Heterogeneity of morphometric similarity networks in health and schizophrenia

Abstract

Reduced structural network connectivity is proposed as a biomarker for chronic schizophrenia. This study assessed regional morphometric similarity as an indicator of cortical inter-regional connectivity, employing longitudinal normative modeling to evaluate whether decreases are consistent across individuals with schizophrenia. Normative models were trained and validated using data from healthy controls (n = 4310). Individual deviations from these norms were measured at baseline and follow-up, and categorized as infra-normal, normal, or supra-normal. Additionally, we assessed the change over time in the total number of infra- or supra-normal regions for each individual. At baseline, patients exhibited reduced morphometric similarity within the default mode network compared to healthy controls. The proportion of patients with infra- or supra-normal values in any region at both baseline and follow-up was low (<6%) and similar to that of healthy controls. Mean intra-group changes in the number of infra- or supra-normal regions over time were minimal (<1) for both the schizophrenia and control groups, with no significant differences observed between them. Normative modeling with multiple timepoints enables the identification of patients with significant static decreases and dynamic changes of morphometric similarity over time and provides further insight into the pervasiveness of morphometric similarity abnormalities across individuals with chronic schizophrenia.

Introduction

Schizophrenia is a severe psychiatric disorder that affects about 1% of the global population¹. Despite decades of research, the prognosis in a substantial proportion of patients remains poor¹. A significant barrier to developing effective, personalized treatments lies in the unresolved neurobiological heterogeneity that characterizes the disease^2,3. While reductions in brain volume and cortical thickness have been observed at the group level in schizophrenia, individual variability in these morphological metrics remains substantial, posing challenges for identifying reliable biomarkers^2–6. The normative modeling framework aims to address the issue of individual phenotypic heterogeneity by establishing normative standards for neurobiological variables and subsequently assessing an individual’s deviation from these norms⁷. Previous studies using normative modeling to examine individual deviations in cortical thickness and white matter structure in schizophrenia have demonstrated that these deviations are not consistently localized to the same regions but are instead embedded within common functional networks that are disrupted in the condition, such as the default mode network (DMN)⁸.

Morphometric similarity is a phenotype that integrates multiple MRI-derived features, such as cortical thickness and volume, into a network-based representation^9,10. Unlike isolated measures such as cortical volume, morphometric similarity provides a multidimensional view of brain organization that reflects structural connectivity patterns and inter-regional relationships⁹. The utility of morphometric similarity for assessing schizophrenia is supported by its strong associations with structural connectivity and its capacity to reflect network-level disruptions^9–11. Morphometric similarity reductions in regions associated with the DMN, replicated across independent samples, underline its potential role in improving our understanding of the pathophysiology of schizophrenia¹¹.

Morphometric similarity shows individual variation across age in the neurotypical population, and has been related to cortical expression of schizophrenia-related genes, making it suitable for normative modeling^9,11,12. By employing a normative modeling framework, morphometric similarity can serve as a proxy for quantifying deviations in network connectivity not just cross-sectionally but also longitudinally. This is particularly valuable for schizophrenia, where disease progression may influence connectivity patterns over time and their relationship with clinical outcomes¹³.

In this study, we apply normative modeling to morphometric similarity for the first time in a longitudinal sample of individuals with schizophrenia. This approach allows us to parse both the cross-sectional and longitudinal heterogeneity of morphometric similarity, offering a more nuanced understanding of how structural connectivity varies across individuals and changes over time within the context of schizophrenia.

