In the life sciences, many measurement methods yield only the relative abundances of different components in a sample. With such relative—or compositional—data, differential expression needs careful interpretation, and correlation—a statistical workhorse for analyzing pairwise relationships—is an inappropriate measure of association. Using yeast gene expression data we show how correlation can be misleading and present proportionality as a valid alternative for relative data. We show how the strength of proportionality between two variables can be meaningfully and interpretably described by a new statistic ϕ which can be used instead of correlation as the basis of familiar analyses and visualisation methods, including co-expression networks and clustered heatmaps. While the main aim of this study is to present proportionality as a means to analyse relative data, it also raises intriguing questions about the molecular mechanisms underlying the proportional regulation of a range of yeast genes.

No abstract

In the life sciences, many assays measure only the relative abundances of components in each sample. Such data, called compositional data, require special treatment to avoid misleading conclusions. Awareness of the need for caution in analyzing compositional data is growing, including the understanding that correlation is not appropriate for relative data. Recently, researchers have proposed proportionality as a valid alternative to correlation for calculating pairwise association in relative data. Although the question of how to best measure proportionality remains open, we present here a computationally efficient R package that implements three measures of proportionality. In an effort to advance the understanding and application of proportionality analysis, we review the mathematics behind proportionality, demonstrate its application to genomic data, and discuss some ongoing challenges in the analysis of relative abundance data.

This study of recidivism among Washington supermax prisoners used a retrospective matched control design, matching supermax prisoners one-to-one with nonsupermax prisoners on mental illness status and up to eight recidivism predictors. Supermax prisoners committed new felonies at a higher rate than nonsupermax controls, but the difference was not statistically significant. Prisoners released directly from supermax to the community, however, showed significantly higher felony recidivism rates than their nonsupermax controls and committed new offenses sooner than supermax prisoners who left supermax 3 months or more before prison release. Limitations, methodological issues, and policy implications are considered.

Whether community mental health treatment affects recidivism cannot be assessed fairly in the absence of higher levels of service during the first months after release. This study also identifies actuarial risk factors that predict new offenses at a level comparable to that of published risk assessment instruments. Commission of less serious offenses that usually precede felonies may provide an early warning of risk for new felonies and an opportunity for strategic intervention. The low rate of serious violence in the community by mentally ill offenders released from prison suggests that the risk of violence may be a weak and potentially counterproductive rationale for community support and mental health treatment of mentally ill offenders.