Instability in Patient Clustering: A Multiverse Analysis of Unsupervised Clustering in the CENTER-TBI cohort

• The acknowledgment names the CENTER-TBI participants and investigators.Source: the SOPRANI collaborators + · p. 1
• Two authors are marked as having contributed equally.Source: the SOPRANI collaborators + · p. 1

• Patients with similar GCS scores can have divergent outcomes, and GCS alone does not capture TBI pathophysiology.The text therefore describes a need for more comprehensive classification.Source: §1 · p. 2
• Clustering choices across preprocessing, features, algorithms, and tuning create many plausible analytic paths that may yield different conclusions.The introduction also questions clustering for risk stratification because it does not incorporate feature or cluster relationships with clinical outcomes.Source: §1 · p. 2
• The study uses a multiverse analysis to test how choices of algorithm, distance metric, and cluster-number criterion affect solutions in 4,509 CENTER-TBI patients.It follows earlier preprocessing and feature selection while systematically varying those clustering choices.Source: §1 · p. 2

2 The CENTER-TBI data

• CENTER-TBI is a multicenter prospective observational TBI cohort spanning the full spectrum of injury severity.Approximately 4,500 patients were enrolled across 63 centers in 18 countries from 2014 to 2017.Source: §2 · p. 3
• The analysis used all 4,509 available patients, seven baseline characteristics, and twelve imaging features, with 6-month GOSE dichotomized at 5.Approximately 25% of patients had an unfavourable outcome.Source: §2 · p. 3

2.1 Data pre-processing

• Preprocessing used single imputation, reduced the twelve imaging features to four principal components, and standardized numerical features.Categorical features were integer-encoded; the authors note that this can make variables with many categories exert greater influence and is unsuitable for nominal features.Source: §2.1 · p. 4

3 Clustering Framework

• The multiverse varies three pipeline choices: clustering algorithm, distance metric, and method for selecting the number of clusters.Source: §3 · p. 4

3.1 Clustering Strategies

• The study compares k-medoids, agglomerative, and spectral clustering as representatives of centroid-based, hierarchical, and graph-based families.Each requires the number of clusters to be specified in advance.Source: §3.1 · p. 4

3.1.1 Centroid based clustering

• K-medoids assigns observations to actual data-point medoids while minimizing total within-cluster dissimilarity.The implementation alternates assignments and medoid updates using a precomputed dissimilarity metric.Source: §3.1.1 · pp. 4–5

3.1.2 Hierarchical clustering

• Agglomerative clustering builds a dendrogram by repeatedly merging the closest clusters; this analysis uses average linkage.Average linkage uses average pairwise dissimilarity and accommodates arbitrary dissimilarity matrices.Source: §3.1.2 · p. 5

3.1.3 Graph-based clustering

• Spectral clustering constructs a patient similarity graph and groups observations with strong within-cluster and weak between-cluster connections.The method can capture more complex, nonconvex structures but is sensitive to graph construction.Source: §3.1.3 · pp. 5–6

3.2 Distance Measures

• Euclidean distance is used for continuous variables, while Gower’s distance supports mixed continuous, ordinal, and nominal features.Euclidean distance is scale-sensitive, so continuous variables were standardized; Gower’s distance averages variable-specific dissimilarities and treats categorical matches as same or different.Source: §3.2 · pp. 6–7

3.3 Choosing the number of clusters

• The silhouette criterion selects the candidate cluster count with the highest average silhouette, whereas the gap statistic compares observed dispersion with a reference distribution.Silhouette cannot select a one-cluster solution; the gap statistic can, using the smallest K within one standard error of the gap at K+1.Source: §3.3 · pp. 7–8

4 Evaluation of clustering solutions

• Without true labels, clustering quality is not directly assessable, so evaluation relies on indirect approaches such as stability analysis.Source: §4 · p. 8

4.1 Clustering Stability

• Stability was assessed by comparing cluster assignments across 200 bootstrap samples with adjusted Rand indices (ARI), averaged over all sample pairs.ARI adjusts pairwise agreement for the agreement expected under random cluster assignment.Source: §4.1 · p. 9

4.2 Clustering Agreement

• UpSet plots show exclusive intersections of patient pairs grouped together by subsets of methods, while ARI quantifies pairwise agreement across clustering solutions.A large exclusive intersection indicates greater agreement within that method subset.Source: §4.2 · pp. 9–10

4.3 Predictive Value of the Identified Clusters

• Clinical discrimination was assessed for 6-month GOSE using cluster outcome proportions and optimism-corrected AUCs, with logistic regression as a reference.The authors caution that outcome discrimination is not a clustering-validity test; clusters may capture structure not reflected in the tested outcomes.Source: §4.3 · p. 10

5 Clustering of the CENTER-TBI data

• Optimal cluster counts ranged from one to 25, and the largest cluster ranged from 869 to all 4,509 patients; four of six algorithm-distance combinations selected one cluster with the gap statistic.Spectral clustering with Euclidean distance and silhouette selection produced 25 clusters, including a cluster of only 10 patients.Source: §5 · p. 11

5.1 Agreement between different clustering strategies

• With Gower’s distance, all three algorithms agreed on 20.4% of patient pairs; with Euclidean distance, agreement was 5.3%.Agglomerative and spectral clustering grouped 47.6% of pairs together with Gower’s distance versus 15.8% with Euclidean distance.Source: §5.1 · p. 11

