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Multiple Comparisons Measures of LD Jess Paulus, ScD January 29, 2013

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Today’s topics 1. Multiple comparisons 2. Measures of Linkage disequilibrium D’ and r 2 r 2 and power

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Multiple testing & significance thresholds Concern about multiple testing Standard thresholds (p<0.05) will lead to a large number of “significant” results Vast majority of which are false positives Various approaches to handling this statistically

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Possible Errors in Statistical Inference Unobserved Truth in the Population H a : SNP prevents DM H 0 : No association Observed in the Sample Reject H 0 : SNP prevents DM True positive (1 – β) False positive Type I error (α) Fail to reject H 0 : No assoc. False negative Type II error (β): True negative (1- α)

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Probability of Errors α =Also known as: “Level of significance” Probability of Type I error – rejecting null hypothesis when it is in fact true (false positive), typically 5% p value = The probability of obtaining a result as extreme or more extreme than you found in your study by chance alone

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Type I Error (α) in Genetic and Molecular Research A genome-wide association scan of 500,000 SNPs will yield: 25,000 false positives by chance alone using α = 0.05 5,000 false positives by chance alone using α = 0.01 500 false positives by chance alone using α = 0.001

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Multiple Comparisons Problem Multiple comparisons (or "multiple testing") problem occurs when one considers a set, or family, of statistical inferences simultaneously Type I errors are more likely to occur Several statistical techniques have been developed to attempt to adjust for multiple comparisons Bonferroni adjustment

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Adjusting alpha Standard Bonferroni correction Test each SNP at the α* =α /m 1 level Where m 1 = number of markers tested Assuming m 1 = 500,000, a Bonferroni-corrected threshold of α*= 0.05/500,000 = 1x10–7 Conservative when the tests are correlated Permutation or simulation procedures may increase power by accounting for test correlation

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Measures of LD Jess Paulus, ScD January 29, 2013

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Haplotype definition Haplotype: an ordered sequence of alleles at a subset of loci along a chromosome Moving from examining single genetic markers to sets of markers

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Measures of linkage disequilibrium Basic data: table of haplotype frequencies AG ag AG ag Ag AG ag AG AG ag AG Ag ag AG ag AG Aa G8050% g26 62.5%37.5%

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D’ and r 2 are most common Both measure correlation between two loci D prime … Ranges from 0 [no LD] to 1 [complete LD] R squared… also ranges from 0 to 1 is correlation between alleles on the same chromosome

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D Deviation of the observed frequency of a haplotype from the expected is a quantity called the linkage disequilibrium (D) If two alleles are in LD, it means D ≠ 0 If D=1, there is complete dependency between loci Linkage equilibrium means D=0

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Aa Gn 11 n 10 n1n1 gn 01 n 00 n0n0 n1n1 n0n0 MeasureFormulaRef. D’Lewontin (1964) 2 = r 2 Hill and Weir (1994) ** Levin (1953) Edwards (1963) QYule (1900)

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AG ag AG ag Ag AG ag AG AG ag AG Ag ag AG ag AG Aa G8050% g26 62.5%37.5% D’ = (8 6 – 0x2) / (8 6) =1 r 2 = (8 6 – 0x2) 2 / (10 6 8 8) =.6 R 2 = D ’ =

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r 2 and power r 2 is directly related to study power A low r 2 corresponds to a large sample size that is required to detect the LD between the markers r 2 *N is the “effective sample size” If a marker M and causal gene G are in LD, then a study with N cases and controls which measures M (but not G) will have the same power to detect an association as a study with r 2 *N cases and controls that directly measured G

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r 2 and power Example: N = 1000 (500 cases and 500 controls) r 2 = 0.4 If you had genotyped the causal gene directly, would only need a total N=400 (200 cases and 200 controls)

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Today’s topics 1. Multiple comparisons 2. Measures of Linkage disequilibrium D’ and r 2 r 2 and power

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