Missing data imputation and haplotype phase inference for genome-wide association studies

Abstract

Imputation of missing data and the use of haplotype-based association tests can improve the power of genome-wide association studies (GWAS). In this article, I review methods for haplotype inference and missing data imputation, and discuss their application to GWAS. I discuss common features of the best algorithms for haplotype phase inference and missing data imputation in large-scale data sets, as well as some important differences between classes of methods, and highlight the methods that provide the highest accuracy and fastest computational performance.

Figure 1

Illustration highlighting major differences between models based on the Li and Stephens framework (2003) and the Browning model (Browning 2006). Excerpts of the models covering three markers (SNPs i-1, i and i+1) are shown. Ovals are hidden states of the models. For the Li and Stephens framework, these states are defined by the reference haplotypes, while for the Browning model the states are localized clusters of haplotypes. Note that the graphical representation of the Browning model is that given in Browning (2008), while earlier representations had states as edges rather than as nodes of the graph. The Browning model will tend to have fewer states at any given marker than will unconstrained models based on the Li and Stephens framework, and the number of states can vary from marker to marker for the Browning model but is fixed in the Li and Stephens framework. Arrows between states from one SNP to the next are transitions of the HMM. For the Li and Stephens framework, transitions with highest prior probability (those seen in the reference haplotypes) are shown with bold arrows, while thin arrows allow for historical recombination. For the Browning model, there are at most k transitions coming out of a state, where k is the number of alleles at the next marker (i.e. 2 for SNPs), which helps to keep the model parsimonious. Arrows coming out of the top of the states are possible emissions of the HMM, which are the observed alleles. For the Li and Stephens framework, emissions with highest prior probability (the alleles on the reference haplotypes) are shown with bold arrows, while thin arrows represent mutations to other alleles. The reference haplotypes here are 011, 010, 101 and 001. For the Browning model, there is only one possible emission from each state, which helps to keep the model parsimonious. The models shown are illustrative only. The actual form of the Browning model will vary depending on the alleles of the reference haplotypes outside this window of markers.