Simultaneous control of error rates in fMRI data analysis.
The key idea of statistical hypothesis testing is to fix, and thereby control, the Type I error (false positive) rate across samples of any size. Multiple comparisons inflate the global (family-wise) Type I error rate and the traditional solution to maintaining control of the error rate is to increase the local (comparison-wise) Type II error (false negative) rates. However, in the analysis of human brain imaging data, the number of comparisons is so large that this solution breaks down: the local Type II error rate ends up being so large that scientifically meaningful analysis is precluded. Here we propose a novel solution to this problem: allow the Type I error rate to converge to zero along with the Type II error rate. It works because when the Type I error rate per comparison is very small, the accumulation (or global) Type I error rate is also small. This solution is achieved by employing the likelihood paradigm, which uses likelihood ratios to measure the strength of evidence on a voxel-by-voxel basis. In this paper, we provide theoretical and empirical justification for a likelihood approach to the analysis of human brain imaging data. In addition, we present extensive simulations that show the likelihood approach is viable, leading to "cleaner"-looking brain maps and operational superiority (lower average error rate). Finally, we include a case study on cognitive control related activation in the prefrontal cortex of the human brain.
Department of Biostatistics, Vanderbilt University, Nashville, TN 37203, USA; Center for Quantitative Sciences, Vanderbilt University, Nashville, TN 37232, USA. Electronic address: hakmook.kang@vanderbilt.edu.
Hakmook
H
Kang
Department of Biostatistics, Vanderbilt University, Nashville, TN 37203, USA.
Jeffrey
J
Blume
Department of Statistics, University of California at Irvine, Irvine, CA 92697, USA.
Hernando
H
Ombao
Department of Cognitive, Linguistic and Psychological Sciences, Brown University, Providence, RI 02912, USA.
David
D
Badre
D001931:Brain Mapping / Q000379:methods*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005625:Frontal Lobe / Q000502:physiology*; D006801:Humans; D016013:Likelihood Functions; D008279:Magnetic Resonance Imaging / Q000379:methods*; D012107:Research Design
Functional magnetic resonance imaging; Likelihood paradigm; Likelihood ratio; Multiple comparison