5.2 Stability of the clustering solutions

• Bootstrap solutions were heterogeneous for most strategies, with selected cluster counts ranging from two to 25; KM-Gow-Gap’s original six-cluster solution never recurred.ARI also varied: SP-Gow-Sil averaged 0.95, while AG-Gow-Sil averaged 0.69 despite both yielding two clusters.Source: §5.2 · p. 12
• ARI = 1 for Euclidean gap-statistic methods reflected frequent single-cluster solutions, whereas SP-Gow-Sil maintained a two-cluster structure at ARI = 0.95.AG-Eucl-Sil’s ARI was 0.88, but its three-cluster partition was highly imbalanced.Source: §5.2 · p. 12

5.3 Discriminative ability of the clustering solutions

• None of the clustering strategies yielded consistently strong prognostic performance; logistic regression achieved an optimism-corrected AUC of 0.87, and a GCS-only model reached 0.81, exceeding all clustering approaches.Source: §5.3 · pp. 12–13

6 Discussion

• Clustering strategies differed substantially in cluster counts, means, and sizes, showed little agreement on patient assignments, and were unstable across bootstrap samples.Euclidean and Gower distances also yielded different apparent subgroup structures.Source: §6 · p. 13
• The 12 strategies showed inconsistent and often limited discriminatory ability, clearly inferior to logistic regression, with some solutions producing very wide AUC confidence intervals.Source: §6 · p. 13
• Prior work also found clustering sensitive to analytic choices, while the authors suggest supervised learning or outcome-integrating models may better suit risk stratification.They note that resampling stability can vary as much as internal fit indices.Source: §6 · pp. 13–14
• The multiverse varied three clustering decisions and assessed stability within and between strategies, evaluating both solution robustness and sensitivity to analytic choices.Source: §6 · p. 14
• The analysis used one dataset and did not vary preprocessing; alternative imputation, feature selection, or imaging reduction could further affect results.The authors also identify a mismatch between unsupervised optimization criteria and clinical risk stratification objectives.Source: §6 · p. 14
• The authors conclude that analytic flexibility can produce divergent results and recommend treating clustering as exploratory rather than using it for important classifications or care decisions.Source: §6 · p. 14

Tables

• 50 [30 - 66] is the reported age median [IQR].Source: Tables · p. 25
• Road traffic accidents accounted for 1,682 (39%), while violence or suicide accounted for 293 (6.7%).Source: Tables · p. 25
• 15 is the reported GCS sum score median [IQR], while GCS Motor is 6.Source: Tables · p. 25
• Both pupils were reactive in 3,802 (90%) of cases; pre-admission hypoxia and hypotension were reported in 299 (7.0%) and 297 (6.9%).Source: Tables · p. 25
• Traumatic SAH was reported in 1,469 (34%), epidural hematoma in 349 (8.0%), and skull fracture in 1,156 (27%).Source: Tables · p. 25
• Table 2 reports average adjusted and unadjusted Rand indices across bootstrap pairs, alongside summaries of cluster counts and sizes.Source: Table 2 · p. 26

Figures

• Figure 1 displays cluster sizes and counts across methods, with identified cluster counts ranging from 1 to 25.Colours are illustrative; matching colours across methods do not indicate the same patients.Source: Figure 1 · p. 27
• Figure 2 uses rows for clustering strategies and vertical bars for exclusive intersections of methods grouping patient pairs together.Percentage labels show the proportion of patient pairs grouped together by the selected methods; horizontal bars show each method’s total.Source: Figure 2 · p. 28
• Figure 3 presents Rand indices in the matrix’s lower triangle and adjusted Rand indices in its upper triangle.Source: Figure 3 · p. 29
• Figure 4 shows the optimal cluster count across bootstrap samples, with a red dotted line marking the original-dataset count.Source: Figure 4 · p. 30
• Figure 5 compares optimism-corrected AUC values across methods, with error bars showing 95% confidence intervals.Source: Figure 5 · p. 31

Supplementary Tables

• Supplementary Table 1 reports results for a single run on the original dataset for each clustering algorithm.Source: Table 1 · pp. 31–32
• The supplied entries report four values each: AG-Eucl-Gap has 1, 4,509, 4,509, and 15.99, while AG-Eucl-Sil has 3, 20, 3,679, and 0.12.Source: Supplementary Tables · p. 31
• Computation time was measured on a MacBook Air with an Apple M3 chip and 8GB RAM; KM used alternate initialization, AG average linkage, and SP three degrees of freedom.Source: Supplementary Tables · p. 32
• Supplementary Table 2 contains bootstrap AUC results.Source: Table 2 · p. 32
• The abbreviations define AG, KM, SP, Eucl, Gow, Sil, Gap, Log-Reg, and GCS.Source: Supplementary Tables · p. 32

Supplementary Figures

• Supplementary Figure 1 reports bootstrap AUCs for 200 bootstrap samples.Source: Figure 1 · p. 33
• The reported AUCs represent discrimination of clustering solutions obtained in bootstrap samples and applied to the original data.Source: Figure 1 · p. 33
• The figure’s stated scope is bootstrap AUCs; the passage does not give numerical values or comparisons.Source: Figure 1 · p. 33