Abstract

Introduction:

Combination antiretroviral therapy (cART) has been shown to reduce inflammation in persons with HIV (PWH), leading to overall improvements in cognition. However, these improvements are patient-dependent and not always observable over short treatment periods.

Methods:

We applied a multimodal integrative model to associate various baseline MR neuroimaging metrics with baseline neurocognitive performance and their longitudinal changes over 12 weeks of cART treatment. Features in our model included volumetric data, cerebral blood flow metrics, cerebrovascular reactivity, and diffusion MRI data from cortical, subcortical, and white matter regions of the brain. Our integrative model, which includes multilayered principal component analysis, penalized regression, and feature weight back-propagation, is designed for “large p, small n” data and offers better interpretability than deep-learning methods.

Results:

There is a modest association between imaging metrics and baseline neurocognitive scores for both PWH and age-matched healthy controls, driven primarily by subcortical regions. In contrast, baseline imaging features exhibited stronger associations with longitudinal changes in cognitive performance over 12 weeks of cART in PWH than with baseline cognitive scores. The multimodal integrative model outperformed all comparable unimodal models in explaining longitudinal cognitive change. Among unimodal analyses, models based on cerebral blood flow and free-water-corrected fractional anisotropy demonstrated the strongest associations. Frequently selected predictors included the frontal pole (cortical gray matter); the amygdala, putamen, and hippocampus (subcortical gray matter); and the posterior limb of the internal capsule (white matter).

Discussion:

Our approach provides an interpretable statistical framework that integrates complementary information across various imaging modalities into a robust and interpretable model for short-term cognitive trajectories in PWH undergoing cART.

1 Introduction

The introduction of combination antiretroviral therapy (cART) has revolutionized the management of HIV infection, significantly reducing morbidity and mortality. One of the critical benefits of cART is its ability to reduce neuroinflammation, which has been linked to improvements in cognition among people with HIV (PWH). Despite these advancements, studies conducted by our team and others showed that cognitive improvements under cART are not uniformly observed across all patients, with some individuals showing significant gains and others exhibiting minimal or no improvement, over relatively short treatment periods (Cysique et al., 2009, Heaton et al., 2015, Gates et al., 2016, Uddin et al., 2021, Weber et al., 2022, Singh et al., 2023). This variability motivated us to seek a deeper understanding of the mechanisms underlying cognitive changes in PWH during cART initiation.

Neurocognitive impairment remains a significant concern for PWH (Heaton et al., 2010), affecting their quality of life and function. Neurocognitive deficits in PWH can be attributed to various factors, including direct effects from viral proteins released by glia cells, chronic neuroinflammation from activated glia cells (Jones and Power, 2006, Killingsworth and Spudich, 2022), and vascular co-morbid conditions (Chow et al., 2012, Chow et al., 2016). These effects eventually lead to brain structural and functional changes, which can be evaluated by various brain imaging markers. Noninvasive brain imaging techniques, such as magnetic resonance imaging (MRI), have been instrumental in identifying structural and functional abnormalities associated with HIV infection. In recent years, studies conducted by our team and others have demonstrated that multiple MRI techniques offer distinct perspectives in assessing differences between PWH and healthy controls, as well as monitoring the recovery in PWH undergoing cART treatment (Chang et al., 1999, Ragin et al., 2004, Strain et al., 2017, Zhuang et al., 2017, Murray et al., 2020, Uddin et al., 2021, Zhuang et al., 2021, Weber et al., 2022, Singh et al., 2023, Uddin et al., 2024).

