Methods for the Analysis of Missing Data in FMRI Studies

Abstract

Functional neuroimaging has provided fundamental advances in our understanding of human brain function and is increasingly used clinically for defining atypical function and surgical planning. For example, functional imaging with blood oxygenation level dependent (BOLD) contrast as a response measure is used as a clinical tool for defining atypical development, pathology, surgical planning, and evaluating treatment outcomes. Despite years of statistical advances in the analysis of complete whole brain data, there has been a limited statistical advance to address the pronounced missingness in many functional imaging studies that use large discovery or small clinical case data. For example, functional magnetic resonance imaging (fMRI) analyses do not always include the entire brain due to image acquisition space limitations and susceptibility artifacts (a loss and spatial distortion of signal that results from a disruption in the magnetic field). The consequence is 'no data' or 'bad data', respectively. No data occurs when the image acquisition doesn't cover the whole head which leads to no values. In addition to susceptibility artifacts, bad data can occur across the brain because of motion artifacts. Because statistic maps with applied effect size or significance thresholds do not typically include information about which voxels were omitted from analyses, missing data can result in Type II errors for regions that were not tested. Missing data in fMRI studies can therefore undermine the benefits provided by high quality imaging technology used to generate data testing predictions about brain function. One approach to this problem is to use appropriate statistical techniques that account for the missing data. However, missing data are almost universally addressed by excluding voxels from analyses. For example, implicit masking in single subject analyses limits the analysis space across subjects when group analyses are performed with spatially varying masked single subject results. As a result, brain regions are excluded from the analysis that may be of theoretical or clinical interest, which directly increases risk for Type II errors. When voxels with incomplete observations are omitted from group-level analyses, the smaller number of tests and less conservative multiple comparison correction can also increase the Type I error rate. If the missing data are non-ignorable, analyzing the space with complete observations only may bias effect size estimates (Figure 1). Missing fMRI data, resulting from incomplete voxel level information, can be missing completely at random (MCAR) because of variation in where images are acquired across the brains of different subjects or because of small variations in the quality of normalization at the edges of the brain across subjects. It can also be MAR because factors such as head size influence the coverage of a bounding box that determines the space of image acquisition. On the other hand, missing fMRI data can be MNAR, perhaps because the tissue is damaged. MCAR data can be addressed by removing voxels from group analyses, but this leads to biased inference if missingness is MAR or MNAR [1-3].