# Presentation: 350403

## Statistical Methodologies for Analyzing Whole Genome Association Data

- John P. Rice, Ph.D.
- Washington University School of Medicine

## Crossing Over During Meiosis

**Crossing Over During Meiosis**

## Definition of centimorgan (cM)

**Definition of centimorgan (cM)**

## Genome Arithmetic

- Kb=1,000 bases; Mb=1,000Kb
- 3.3 billion base pairs; 3,300 cM in genome
- 		3,300,000,000/3,300 = 1 Mb/cM
- 33,000 genes
- 		33,000/3,300 Mb = 10 genes / Mb
-  Thus, 20 cM region may have 200 genes to examine
- Erratum – closer to 20,000 genes in humans

## Linkage Vs. Association

- Linkage:
-       -Disease travels with marker within families
-       -No association within individuals
-       -Signals for complex traits are wide (20MB)
- Association:
-       -Can use case/control or case/parents design
-       -Only works if association in the population
-       -Allelic heterogeneity (eg, BRAC1) a problem
- Linkage – large scale; Association fine scale (<200kb)

## Exanple of a LOD Curve

## Disequilibrium  

- Let  P(A1)=p1
- Let  P(B1)=q1
- Let  P(A1B 1)=h11
- No association if h11=p1q1
- D = h11-p1q1

- A1                   A2
- B1		  B2

## D ́ and r2

-  D tends to take on small values and depends on marginal gene frequencies
-   D =  D / max(D)
-    r2 = D2 / (p1p2 q1q2)
-       =  square of usual correlation coefficient ()
- Note: r2 = 0   D  = 0
- D  = ±1 if one cell is zero
- r2 can be small even when D  = ±1
- Prediction of one SNP by another depends  on r2

## Basic Idea

- If SNP A is a disease susceptibility gene, and if we genotype SNP B (for example in a whole genome association study), and if A and B are in disequilibrium, then cases and controls will have different frequencies of alleles at B
- Power to detect A is related to N/r2

## D  = 1, r2 = .1

**D ******** = 1, r****2**** = .1**

## D  = 1, r2 = .01 

**D ******** = 1, r****2**** = .01**

## Blocks and Bins

- Predictability of one SNP by another best described by r2 – basic statistics
- Block – set of SNPs with all pair-wise LD high (Please specify measure)
- If one uses r2 – insert a SNP with low frequency in between SNPs with freqs close to 0.5, then block breaks up!
- Perlegen (Hinds et al, Science, 2005) -– use bins where a tag SNP has r2  of 0.8 with all other SNPs.  Bins may not be contiguous.

## Slide 13

## Summary (Blocks and Bins)

- Blocks using **D ******** **may have a “biological” interpretation (long stretches with |**D ********| **=1)
- Selection of Tag SNPs is a statistical issue, want to predict untyped SNPS from those that are typed – r2 is natural measure
- Phase of SNPs is important – usually ignored
- Most current WGA studies use bins based on r2 (typically r2 > 0.8)
- There is an art to selecting tag SNPs

## Statistical Analysis

- Case/Control Design
- Use standard statistical tests (logistic regression) to test whether the distribution of the SNP differs between cases and controls
- Sensitive to population stratification
- Family Based Design

- Alleles 1 and 4 are transmitted -- CASE
- Alleles 2 and 3 are non-transmitted –CONTROL
- NOTE:  Genotype 3 people to get 1 case and 1 control
- NOT sensitive to population stratification

## Problem of Multiple Tests

- Significant level = α
- We perform N (independent) tests
- We expect to reject Nα tests if null hypothesis is true for each test.
_**Example**_**:**
- 	N = 100, α = .05, x = # of rejections
- 	P(x _>_ 1) = 1 – P(x = 0)
- 		= 1 –( 1 – α)100
- 		= .99408
- Note:	1 –( 1 – α)N ≈ Nα  for α small
- Choose α′ = α/N = .0005
- The 1 – (1 - α′)100 = .0488
**Bonferroni Correction**
**Problem:**  Power goes down as α decreases

## Multiple tests for association

- Intuition:  LD  extents over smaller regions than linkage
- More “independent” tests for LD -- There must be at the equivalent of at least 200,000 independent tests in one experiment (linkage about 2,000 independent tests)
- Multiple testing for whole genome association studies will be problematic
- Practical question – How to correct for multiple tests

## Multiple Testing

- Suppose we use 600,000 SNPs, and there are 10 true susceptibility loci. Test at significance level p=0.001, and power is 60%
- We expect 10 x .6 = 6 true positives, and       600,000 x .001= 600 false positives.  We expect one false positive to be significant at the 0.0000002 level.
- Tests are not independent, so use of Bonferroni correction of 0.05/600,000=.000000008 is too conservative.  Even with appropriate p-value, there would be little power without massive sample sizes.  A gene with the effect size needed to be detected would already be known.

## False Discovery Rate (FDR)

- V= # true null hypotheses called significant
- 	S= # non-true hypotheses called significant
- 	Q=V/(V + S)    (false positives/all positives)
- 	FDR = E(Q)
- Benjamini & Hochberg (1995)
- 	When testing m hypotheses H1,...,Hm, order p-values
- 	p1, ... pm , let k be largest i for which pi ≤ (i/m) q*
- 	Then reject H1, ... Hm
- Theorem:  Above controls FDR at q*
- Computer program: QVALUE

## Multiple Testing

- FDR helps and is commonly used
- Question:  Should all markers be tested using same p-value?
- Roeder et al (2006) Am J Hum Genet, 78:243
- 	Use a set of weights in the FDR computations.
- 	If a small proportion are over-weighted, does not reduce the power to detect the others very much, but helps the detection of the ones to “bet” on.
- 	Use of prior linkage evidence may be a way to  increase power.

## Example: Top 10 SNPs from Analysis of 1,500 SNPs

**Example: Top 10 SNPs from Analysis of 1,500 SNPs**

## Conclusions

- WGA studies will be done (6 GAIN studies have just been selected) and be in the public domain
- Candidate gene studies have been problematic (the prior probability of selecting the right gene may be 1/10,000), so may be very low power.
- Multiple testing issues a major challenge for WGA studies, but these will be overcome