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Statistical power of model selection strategies for genome-wide association studies.

Wu Z, Zhao H - PLoS Genet. (2009)

Bottom Line: Because many genes are potentially involved in common diseases and a large number of markers are analyzed, it is crucial to devise an effective strategy to identify truly associated variants that have individual and/or interactive effects, while controlling false positives at the desired level.After the accuracy of our analytical results is validated through simulations, they are utilized to systematically evaluate and compare the performance of these strategies in a wide class of genetic models.For a specific genetic model, our results clearly reveal how different factors, such as effect size, allele frequency, and interaction, jointly affect the statistical power of each strategy.

View Article: PubMed Central - PubMed

Affiliation: Department of Epidemiology and Public Health, Yale University School of Medicine, New Haven, Connecticut, United States of America.

ABSTRACT
Genome-wide association studies (GWAS) aim to identify genetic variants related to diseases by examining the associations between phenotypes and hundreds of thousands of genotyped markers. Because many genes are potentially involved in common diseases and a large number of markers are analyzed, it is crucial to devise an effective strategy to identify truly associated variants that have individual and/or interactive effects, while controlling false positives at the desired level. Although a number of model selection methods have been proposed in the literature, including marginal search, exhaustive search, and forward search, their relative performance has only been evaluated through limited simulations due to the lack of an analytical approach to calculating the power of these methods. This article develops a novel statistical approach for power calculation, derives accurate formulas for the power of different model selection strategies, and then uses the formulas to evaluate and compare these strategies in genetic model spaces. In contrast to previous studies, our theoretical framework allows for random genotypes, correlations among test statistics, and a false-positive control based on GWAS practice. After the accuracy of our analytical results is validated through simulations, they are utilized to systematically evaluate and compare the performance of these strategies in a wide class of genetic models. For a specific genetic model, our results clearly reveal how different factors, such as effect size, allele frequency, and interaction, jointly affect the statistical power of each strategy. An example is provided for the application of our approach to empirical research. The statistical approach used in our derivations is general and can be employed to address the model selection problems in other random predictor settings. We have developed an R package markerSearchPower to implement our formulas, which can be downloaded from the Comprehensive R Archive Network (CRAN) or http://bioinformatics.med.yale.edu/group/.

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Comparisons among model selection power for detecting the true model or both true SNPs in marginal search over genetic model space.The power differences between marginal search and exhaustive search in the left column, between marginal search and forward search in the middle column, and between forward search and exhaustive search in the right column. Green areas indicate positive values of difference, and red areas indicate negative values of difference. We consider genetic models with the main effects b1 = b2 varying from −1 to 1 and the epistatic effect b3 varying from −1 to 1. The allele frequency qj = 0.3, j = 1, …, p, and the false discovery number R is set to be 1 in row 1 and 10 in row 2.
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pgen-1000582-g002: Comparisons among model selection power for detecting the true model or both true SNPs in marginal search over genetic model space.The power differences between marginal search and exhaustive search in the left column, between marginal search and forward search in the middle column, and between forward search and exhaustive search in the right column. Green areas indicate positive values of difference, and red areas indicate negative values of difference. We consider genetic models with the main effects b1 = b2 varying from −1 to 1 and the epistatic effect b3 varying from −1 to 1. The allele frequency qj = 0.3, j = 1, …, p, and the false discovery number R is set to be 1 in row 1 and 10 in row 2.

Mentions: In order to better visualize the difference of model selection methods, we show the power differences between different methods. The left, middle, and right columns of Figure 2 and Figure 3 present the power difference between marginal search and exhaustive search, between marginal search and forward search, and between forward search and exhaustive search, respectively. For a specific comparison, the red areas represent negative values, indicating the former method has lower power, and the green areas represent positive values, indicating the former method has higher power. The dashed contours in these plots represent the heritability of the genetic model, i.e., the proportion of the total variation due to genetic effects, which is defined asUnder our model set-up,In each plot, there are two areas in which the difference of power is close to 0. First, in the central area where the signal is weak (small H2), all model selection procedures have low power and tend to fail to pick up the true SNPs. Second, in the edge areas where the signals are strong, all model selection procedures have similarly good power. The light colored areas represent these two special situations in which there is little difference in power among model selection methods.


