Model selection for genetic and epidemiological data

Approximate Bayesian computation (ABC) have become a essential tool for the analysis of complex stochastic models. Having implemented ABC-based model choice in a wide range of phylogenetic models in the DIY-ABC software (Cornuet et al., 2008), we first present theoretical background as to why a generic use of ABC for model choice is ungrounded, since it depends on an unknown amount of information loss induced by the use of a summary statistic (Robert et al., 2011). We then present necessary and sufficient conditions on the summary statistics for ABC based model choice procedure to be consistent, a solution that avoids the call to additional empirical verifications of the performances of the ABC procedure as those available in DIYABC and advocated in Ratman et al. (2011).

Note: these are joint works with J.M. Cornuet, J.M. Marin, N. Pillai and J. Rousseau.
Refs.: http://arxiv.org/abs/1101.0955
          http://arxiv.org/abs/1102.4432
          http://arxiv.org/abs/1110.4700

There is continued discussion regarding the so called "missing heritability" problem. By applying a linear mixed model to whole-genome SNP data, a series of papers headed by Yang et. al. have presented strong evidence that many complex traits are highly polygenic, so that while common variants can explain most of the heritability, each on average has such a small contribution to make their detection by standard size GWAS almost impossible. We have investigated use of the linear mixed model for heritability estimation, finding that it is highly sensitive to the correlations induced by linkage disequilibrium (LD). In particular, it will struggle to pick up the variance explained by rarer variants, even if typed, as their signals will be on average more poorly represented by the SNP array. We have devised a solution to this problem, allowing unbiased estimates of heritability in spite of LD. Using our revised method, we have been able to show that almost all of the heritability for epilepsy can be explained by common SNPs, suggesting that effective prediction models should be possible.

At first glance, the linear mixed model, which assumes a polygenic model where every SNP contributes to the phenotype, would appear completely unsuited to model selection, where we hope to find the relatively small number of SNPs which have the (most) influence on the outcome. But this is not the case, as a subsequent paper involving Yang proceeded to demonstrate by partitioning the genome and assessing the heritability explained by each region. For example, they were able to examine the contributions of individual chromosomes or test whether the causal variants were most likely to be inter or intra genic. We have extended their analysis, showing how localised heritability estimates can be used to guide model selection algorithms. Additionally, we have used the mixed model to develop tests of homogeneity across traits. For example, by demonstrating a concordance between epilepsy and other neurological conditions, this provides justification for combining studies to improve detection power.

References:
Common SNPs explain a large proportion of the heritability for human height; J. Yang, P. Visscher et. al., Nature Genetics 2010

Genome partitioning of genetic variation for complex traits using common SNPs; J. Yang, P. Visscher et. al. Nature Genetics 2011