Modeling dose-dependent neural processing responses using mixed effects spline models: With application to a PET study of ethanol

For functional neuroimaging studies that involve experimental stimuli measuring dose levels, e.g. of an anesthetic agent, typical statistical techniques include correlation analysis, analysis of variance or polynomial regression models. These standard approaches have limitations: correlation analysis only provides a crude estimate of the linear relationship between dose levels and brain activity; ANOVA is designed to accommodate a few specified dose levels; polynomial regression models have limited capacity to model varying patterns of association between dose levels and measured activity across the brain. These shortcomings prompt the need to develop methods that more effectively capture dose-dependent neural processing responses. We propose a class of mixed effects spline models that analyze the dose-dependent effect using either regression or smoothing splines. Our method offers flexible accommodation of different response patterns across various brain regions, controls for potential confounding factors, and accounts for subject variability in brain function. The estimates from the mixed effects spline model can be readily incorporated into secondary analyses, for instance, targeting spatial classifications of brain regions according to their modeled response profiles. The proposed spline models are also extended to incorporate interaction effects between the dose-dependent response function and other factors. We illustrate our proposed statistical methodology using data from a PET study of the effect of ethanol on brain function. A simulation study is conducted to compare the performance of the proposed mixed effects spline models and a polynomial regression model. Results show that the proposed spline models more accurately capture varying response patterns across voxels, especially at voxels with complex response shapes. Finally, the proposed spline models can be used in more general settings as a flexible modeling tool for investigating the effects of any continuous covariates on neural processing responses.