PWH treated with cART show, as a group, stable cognitive performance over several years, but continue to have worse cognitive performance compared to healthy controls. Neuroimaging differences also continue to persist when comparing these two groups. In this regard, cART naïve PWH are more likely, at least in the short term, to show cognitive improvement and changes in neuroimaging markers (Zhuang et al., 2017, Weber et al., 2022). However, which specific imaging modality or combination of modalities is best to predict cognitive changes remains to be determined. This is partly because most individual markers from a single imaging modality may show weak associations with the outcome variable. It is a standard clinical practice to use multiple imaging modalities to assess the presence of brain pathology. It is therefore natural to consider a multimodal statistical model to integrate various types of imaging metrics and develop a strong predictor for the outcome variable. However, integrating multimodal imaging data faces two main challenges. First, compared with a typical unimodality study, it takes more resources and broader expertise to collect and process brain imaging data across multiple modalities within a single clinical study. Secondly, it is also statistically challenging to train a reliable and interpretable multimodality statistical model in an under-determined (“large p, small n”) situation. For example, cross-validation (CV), a standard validation technique in machine learning, are known to be highly unstable in small sample settings (Hawkins et al., 2003, Varoquaux, 2018) and may lead to “optimizer’s curse,” in which the validation performance is significantly over-optimistic compared to true test set error (Smith and Winkler, 2006, Gupta and Rusmevichientong, 2021, Cory-Wright and Gómez, 2025). In this study, we introduce a multimodal integrative model that combines feature screening, multi-layered principal component analysis (PCA), and regression with AIC-based model selection to rigorously control model complexity. A key contribution is that we developed an equivalent weight back-propagation algorithm that translates a complex predictive model based on multi-layered PCA back to the original feature space, which produces standard-deviation-adjusted weights for users to rank and directly interpret the original imaging features. This level of biological interpretability is often lacking from “black-box” style machine learning approaches. Using this approach, we studied the associations between baseline brain imaging metrics and both baseline neurocognitive scores and their changes over a 12-week period from cART treatment initiation.

Our investigation focuses on the following MRI modalities: T1-weighted MRI derived subcortical volumes (Vol), cortical thickness (CT), fractal dimensionality (FD); diffusion MRI derived extracellular free water (FW), fractional anisotropy (FA), mean diffusivity (MD); arterial spin labeling (ASL) derived cerebral blood flow (CBF); resting-state fMRI based cerebrovascular reactivity (CVR). Those measurements are collected from various regions of interest (ROIs) that can be divided into three key brain areas: cortical gray matter, subcortical gray matter, and white matter. We hypothesized that our multimodal integrative model would outperform unimodal models in predicting longitudinal changes in neurocognitive scores, providing a robust tool for understanding and potentially forecasting cognitive trajectories in this population.

2 Materials and methods2.1 Research subjects

Forty-five treatment-naïve PWH and 92 HIV uninfected (HIV–) participants were enrolled in a study assessing the potential neurotoxicity of combination antiretroviral therapy treatment (cART) at the University of Rochester Medical Center. Of them, 30 PWH and 56 controls had complete multimodality data, and they comprise the 86 subjects analyzed in this study. It should be noted that the age and sex of the PWH cART-naïve individuals recruited reflected those of individuals infected who were receiving care during the study period. All participants provided written informed consent before enrollment according to the institutional protocol and underwent clinical, laboratory, and brain MRI exams. All experiments were performed in accordance with relevant guidelines and regulations. The details of the study have been provided elsewhere (Weber et al., 2022).

Data used in this study include: (a) various types of MRI metrics in PWH, cART naïve collected at the baseline (prior to starting cART) and after 12 weeks of cART treatment, (b) neuropsychological assessments measured at both the baseline and after 12 weeks of cART treatment in PWH. These two visits were chosen to represent the clearest difference in cognitive performance within the PWH group. Demographic information about study participants is provided in Table 1; more details can be found in Table 1 of Weber et al. (2022).

VariableControlPWHN = 56N = 30Age, years, mean ± SD41.3 ± 15.033.3 ± 13.1Gender, n (%)Female24 (42.9%)2 (6.67%)Male32 (57.1%)28 (93.3%)Ethnicity, n (%):Hispanic or Latino2 (3.57%)3 (10.0%)Not Hispanic or Latino54 (96.4%)27 (90.0%)Race, n (%)Black5 (8.93%)14 (46.7%)Other4 (7.14%)0 (0.00%)White47 (83.9%)16 (53.3%)Bachelor’s degree, n (%)Yes40 (71.4%)9 (30.0%)No16 (28.6%)21 (70.0%)

Participant characteristics, stratified by the HIV status.

