Abstract
Third variable effect refers to the effect from a third variable that explains an observed relationship between an exposure and an outcome. Depending on whether there is causal relationship, typically, a third variable takes the format of a mediator or a confounder. A moderation effect is a special case of the third-variable effect, where the moderator and other variables have an interactive effect on the outcome. In this paper, we extend the R package 'mma' for moderation analysis so that third-variable effects can be reported at different levels of the moderator. The proposed moderation analysis use tree-structured models to automatically detect moderation effects and can handle both categorical and numerical moderators. We propose algorithms and graphical methods for making inference on moderation effects and illustrate the method under different scenarios of moderation effects. Finally, we apply the proposed method to explore the trend of racial disparities in the use of Oncotype DX recurrence tests among breast cancer patients. We found that the unexplained racial differences in using the tests have decreased from 2010 to 2015.