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Multiple Comparisons Measures of LD Jess Paulus, ScD January 29, 2013 Today’s topics 1. 2. Multiple comparisons Measures of Linkage disequilibrium • D’ and r2 • r2 and power 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 Possible Errors in Statistical Inference Unobserved Truth in the Population Observed in the Sample Reject H0: SNP prevents DM Fail to reject H0: No assoc. Ha: SNP prevents DM H0: No association True positive (1 – β) False positive Type I error (α) False negative Type II error (β): True negative (1- α) 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 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 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 Adjusting alpha Standard Bonferroni correction Test each SNP at the α* =α /m1 level Where m1 = number of markers tested Assuming m1 = 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 Measures of LD Jess Paulus, ScD January 29, 2013 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 Measures of linkage disequilibrium a g a g A G A G A G A G A g a g a g A g A G A G A G A G a g a g Basic data: table of haplotype frequencies A a G 8 0 50% g 2 6 50% 62.5% 37.5% D’ and r2 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 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 G g Measure D’ 2 = r2 A n11 n01 n1 a n10 n00 n0 n1 n0 Formula n 11 n 00 n 10 n 01 min( n 1n 0 , n 0 n 1 ) n 11 n 00 n 10 n 01 2 n 1n 0 n 1 n o * n 11 n 00 n 10 n 01 n 11 n 00 n 11 n 0 Ref. Lewontin (1964) Hill and Weir (1994) Levin (1953) Edwards (1963) n 10 n 01 Q n 11 n 00 n 10 n 01 n 11 n 00 n 10 n 01 Yule (1900) a g a g A G A G A G A G A g a g a g A g A G A G A G A G a g a g D’ = n 11 n 00 n 10 n 01 min( n 1n 0 , n 0 n 1 ) A G 8 g 2 62.5% a 0 6 37.5% D’ =(86 – 0x2) / (86) =1 R2 = 50% 50% n 11 n 00 n 10 n 01 2 n 1n 0 n 1 n o r2 = (86 – 0x2)2 / (10688) = .6 r2 and power r2 is directly related to study power A low r2 corresponds to a large sample size that is required to detect the LD between the markers r2*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 r2*N cases and controls that directly measured G r2 and power Example: N = 1000 (500 cases and 500 controls) r2 = 0.4 If you had genotyped the causal gene directly, would only need a total N=400 (200 cases and 200 controls) Today’s topics 1. 2. Multiple comparisons Measures of Linkage disequilibrium • D’ and r2 • r2 and power