A Novel Algorithmic Approach to Bayesian Logic Regression

Logic regression was developed more than a decade ago as a tool to
construct predictors from Boolean combinations of binary covariates. It has been
mainly used to model epistatic effects in genetic association studies, which is very
appealing due to the intuitive interpretation of logic expressions to describe the interaction
between genetic variations. Nevertheless logic regression has (partly due
to computational challenges) remained less well known than other approaches to
epistatic association mapping. Here we will adapt an advanced evolutionary algorithm
called GMJMCMC (Genetically modified Mode Jumping Markov Chain
Monte Carlo) to perform Bayesian model selection in the space of logic regression
models. After describing the algorithmic details of GMJMCMC we perform
a comprehensive simulation study that illustrates its performance given logic regression
terms of various complexity. Specifically GMJMCMC is shown to be able
to identify three-way and even four-way interactions with relatively large power,
a level of complexity which has not been achieved by previous implementations
of logic regression. We apply GMJMCMC to reanalyze QTL (quantitative trait
locus) mapping data for Recombinant Inbred Lines in Arabidopsis thaliana and
from a backcross population in Drosophila where we identify several interesting
epistatic effects. The method is implemented in an R package which is available
on github.