2.2 Data acquisition2.2.1 Neuropsychological assessments

The neurocognitive evaluation was performed by staff trained and supervised by a clinical neuropsychologist. Tests of Executive Function (Trailmaking Test Parts A and B, Stroop Interference task), Speed of Information Processing (Symbol Digit Modalities Test and Stroop 2 Color Naming), Attention and Working Memory [CalCAP(CRT4) and WAIS-III Letter-Number Sequencing], Learning [Rey Auditory Verbal Learning Test AVLT (trials 1–5), Rey Complex Figure Test Immediate Recall], Memory (Rey Auditory Verbal Learning Test RAVLT Delayed Recall, Rey Complex Figure Test Delayed Recall), and Motor (Grooved Pegboard, left and right hand) were administered at each visit. Premorbid intellectual functioning ability was estimated via WRAT-4 Reading at the baseline visit only. Raw scores were converted to z-scores using test manual norms, but the z-scores were cut off at ± 3 standard deviations (SD) above and below the mean values. Cognitive domain scores were created by averaging the z-scores of tests within each domain. A total summary score was calculated by summing the z-scores of the six cognitive domains measured (Executive Function, Speed of Information Processing, Attention and Working Memory, Learning, Memory, and Motor).

2.2.2 Magnetic resonance imaging

MRI was performed on 3T scanner (MAGNETOM Trio, Siemens, Erlangen, Germany) equipped with 32-channel head coil.

2.2.2.1 Anatomical imaging

The T1-weighted (T1w) images were acquired using a 3D magnetization prepared rapid acquisition gradient-echo (MPRAGE) sequence with inversion time (TI) = 1,100 ms, repetition time (TR) = 2,530 ms; echo time (TE) = 3.44 ms; flip angle = 7°; field of view (FOV) = 256 × 256; GRAPPA = 2; number of slices = 192; voxel size = 1.0 × 1.0 × 1.0 mm3.

2.2.2.2 Diffusion tensor imaging

Diffusion weighted images (DWI) were acquired using a single shot spin echo echo-planar imaging (SE-EPI) sequence with the following scan parameters: 60 diffusion-encoded images (b = 1,000 s/mm2), 10 non-diffusion weighted reference images (b = 0 s/mm2); TR = 8,900 ms; TE = 86 ms; FOV = 256 × 256; GRAPPA = 2; number of slices = 70; voxel size = 2.0 × 2.0 × 2.0 mm3. In order to correct for EPI distortions, a double-echo gradient echo field map sequence was also acquired (TR = 701 ms; TE1 = 5.19 ms; TE2 = 7.65 ms; FOV = 256 × 256; flip angle = 60°; number of slices = 70; voxel size = 2.0 × 2.0 × 2.0 mm3).

2.2.2.3 Resting-state fMRI (rs-fMRI)

The rs-fMRI scans were acquired using a gradient echo-echo planar imaging (GE-EPI) sequence with parameters TR = 2,000 ms, TE = 30 ms, 150 volumes, and voxel size = 4.0 × 4.0 × 4.0 mm3. Participants were instructed to keep their eyes closed throughout the scan.

2.2.2.4 Perfusion imaging

A pseudo-continuous arterial spin labeling (pCASL) sequence was used to acquire perfusion MRI images with scan parameters—TR = 3,530, TE = 22.62 ms and voxel size = 3.8 × 3.8 × 5 mm3. A tag-control pair technique with 36 averages was used, incorporating a labeling duration of 1.5 s and a single post-label delay (PLD) of 1.5 s. Additionally, the equilibrium magnetization of arterial blood (M0) image was acquired with one average using a TR of 5,000 ms.

2.3 Data analysis

Image analyses were conducted using multiple image processing tools, including FMRIB’s Software Library (Jenkinson et al., 2012) (FSL),1 ANTs (Avants et al., 2009),2 FreeSurfer (Fischl, 2012),3 and MATLAB (version 2022b; MathWorks, Natick, MA). All MRI images were visually inspected for any severe artifacts including motion and signal dropout.

2.3.1 Anatomical imaging

T1-weighted images were reoriented, cropped, bias-field corrected, skull-stripped, registered both linearly and nonlinearly to MNI152 2 mm standard space, and segmented by tissue type using FSL’s (version 5.11) anatomical processing script, fsl_anat (Smith et al., 2004, Woolrich et al., 2009).