Materials and methods

Sample

Eleven datasets were combined to create the full sample. These datasets are described in Fig. 1, including the sample size, age, and sex distribution of each dataset. We included healthy participants from ten publicly available datasets: the Amsterdam Open MRI Collection (aomic) (id1000, piop1 and piop2) datasets¹⁴, the Cambridge Centre for Ageing and Neuroscience (camcan) dataset¹⁵, the Dallas Longitudinal Brain Study (dlbs) dataset¹⁶, the Information eXtraction from Images (ixi) dataset (http://brain-development.org/ixidataset/), the Narratives (narratives) dataset¹⁷, the Open Access Series of Imaging Studies (oasis3) dataset¹⁸, the NKI-Rockland (rockland) dataset¹⁹ and the Southwest University adult lifespan (sald) dataset²⁰. One dataset is not publicly available and consisted of a large longitudinal sample of individuals with schizophrenia and healthy participants aged 16-68 years (at baseline) from the Utrecht Schizophrenia project and the Genetic Risk and Outcome of Psychosis (GROUP) consortium. From this longitudinal clinical sample, we included individuals who had T1-weighted magnetic resonance imaging (MRI) scan acquisitions at baseline and follow-up. Two identical scanners were used, and all included participants had their baseline and follow-up scans acquired on the same scanner. Detailed information regarding diagnostic criteria, clinical assessments, MRI acquisition, and image quality control assessment of the Utrecht Schizophrenia project and the GROUP consortium is described in refs. ^21–23. Additional demographic, cognitive, and clinical characteristics of the longitudinal clinical sample are provided in Table 1A. All participants provided written informed consent. Subject recruitment procedures and informed consent forms, including consent to share de-identified data, were approved by the corresponding institutional review board where data were collected.

Fig. 1. Age distributions of datasets.

Eleven datasets were used in the study. Ten datasets were cross-sectional and included healthy participants. For each of these ten datasets, 90% of individuals were included in the training set and 10% were part of the test set. One longitudinal clinical dataset (two timepoints) included healthy controls and individuals with chronic schizophrenia. Of the healthy controls belonging to the longitudinal clinical dataset, 20% were included in the training set and 80% in the test set. All individuals with schizophrenia were included in the test set. The age distribution for each dataset within the training/test samples is shown. The table shows the descriptives per dataset. N, number of subjects.

Table 1.

(A) Demographic, cognitive, imaging, and clinical characteristics of the clinical dataset. (B) Results of statistical tests for case-control differences in z-scores averaged across regions belonging to the seven functional brain networks²⁸.

(A)
	Healthy		Schizophrenia
	Baseline (N = 292)	Follow-up (N = 292)	Baseline (N = 167)	Follow-up (N = 167)
Age (years)	30.44 (11.02)	34.39 (11.31)	29.90 (9.31)	34.02 (9.60)
Sex (N, (%F))	130 (44.5)		38 (22.8)
Education (years)	21.92 (25.33)		20.31 (25.84)
IQ total	110.28 (15.79)	113.89 (16.65)	97.82 (16.60)	103.13 (20.34)
Time between scans (years)	3.95 (1.03)		4.11 (0.95)
Age of onset (years)			22.14 (5.28)
Illness duration at scan (years)			6.41 (6.66)	11.08 (7.72)
PANSS total			63.22 (19.38)	50.17 (14.28)
Total positive			14.91 (5.85)	12.38 (4.65)
Total negative			16.25 (6.25)	12.83 (5.66)
Total general			31.15 (11.26)	24.97 (7.04)

(B)
Timepoint	Network	z-scores
		t-statistic	p-value
Baseline	Visual	1.451	0.148
	Somato motor	2.940	0.003*
	Dorsal attention	−0.844	0.399
	Ventral attention	−0.075	0.940
	Limbic	−1.902	0.058
	Fronto parietal	−0.805	0.421
	Default mode	−3.665	0.0002*
Follow-up	Visual	1.519	0.130
	Somato motor	1.675	0.095
	Dorsal attention	−0.867	0.387
	Ventral attention	−0.819	0.413
	Limbic	−0.617	0.537
	Fronto parietal	−0.361	0.718
	Default mode	−2.046	0.041

All descriptors are mean (standard deviation) unless otherwise specified.

A positive t-statistic indicates that the group of individuals with schizophrenia has a higher mean than the group of healthy controls, while a negative t-statistic indicates that the group of individuals with schizophrenia has a lower mean MS than the group of healthy controls.

N number of subjects, F female, PANSS positive and negative syndrome scale24.

^*P_FDR < 0.05.

