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  • Review Article
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Statistical analysis strategies for association studies involving rare variants

Nature Reviews Genetics volume 11, pages 773–785 (2010)Cite this article

Subjects

Key Points

  • We review the motivation for exploring the role of rare variants in phenotypic expression.

  • There are several problems with capturing the effects of rare variants in association studies using current statistical analysis methods.

  • We discuss the concept and use of collapsing sets of rare variants into predictors of phenotypic expression, to aid statistical analyses of rare variant associations.

  • Functional annotations of specific variants and genomic regions can be used to define collapsed sets of rare variants.

  • A range of statistical analysis models and inference-making procedures could be exploited to assess the association between rare variants and phenotypic expression. We discuss the relative merits of these approaches.

  • We compare moving window and defined region approaches to the analysis of rare variant effects.

  • We discuss the importance for rare variant analysis of the flexibility of statistical analysis models and methods in accommodating factors, including common variants, interactions between variants, beneficial and deleterious effects of variants and environmental factors.

Abstract

The limitations of genome-wide association (GWA) studies that focus on the phenotypic influence of common genetic variants have motivated human geneticists to consider the contribution of rare variants to phenotypic expression. The increasing availability of high-throughput sequencing technologies has enabled studies of rare variants but these methods will not be sufficient for their success as appropriate analytical methods are also needed. We consider data analysis approaches to testing associations between a phenotype and collections of rare variants in a defined genomic region or set of regions. Ultimately, although a wide variety of analytical approaches exist, more work is needed to refine them and determine their properties and power in different contexts.

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Figure 1: Sample size requirements and statistical power for variants of different frequencies.
Figure 2: Scenarios in which DNA sequence variants distinguish cases and controls.

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Acknowledgements

This work was supported in part by the following research grants: U19 AG023122-05, R01 MH078151-03, N01 MH22005, U01 DA024417-01, P50 MH081755-01, R01 AG030474-02, N01 MH022005, R01 HL089655-02, R01 MH080134-03, U54 CA143906-01, UL1 RR025774-03 as well as the Price Foundation and Scripps Genomic Medicine. O.L. is also supported by a grant from Charles University: GAUK 134,609. The authors would like to thank E. Topol, S. Murray, S. Levy and the entire team at The Scripps Translational Science Institute for support.

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Author notes

  1. Vikas Bansal, Ondrej Libiger and Ali Torkamani: These authors contributed equally to this Review.

Authors and Affiliations

  1. The Scripps Translational Science Institute, 3344 North Torrey Pines Court, Suite 300, La Jolla, 92037, California, USA

    Vikas Bansal, Ondrej Libiger, Ali Torkamani & Nicholas J. Schork

  2. Department of Molecular and Experimental Medicine, The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, 92037, California, USA

    Ondrej Libiger, Ali Torkamani & Nicholas J. Schork

  3. Lekarska Fakulta v Hradci Kralove, Charles University, Faculty of Medicine in Hradec Kralove, PO BOX 38, Simkova 870, 500 38, Hradec Kralove 1, Czech Republic

    Ondrej Libiger

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Sequence Variant Analyzer

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Glossary

Contingency table

A way of representing categorical data in a matrix that is often used to record and analyse the relationship between two or more categorical variables. Also referred to as cross-tabulation or a cross-tab table.

Regression method

A statistical method for predicting or relating a variable (or set of variables) known as the dependent variable to another variable (or set of variables) known as the independent or predictor variable. The resulting relationship defines a regression function.

Compound heterozygosity

A situation in medical genetics in which two normally recessive alleles of a gene cause disease when they are located on different chromosome homologues in the same individual.

Population stratification

The phenomenon of an apparently homogeneous population that is actually composed of subgroups of individuals with distinct ancestral origins and differing allele frequencies at many loci. This leads to bias in assessing the significance of associations of a trait with particular loci.

Multiple testing

In statistics, multiple testing occurs when one considers more than one statistical inference from a single data set. Errors in inference are more likely to occur when one considers all the inferences as a whole.

Imputation

Based on the known linkage disequilibrium structure in fully genotyped individuals, the genotype of untyped variants can be inferred or imputed in individuals who are genotyped for a smaller number of variants.

Conditional test

In regression analysis, the importance of additional variables (or covariates) can be included in the model — that is, the model can be conditioned on the additional variables. A conditional test of the relationship between the primary independent variable and the dependent variable can therefore be performed.

Covariate effect

The influence of non-primary independent variables on the relationship between a primary independent variable and a dependent variable in a regression analysis setting.

Quantile

A point taken at regular intervals in the cumulative distribution function of a random variable. Quantiles are used to define discrete categories of the variable.

Stratified analysis

A data analysis that proceeds by dividing the units of observation into groups and analysing these groups independently.

Group summary information

Statistics that capture frequencies, counts and other measures that reflect information at the population or sample level, in contrast to measures reflecting information that is unique to each individual.

Moving window

A method for testing genetic associations in which a subregion of a larger region is defined. Variants within the defined region are tested for association, then the region is shifted to an adjacent region and the process is repeated until all the subregions have been assessed.

Type I error rate

The probability of a false-positive result from a statistical hypothesis test.

Permutation method

A strategy for assessing the probability of observing the value of a particular statistic. The probability is computed from a data set in which the data are randomly shuffled and the statistic is recomputed from the shuffled data many times and ultimately compared to the value of the statistic obtained with the non-shuffled data.

Phase information

The nucleotide content of each of the homologous chromosomes in a diploid individual.

Fst and Gst statistics

Two classical measures of population differentiation at the nucleotide level. Essentially, Fst and Gst capture and quantify the allele frequency differences between populations.

Logic regression

A regression analysis procedure in which sets of independent variables are grouped together using logical operators such as 'AND' and 'OR.' These sets of independent variables, rather than the individual variables themselves, are tested for association with a dependent variable.

Non-parametric approach

A statistical analysis method that does not rely on specific distributional assumptions (for example, normality) for the variables being analysed.

Multicolinearity

The situation in which two or more predictors (or subsets of predictors) are strongly (but not perfectly) correlated to one another, making it difficult to interpret the strength of the effect of each predictor (or predictor subset). For example, it would be hard to detect a gene if its effect is 'absorbed' (or masked) by combinations of genetic background action or interaction parameters in the model.

Overfitting

A phenomenon in which the predictions of a dependent variable, based on a set of independent variables in a regression setting, are complicated by the fact that there are many more independent variables used in the prediction than there are individuals who have been measured on these independent variables.

Regularization and shrinkage

A method for combating overfitting in regression models. Most independent variables are assumed to make only a small or non-existent contribution to the prediction of a dependent variable. Hence their impact is shrunk or regulated to be close to zero when estimating relevant parameters that govern the regression model.

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Bansal, V., Libiger, O., Torkamani, A. et al. Statistical analysis strategies for association studies involving rare variants. Nat Rev Genet 11, 773–785 (2010). https://doi.org/10.1038/nrg2867

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