2.3.2 Volumetric and cortical thickness (CT)

Volumetric and cortical thickness (CT) measurements were conducted using FreeSurfer (version 6.0.0) (Dale et al., 1999, Desikan et al., 2006, Livingston et al., 2020). In summary, the preprocessing steps included removing non-brain tissue via surface deformation, segmenting subcortical gray matter structures, correcting for motion artifacts, normalizing intensity, and performing automated Talairach transformation. For subcortical volumes, values for bilateral regions of interest were averaged across the left and right hemispheres.

2.3.3 Fractal dimensionality (FD)

Fractal dimensionality (FD) is a scale-invariant mathematical measure that quantifies the complexity of shapes at both macroscopic and microscopic levels, often interpreted as geometric fractals. FD was calculated for various brain regions, including the cortical ribbon (unparcellated gray matter), frontallobe, temporal lobe, occipital lobe, parietal lobe, and subcortical structures, using the calcFD toolbox4 (Madan and Kensinger, 2016, Madan and Kensinger, 2017). The calcFD toolbox, compatible with intermediate files from the FreeSurfer pipeline, calculates the FD of 3D brain structures. This is achieved through the box-counting algorithm, where the brain is treated as a 3D structure within a grid. Voxels containing portions of the structure are counted, and the process is repeated iteratively with progressively larger box sizes, with the filled boxes being recounted at each step. The relationship between box sizes and their respective counts are fitted using a power-law model, where the resulting FD is the exponent of the fitted model (Madan and Kensinger, 2016, Madan and Kensinger, 2017).

2.3.4 Diffusion tensor imaging (DTI)

Diffusion weighted images were corrected for eddy current-induced distortion, susceptibility-induced distortion, and motion correction using TOPUP and EDDY tools in FSL (Andersson et al., 2003). DTI metrics, including fractional anisotropy (FA) and mean diffusivity (MD), were calculated using DTIFIT tool in FSL (Behrens et al., 2003). Free water (FW) index and free water corrected DTI metrics (FA and MD) were computed with a bi-tensor model applied to the DWI data, following a previously established algorithm (Dumont et al., 2019). The processing pipeline was implemented using Nextflow pipeline (Di Tommaso et al., 2017) with all software dependencies encapsulated in a Singularity Container (Kurtzer et al., 2017). In this work, free water corrected FA and MD metrics were used.

2.3.5 Cerebral blood flow (CBF) and cerebrovascular reactivity (CVR)

ASL images were processed using the Oxford ASL tool (Chappell et al., 2008). Preprocessing steps included motion correction with MCFLIRT, slice-timing correction, distortion correction, spatial regularization, partial volume correction, and registration to high-resolution anatomical space using the boundary-based registration (BBR) algorithm. Additionally, images were registered to 2 mm MNI-152 standard space using FNIRT nonlinear registration (Greve and Fischl, 2009, Glasser et al., 2022). Cerebral blood flow (CBF) quantification was performed in three steps: (1) Bayesian inference for CBF based on the Buxton kinetic curve model, (2) Bayesian inference of additional parameters applicable to single-post label delay data, and (3) Bayesian inference with spatial priors to refine model parameters, initialized with high-resolution anatomical image (Buxton et al., 1998, Chappell et al., 2008).

CVR maps were calculated using the global signal regression coefficient method applied to rs-fMRI BOLD images (Liu et al., 2017), providing qualitative reactivity indices for each subject at each study visit. Preprocessing steps included motion correction, spatial smoothing with a Gaussian filter [full-width at half-maximum (FWHM) of 4 mm], and linear detrending. Building on previous findings in healthy controls that linked global resting-state BOLD fluctuations to natural variations in ETCO2 levels within the 0.02–0.04 Hz frequency range, we applied a band-pass filter to isolate this specific frequency range in the rs-BOLD data. Gray matter tissue segmentation was used as a mask to compute the global average gray matter rs-fMRI signal, which served as a regressor for voxel-wise BOLD signals. The global signal, previously demonstrated to reflect respiratory and cardiac fluctuations, was regressed against the preprocessed BOLD signal at each voxel. The slope of this regression was taken as the CVR index. Finally, normalization of this index by the whole-brain average provided a qualitative measure of CVR (Liu et al., 2017).