Image processing and quality control

All T1-weighted images from all datasets were processed centrally using the FreeSurfer analysis suite (v7.1) with default settings²⁴. Estimates of (1) cortical volume, (2) surface area, (3) average cortical thickness, (4) average curvature, and (5) Gaussian curvature were calculated for each of the 62 regions of the Desikan–Killany–Tourneville (DKT) atlas²⁵. The Freesurfer Euler number was extracted as a proxy for image quality²⁶. Subjects were removed if the maximum, absolute, within-dataset centered Euler number was larger than 10, and 29 subjects were removed²⁷. For the clinical sample, we applied extensive visual and non-visual image quality control procedures as described in refs. ^22,23. For the clinical sample, we applied extensive visual and non-visual image quality control procedures as described in refs. ^22,23. Briefly, the non-visual quality control procedures included calculating measurements based on the ones proposed by the PCP quality assessment protocol: signal-to-noise ratio, contrast-to-noise ratio, Foreground to background Energy Ratio, percent artifact Voxels, and Entropy Focus Criterion. Following ENIGMA criteria, we defined the threshold for outliers as [mean − (2.698 × SD)]. Next, for each scan, the whole brain mean cortical thickness, total cortical surface area, total white matter volume, total gray matter volume, subcortical gray matter volume, and intracranial volume were calculated. Then, we summed for each image the number of outliers over all measures and calculated the mean + (2.698 × SD) for the number of outliers over the whole sample and designated those above the threshold as outliers.

Morphometric similarity

Using regional measurements of cortical thickness, surface area, cortical volume, mean curvature, and Gaussian curvature, we calculated regional morphometric similarity following a previously published protocol⁹, see Fig. 2A, B. We assessed the replicability of our approach by comparing regional morphometric similarity maps to previously published maps¹¹. The correlation between our regional morphometric similarity maps and the previously published maps by ref. ¹¹ was 0.8, thus indicating good replicability; see the Supplemental text and Supplemental Fig. 1 for details.

Fig. 2. Study overview.

A Ten cross-sectional datasets consisting of healthy individuals only and one longitudinal dataset consisting of healthy controls and individuals with chronic schizophrenia (Utrecht) were used in the study. B morphometric similarity matrices were constructed following established protocols using cortical thickness, cortical volume, surface area, mean curvature, and Gaussian curvature extracted for each cortical region⁹. C Example centile plot from normative modeling of regional morphometric similarity of the left hemispheric superior frontal gyrus for assessing individual deviance (Z). Normative modeling was done following established protocols⁴⁰ using prediction on unseen test data following training of the model. D Cortical maps depicting percentage of extreme deviance below the norm, i.e., infra-normal deviance, in individuals with schizophrenia and healthy individuals. n number of subjects, CT cortical thickness, SA surface area, CV cortical volume, MC mean curvature, GC Gaussian curvature, MS morphometric similarity.

Mapping the DKT atlas regions to functional networks

Ref. ¹¹ reported altered group-level morphometric similarity in schizophrenia in three out of seven functional networks as described by ref. ²⁸. In order to replicate the findings by ref. ¹¹ we focused on these seven widely recognized functional brain networks derived from an analysis of an independent resting state fMRI dataset²⁸, see Supplemental Fig. 2. To obtain a correspondence between the regions of the DKT atlas and the seven functional networks we followed the approach by ref. ²⁹. Briefly, for each region of the DKT atlas, we calculated the overlap (as the number of vertices) between each region of the DKT atlas and each of the seven functional networks. Afterwards, each region was assigned to the functional network with which it exhibited the greatest overlap. This resulted in a mapping of each region to one of the seven functional networks.

Normative modeling of morphometric similarity

For normative modeling, each of the ten datasets containing only healthy controls was split into a training set (≈90%) and a test set (≈10%)³⁰, see Fig. 1. Following recommendations by ref. ⁷ and as for example in refs. ^27,31,32, only healthy controls were included in the training set. For the clinical dataset, all individuals with schizophrenia, as well as 80% of the healthy controls, were included in the test set, while the remaining healthy controls (20%) were included in the training set. The per-dataset splits were created using the createDataPartition function from the caret R package, preserving the distribution of age, sex, and scanner (some datasets contained multiple scanners) in both the training and the test split of each dataset. By preserving the distributions across splits, the inclusion percentages become approximate, not exact. The training set included 4310 participants and the test set 859 participants. Bayesian linear regression (BLR) with likelihood warping using a B-spline (spline order = 3, number of knots = 5) was used to predict morphometric similarity from a vector of covariates (age, sex, Euler number, and scanner)²⁷. In order to reduce residual variance due to differences in image quality across subjects, we decided to include the Euler number as a variable in our normative models. For a complete mathematical description and explanation of this implementation, see ref. ³³. Briefly, for each brain region of interest (r),

$$y_r=w^T\varphi \left(X\right)+{ϵ}_s$$ 1

where y is the predicted distribution of morphometric similarity for region r, $w^T$ is the estimated weights vector, $X$ is the set of covariates, $\varphi \left(X\right)$ the B-spline basis expansion applied to them, and ${ϵ}_s$ a Gaussian noise distribution term for scanner s.

