Statistical Issues in Genetic Association Studies Eleanor Feingold, Ph.D. University of Pittsburgh March, 2011

Underlying Principle of Genetic Mapping People who have similar traits (phenotypes) should have greater than expected sharing of genetic material near the genes that influence those traits.

Basic study designs for gene mapping families unrelated individuals

Basic study designs for gene mapping families unrelated individuals linkage analysis (or association) association analysis

Basic study designs for gene mapping families unrelated individuals semi-related individuals in an inbred population association analysis linkage analysis (or association) ?

Basic study designs for gene mapping families unrelated individuals semi-related individuals in an inbred population association analysis linkage analysis (or family- based association) ?

Association analysis (circa 2000) 1) Collect cases and controls. aa 2) Genotype everyone at a marker. AA Aa 3) Test genotype/phenotype association. 4) Call it a day and go out for a beer with your co-investigators. AA Aa aa cases 65 133 202 controls 16 81 316

GWAS Study circa 2010 Repeat 1,000,000 times! 1) Collect cases and controls. 2) Genotype everyone at a marker. AA Aa aa 3) Test genotype/phenotype association. 4) Call it a day and go out for a beer with your co-investigators. AA Aa aa cases 65 133 202 controls 16 81 316

So what’s the BIG DEAL? Well, not much, until you get into 1) the complexities of array data, and 2) the real science of genetics.

One important genetic subtlety Even in a GWAS study, we can’t test every variant on the genome. So at the design phase, we have to pick markers (SNPs) that we hope will “cover” as well as possible, and at the testing phase, we do not expect that the marker we are testing is actually the “causal variant” - we are usually hoping (at best) that it is correlated with the true causal genetic variable.

Gene in here somewhere

Gene in here somewhere

After many generations ...

Within a population, genotypes at nearby SNPs are correlated due to population history. This correlation is called linkage disequilibrium.

“Tag” SNPs Find a set of SNPs that captures most information at least cost. How? Find clusters of SNPs that are highly correlated and then choose one representative from each cluster to genotype. Easily-available relatively idiot-proof software (e.g. Tagger). Caveat 1: You need a database that knows lots of SNPs in your gene and has genotyped them in a fair number of people in the population you are studying (Hapmap, Seattle SNPs). Caveat 2: Beware of overly-aggressive “tagging.”

Conventional association vs. candidate gene sequencing Candidate gene sequencing study 1) Expensive - fewer genes and fewer people, so lower power overall. 2) Find both common and rare variation. 3) Find functional variants. GWAS (tag SNP) study 1) Cheaper - more genes and more people, so higher power. 2) Find only common variation. 3) Probably do not find functional variants.

GWAS Analysis Genotype calling Data cleaning Single-SNP analysis Other analyses CNVs

Genotype “calling” Generally done before you see the data. But plenty of open questions about how to do it. - best clustering methods? salvage data from messy clusters? BB AB AA

Data cleaning Somewhat dependent on which chip you are using. Throw out “bad” SNPs and “bad” samples. (% of genotypes “called” for each person and each SNP) Hardy-Weinberg testing Relationship testing Find major chromosomal anomalies Look for population stratification Look for signs of systematic problems (e.g. allele frequencies differ by sample processing date).

Data cleaning examples

Plate effect on missing call rate per sample ANOVA p-value = 6e-48 But no significant association between plate and case status (p=0.20)

Gender Check

chromosomal anomalies

Testing Hardy-Weinberg Hardy-Weinberg Equilibrium (HWE) means that your three genotype groups occur in the expected p2, 2pq, q2 proportions. Departure from HWE most often indicates genotyping problems. But it can also indicate an actual genetic effect. (Check for case-control differences). Do your HWE tests by ethnicity, but don’t expect admixed groups (hispanics, African-Americans) to be in HWE.

