Using normative models pre-trained on cross-sectional data to evaluate intra-individual longitudinal changes in neuroimaging data

Abstract

Longitudinal neuroimaging studies offer valuable insight into brain development, ageing, and disease progression over time. However, prevailing analytical approaches rooted in our understanding of population variation are primarily tailored for cross-sectional studies. To fully leverage the potential of longitudinal neuroimaging, we need methodologies that account for the complex interplay between population variation and individual dynamics. We extend the normative modelling framework, which evaluates an individual's position relative to population standards, to assess an individual's longitudinal change compared to the population's standard dynamics. Using normative models pre-trained on over 58,000 individuals, we introduce a quantitative metric termed 'z-diff' score, which quantifies a temporal change in individuals compared to a population standard. This approach offers advantages in flexibility in dataset size and ease of implementation. We applied this framework to a longitudinal dataset of 98 patients with early-stage schizophrenia who underwent MRI examinations shortly after diagnosis and 1 year later. Compared to cross-sectional analyses, showing global thinning of grey matter at the first visit, our method revealed a significant normalisation of grey matter thickness in the frontal lobe over time-an effect undetected by traditional longitudinal methods. Overall, our framework presents a flexible and effective methodology for analysing longitudinal neuroimaging data, providing insights into the progression of a disease that would otherwise be missed when using more traditional approaches.

Keywords: MRI; human; neuroimaging; neuroscience; normative modelling; psychosis; schizophrenia.

Figure 1.. Visualisations of the core assumptions of normative modelling.

(A) The parameters of the fitted normative model are independent of the time of sampling. (B) People of the same age are comparable irrespective of their year of birth (datasets sampled at different times can be combined).

Figure 2.. Simulated detection rate of a true disruption Δ for various values of autocorrelation ρ (individual subplots) comparing the performance of our z-diff method against the naïve subtraction of z-scores.

The right column highlights the false-positive rate across various degrees of autocorrelation for the two approaches. We use ${\displaystyle {\sigma }^2=1}$ and θ = 0.05.

Figure 3.. The overview of the analytical pipeline for our schizophrenia patients: First, data are preprocessed using FreeSurfer’s longitudinal pipeline.

Subsequently, the pre-trained models are adjusted to a local sample of healthy controls. The site-specific measurement noise variance ${\displaystyle {\sigma }_{\xi }^2}$ in healthy subjects is estimated using held-out controls, and finally, the z-diff score is computed.

Figure 4.. The effect of preprocessing across all subjects and image-derived phenotypes (IDPs).

(A) Cross-sectional preprocessing: Heatmap of the difference of the original ${\displaystyle z}$-scores (${\displaystyle z^{(2)}-z^{(1)}}$) on held-out controls. (B) Longitudinal preprocessing: Heatmap of the difference of the original ${\displaystyle z}$-scores (${\displaystyle z^{(2)}-z^{(1)}}$) on held-out controls. (C) Histogram of the average (${\displaystyle z}$) across all IDPs stratified by health status and preprocessing. (D) Histogram of the average (${\displaystyle z^{(2)}-z^{(1)}}$) of each subject stratified by health status and preprocessing.

Figure 5.. Cross-sectional results for each visit separately: p-Values of Mann-Whitney U test between patients and held-out controls surviving Benjamini-Hochberg correction.

The sign indicates the direction of change (negative means lower thickness in patients).

Figure 6.. Regions significantly changed between the visits: Map of regions significantly changed between the two visits (centre).

Each region is described using a scatter plot of ${\displaystyle z}$-scores across all patients for both visits (the x-axis describes age and the y-axis depicts the ${\displaystyle z}$-score. Blue dots represent the first and pink dots represent the second visit). The grey dashed line highlights ${\displaystyle z}$ = 0. Histograms in the golden circles depict the distribution of the z-diff score.

Figure 7.. Results of the PCA.

(A) Scree plot of the explained variance of PCA components. (B) Scatter plot of change in the Global Assessment of Functioning (GAF) scale vs. the change in the Positive and Negative Syndrome Scale (PANSS) scale. (C, left) Scatter plot of the first PCA component and difference in the GAF scale. (C, right) Heatmap of PCA loadings for the first component. (D, left) Scatter plot of the second PCA component and difference in the PANSS scale. (D, right) A heatmap of PCA loadings for the second component. (E) Average z-diff score.

Appendix 2—figure 1.. ρ^ estimates derived from the data.

Appendix 3—figure 1.. Probability of detecting a true disruption Δ for various values of autocorrelation ρ (rows) and variances σ2 (columns) comparing the performance of our z-diff method against the naïve subtraction of z-scores.

We use θ = 0.05.

Appendix 4—figure 1.. Quality of fit as measured by Rho for the first and the second visit.

Appendix 5—figure 1.. Regions significantly changed between the visits (longitudinal preprocessing): Map of regions significantly changed between the two visits (centre).

Each region is described using a scatter plot of z-diff across all patients for both visits (the x-axis describes age and the y-axis depicts the z-diff. Blue dots represent individual patients and the pink line shows a trend of z-diff change). The grey dashed line highlights z=0. Histograms in the golden circles depict the distribution of the z-diff score.

Appendix 5—figure 2.. Regions significantly changed between the visits (cross-sectional preprocessing): Map of regions significantly changed between the two visits (centre).

Each region is described using a scatter plot of z-diff scores across all patients for both visits (the x-axis describes age and the y-axis depicts the z-diff score). The grey dashed line highlights ${\displaystyle z}$=0. Histograms in the golden circles depict the distribution of the z-diff score.

Appendix 5—figure 3.. Raw changes in grey matter thickness: Each significantly changed region is presented twice, once as a scatter plot containing the original grey matter thickness for both visits (left); females are plotted in pink, males in blue.

The figure on the right depicts visit 2 minus visit 1 in raw thicknesses (separately for females—pink, and males—blue).