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More Powerful Genome-wide Association Methods for Case-control Data

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More Powerful Genome-wide Association Methods for Case-control Data

Robert C. Elston, PhD

Case Western Reserve University

Cleveland Ohio

Kim S, Morris NJ, Won S, Elston RC

Genetic Epidemiology, in press

- A genome-wide association study with case-control data aims to localize disease susceptibility regions in the genome
- Single Nucleotide Polymorphism (SNP) markers, which are usually diallelic, have been used to cover the whole genome
- Two categories of tests have been applied to these data
- single marker association tests, which examine association between affection status and the SNP data one SNP at a time
- multi-marker association tests, which examine association between affection status and multiple SNP data simultaneously

Information for association

- Allele frequency trend test

Association Analysis

HWD trend test

Allele

LD contrast test

a

d. genotype frequency test

HWD

LD

d

e

haplotype-based test with HWE

g

b

c

f

f. ???

g. phase-known genotype-based test

- The allele frequency, HWD and LD contrast tests are typically developed in what has been termed a retrospective context; i.e. case-control status is considered fixed and the genotypes are considered random
- For case-control data, epidemiologists typically take advantage of the properties of the odds ratio and use the prospective logistic regression model, making the case-control status the random variable dependent on the predictors
- Prospective modeling tends to allow for greater flexibility, especially when adjusting for covariates
- It also provides a natural way to adjust for any correlations between the tests or other covariates, and can be extended to quantitative traits

- We suppose there are two diallelic SNP markers, A and B having alleles {A1,A2} and {B1,B2}, respectively, where A1 and B1 are the minor alleles

- IcaseandIctrldenote the sets of cases and controls
- We make minimal assumptions about the general population sampled; in particular, we do not assume HWE in the population
- μX, andσXYdenote the expected value of X, the variance of X and the covariance of X and Y, respectively

- The HWD parameter for marker A is given by
- The HWD parameter can be expressed as
- This means that the HWD parameter, dA, is half the deviation of the variance from the variance expected under HWE
- The composite LD parameter for alleles A1 and B1 of markers A and B is

- The joint test of allele frequency and HWD contrasts between cases and controls tests the null hypothesis H0: (pA|casedA|case) = (pA|ctrldA|ctrl)
- Let Zi= (Xi )’; the sample mean Z is a sufficient statistic for (pAdA)’
- The Allelic-HWD contrast test can be performed by comparing Zcase and Zctrl. The T2 statistic for this test is

_

_

_

_

Z

- Let Zi = (Xi YiXiYi)’; is a sufficient statistic for (pApBΔ)’

- The Allelic-LD contrast test can be performed using a version of Hotelling’s T2
- The additional case-control differences can be captured by the HWD and LD contrast tests, given the allele frequency contrast(s)
- The Allelic-HWD-LD contrast test can be constructed in a similar manner by contrasting the mean vector of Zi = (Xi YiXiYi )’ between cases and controls

- “Self-replication” if the tests are independent
- Sequential tests
E.g. The HWD contrast test adjusted for allele frequency information which is used in the first stage can be performed by the test of

- Let D denote the disease genotype variable coded as

- We write the penetrance model as:

- Given the true disease model and the LD structure, we can set up the true single-marker associationmodel between the phenotype and single-marker data X:

- This true association model has the same form as the penetrance model

- When (1 – 2pD) - ≠ 0, the coefficient of the
- quadratic terms generally approaches 0 faster than does that of the linear term

γD

γD2

- T2 test in a retrospective model and the score test and LRT in a prospective logistic model are expected to perform similarly
- The noncentrality parameter of the T2 test for test 2-5 is

- The noncentrality parameters for the other tests can be obtained by using the corresponding sub-matrices of (μcase – μctrl) and (Σcase + Σctrl)
- Then

For each of the four disease models, parameters were set as follows:

pD = 0.2, pA = 0.3, K = 0.05, DXD = 0.048(D’ = 0.8), n = 2,000 (500 for recessive), α = 0.05/500,000

Empirical power is obtained by the ratio of the number of rejected replicates to the total 100,000 replicates.

- We estimated LD parameters and marker allele frequencies from the HapMap CEU population
- The data consist of 120 haplotypes estimated from 30 parent-offspring trios
- We split chromosome 11 into mutually exclusive consecutive regions containing 3 SNPs each
- For each region we estimated the LD and allele frequency parameters
- We excluded regions where the minor allele frequencies of three consecutive markers were less than 0.1, leaving 4,648 regions
- We chose the disease SNP to be the one with the smallest allele frequency
- Parameters other than the allele frequency and LD parameters were set to be the same as before

- The best two marker test always appear to be more powerful than either the best single-marker test or the haplotype-based test
- It should be possible, by examining the LD structure of the markers, to predict which will be the best two-marker test to perform
- We need to study > two marker tests

http://darwin.case.edu/sage.html

http://darwin.case.edu/