Statistical power of model selection strategies for genome-wide association studies.

Wu Z, Zhao H - PLoS Genet. (2009)

Comparisons among model selection power for detecting the true model or both true SNPs in marginal search over genetic model space.The power differences between marginal search and exhaustive search in the left column, between marginal search and forward search in the middle column, and between forward search and exhaustive search in the right column. Green areas indicate positive values of difference, and red areas indicate negative values of difference. We consider genetic models with the main effects b1 = b2 varying from −1 to 1 and the epistatic effect b3 varying from −1 to 1. The allele frequency qj = 0.3, j = 1, …, p, and the false discovery number R is set to be 1 in row 1 and 10 in row 2.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2712761&req=5

pgen-1000582-g002: Comparisons among model selection power for detecting the true model or both true SNPs in marginal search over genetic model space.The power differences between marginal search and exhaustive search in the left column, between marginal search and forward search in the middle column, and between forward search and exhaustive search in the right column. Green areas indicate positive values of difference, and red areas indicate negative values of difference. We consider genetic models with the main effects b1 = b2 varying from −1 to 1 and the epistatic effect b3 varying from −1 to 1. The allele frequency qj = 0.3, j = 1, …, p, and the false discovery number R is set to be 1 in row 1 and 10 in row 2.
Mentions: In order to better visualize the difference of model selection methods, we show the power differences between different methods. The left, middle, and right columns of Figure 2 and Figure 3 present the power difference between marginal search and exhaustive search, between marginal search and forward search, and between forward search and exhaustive search, respectively. For a specific comparison, the red areas represent negative values, indicating the former method has lower power, and the green areas represent positive values, indicating the former method has higher power. The dashed contours in these plots represent the heritability of the genetic model, i.e., the proportion of the total variation due to genetic effects, which is defined asUnder our model set-up,In each plot, there are two areas in which the difference of power is close to 0. First, in the central area where the signal is weak (small H2), all model selection procedures have low power and tend to fail to pick up the true SNPs. Second, in the edge areas where the signals are strong, all model selection procedures have similarly good power. The light colored areas represent these two special situations in which there is little difference in power among model selection methods.

Bottom Line: Because many genes are potentially involved in common diseases and a large number of markers are analyzed, it is crucial to devise an effective strategy to identify truly associated variants that have individual and/or interactive effects, while controlling false positives at the desired level.After the accuracy of our analytical results is validated through simulations, they are utilized to systematically evaluate and compare the performance of these strategies in a wide class of genetic models.For a specific genetic model, our results clearly reveal how different factors, such as effect size, allele frequency, and interaction, jointly affect the statistical power of each strategy.

View Article: PubMed Central - PubMed

Affiliation: Department of Epidemiology and Public Health, Yale University School of Medicine, New Haven, Connecticut, United States of America.

ABSTRACT
Genome-wide association studies (GWAS) aim to identify genetic variants related to diseases by examining the associations between phenotypes and hundreds of thousands of genotyped markers. Because many genes are potentially involved in common diseases and a large number of markers are analyzed, it is crucial to devise an effective strategy to identify truly associated variants that have individual and/or interactive effects, while controlling false positives at the desired level. Although a number of model selection methods have been proposed in the literature, including marginal search, exhaustive search, and forward search, their relative performance has only been evaluated through limited simulations due to the lack of an analytical approach to calculating the power of these methods. This article develops a novel statistical approach for power calculation, derives accurate formulas for the power of different model selection strategies, and then uses the formulas to evaluate and compare these strategies in genetic model spaces. In contrast to previous studies, our theoretical framework allows for random genotypes, correlations among test statistics, and a false-positive control based on GWAS practice. After the accuracy of our analytical results is validated through simulations, they are utilized to systematically evaluate and compare the performance of these strategies in a wide class of genetic models. For a specific genetic model, our results clearly reveal how different factors, such as effect size, allele frequency, and interaction, jointly affect the statistical power of each strategy. An example is provided for the application of our approach to empirical research. The statistical approach used in our derivations is general and can be employed to address the model selection problems in other random predictor settings. We have developed an R package markerSearchPower to implement our formulas, which can be downloaded from the Comprehensive R Archive Network (CRAN) or http://bioinformatics.med.yale.edu/group/.

Show MeSH