Nathan Sanders - The Performance of Model Averaging Relative to Individual Models for Testing Hormesis

Abstract

In cancer studies, hormesis is a phenomenon where low doses of a carcinogen reduces the risk of cancer while high doses increase the risk. There are several models to test for hormesis, however some are not flexible enough to detect hormesis. Our research objective was to compare five individual models as well as the method of model averaging (MA). The MA method utilizes multiple models for the hypothesis testing, and a simpler model with better fit has greater contribution in the procedure.  We hypothesized that the MA method would avoid the worst individual result and perform closely to the best individual result.  We designed sixteen simulation scenarios to emulate various cases occurred in real life experiments. Five monotonic scenarios were designed to test a significance level (α = .05), and eleven non-monotonic (hormetic) scenarios were designed to test statistical power. In the results, when the null hypothesis was true there was an instance when an individual model violated α = .05 and the MA method relieved the violation. When the alternative hypothesis was true the MA method relieved significantly low power. However when the truth was one of the models in MA, the MA method performed worse than we expected.