000130 (2008). Refs 74 and 75 introduced regularized regression techniques for accommodating a large number of predictors in a genetic association study and to separate causally associated from non-causally associated variants. sourceNot checked yet

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• cites [76] Zhou, H., Sehl, M. E., Sinsheimer, J. S. & Lange, K. Association screening of common and rare genetic variants by penalized regression. Bioinformatics 6 Aug 2010 (doi:10.1093/bioinformatics/btq448). sourceNot checked yet

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The choice of a distance measure can impact the interpretation of within-species ancestral relationships based on DNA sequence.

“For within-species studies assessing the ancestral relationships between populations based on DNA sequence, it has been shown that the choice of a distance measure can impact the interpretation of the results50, 128.”

• cites [50] Jost, L. GST and its relatives do not measure differentiation. Mol. Ecol. 17, 4015–4026 (2008). sourceNot checked yet

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• cites [128] Libiger, O., Nievergelt, C. M. & Schork, N. J. Comparison of genetic distance measures using human SNP genotype data. Hum. Biol. 81, 389–406 (2009). sourceNot checked yet

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Pairwise sequence similarity statistics would be highly appropriate in the extreme allelic heterogeneity situation, in which a group of individuals such as cases is hypothesized to possess more unique variants or more unique combinations of variants than another group such as controls in a defined genomic region.

“Such statistics would be highly appropriate in situations, such as the EAH situation, in which a group of individuals (e.g., cases) are hypothesized to simply possess more unique variants or more unique combinations of variants than another group of individuals (e.g., controls) in a defined genomic region.”

When many individual common and rare variants plus collapsed sets are included, a large number of candidate predictors will probably be available.

“In addition, there will likely be many potential predictor variables to choose from if many individual common and rare variants, as well as collapsed sets of variants, are considered.”

If enough rare variants are studied, each individual in a sample of cases and controls may have their own unique haplotypes, making summary statistic approaches impossible.

“In addition, if enough rare variants are studied, each individual in a sample of cases and controls may have their own unique haplotypes, making summary statistic approaches impossible.”

The choice of a q value for association studies based on diversity indices may be problematic because a genomic region may harbor common, moderately common, and rare variants, some of which may influence phenotypic expression.

“Since a genomic region may harbor common, moderately common, and rare variants, some of which may influence phenotypic expression, the choice of a q value for association studies based on diversity indices may be problematic.”

Statistics that exploit pairwise sequence similarity can be used as alternatives to classical summary statistic measures of sequence diversity differences between groups.

“Alternatively, statistics that exploit pairwise sequence similarity can be used65 as alternatives to classical summary statistic measures of sequence diversity differences between groups.”

• cites [65] Anderson, M. J. Distance-based tests for homogeneity of multivariate dispersions. Biometrics 62, 245–253 (2006). sourceNot checked yet

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Regression models provide a flexible framework for assessing the contribution of collections of rare variants to a phenotype.

“Such methods provide a flexible framework for assessing the contribution of collections of rare variants to a phenotype.28, 33”

• cites [28] Li, B. & Leal, S. M. Methods for detecting associations with rare variants for common diseases: application to analysis of sequence data. Am. J. Hum. Genet. 83, 311–321 (2008). One of the first papers to comprehensively evaluate statistical methods for testing collapsed sets of rare variants to a trait. The paper discussed both distance-based and regression approaches. sourceNot checked yet

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• cites [33] Morris, A. P. & Zeggini, E. An evaluation of statistical approaches to rare variant analysis in genetic association studies. Genet. Epidemiol. 34, 188–193 (2010). sourceNot checked yet

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Other summary statistic methods that ignore direction of effect may be problematic in settings in which rare variants are not necessarily more frequent in disease or certain a priori defined phenotypic states.

“Other summary statistic methods essentially ignore direction of effect and hence may be problematic in settings in which rare variants are not necessarily more frequent in disease or certain a priori defined phenotypic states.”

Many forms of structural variation are thought to exert or manifest their effects throughout the genome and not necessarily as a group of variants in a singular region of the genome.

“However, many of these forms of variation are thought to exert or manifest their effects throughout the genome and not necessarily as a group of variants in a singular region of the genome.”

• cites [3] Pinto, D. et al. Functional impact of global rare copy number variation in autism spectrum disorders. Nature 466, 368–372 (2010). sourceNot checked yet

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• cites [37] Sebat, J., Levy, D. & McCarthy, S. E. Rare structural variants in schizophrenia: one disorder, multiple mutations; one mutation, multiple disorders. Trends Genet. 25, 528–535 (2009). sourceNot checked yet

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Morris and Zeggini found that simple regression methods for testing collapsed sets of rare variants for association with a quantitative trait are intuitive, flexible and powerful.

