Multivariate data analysis for neuroimaging data: overview and application to Alzheimer's disease

Abstract

As clinical and cognitive neuroscience mature, the need for sophisticated neuroimaging analysis becomes more apparent. Multivariate analysis techniques have recently received increasing attention as they have many attractive features that cannot be easily realized by the more commonly used univariate, voxel-wise, techniques. Multivariate approaches evaluate correlation/covariance of activation across brain regions, rather than proceeding on a voxel-by-voxel basis. Thus, their results can be more easily interpreted as a signature of neural networks. Univariate approaches, on the other hand, cannot directly address functional connectivity in the brain. The covariance approach can also result in greater statistical power when compared with univariate techniques, which are forced to employ very stringent, and often overly conservative, corrections for voxel-wise multiple comparisons. Multivariate techniques also lend themselves much better to prospective application of results from the analysis of one dataset to entirely new datasets. Multivariate techniques are thus well placed to provide information about mean differences and correlations with behavior, similarly to univariate approaches, with potentially greater statistical power and better reproducibility checks. In contrast to these advantages is the high barrier of entry to the use of multivariate approaches, preventing more widespread application in the community. To the neuroscientist becoming familiar with multivariate analysis techniques, an initial survey of the field might present a bewildering variety of approaches that, although algorithmically similar, are presented with different emphases, typically by people with mathematics backgrounds. We believe that multivariate analysis techniques have sufficient potential to warrant better dissemination. Researchers should be able to employ them in an informed and accessible manner. The following article attempts to provide a basic introduction with sample applications to simulated and real-world data sets.

Fig. 1

Visual illustrations of the binary pattern v (left panel) and the subject scores z_young and z_old

Fig. 2

Simulation results: upper row, the thresholded univariate T-fields are shown for noise levels σ = 2, 5, 10. One can appreciate the decreasing true-positive rate. At σ = 10, no signal is recovered, while the stringent Bonferroni correction for 10,000 comparisons makes sure there are no false positives. Lower row: the results of the PCA are shown for σ = 10: the subject scores of the first PC show a significant group difference between old and young. Further, the topographic composition of the first PC is visually similar to the binary target pattern

Fig. 3

Comprehensive display of univariate true-positive rate (blue), topographic correlation between first PC and binary pattern (green), and correlation between subject scores of first PC and binary pattern (red)

Fig. 4

Empirical histogram generated for the subject score of the first PC obtained in 10,000 Monte-Carlo simulations of Gaussian IID noise and theoretical curve for a T-distribution with 99 degrees of freedom. Increased false positives for the multivariate technique would imply “fat” tails, i.e., a histogram that was much wider than the theoretical T-distribution; fortunately, this is not the case

Fig. 5

Schematic figure for illustration of the bootstrap procedure for assessing the robust of individual voxel weights in the covariance pattern. Sampling from the pool of subjects with replacement results in some subjects being dropped, while others are represented more than once in the associated data and design matrix Y* and X*, respectively. The algorithm that was applied to XY to derive a covariance pattern v is performed on Y*X* to obtain v*. Resampling and subsequent pattern derivations are repeated ~ 500 times. From all 500 bootstrap patterns, a Z-map can finally be computed

Fig. 6

Schematic figure to illustrate our split sample simulations for the empirical comparison of different classifier’s prediction performance. The data sample of 40 ADs and 40 HCs is split into a 30/30 derivation, and a 10/10 replication sample. A classifier C is derived in the derivation sample and then prospectively applied to the replication sample with predictions of the class labels {± 1}, corresponding to the diagnostic status “AD” (label = 1), or “HC” (label = −1). Total prediction error, false-positive rate and false-negative rate are recorded each time and enable an empirical comparison of different classifiers’ performances