A comparative study of one-level and two-level semiparametric estimation of hemodynamic response function for fMRI data.

Functional magnetic resonance imaging (fMRI) is emerging as a powerful tool for studying the process underlying the working of the many regions of the human brain. The standard tool for analyzing fMRI data is some variant of the linear model, which is restrictive in modeling assumptions. In this paper, we develop a semiparametric approach, based on the cubic smoothing splines, to obtain statistically more efficient estimates of the underlying hemodynamic response function (HRF) associated with fMRI experiments. The hypothesis testing of HRF is conducted to identify the brain regions which are activated when a subject performs a particular task. Furthermore, we compare one-level and two-level semiparametric estimates of HRF in significance tests for detecting the activated brain regions. Our simulation studies demonstrate that the one-level estimates combined with a bias-correction procedure perform best in detecting the activated brain regions. We illustrate this method using a real fMRI data set and compare it with popular methods offered by AFNI and FSL.