“Recently, Morris and Zeggini33 assessed the power of simple regression methods for testing collapsed sets of rare variants for association with a quantitative trait and found that such approaches are indeed intuitive, flexible and powerful.”

• cites [33] Morris, A. P. & Zeggini, E. An evaluation of statistical approaches to rare variant analysis in genetic association studies. Genet. Epidemiol. 34, 188–193 (2010). sourceNot checked yet

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A limitation of similarity-based methods is that a specific DNA similarity or distance measure or metric must be chosen, and this can be problematic.

“In addition, a limitation of these methods is that a specific DNA similarity or distance measure or metric must be chosen and this can be problematic (Box 3).59”

• cites [59] Ickstadt, K., Selinski, S. & Muller, T. D. in SFB 475 Komplexitatsreduktion in Multivariaten Datenstrukturen (Univ. Dortmund, Germany, 2005).Not checked yet

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Price et al. showed that their method with optimal or variable weighting is more powerful than approaches that consider fixed weights.

“Price et al.35 showed that their method is more powerful than approaches that consider fixed weights.”

• cites [35] Price, A. L. et al. Pooled association tests for rare variants in exon-resequencing studies. Am. J. Hum. Genet. 86, 832–838 (2010). This paper describes a method for explicitly incorporating information about the likely functional effect of specific rare variants into the formulation of an association statistic. However, the proposed method only considers coding variations. sourceNot checked yet

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Similarity-based strategies can be as powerful, if not more so, than some traditional tests of association in many settings involving common variations.

“Many recent papers have described flexible strategies for testing genetic associations that leverage individual sequence similarity information,20, 52–57 and it has been shown that such strategies can be as powerful, if not more so, than some traditional tests of association in many settings involving common variations.58”

• cites [58] Lin, W. Y. & Schaid, D. J. Power comparisons between similarity-based multilocus association methods, logistic regression, and score tests for haplotypes. Genet. Epidemiol. 33, 183–197 (2009). sourceNot checked yet

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Applying multiple regression by simply extending Morris and Zeggini's approach to many individual rare variants or collapsed variant sets could be problematic.

“However, their direct application via simple extensions of the methods described by Morris and Zeggini33 to the analysis of multiple individual rare variants or collapsed sets of variants may be problematic.”

• cites [33] Morris, A. P. & Zeggini, E. An evaluation of statistical approaches to rare variant analysis in genetic association studies. Genet. Epidemiol. 34, 188–193 (2010). sourceNot checked yet

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• AssumptionRests on an assumption: In traditional linear regression, severe multicollinearity leads to numerical and interpretive problems.
• AssumptionRests on an assumption: When a standard linear regression has many predictors, or more predictors than subjects, it is prone to numerical instability and overfitting.

Not all approaches to linkage analysis are very powerful, especially non-parametric approaches involving small families.

“However, not all approaches to linkage analysis are very powerful, and this is especially true for non-parametric approaches involving small families69, 70, although transmission/disequilibrium tests may have merit in the analysis of rare variants.71”

• cites [69] Kruglyak, L., Daly, M. J., Reeve-Daly, M. P. & Lander, E. S. Parametric and nonparametric linkage analysis: a unified multipoint approach. Am. J. Hum. Genet. 58, 1347–1363 (1996).Not checked yet

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• cites [70] Risch, N. & Merikangas, K. The future of genetic studies of complex human diseases. Science 273, 1516–1517 (1996). sourceNot checked yet

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Two recent papers suggest that leveraging functional annotations and computational methods for predicting the consequences of specific rare variants can be used to great advantage in identifying disease-predisposing variants, at least for rare monogenic conditions.

“In fact, two recent papers23, 36 suggest that leveraging functional annotations and computational methods for predicting the consequences of specific rare variants can be used to great advantage in the identification of disease-predisposing variants, at least for rare monogenic conditions.”

• cites [23] Ng, S. B. et al. Exome sequencing identifies the cause of a Mendelian disorder. Nature Genet. 42, 30–35 (2010). sourceNot checked yet

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• cites [36] Ng, S. B. et al. Targeted capture and massively parallel sequencing of 12 human exomes. Nature 461, 272–276 (2009). sourceNot checked yet

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If a large enough genomic region is considered, one could collapse all variants unique to each case and then unique to each control, resulting in a set of variants that completely and perfectly discriminates cases from controls.

“In addition, if a large enough genomic region is considered, then one could merely ‘collapse’ all variants unique to each case and then unique to each control, resulting in a set of variants that completely and perfectly discriminate cases from controls.”

