Logistic Regression and Decision Tree Predictive Modeling: A Fit Function Comparison

Abstract

Investigations of differential treatment effects through the inclusion of moderating variables advance individualized treatment decisions through improved knowledge of treatment effectiveness across individuals and contexts. Literature has explored planning strategies for partially nested designs with heterogeneous treatment effects but statistical power formulas for detecting moderated effects when the moderator-outcome relationship varies across clusters (i.e., random slopes) are currently unavailable. We derive these formulas and probe the roles of the governing parameters and likely scale required for detecting these moderation effects. Simulation study results suggest that substantial moderation effect heterogeneity warrants much larger sample sizes to consistently detect moderation effects. Power formulas are implemented in R (see Supplemental Materials).