Accuracy and Computational Efficiency of a Graphical Modeling Approach to Linkage Disequilibrium Estimation

Abstract

We develop recent work on using graphical models for linkage disequilibrium to provide efficient programs for model fitting, phasing, and imputation of missing data in large data sets. Two important features contribute to the computational efficiency: the separation of the model fitting and phasing-imputation processes into different programs, and holding in memory only the data within a moving window of loci during model fitting. Optimal parameter values were chosen by cross-validation to maximize the probability of correctly imputing masked genotypes. The best accuracy obtained is slightly below than that from the Beagle program of Browning and Browning, and our fitting program is slower. However, for large data sets, it uses less storage. For a reference set of n individuals genotyped at m markers, the time and storage required for fitting a graphical model are approximately O(nm) and O(n+m), respectively. To impute the phases and missing data on n individuals using an already fitted graphical model requires O(nm) time and O(m) storage. While the times for fitting and imputation are both O(nm), the imputation process is considerably faster; thus, once a model is estimated from a reference data set, the marginal cost of phasing and imputing further samples is very low.

Employing MCMC under the PPL framework to analyze sequence data in large pedigrees

“…Founder haplotype models can be derived under the assumption of linkage equilibrium from the allele frequencies in a sample. It is also possible to estimate models under LD using the FitGMLD program that is also available in JPSGCS, as described by Thomas (2010) and Abel and Thomas (2011). In the case that LD is allowed, only locus block Gibbs updates can be made which typically leads to poorer mixing of the MCMC sampler.…”

Pairwise shared genomic segment analysis in three Utah high-risk breast cancer pedigrees

“…We used FitGMLD to obtain a LD model based on the 224 local control samples using default parameters [15]. This program applies graphical models to estimate a general finite multivariate distribution for allelic association between genetic loci in each autosomal chromosome.…”

“…The method incorporates an error model for genotyping. The program takes computation time in the magnitude of O ( nm ), given n individuals with m genotyped markers [15]. …”

Modelling and visualizing fine-scale linkage disequilibrium structure

“…MCMC sampling from this model class may be performed more efficiently [13,14]. This work was extended in [15] to a more general subclass of decomposable models, namely those in which distant marker pairs (i.e., with more than a given number of intervening markers) are conditionally independent given the intervening markers.…”

“…For phase estimation and imputation BEAGLE uses an iterative scheme analogous to the EM algorithm, alternating between sampling from a haplotype-level model given the observed genotype data (the E-step) and selecting a haplotype-level model given the samples (the M-step). A similar computational scheme for decomposable graphical models has been described and implemented in the FitGMLD program [15]. …”