Increasing Power in Association Studies by using Linkage Disequilibrium Structure and Molecular Function as Prior Information

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Increasing Power in Association Studies by using
Linkage Disequilibrium Structure and Molecular
Function as Prior Information

• Eleazar Eskin
• UCLA

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Motivation

• Whole genome association study
• How to perform multiple hypothesis correction
• To increase statistical power
• Incorporate prior information on molecular
  function of associated loci
• Information on linkage disequilibrium structure

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Main idea

• Traditional method
• Use a single significance threshold
• In practice, markers are not identical
• Set a different threshold at each marker, which
  reflects both intrinsic (e.g. LD, allele freq.)
  and extrinsic information on the markers

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Standard Association Study

• M markers in N cases and N controls
• fi minor allele frequency at marker i
• True case/control allele frequency
• Marker d casual variant with a relative risk

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Standard Association Study

• Test statistic
• N( ,1)
• Power at a single marker (probability of
  detecting an association with N individuals at
  p-value or significance threshold t

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Multiple Hypothesis correction

• Fix the false positive rate at each marker so
  that the total false positive rate is a
• Bonferroni correction
• ti a/M
• Expected power
• where ci is the probability of marker i to be
  causal
• ? Probability of rejecting the correct null
  hypothesis

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Multi-Threshold Association

• Allow a different threshold ti for each marker
• Power
• with adjusted false positive rate
• Goal set values for ti to maximize the power
  subject to the constraints

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Maximizing the Power

• Gradient at each marker will be equal at the
  optimal point
• Given a value of gradient, solve for the
  threshold at each marker to achieve that gradient
• Do binary search over the gradient until
  thresholds sum to a

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Maximizing Power for Proxies

• In practice, markers are tags for causal
  variation
• Given K variants, assign each potential causal
  variation vk to the best marker i
• The effective non-centrality parameter is reduced
  by a factor of rki where rki is the correlation
  coefficient between variant k and marker i.
• If vk is causal, the power function when
  observing proxy marker i is

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Maximizing Power for Proxies

• Each variant k has a prob of being causal ck
• The total power captured by each marker i
• The total power of the association study

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Candidate Gene study

• 1000 cases and controls over ENCODE regions using
  markers in Affymetrix 500k genechip

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Robustness over relative risks
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Whole Genome Association

• Assumption
• Each SNP is equally likely to be causal with
  relative risk of 2
• Power for traditional study and multi-threshold
  association for 2,614,057 SNPs
• avg 0.593 / 0.610
• Avg over power in 0.1, 0.9 0.568 / 0.615

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Impact of extrinsic information

• cSNPs are more likely to be involved in disease
• Add information on se of genes which are more
  likely to be involved in specific disease
• 30,700 cSNPs in HapMap contributes to 20 of the
  disease causing variation
• Cancer Gene Census 363 genes in which mutations
  have been implicated in cancer. 20 of causal
  variation is assumed in these genes

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