TV‐L1 Ordinal Logistic Regression Reveals New Morphometric Patterns Related to Parkinsonian Symptom Severity: An ENIGMA‐PD study

Background Parkinson’s disease (PD) is heterogeneous, both phenotypically and in terms of temporal progression. The Hoehn and Yahr (HY) scale is a well‐established PD staging approach, and identifies 5 stages of the disease. Morphometric effects in deep gray matter regions of the brain associated with HY stages are complex; a recent large‐scale ENIGMA‐PD study showed higher local subcortical volumes in early HY stages relative to controls, followed by a precipitous decrease after stage 2 [1]. This finding motivates a closer look at fine‐level morphometry beyond gross volume measures. Here, we developed and applied a novel machine learning algorithm to reveal the subcortical shape signatures of HY staging. Method We computed shape features in 7 bilateral subcortical regions [2] based on T1‐weighted MRI data from 2,322 PD subjects and 1,207 controls from 20 ENIGMA‐PD cohorts (HY stages in Table 1). We developed a sparse, spatially coherent (total variation/TV‐L1) ordinal linear logistic classifier [3] to predict HY stages with a single linear model. We applied the model to vertex‐wise medial thickness features. We optimized regularization parameters for balanced recall (sensitivity) and precision using a 4‐fold cross‐validation grid search. Very low numbers of HY4 and HY5 samples necessitated merging stages 3‐5 into one category. For comparison, we also trained 4 binary TV‐L1 logit models on the same features [4], discriminating (1) PD‐Control; (2) HY1‐HY2; (3) HY1‐HY345; (4) HY2‐HY345, using ROC area‐under‐the‐curve (AUC) evaluation. Result Across‐stage mean out‐of‐sample precision and recall were 0.43, and 0.393, respectively (chance=0.33). Table 2 shows the confusion matrix and precision/recall for each HY stage. All models’ linear coefficient maps are displayed in Figures 1,2. Binary classification ROC‐AUC was 0.66 for PD‐Control, and ranged from 0.62 to 0.73 for HY prediction (Figure 2). Conclusion We developed an ordit machine learning model for morphometric shape‐based ordinal classification of disease stages, training it for Parkinson’s Disease Hoehn and Yahr stage prediction on a large MRI collection. Performance was substantially above chance. Model weight maps indicate early increased thalamic thickness, followed by a complex thinning pattern associated with later HY stages.