An application of multivariate ranks to assess effects from combining factors: Metal exposures and semen analysis outcomes

In studies of environmental effects on human health outcomes, it is often difficult to assess the effects of a group of exposure variables when the individual exposures do not appear to have statistically significant effects. To address this situation, we propose a method of U-scores applied to subsets of multivariate data. We illustrate the usefulness of this approach by applying it to data collected as part of a study on the effects of metal exposure on human semen parameters. In this analysis, profiles (pairs) of metals containing copper and/or manganese were negatively correlated with total motile sperm and profiles containing copper were negatively correlated with sperm morphology; profiles containing selenium and chromium were positively correlated with total motile sperm.