Motivation: The genomic architecture of human complex diseases is thought to be attributable to single markers, polygenic components and epistatic components. No study has examined the ability of tree-based methods to detect epistasis in the presence of a polygenic signal. We sought to apply decision tree-based methods, C5.0 and logic regression, to detect epistasis under several simulated conditions, varying strength of interaction and linkage disequilibrium (LD) structure. We then applied the same methods to the phenotype of educational attainment in a large population cohort. Results: LD pruning improved the power and reduced the type I error. C5.0 had a conservative type I error rate whereas logic regression had a type I error rate that exceeded 5%. Despite the more conservative type I error, C5.0 was observed to have higher power than logic regression across several conditions. In the presence of a polygenic signal, power was generally reduced. Applying both methods on educational attainment in a large population cohort yielded numerous interacting SNPs; notably a SNP in RCAN3 which is associated with reading and spelling and a SNP in NPAS3, a neurodevelopmental gene. Availability and implementation: All methods used are implemented and freely available in R. Supplementary information: Supplementary data are available at Bioinformatics online.

A recent study examined the stability of rankings from random forests using two variable importance measures (mean decrease accuracy (MDA) and mean decrease Gini (MDG)) and concluded that rankings based on the MDG were more robust than MDA. However, studies examining data-specific characteristics on ranking stability have been few. Rankings based on the MDG measure showed sensitivity to within-predictor correlation and differences in category frequencies, even when the number of categories was held constant, and thus may produce spurious results. The MDA measure was robust to these data characteristics. Further, under strong within-predictor correlation, MDG rankings were less stable than those using MDA.

BACKGROUND: Random forests (RF) have been increasingly used in applications such as genome-wide association and microarray studies where predictor correlation is frequently observed. Recent works on permutation-based variable importance measures (VIMs) used in RF have come to apparently contradictory conclusions. We present an extended simulation study to synthesize results. RESULTS: In the case when both predictor correlation was present and predictors were associated with the outcome (HA), the unconditional RF VIM attributed a higher share of importance to correlated predictors, while under the null hypothesis that no predictors are associated with the outcome (H0) the unconditional RF VIM was unbiased. Conditional VIMs showed a decrease in VIM values for correlated predictors versus the unconditional VIMs under HA and was unbiased under H0. Scaled VIMs were clearly biased under HA and H0. CONCLUSIONS: Unconditional unscaled VIMs are a computationally tractable choice for large datasets and are unbiased under the null hypothesis. Whether the observed increased VIMs for correlated predictors may be considered a "bias" - because they do not directly reflect the coefficients in the generating model - or if it is a beneficial attribute of these VIMs is dependent on the application. For example, in genetic association studies, where correlation between markers may help to localize the functionally relevant variant, the increased importance of correlated predictors may be an advantage. On the other hand, we show examples where this increased importance may result in spurious signals.

MOTIVATION: The advent of high-throughput genomics has produced studies with large numbers of predictors (e.g. genome-wide association, microarray studies). Machine learning algorithms (MLAs) are a computationally efficient way to identify phenotype-associated variables in high-dimensional data. There are important results from mathematical theory and numerous practical results documenting their value. One attractive feature of MLAs is that many operate in a fully multivariate environment, allowing for small-importance variables to be included when they act cooperatively. However, certain properties of MLAs under conditions common in genomic-related data have not been well-studied--in particular, correlations among predictors pose a problem. RESULTS: Using extensive simulation, we showed considering correlation within predictors is crucial in making valid inferences using variable importance measures (VIMs) from three MLAs: random forest (RF), conditional inference forest (CIF) and Monte Carlo logic regression (MCLR). Using a case-control illustration, we showed that the RF VIMs--even permutation-based--were less able to detect association than other algorithms at effect sizes encountered in complex disease studies. This reduction occurred when 'causal' predictors were correlated with other predictors, and was sharpest when RF tree building used the Gini index. Indeed, RF Gini VIMs are biased under correlation, dependent on predictor correlation strength/number and over-trained to random fluctuations in data when tree terminal node size was small. Permutation-based VIM distributions were less variable for correlated predictors and are unbiased, thus may be preferred when predictors are correlated. MLAs are a powerful tool for high-dimensional data analysis, but well-considered use of algorithms is necessary to draw valid conclusions. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Risk for complex disease is thought to be controlled by multiple genetic risk factors, each with small individual effects. Meta-analyses of several independent studies may be helpful to increase the ability to detect association when effect sizes are modest. Although many software options are available for meta-analysis of genetic case-control data, no currently available software implements the method described by Kazeem and Farrall (2005), which combines data from independent family-based and case-control studies. RESULTS: I introduce the package catmap for the R statistical computing environment that implements fixed- and random-effects pooled estimates for case-control and transmission disequilibrium methods, allowing for the use of genetic association data across study types. In addition, catmap may be used to create forest and funnel plots and to perform sensitivity analysis and cumulative meta-analysis. catmap is available from the Comprehensive R Archive Network http://www.r-project.org. CONCLUSION: catmap allows researchers to synthesize data to assess evidence for association in studies of genetic polymorphisms, facilitating the use of pooled data analyses which may increase power to detect moderate genetic associations.

UNLABELLED: snp.plotter is a newly developed R package which produces high-quality plots of results from genetic association studies. The main features of the package include options to display a linkage disequilibrium (LD) plot below the P-value plot using either the r2 or D' LD metric, to set the X-axis to equal spacing or to use the physical map of markers, and to specify plot labels, colors, symbols and LD heatmap color scheme. snp.plotter can plot single SNP and/or haplotype data and simultaneously plot multiple sets of results. R is a free software environment for statistical computing and graphics available for most platforms. The proposed package provides a simple way to convey both association and LD information in a single appealing graphic for genetic association studies. AVAILABILITY: Downloadable R package and example datasets are available at http://cbdb.nimh.nih.gov/~kristin/snp.plotter.html and http://www.r-project.org.