Beyond the one-way ANOVA for ’omics data

Kirsty L. Hassall, Andrew Mead

With ever increasing accessibility to high throughput technologies, more complex treatment structures can be assessed in a variety of 'omics applications. This adds an extra layer of complexity to the analysis and interpretation, in particular when inferential univariate methods are applied en masse. It is well-known that mass univariate testing suffers from multiplicity issues and although this has been well documented for simple comparative tests, few approaches have focussed on more complex explanatory structures. Two frameworks are introduced incorporating corrections for multiplicity whilst maintaining appropriate structure in the explanatory variables. Within this paradigm, a choice has to be made as to whether multiplicity corrections should be applied to the saturated model, putting emphasis on controlling the rate of false positives, or to the predictive model, where emphasis is on model selection. This choice has implications for both the ranking and selection of the response variables identified as differentially expressed. The theoretical difference is demonstrated between the two approaches along with an empirical study of lipid composition in Arabidopsis under differing levels of salt stress. Multiplicity corrections have an inherent weakness when the full explanatory structure is not properly incorporated. Although a unifying 'single best' recommendation is not provided, two reasonable alternatives are provided and the applicability of these approaches is discussed for different scenarios where the aims of analysis will differ. The key result is that the point at which multiplicity is incorporated into the analysis will fundamentally change the interpretation of the results, and the choice of approach should therefore be driven by the specific aims of the experiment.