Individual deviations: infra- and supra-normal morphometric similarity

We followed the method proposed by ref. ³⁴ who showed that longitudinal normative modeling metrics (see Statistics) for adult individuals with schizophrenia and healthy participants can be calculated from a large cross-sectional normative model of healthy participants. We created morphometric similarity normative charts for each region using the training set consisting of healthy participants. Thereafter, individuals from the test set were positioned on the morphometric similarity normative charts. For each individual deviation (z) scores, quantifying individual deviation from the normative range, were calculated for all brain regions (r) and all participants (n), as follows:

$$z_{nr}=\frac{y_{nr}-\widehat{y_{nr}}}{\sqrt{{\sigma }_r^2+{\sigma }_{*r}^2}}$$ 2

where $y_{\mathit{nr}}$ means the true morphometric similarity value and ${\hat{y}}_{\mathit{nr}}$ is the predicted mean morphometric similarity value. The difference in these values is normalized to account for two different sources of variation; (i) ${\sigma }_r^2$, which is the aleatoric uncertainty and reflects the variation between individuals across the population, and (ii) the epistemic uncertainty, ${\sigma }_{*r}^2$, which accounts for the variance associated to modeling uncertainty introduced by the model assumptions or parameter selection. z-scores were then categorized as either: (i) normal, i.e., within the normative range of variation for healthy individuals with the same age range, sex, Euler number, and scanner; (ii) supra-normal: significantly exceeding the normative range; or, (iii) infra-normal: significantly below the normative range. As per previous studies^{23,27,32,35–38}, we considered a z-score ≧ 1.96 as supra-normal and a z-score ≦ −1.96 as infra-normal.

Evaluation of the normative model

The unseen data in the complete test set was used to evaluate the normative model. The evaluation included Q–Q plots, and the metrics proportion of explained variance, mean standardized log loss, standardized mean square error, root mean square error, rho, skewness, and kurtosis (see Supplemental Fig. 3).

Statistical analyses

Effects of diagnosis on morphometric similarity of functional networks

In order to replicate the findings by ref. ¹¹, averaged z-scores of the seven functional networks were compared between healthy controls and individuals with schizophrenia at baseline using Welch t-tests. Effect sizes are given as Cohen’s d. Only p-values that survived FDR correction for multiple comparisons were considered significant.

The percentage of individuals with infra- or supra-normal deviance per region

We calculated for each region (r) and at each timepoint (t = t1 or t2) the percentage of patients and healthy controls that had supra- or infra-normal z-scores:

$$percentag{eoutliers}_r\left(t\right)=\frac{{\sum }_{n=1}^{N_{total}\left(t\right)}{\delta }_{rn}\left(t\right)}{N_{total}\left(t\right)}\cdot 100\%$$ 3

where ${\delta }_{\mathit{rn}}$(t) equals 1 if participant n = 1,…,$N_{total}\left(t\right)$ has |z| > 1.96 in region r at time point t, and equals 0 otherwise, and $N_{\mathit{total}}$ is the total number of participants at time point t. Group differences for each region and at each time point in the proportion of individuals with supra- or infra-normal z-scores were examined using the two-proportions z-test.

Differences in z-scores over time by region are calculated by implementing the z-diff approach, which takes into account the typical variation over time³⁴. Z-diff was calculated as follows:

$${Zdiff}_{SZ}=\frac{\left(Y_{SZ,V2}-\widehat{Y_{SZ,V2}}\right)-\left(Y_{SZ,V1}-\widehat{Y_{SZ,V1}}\right)}{\sqrt{Var\left[\left(Y_{HCvar,V2}-\widehat{Y_{HCvar,V2}}\right)-\left(Y_{HCvar,V1}-\widehat{Y_{HCvar,V1}}\right)\right]}}$$

Where $Y$ represents the true morphometric similarity, $\hat{Y}$ denotes the predictions, v1 and v2 correspond to visit one and visit two, respectively, and $\mathit{HC}\mathrm{var}$ refers to healthy control subjects that were only used for variance calculation. Group differences for each region were assessed using Welch t-tests.

