Journal of Data Science

Abstract: Various statistical models have been proposed to analyze fMRI data. The usual goal is to make inferences about the effects that are related to an external stimulus. The primary focus of this paper is on those statistical methods that enable one to detect ‘significantly activated’ regions of the brain due to event-related stimuli. Most of these methods share a common property, requiring estimation of the hemodynamic response function (HRF) as part of the deterministic component of the statistical model. We propose and investigate a new approach that does not require HRF fits to detect ‘activated’ voxels. We argue that the method not only avoids fitting a specific HRF, but still takes into account that the unknown response is delayed and smeared in time. This method also adapts to differential responses of the BOLD response across different brain regions and experimental sessions. The maximum cross-correlation between the kernel-smoothed stimulus sequence and shifted (lagged) values of the observed response is the proposed test statistic. Using our recommended approach we show through realistic simulations and with real data that we obtain better sensitivity than simple correlation methods using default values of SPM2. The simulation experiment incorporates different HRFs empirically determined from real data. The noise models are also different AR(3) fits and fractional Gaussians estimated from real data. We conclude that our proposed method is more powerful than simple correlation procedures, because of its robustness to variation in the HRF.

In this article, we considered the analysis of data with a non-normally distributed response variable. In particular, we extended an existing Area Under the Curve (AUC) regression model that handles only two discrete covariates to a general AUC regression model that can be used to analyze data with unrestricted number of discrete covariates. Comparing with other similar methods which require iterative algorithms and bootstrap procedure, our method involved only closed-form formulae for parameter estimation. Additionally, we also discussed the issue of model identifiability. Our model has broad applicability in clinical trials due to the ease of interpretation on model parameters. We applied our model to analyze a clinical trial evaluating the effects of educational brochures for preventing Fetal Alcohol Spectrum Disorders (FASD). Finally, for a variety of simulation scenarios, our method produced parameter estimates with small biases and confidence intervals with nominal coverage probabilities.