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

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

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

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 /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

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 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%

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

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

Aa Gn 11 n 10 n1n1 gn 01 n 00 n0n0 n1n1 n0n0 MeasureFormulaRef. D’Lewontin (1964)  2 = r 2 Hill and Weir (1994) ** Levin (1953)  Edwards (1963) QYule (1900)

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 ’ =

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

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)

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

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