To assess the spatial distribution of infra- and supra-normal deviations, we built diagnostic-wise brain maps, see Fig. 2E.

Effects of diagnosis on the number of outlier regions per participant

Here we determine the change over time in the total number of outlier regions per participant as follows:

$$changeinoutliercoun{t}_n\left(t\right)=\sum _{r=1}^{62}{\delta }_{rn}\left(t1\right)-\sum _{r=1}^{62}{\delta }_{rn}\left(t2\right)$$ 5

where δ_rn(t) equals 1 if participant n has |Z| > 1.96 for region r = 1,…, 62, and equals 0 otherwise. Diagnostic group differences in the change in total number of outlier regions by participant were examined using a Welch t-test. In the group of individuals with schizophrenia, we tested for associations between baseline z-scores and change in outlier count over time with IQ and PANSS total, positive, negative, and general scores using Pearson correlation.

Effect of diagnosis on z-scores vs ‘raw’ morphometric similarity

We assessed whether using z-scores from normative modeling led to stronger diagnostic group results as compared to using ‘raw’ morphometric similarity (i.e., the traditional approach). Therefore, we averaged ‘raw’ morphometric similarity across the regions belonging to each of the functional networks. To investigate the diagnostic differences of ‘raw’ morphometric similarity scores for each functional network, we used seven separate generalized additive models (one for each functional network) to residualize the ‘raw’ morphometric similarity for age (included as a smooth term to allow for the potentially non-linear association between morphometric similarity and age), sex, Euler number, and scanner⁵. For the diagnostic comparison of the residualized ‘raw’ morphometric similarity, we used Welch t-tests.

Supplemental analyses

Firstly, we calculated infra- and supra-normal deviance for males and females separately to assess whether results differed by sex. Secondly, we averaged morphometric similarity across all regions and hemispheres to determine whole brain morphometric similarity and compared this between cases and controls. The results of these analyses are included in the Supplement.

Results

Visualization and evaluation of the normative models

An exemplary normative model plot with percentile curves for the left hemispheric superior frontal gyrus can be seen in Fig. 2C. Distributions of the evaluation metrics of the normative models can be found in Supplemental Fig. 3.

Effects of diagnosis on morphometric similarity of functional networks

At baseline, the group of individuals with schizophrenia had a positive average deviance of morphometric similarity for the somatosensory network, which differed significantly from the negative average deviance of morphometric similarity in healthy controls (d = 0.30; p < 0.01). Individuals with schizophrenia had a negative average deviance of morphometric similarity for the DMN, which differed significantly from the positive average deviance of morphometric similarity in healthy controls (d = −0.36; p < 0.001), see Table 1B and Figs. 3 and 4. At follow-up, the group of individuals with schizophrenia maintained the negative morphometric similarity for the DMN compared to healthy controls, but this difference did not withstand correction for multiple comparisons, see Fig. 4.

Fig. 3. Group comparisons of network z-scores.

Violin plots of significant (FDR-corrected) differences in z-scores of morphometric similarity of two functional networks that differed significantly between the group of healthy controls and the group of individuals with schizophrenia at baseline.

Fig. 4. Cortical maps showing the percentage of individuals with infra- and supra-deviance morphometric similarity per region.

A At baseline and B follow-up. C Group differences in the change in z-scores over time, with light red indicating uncorrected group differences and dark red indicating FDR-corrected group differences. No corrected significant group differences were observed.

The percentage of individuals with infra- or supra-normal deviance per region

The percentage of individuals from the test set with either infra- or supra-normal deviance was below 6% for both the healthy individual and the schizophrenia samples at the baseline and follow-up visits (see Fig. 5A, B). At both timepoints, the percentage of infra-normal regional morphometric similarity z-scores ranged between 0 and 6.0% for individuals with schizophrenia and between 0 and 4.3% for healthy individuals; for supra-normal morphometric similarity z-scores, percentage ranges were 0–5.4% and 0–6.0%, respectively. There were no significant differences between patients and controls in the percentage of participants with infra- or supra-normal regional values at either baseline or follow-up (p > 0.05). At baseline and follow-up, the percentages of individuals with schizophrenia with infra-normal deviance were highest in the superior temporal and superior frontal regions. For both diagnostic groups, the percentages of participants with supra-normal deviance were highest in the occipital lobe and postcentral gyrus (see Fig. 5A, B).