2.3.6 ROI analysis

T1-weighted images were used for co-registration of the DTI, rs-fMRI, and perfusion MR images to anatomical and standard spaces. Tissue maps were used to account for partial volume effects in functional processing. Regions of interests (ROIs) were determined based on previous literature (Tate et al., 2011, Thompson and Jahanshad, 2015, Uddin et al., 2021, Minosse et al., 2023, O’Connor et al., 2023, Uddin et al., 2024)and extracted using the Harvard-Oxford cortical and subcortical atlases available in FSL. Each ROI was warped from standard to native spaces and binarized before being applied as a mask against each imaging metric map. The mean and standard deviation of each metric were calculated using FSL’s fslstats tool within each ROI. The following ROIs were included in the analysis. Cortical gray matter: Frontal Pole (FRP), Pars Opercularis (IFG_O), Superior Temporal Gyrus (STG), Postcentral Gyrus (POC), Parahippocampal Gyrus (PHG), Lingual Gyrus (LNG), Insula (ICX), Lateral Occipital Lobe (LOC), Temporal Pole (TMP), Superior Parietal Lobule (SPL), Precuneus (PUC); subcortical gray matter: Caudate Nucleus (CN), Putamen (PUT), Globus Pallidus (GP), Thalamus (TH), Amygdala (Amyg), Accumben Nucleus (AccN), Hippocampus (Hippo); white matter: Splenium of Corpus Callosum (SCC), Genu of Corpus Callosum (GCC), Body of Corpus Callosum (BCC), Posterior Limb of Internal Capsule (PLIC), Anterior Limb of Internal Capsule (ALIC), Superior Longitudinal Fasciculus (SLF), Anterior Corona Radiata (ACR). Bilateral ROIs were merged prior to calculating metric means.

3 Statistical methods

We analyzed the following datasets: Cortical gray matter—CT, FD, FW, FA, MD, CBF, CVR; subcortical gray matter—volumes, FD, FW, FA, MD, CBF, CVR; white matter—FW, FA and MD. A total of 147 candidate imaging features, representing four imaging modalities: volumetric measures (volumes, cortical thickness and FD); Diffusion MRI (FW, FA, and MD); perfusion MRI (CBF), and rs-fMRI-based cerebrovascular reactivity (CVR). Out of them, 77 are collected from ROIs in cortical gray matter regions, 49 are from subcortical gray matter regions, and 21 are from white matter regions.

For each feature, we apply an initial screening using a two-sample Welch t-test for identifying mean differences between the PWH group and healthy controls at the baseline visit (n = 86 subjects). Given the high-dimensional nature of our study, we adopt a liberal selection threshold of p < 0.2. This “soft” screening method is commonly used in high-dimensional statistical learning to retain features with relatively weak marginal associations for model development. A feature is selected for further analysis if the resulting p-value is less than 0.2. Based on this criterion, we identified 39 (11 cortical gray matter, 23 subcortical gray matter, and 5 white matter) features to be used for multimodal integrative analysis. A complete list of these features, an ROI-abbreviation legend, and the corresponding results from Welch t-test are provided in Supplementary Table 1.

3.1 Multimodal integrative analysis

Two outcome variables are considered in this study. The first, denoted as Z0, is the overall cognitive z-score measured at baseline. This data is available for both PWH and controls (n = 86). The second, denoted as ΔZ, is the temporal change in z-scores between the baseline and the second visit following 12 weeks of cART treatment. This data is defined only for PWH and is available for 27 subjects (three PWH lacked cognitive data at the 12-week follow-up).

Our main objective was to develop interpretable, regression-based predictors for the two outcome variables. As a secondary objective, we identify the features, as well as the corresponding brain regions and imaging modalities, that are most informative for predicting these outcome variables. Due to the large number of features used in this study, it is reasonable to consider applying dimensionality reduction and model selection steps in training the predictive models for the two outcome variables. Below, we summarize the two approaches we attempted in this study.

