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Haplotypes and Imputation

When multiple markers/SNPs are genotyped in a gene or gene region, the SNPs may be in linkage disequilibrium (LD). Each individual test of association with a marker is correlated with all tests for other markers in LD with that marker.

So, instead of testing the individual markers for association, we may want to test haplotypes of markers for association.

Review: A haplotype is a combination of alleles at multiple loci that are transmitted together on the same chromosome. It should provide the alleles present on the locus and which alleles are on the same chromosome. For example, if we have 2 SNPs with alleles (A, a) and (B, b) then we have 2x2= 4 possible haplotypes: AB, Ab, aB, ab.

For linked SNPs within a gene or small chromosomal region there are typically far fewer haplotypes observed than are theoretically possible (as a consquence of LD).

Reasons to Care About Haplotypes

  1. We haven't typed the casual variant. The haplotype that the variant lies on is a better surrogate for the variant than any one SNP in the haplotype.

    image-1667409934425.png

  2. The "causal" genetic variant is actually the haplotype, not any one variant -- The haplotype confers risk rather than an individual SNP allele.

    image-1667409958708.png

  3. They allow us to impute additional ungenotyped variants

Often we don't have family data to help us. Haplotype phase is ambiguous only if there are 2 or more heterozygous genotypes. For example, Aa Bb genotype has two possible phases:image-1667411325955.png

All multi-locus genotypes that consist of 2 or more heterozygotes have ambiguous phase.

When family data is not available to determine haplotypes, multi-locus haplotype probabilities and frequencies can be estimated.

Haplotype Inference

The goal is to get the probability of a haplotype given the individual's genotype. There are two classes of algorithms: EM or MCMC

  • EM requires HWE assumption; MCMC does not
  • EM algorithm is memory demanding to infer haplotypes for a large number of SNPs; MCMC method requires much less memory but more time

There are many options for software for phasing with and without family data.

The basic idea is to determine haplotype frequencies for sets of SNPs in close proximity on a chromosome, and compare frequencies in cases and controls or by quantitative phenotype.

Which SNPs should we use to test with Haplotypes?
  • Options include:
    • All SNPs on a chromosome
    • All SNPs on a "haplotype block" (chromosome segment where all variants are in high LD)
    • Sliding windows of 2-5 SNPs across region of interest
  • Unless there is high LD, there will be more haplotypes than SNPs -> create haplotypes from SNPs that are in LD

Regression with Haplotypes/Likelihood-Based Tests

Take the following example with 3 SNPs and 4 observed Haplotypes, where each person i has 2 haplotypes:
image-1667414339979.png

We can use variables to count the number of each haplotype type per person. This coding works for any type of multi-allelic marker, not just haplotypes.

We can use a linear regression model with the haplotype counts as predictors:
image-1667415990954.png

Note we do not include H1 in the model. Since H1 + H2 + H3 + H4 = 2, we already know H1 once we know the remaining haplotypes. Think of H1 as a reference haplotype.

Each individual will have a 0, 1, or 2 for each of the 3 indicator variables for the haplotypes.

For 4 haplotypes, the general (Omnibus) test for association would be:
H0: Beta1 = Beta2 = Beta3 = 0; df = 3
If we reject the null, the do tests on individual haplotypes

Global (omnibus) tests of haplotype association provide some protection from  the multiple testing problem, as it tests whether the haplotype distribution is associated with phenotype.

In reality we rarely know haplotypes with certainty. Instead, for each individual haplotype estimation produces the probability of each possible haplotype pair. Can use the same model, but replace the observed haplotype counts with the expected counts (determined by probabilities).

SNP Imputation

The most recent application of haplotypes is imputation. The idea is we use a reference population that has denser genotyping of whole genome sequencing on your subset of SNPs plus many additional SNPs to impute the SNPs not typed on your chip.

A reference population is a set of indivduals who have been genotyped or sequenced in a comprehensive manner. Typically these are for the whole genome sequenced (all the SNPs are included in the sample, plus many additional).

The HapMap project was the first available reference popualtion.

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