Fig. 5. ‘Raw’ morphometric similarity.

Violin plots of significant (FDR-corrected) differences in z-scores and ‘raw’ morphometric similarity (i.e., traditional values rather than normative modeling-based z-scores) of two functional networks between the group of healthy controls and the group of individuals with schizophrenia. MS, morphometric similarity.

We then assessed differences in longitudinal change in the z-scores for each region between cases and controls, using the z-diff approach. After correction for multiple comparisons, there were no significant differences between diagnostic groups (see Fig. 5C). This indicated that, on average, patients did not show progressive changes of morphometric similarity over time.

Effects of diagnosis and symptom severity on the amount of outlier regions per participant and z-scores

No significant group differences for the average cross-sectional total outlier count and change in total outlier region count over time were found between healthy controls and individuals with schizophrenia (see Supplemental Fig. 4). No significant correlations were observed between total PANSS scores and baseline z-scores (maximum r = 0.14, see Supplemental Fig. 5). In the group of individuals with schizophrenia no significant correlations were found between cross-sectional outlier region count or change in outlier region count over time and IQ and PANSS scores.

Effect of diagnosis on z-scores vs ‘raw’ morphometric similarity

We replicated the finding of lower average deviance morphometric similarity for the DMN for the group of individuals with schizophrenia compared to healthy controls in the analyses using raw values at baseline, albeit with a smaller effect size (d = −0.27, p < 0.01) compared to the normative-modeling based z-scores (see Supplemental Table A and Fig. 5).

Discussion

To the best of our knowledge, this study is the first longitudinal study of morphometric similarity, as well as the first to assess morphometric similarity in a normative modeling framework. We established regional age-dependent normative trajectories for morphometric similarity across the adult age range. Our normative models showed that, overall, mean regional morphometric similarity converged towards zero with increasing age, which is coherent with a prior study¹².

Morphometric similarity is increasingly recognized as a biologically meaningful marker due to its association with underlying microstructural connectivity^37,39. Recent research has demonstrated that morphometric similarity correlates positively with the likelihood of cellular network structures forming axonal connections⁴⁰. This relationship with cellular architecture and axonal pathways enhances the biological relevance of morphometric similarity, positioning it as a potential link between structural deficits, functional impairments, and behavioral symptoms in schizophrenia^9,11,41.

Our cross-sectional findings revealed that, at baseline, individuals diagnosed with schizophrenia exhibited increased morphometric similarity in regions associated with the somatomotor network and decreased morphometric similarity in regions associated with the DMN compared to healthy controls. The reduced morphometric similarity in the DMN is consistent with prior functional connectivity studies reporting general DMN dysfunction in schizophrenia across high-risk, early-onset, and chronic stages of the disorder^42–44. The DMN has been implicated in higher-order cognitive functions such as self-referential thought, social cognition, and introspection, all of which are frequently impaired in schizophrenia⁴⁵. Thus, reductions in DMN morphometric similarity may reflect disruptions in these processes, linking structural abnormalities to behavioral and cognitive deficits in psychiatric conditions such as schizophrenia.

The increased morphometric similarity observed in the somatomotor network represents an underexplored finding. Psychiatric models of schizophrenia have traditionally overlooked the somatomotor network, yet alterations in this network may reflect compensatory mechanisms. For example, individuals with schizophrenia may rely more heavily on somatomotor processing due to dysfunctions in other networks, such as the DMN or executive control networks. Supporting this notion, recent resting-state fMRI studies have highlighted altered somatomotor network connectivity in psychiatric disorders such as schizophrenia, schizoaffective disorder and bipolar disorder, associating it with cognitive impairments, impulsivity, and other psychopathological features⁴⁶. These findings suggest that increased morphometric similarity in the somatomotor network may not merely reflect structural changes but could also have implications for motor behaviors and sensorimotor integration deficits in schizophrenia.