Model 1: We apply the first layer of principal component analyses (PCA) separately on the set of features collected in each brain region (cortical gray matter, subcortical gray matter, and white matter). A second layer of PCA is then applied to the principal components (PCs) defined in the first step to further reduce the dimensionality. For both principal component analyses, numbers of top PCs are selected by the proportion of variance explained (PVE), with the following two options: PVE = 0.8 (80% of total variance) or PVE = 0.9 (90% of total variance). Top PCs defined in the second PCA are used as features in multiple regression models to predict the two outcome variables in the output model. A bi-directional stepwise model selection procedure based on Akaike Information Criterion (AIC) is applied to reduce the complexity and prevent overfitting for the output model.

Model 2: Much like Model 1, except that top PCs identified in the first layer PCA are used directly as features in the output model to predict the outcome; no second layer PCA is applied.

Of note, we also explored an alternative approach with the output regression model replaced by an elastic-net regression, implemented in R package glmnet. However, its performance was significantly worse than our primary approach; therefore, this approach is not presented here.

A schematic representation of this multimodal integrative analysis pipeline is shown in Figure 1.

Top row: Schematic representation of the analytic pipeline. After image preprocessing and feature selection, principal components (PCs) are extracted separately for each imaging modality. These modality-specific PCs may be concatenated and optionally reduced via a second-layer (global) PCA. Retained PCs (plus any covariates) are used to fit multiple linear regression model (with model selection or penalty) to predict either the baseline cognitive score (Z) or 12-week changes (ΔZ). Finally, linear coefficients in the PC space are algebraically back-propagated to produce equivalent and scale-adjusted input-space weights (wj). These adjusted feature weights represent changes in predicted outcome per one standard-deviation change in feature j, which can be used to rank features across regions and modalities. Bottom left: An illustration of the per-modality PCA →regression pipeline (Vol, FD, FW are example modalities). Bottom right: An alternative approach with an additional global PCA step to further reduce modeling complexity.

3.2 Unimodality and modality-region models for ΔZ

One drawback of the multimodality models is that, by incorporating all imaging modalities across all brain regions, they do not reveal which specific modality or region is most predictive of the outcome variables. To address this deficiency, we developed unimodality models for each of the eight imaging metrics used in this study: Vol, CT, FD, FW, FA, MD, CBF, and CVR. Each model uses only features in that category, selected by the marginal screening procedure based on Welch two sample t-test for HIV status. Compared with multimodality models, these unimodality models use far fewer features; therefore, there is no need for dimensionality reduction prior to regression. We decided to employ the same AIC-based stepwise selection procedure to exclude uninformative features and reduce model complexity.

In addition, we developed 17 experimental modality-region models, each using just one modality from a single brain region, e.g., FW measures from the cortical region, to predict Z or ΔZ. Because each modality-region contains far fewer features than the pooled unimodality models, we decided to skip the feature screening step based on HIV status. As a result, modality-region models reflect the general association between various imaging markers to longitudinal changes of cognitive scores, not just those strongly related to the HIV infection revealed in multimodality and unimodality models. Again, modality-region models use relatively few features; therefore, we do not need to apply a dimensionality reduction procedure before regression analyses. The same AIC-based stepwise selection procedure is used to keep model complexity in check.

3.2.1 Assign weights to original features for multimodality models

Although unimodality and modality-region models offer insight into which specific modalities and brain regions are most associated with cognitive outcomes, these models are certainly not equivalent to the superior multimodality models, because each such model can only use a small subset of features. In this section, we introduce an algorithm that assigns equivalent weights to the original features in multimodality models, allowing us to rank these imaging measures directly.

Mathematically, the final predictor of our multimodality models can be represented as follows:

Here is the predicted outcome value (Z0 or ΔZ) for the ith subject; PCil is the lth PC score pertain to the ith subject; is the intercept, and are the linear coefficients associated with PC⋅l. For Model 1, PCil are the second-layer PC scores; for Model 2, PCil are scores of the first and only PCA.