Functional nucleotide content, meaning the nucleotides and nucleotide combinations an individual possesses that impact function, determines gene activity rather than the phylogenetic origins of those nucleotides.

“The problem of choosing a DNA sequence similarity measure based purely on nucleotide content matching or genealogical or cladistic distance is rooted in the fact that, ultimately, functional nucleotide content (i.e., what nucleotides and nucleotide combinations an individual possesses that impact function) determines gene activity, rather than the phylogenetic origins of those nucleotides.”

Madsen and Browning showed that their proposed frequency-weighted statistic is more powerful than either the CAST or CMC methods in a number of settings.

“Madsen and Browning showed that their proposed statistic is more powerful than either the CAST or CMC methods in a number of settings, but more work in this area is needed to clarify the advantages, if any, of each.34”

• cites [34] Madsen, B. E. & Browning, S. R. A groupwise association test for rare mutations using a weighted sum statistic. PLoS Genet. 5, e1000384 (2009). sourceNot checked yet

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Traditional family-based linkage analyses are fairly robust to allelic heterogeneity.

“As a result, such methods are fairly robust to allelic heterogeneity.68”

• cites [68] Ott, J. Analysis of Human Genetic Linkage (Johns Hopkins Univ. Press, Baltimore, 1991).Not checked yet

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Measures of nucleotide similarity for comparing DNA sequences between pairs of individuals within a species are problematic.

“Measures of nucleotide similarity for the comparison of DNA sequences between pairs of individuals within a species are also problematic for this reason.”

• cites [50] Jost, L. GST and its relatives do not measure differentiation. Mol. Ecol. 17, 4015–4026 (2008). sourceNot checked yet

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Morris and Zeggini found that using a tally of the number of rare variants possessed by an individual across a large region as a predictor may be more powerful than using a simple indicator of possession of any rare variant.

“They found that the use of a tally may be more powerful.33”

• cites [33] Morris, A. P. & Zeggini, E. An evaluation of statistical approaches to rare variant analysis in genetic association studies. Genet. Epidemiol. 34, 188–193 (2010). sourceNot checked yet

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Searching for an optimal subset of variants that maximally discriminates between groups based on distances between sequences can be computationally intensive.

“Although intuitively appealing, such methods are problematic in that the determination of an optimal subset of variants based on group differences can be computationally-intensive.”

Using different q values in the construction of Δ measures for comparing genetic diversities of two or more populations has the same effect: small q values impact differences in rare variants and large q values emphasize differences in common variants.

“The use of different q values in the construction of Δ measures for the comparison of the genetic diversities of two (or more) populations will have the same effect50, 130, 131: small q values will impact differences in rare variants and large q values emphasize differences in common variants132.”

• cites [50] Jost, L. GST and its relatives do not measure differentiation. Mol. Ecol. 17, 4015–4026 (2008). sourceNot checked yet

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• cites [130] Keylock, C. J. Simpson diversity and the Shannon–Wiener index as special cases of a generalized entropy. Oikos 109, 203–207 (2005). sourceNot checked yet

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• cites [131] Lande, R. Statistics and partitioning of species diversity, and similarity among multiple communities. Oikos 76, 5–13 (1996). sourceNot checked yet

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The choice of a similarity or diversity measure can impact the interpretation of results in genetic association studies.

“Exploiting sequence similarity or diversity in genetic association studies can be problematic due to the fact that the choice of a similarity or diversity measure can impact the interpretation of the results.”

• cites [59] Ickstadt, K., Selinski, S. & Muller, T. D. in SFB 475 Komplexitatsreduktion in Multivariaten Datenstrukturen (Univ. Dortmund, Germany, 2005).Not checked yet

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• cites [126] Everitt, B. S. Cluster Analysis (John Wiley and Sons, New York, 2009).Not checked yet

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• cites [127] Wong, K. M., Suchard, M. A. & Huelsenbeck, J. P. Alignment uncertainty and genomic analysis. Science 319, 473–476 (2008). sourceNot checked yet

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In many standard GWA studies, multiple regression models have been used to pinpoint probable causal variants within genomic regions containing numerous associated variants.

“Multiple regression models have been applied in many standard GWA studies in an effort to identify the most likely causal variants in a particular genomic region harboring many associated variants72, 73.”

• cites [72] Haiman, C. A. et al. Multiple regions within 8q24 independently affect risk for prostate cancer. Nature Genet. 39, 638–644 (2007). sourceNot checked yet

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• cites [73] Clarke, R. et al. Genetic variants associated with Lp(a) lipoprotein level and coronary disease. N. Engl. J. Med. 361, 2518–2528 (2009). sourceNot checked yet

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In non-genetic settings, Tibshirani contrasted stepwise regression, ridge regression, and LASSO, finding each best for different situations based on predictor count and effect magnitude.