By applying a normative modeling framework, we observed infra-normal and supra-normal deviations of morphometric similarity in a small subset of individuals with schizophrenia (<6%), similar to the variability seen in healthy controls and patients^8,37,47. This suggests that, while morphometric similarity abnormalities exist, they largely fall within the spectrum of normative variation. However, previous studies have found significant differences in extreme deviation scores between cases and controls when summing over regions⁴⁷. These studies assessed gray matter volume, which, together with regional cortical thickness changes or functional connectivity alterations, may offer greater sensitivity to disease effects⁸.

Longitudinal analyses revealed no significant differences in the change of z-scores over time between individuals with schizophrenia and healthy controls, indicating that schizophrenia does not involve an accelerated accumulation of structural abnormalities in morphometric similarity over time. This stands in contrast to Alzheimer’s disease, where increased outlier counts for cortical thickness have been shown to track neurodegeneration over time⁴⁸. For schizophrenia, this stability may reflect a plateau in morphometric similarity changes after the early stages of illness or the influence of treatment and environmental factors in mitigating progressive changes in morphometric similarity.” This would be in line with a recent ten-year longitudinal normative modeling study showing that cortical thinning was present early on in schizophrenia but thereafter attenuated over time⁴⁹.

Despite the lack of significant longitudinal change in outlier counts, the ability of normative modeling to detect deviations in morphometric similarity highlights its potential utility. Normative modeling provides a powerful framework for understanding individual-level deviations in brain structure, which can be linked to behavioral outcomes, treatment responses, and genetic predispositions. For instance, integrating morphometric similarity with behavioral data could help clarify the relationship between structural deviations and specific cognitive or clinical profiles in schizophrenia⁴¹. Additionally, exploring genetic correlates of morphometric similarity deviations may yield insights into the heritable aspects of structural connectivity and its disruption in schizophrenia¹¹.

Z-scores of regional deviations were unrelated to symptom severity and cognition. Furthermore, results must be interpreted with caution as the explained variance differed among regions, with some regions showing low variance, suggesting that age-dependency differs considerably among regions. Thus, while morphometric similarity has shown promise as a phenotype for identifying macroscopic brain abnormalities, our findings suggest that its utility in schizophrenia may be nuanced. Furthermore, the explained variance differed among regions, with some regions showing low variance, suggesting that age-dependency differs considerably among regions. Regional cortical thickness changes or functional connectivity alterations assessed through normative modeling may offer greater sensitivity to disease effects⁸. Nonetheless, morphometric similarity remains valuable for understanding the underlying architecture of brain networks and their relevance to psychiatric conditions. Normative models may be better able to detect diagnosis-related effects compared to raw, i.e., traditional, data models because normative modeling allows for the consideration of numerous sources of variance. Some of these sources may not carry clinical significance (e.g., scanner variability, Euler number), while others simultaneously encapsulate clinically relevant information within the framework of a reference cohort. Our supplemental results are in line with this, i.e., our study demonstrated increased statistical significance using normative models when compared to raw data models. Thus, normative modeling may possess the capacity to capture overarching population patterns, discern clinical disparities between groups, and retain the ability to investigate individual differences²⁷. Future research integrating normative modeling with multimodal data—encompassing behavior, genetics, and functional connectivity—may provide a more comprehensive understanding of the pathophysiology of schizophrenia and its individual variability.

This study has limitations. For clinical translation, progress in normative modeling stands as a crucial prerequisite, underscoring the necessity for a broadened diversification of datasets. While the present study benefited from a substantial training set, larger and more heterogeneous datasets, incorporating not solely European ancestry data, are imperative for a more accurate representation of the underlying population⁵⁰. An alternative strategy for normative modeling would be to include non-healthy individuals in the training set. This may increase the generalizability of the model. However, we followed customary practices by training the model on healthy controls only^7,51. The normative modeling framework employed herein treats each region as independent, notwithstanding potential correlations among z-scores from neighboring regions. To mitigate this challenge, one plausible strategy involves implementing data reduction techniques, such as principal component analysis applied to the z-scores⁵¹. In addition, by definition, normative models can only detect deviations from the norm but not whether these are specific to a particular condition, thereby limiting their usefulness as a biomarker indicator. Of course, the normative modeling could be made part of a two-step procedure, where, in the second step, the z-scores and diagnostic labels are used as inputs for a classification algorithm. The classifier could be trained to discriminate between different disorders and would also indicate which regions are most important for this. We used the seven network solution as put forward by ref. ²⁸ to replicate the findings by ref. ¹¹. It must be recognized that our findings and those by ref. ¹¹ only apply to this network solution and that alternative network solutions may provide different results. While our sample size of individuals with schizophrenia was comparable to previous normative modeling studies, larger (multicenter) clinical samples may enable the identification of distinct clusters of patients exhibiting significant deviance.