By design, represents the importance of the lth PC, not the original features (denoted as xij for the ith subject and the jth feature). Because PC⋅l is a linear combination of all x⋅j, it is not obvious how much each xij contributes to the predicted value .

A weight back-propagation algorithm originally developed in our recent study (McCall et al., 2021) enables direct interpretation of our multilayer PC–regression models by mapping principal-component weights () back to the original feature space. Specifically, it computes an equivalent weight vector , such that , where Xij is original feature j for subject i. Due to this mathematical equivalence, the magnitude of quantifies the contribution of X⋅j to the predictions.

In this study, we introduce two important refinements tailored to multimodality imaging analysis:

PCA on the Pearson correlation matrix. Because our imaging features span many different modalities with very different natural scales, we apply a variant of PCA based on the eigen-decomposition of the sample Pearson correlation matrix instead of sample covariance matrix. This choice prevents any single modality from dominating the principal components, thus ensures a balanced representation of all modalities in top PCs.

Standard-deviation-adjusted weights. Instead of ranking the importance of image metrics by directly, we define the adjusted weights to be , where is the sample standard deviation of X⋅j. By construction, wj represents the expected change in the predicted value () associated with one STD change in X⋅j, which remains invariant under any rescaling of X⋅j. This invariance makes these adjusted weights directly comparable across features and modalities.

Based on these refinements, the adjusted weights are more appropriate than the unadjusted weights for prioritizing features with vastly different scales. In Tables 2, 3, we see that the adjusted weights are much more comparable to each other than the unadjusted weights.

FeaturesAdjusted weights (wj)Unadjusted weights ()MeanSTDAmyg.CBF.sub–0.864–6.6320.8280.130PUC.CVR.cor0.7421.8731.5790.396GP.Vol.sub–0.718–45.1220.1310.016PUT.FW.sub0.699132.5020.0080.005CN.MD.sub0.56813407.9300.0010.000GP.FA.sub–0.541–22.3110.3720.024AccN.CBF.sub0.5012.3941.2610.209CN.Vol.sub0.50115.7970.2410.032

Equivalent weights of imaging features in Model 2 (with PVE = 0.9) for predicting the baseline total Z-scores (Z) using baseline data from n = 86 subjects.

Features reported in this table are ranked by the adjusted weights (wj) and selected based on |wj| = 0.5. Features are represented as ROI.MRI-metric.region. ROIs: Amyg–Amygdala; PUC, Precuneus; GP, Globus Pallidus; PUT, Putamen; CN, Caudate Nucleus; AccN, Accumben Nucleus. Metrics: CBF, cerebral blood flow; CVR, cerebrovascular reactivity; Vol, subcortical volume; FW, extracellular free water; MD, mean diffusivity; FA, fractional anisotropy. Regions: sub, subcortical gray matter; cor, cortical gray matter.

FeaturesAdjusted weights (wj)Unadjusted weights ()MeanSTDALIC.FW.wm4.338901.1430.0020.005LNG.FD.cor–1.798–53.2682.0890.034Hippo.CVR.sub1.7046.1690.9780.276PUT.FW.sub–1.494–283.0280.0080.005ICX.CBF.cor–1.284–8.2081.2590.156Hippo.FW.sub–1.211–25.5130.2080.047Hippo.FA.sub–1.058–57.3280.2230.018TH.CVR.sub–0.960–2.7590.9220.348GP.Vol.sub0.95359.8700.1310.016CN.Vol.sub–0.916–28.8950.2410.032IFG-O.CBF.cor–0.867–4.0161.5890.216AccN.FA.sub–0.850–56.7330.1840.015Amyg.MD.sub0.8184299.2610.0010.000IFG-O.CT.cor–0.816–5.5672.6400.147FRP.FA.cor–0.803–55.0270.1290.015FRP.CBF.cor0.7352.8661.2450.257Amyg.FW.sub–0.714–19.0080.1720.038Amyg.CBF.sub0.7015.3780.8280.130AccN.CBF.sub–0.700–3.3441.2610.209PLIC.FA.wm0.66128.7480.5780.023PUT.CVR.sub0.6031.9160.8110.315PUT.CBF.sub0.5954.4001.0030.135