Theoretical Improvements and Practical Software for Standardized Effect Size Estimation with Applications to Neuroimaging and Machine Learning
Standardized effect sizes provide a unitless measure of the magnitude of associations. Unlike p-values, the target quantity is not dependent on sample size, facilitating interpretation and comparison across studies. When coupled with confidence intervals, standardized effect size estimates further quantify the range of plausible strengths of association. My dissertation work develops theoretically grounded tools for standardized effect size reporting through three projects. In the first chapter, I introduce the RESI R package, which allows researchers to report estimates of the Robust Effect Size Index (RESI) with confidence intervals for a wide range of common model types. The remaining chapters explore predictive accuracy as a standardized effect size for machine learning brain-phenotype associations. I distinguish between types of predictive accuracy, including the trained predictive accuracy (TPA) of a particular fitted model and the Maximum Achievable Predictive Accuracy (MAPA) for a modeling pipeline for a given brain-phenotype association. As predictive neuroimaging is still in a phase of uncovering potentially useful biomarkers while dealing with the challenge of relatively small sample sizes, estimating MAPA can be especially useful, yet standard methods target TPA. Using semiparametric influence function methods, I provide improved model-agnostic estimators and valid large-sample confidence intervals for MAPA. The second chapter develops the method in the context of Pearson’s correlation for continuous phenotypes, and the third chapter extends the methodology to area under the curve (AUC) estimation for binary phenotypes. I demonstrate these methods through applications to psychopathology factor scores and Alzheimer’s Disease classification, comparing machine learning pipelines using MAPA. I introduce an additional R package, MAPA, to enable researchers to estimate this effect size for their own machine learning models. Taken together, these projects demonstrate the utility of standardized effect size reporting in both associational analyses and predictive machine learning. While I focus on the neuroimaging context, the methodology and software tools are widely applicable.