Abstract
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 mapping data for Recombinant Inbred Lines in \textit{Arabidopsis thaliana} and from a backcross population in \textit{Drosophila} where we identify several interesting epistatic effects. The method is implemented in an R package which is available on github.
Highlights
Logic regression was developed as a general tool to obtain predictive models based on Boolean combinations of binary covariates (Ruczinski et al, 2003)
It is even difficult to specify q, the total number of feasible trees. To solve this problem we present an adaptive algorithm called Genetically Modified mode jumping Markov Chain Monte Carlo (MJMCMC) (GMJMCMC), where MJMCMC is embedded in the iterative setting of a genetic algorithm
For Scenarios 1 and 2 we report the results for Cmax = 2, which were the values used in the original study of Fritsch (2006) and which we used here for Monte Carlo logic regression (MCLR) and full Bayesian version of logic regression (FBLR)
Summary
Logic regression (not to be confused with logistic regression) was developed as a general tool to obtain predictive models based on Boolean combinations of binary covariates (Ruczinski et al, 2003). Important contributions to the development of logic regression were later made by the group of Katja Ickstadt (Fritsch, 2006; Schwender and Ickstadt, 2008), which provided a comparison of different implementations of logic regression (Fritsch and Ickstadt, 2007). A Novel Algorithmic Approach to Bayesian Logic Regression based on Cockerham’s coding to detect interactions illustrated the advantages of logic regression to detect epistasic effects in QTL mapping (Malina et al, 2014). Given the potential of logic regression to detect interpretable interaction effects in a regression setting it is rather surprising that it has not yet become wider addressed in applications
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