HWE 10-4 < p < 0.5

HWE p < 10-4

population stratification via principle components

Analysis

Simple association test at every SNP Case-control association test by allele ... case 2 x 2 table (Fisher’s exact test or chi-squared test) control And by genotype ... AA Aa aa 2 x 3 table (Fisher’s exact test or chi-squared test or Armitage trend test) case control

Or use logistic regression Lets you incorporate other predictors (age, sex, diet, whatever). G + E (genotype + environment model) G + E + GxE (interaction model)

GWAS results Manhattan plot and qq plot

What’s the best single-SNP association test? Not as “solved” a problem as you’d think. If you knew the true model for the gene effect, you’d just fit that model. But you don’t. So which tests are robust over lots of models?

============= MIN 4P ============== Chia-Ling Kuo’s work ===== MIN 2P ===== ======== MIN 3P ======= ============= MIN 4P ==============

Scan with Covariates Which logistic regression model is best for testing GENETIC EFFECT? G: LR(G, NULL) ~ X2(1) G+E: LR(G+E, E) ~ X2(1) G+E+GE: LR(G+E+GE, E) ~ X2(2)

Results Combination statistics (best of several statistics) are most robust, even after correction for multiple comparisons, but linear trend test is also a good choice. To test for genetic effect, the G + E is almost never advantageous. Just test G, or fit G + E + GxE if you’re pretty sure there’s an interaction. BIG CAVEAT: This assumes G and E are independent – if you are worried about confounding, you DO need to control for E when testing G.

More generally, should you use the same statistics you used for a small-scale study? What do I mean? • Statisticians develop tests that behave sensibly on average. • But in genomic problems, we do 10,000 or 500,000 of the same test and then follow up the top 100 results. • So we need test statistics for which the extreme values are well-behaved, not so much the averages. Maybe not. Problem Need to worry about the statistical properties of the extreme values of the test statistics.

Example from expression arrays: “10,000 t-tests” analysis Compute t-statistic for each gene. Rank by absolute value of t-statistic.

Ranked list is dominated by small-variance genes. Problem Ranked list is dominated by small-variance genes. 2 ways to get a large t-statistic large difference between the means small SE With a small sample size, the SE estimates are very poor. If you estimate an SE poorly 10,000 times, some of the estimates will come out very small.

Solution Shrinkage estimator! (Add a fudge factor to the denominator of the t-statistic.)

Back to association studies ... Whatever statistic you are using (1,000,000 times), you need to know the statistical behavior of the 1st - 50th highest order statistics, not the statistical behavior on average. This issue has not really been dealt with in the association study literature.

A few other open statistical issues

Multiple testing The problem The solution If you do 1,000,000 tests, you will produce a lot of false positives. The solution There isn’t one! • Be realistic about hypothesis generating vs. hypothesis testing. • False discovery rate - controls percent of genes on list that are false. • Permutation testing - controls for lots of correlated tests.

“Imputaton” at untyped SNPs The idea Use Hapmap database to impute genotypes for your samples at all the SNPs in-between the ones you genotyped. Do a test at each of those SNPs in addition to the typed ones. Should increase overall study power even if multiple comparisons are correctly controlled for. typed SNP untyped SNP “blue” at typed SNP => “blue” at untyped one as well

“Imputaton” at untyped SNPs The best thing Allows joint analyses of datasets that were genotyped with different chips! Limitations Only helpful if correlation structure in Hapmap is valid for your population. Only helpful for SNPs in the database (contrast to haplotype analysis). Open questions • Best imputation methods in theory and practice? • What populations should you base the imputation on? • Imputed SNPs have different statistical properties (e.g. slightly higher variance) – how do we account for that?

Meta-analysis Typical GWAS papers now combine results from many studies. What are the best meta-analysis methods for doing this? - What if same SNPs not typed in all studies? - What if phenotype not measured the same way? - What if some SNPs are imputed?

Software for genetic association studies PLINK is the primary tool. Bioinformatics is incorporated. There are some useful R packages as well. Need R for fancier analyses – typically integrate it with PLINK. Lots of new stuff constantly under development for large-scale data management and viewing – WGAViewer, LocusZoom Lots of specialty packages for: HWE haplotype analysis family association other stuff