“Tibshirani82 compared the relative merits of standard stepwise regression, ridge regression, and the LASSO in different non-genetic contexts and concluded that each method seems is best suited for different specific settings, depending on the number and effect sizes of the predictors.”

• cites [82] Tibshirani, R. Regression shrinkage and selection via the Lasso. J. R. Stat. Soc. Series B Stat. Methodol. 58, 267–288 (1996). sourceNot checked yet

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Researchers have conducted power studies that compare newer rare variant methods against simpler ones.

“However, power studies comparing newer methods with more simplistic methods for rare variant analysis have been pursued (Table 3).”

The majority of studies linking rare variants to phenotypes have used straightforward collapsing approaches.

“Most studies assessing associations between rare variants and a phenotype have relied on rather simple collapsing strategies (Table 1).”

Approaches that capture subtle synergistic effects among many loci in a region, or among different variant types affecting gene function, such as sequence- or functional-similarity-based methods, are probably also suitable.

“However, methods which can account for subtle synergistic effects of many loci within a defined region and/or different forms of variation that might contribute to gene function, such as those rooted in sequence or functional similarity56, 57, 87, 88 are also likely to be appropriate.”

• cites [56] Clayton, D., Chapman, J. & Cooper, J. Use of unphased multilocus genotype data in indirect association studies. Genet. Epidemiol. 27, 415–428 (2004). sourceNot checked yet

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• cites [57] Tzeng, J. Y., Zhang, D., Chang, S. M., Thomas, D. C. & Davidian, M. Gene–trait similarity regression for multimarker-based association analysis. Biometrics 65, 822–832 (2009). sourceNot checked yet

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• cites [87] Wessel, J., Schork, A. J., Tiwari, H. K. & Schork, N. J. Powerful designs for genetic association studies that consider twins and sibling pairs with discordant genotypes. Genet. Epidemiol. 31, 789–796 (2007). sourceNot checked yet

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• cites [88] Nievergelt, C. M., Libiger, O. & Schork, N. J. Generalized analysis of molecular variance. PLoS Genet. 3, e51 (2007). sourceNot checked yet

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Because these methods are relatively new, no one has had sufficient time to compare all of them in a single large study.

“Other obvious issues with the current assessments of the power and other properties of rare variant analysis methods concern the simple fact that not enough time has elapsed since their introduction for someone to compare them all in a large study.”

Determining which rare variants in a set are causal may be harder than determining causality for a single common variant.

“Thus, the problem of assigning causality to rare variants in a set may be more pronounced than it is in assigning causality to a single common variant.”

In genetic association studies, a difficulty arises because the number of common, rare, or collapsed variant sets affecting a phenotype, and the nature of their effects, cannot be known in advance.

“This is problematic in the context of genetic association analyses since one will not necessarily know a priori how many common, rare, or collapsed sets of variants might influence a phenotype, nor what kind of effects those variants have.”

• AssumptionRests on an assumption: The number of common, rare, or collapsed variant sets that affect a phenotype, and the nature of their effects, cannot be known in advance.

Logic regression, first introduced for sequence data analysis, does not require variants to be collapsed beforehand.

“Logic regression, which is similar in ways to the method proposed by Han and Pan,40 was initially proposed for analyzing sequence data and does not assume that variants have been collapsed a priori.”

• cites [67] Kooperberg, C., Ruczinski, I., LeBlanc, M. L. & Hsu, L. Sequence analysis using logic regression. Genet. Epidemiol. 21 (Suppl. 1), S626–S631 (2001). One of the first papers to consider statistical methods for identifying optimal sets of predictors of a phenotype from sequence data based purely on the strength of statistical association. This paper proposed a novel regression method for this task. sourceNot checked yet

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• cites [40] Han, F. & Pan, W. A data-adaptive sum test for disease association with multiple common or rare variants. Hum. Hered. 70, 42–54 (2010). sourceNot checked yet

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Several methods for rare variant association analysis have been introduced, all relying on grouping variants by functional annotation or by genomic position or window.

“A number of rare variant association analysis methods have been proposed that build off the notion of collapsing variants into groups based on either functional annotations of the genomic regions they reside in or on their location in a defined genomic region or ‘window.’”

Certain methods are highly specialized and probably will not perform well outside the contexts they were built for.

“In addition, some methods are clearly nuanced and are unlikely to work in situations other than those for which they were designed.”

A collective association between a set of rare variants and a phenotype does not imply that every variant in the set is functional or causal.

“In this context merely finding that a set of rare variants appears to be collectively associated with a phenotype in no way suggests that all those variants are indeed functional or causally related to the phenotype.”