Spatiotemporal linear mixed effects modeling for the mass-univariate analysis of longitudinal neuroimage data

Abstract

We present an extension of the Linear Mixed Effects (LME) modeling approach to be applied to the mass-univariate analysis of longitudinal neuroimaging (LNI) data. The proposed method, called spatiotemporal LME or ST-LME, builds on the flexible LME framework and exploits the spatial structure in image data. We instantiated ST-LME for the analysis of cortical surface measurements (e.g. thickness) computed by FreeSurfer, a widely-used brain Magnetic Resonance Image (MRI) analysis software package. We validate the proposed ST-LME method and provide a quantitative and objective empirical comparison with two popular alternative methods, using two brain MRI datasets obtained from the Alzheimer's disease neuroimaging initiative (ADNI) and Open Access Series of Imaging Studies (OASIS). Our experiments revealed that ST-LME offers a dramatic gain in statistical power and repeatability of findings, while providing good control of the false positive rate.

Keywords: Linear Mixed Effects models; Longitudinal studies; Mass-univariate analysis; Statistical analysis.

Figure 1

Empirical sensitivity (statistical power) as a function of FDR q-value on AD+HC sub-samples with 2N = 30, randomly drawn from the complete ADNI data (800 random sub-samples). Sensitivity is quantified as the fraction of instances, where the corresponding statistical method detected some group difference at a given FDR q-value. X-Slope: vertex-wise cross-subject analysis of cortical thinning rates estimated by fitting a line to serial measurements; V-LME: vertex-wise application of the LME approach to longitudinal thickness data; ST-LME: the proposed spatiotemporal LME modeling method applied to longitudinal thickness data.

Figure 2

Statistical power as a function of sample size (2N) with FDR q-value = 0.05. See caption of Figure 1 for further details.

Figure 3

Repeatability quantified as the agreement (area overlap) of the detected regions between two independent samples (400 independent AD+HC sample pairs of size 2N=30) as a function of FDR q-value. Error bars show standard error of the mean. See caption of Figure 1 for legend.

Figure 4

Repeatability quantified as the agreement (area overlap) of the detected regions between two independent samples as a function of sample size (with FDR q-value = 0.05). See caption of Figure 3 for further details.

Figure 5

Uncorrected statistical significance –negative log10(p-value)- maps comparing longitudinal cortical thinning rates between HC (N=210) and AD (N=188) subjects (from the entire ADNI sample) visualized on the pial surface of the FreeSurfer template (fsaverage): (A) ST-LME method and (B) X-Slope method. The left hemisphere is shown on the left, and the right hemisphere is on the right. Vertices that have an uncorrected p-value less than 0.05 are shown in color. The odd-numbered rows show the lateral, superior, and anterior views. The even-numbered rows show the medial, inferior, and posterior views. Colorbar shows the corresponding significance value.

Figure 6

Cortical regions exhibiting a statistically significant difference in longitudinal thinning between HC and AD subjects (in red) on the entire ADNI sample. These maps were derived by thresholding the values shown in Figure 5 with an FDR correction at q=0.05. (A) ST-LME method and (B) X-Slope method. ST-LME reveals a much wider extent of significant thinning in AD.

Figure 7

Uncorrected statistical significance –negative log10(p-value)- maps comparing longitudinal cortical thinning rates between stable MCI (N=227) and converter MCI (N=166) subjects (from the entire ADNI sample) visualized on the pial surface of the FreeSurfer template (fsaverage): (A) ST-LME method and (B) X-Slope method. See caption of Figure 5 for further details.

Figure 8

Cortical regions exhibiting a statistically significant difference in longitudinal thinning between stable and converter MCI subjects (in red). These maps were derived by thresholding the values shown in Figure 7 with an FDR correction at q=0.05. (A) ST-LME method and (B) X-Slope method. ST-LME reveals a much more dramatic extent of significant thinning differences between two groups.