In conclusion, the current study used normative modeling to show decreased morphometric similarity of the DMN in a group of individuals with chronic schizophrenia, replicating previous findings in groups of individuals with first-episode psychosis. Using a longitudinal design, we showed that the change in the total number of outlier regions over time was not different between cases and controls. Assessment of change in regional z-scores over time did not reveal diagnostic differences, indicating that morphometric similarity abnormalities were not progressive over time. Normative modeling demonstrated that significant cross-sectional reductions and longitudinal changes of morphometric similarity are only present in a minority of individuals with schizophrenia. Our study provides a layout for future studies using normative modeling, including cross-sectional and longitudinal neuroimaging phenotypes.

Author contributions

Substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work: Joost Janssen, Ana Guil Gallego, Hugo G. Schnack, and Covadonga Martínez Díaz-Caneja. Drafting the work or revising it critically for important intellectual content: Joost Janssen, Ana Guil Gallego, Hugo G. Schnack, Pedro Macias Gordaliza, Neeltje van Haren, and Celso Arango. Final approval of the version to be published: Joost Janssen, Ana Guil Gallego, Covadonga Martínez Díaz-Caneja, Noemi Gonzalez Lois, Niels Janssen, Javier González-Peñas, Pedro Macias Gordaliza, Elizabeth Buimer, Neeltje van Haren, Celso Arango, René Kahn, Hilleke E. Hulshoff Pol, and Hugo G. Schnack. Agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved: Joost Janssen, Ana Guil Gallego, and Hugo G. Schnack.

Data availability

The study IDs of the included participants from the ten publicly available datasets, the five regional metrics and regional morphometric similarity from the ten publicly available datasets, the overlap between the DKT atlas and the seven functional networks, the normative model plots with percentile curves, the Q–Q plots, the information and usage instructions about the docker we created for normative modeling are all available at https://github.com/iamjoostjanssen/NormModel_MorphoSim_SZ. The data from the clinical dataset (Utrecht) cannot be made publicly available. The publicly available datasets are accessible from the following repositories: Aomic (id1000, piop1 and piop2) is available at https://openneuro.org/datasets/ds003097, https://openneuro.org/datasets/ds002785 and https://openneuro.org/datasets/ds002790, camcan is available at https://camcan-archive.mrc-cbu.cam.ac.uk, dlbs is available at https://fcon-1000.projects.nitrc.org/indi/retro/dlbs, ixi is available at http://brain-development.org/ixidataset, narratives is available at https://openneuro.org/datasets/ds002345, oasis3 is available at www.oasis-brains.org, rockland is available at http://fcon-1000.projects.nitrc.org/indi/enhanced and sald is available at http://fcon-1000.projects.nitrc.org/indi/retro/sald.

Code availability

All code used to perform the analyses can be found at https://github.com/iamjoostjanssen/NormModel_MorphoSim_SZ.

Competing interests

Dr. Díaz-Caneja has received honoraria from Angelini and Viatris. Dr. Arango has been a consultant to or has received honoraria or grants from Acadia, Angelini, Gedeon Richter, Janssen-Cilag, Lundbeck, Otsuka, Roche, Sage, Servier, Shire, Schering-Plough, Sumitomo Dainippon Pharma, Sunovion, and Takeda. Dr. Cahn has received unrestricted research grants from or served as an independent symposium speaker or consultant for Eli Lilly, Bristol-Myers Squibb, Lundbeck, Sanofi-Aventis, Janssen-Cilag, AstraZeneca, and Schering-Plough. The other authors report no financial relationships with commercial interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41537-025-00612-2.