Supplementary Table 1: Distribution of per-participant rib-side counts among the candidate cohort. The inclusion criterion (Methods §2.5) requires exactly 24 rib sides; participants with different counts are excluded. Low counts (≤ 23) are consistent with transitional thoracolumbar vertebrae, missing segmentations or merged segmentations; high counts (≥ 25) with supernumerary cervical or lumbar ribs.
Rib sides per participant
n participants
%
8
1
0.0%
12
1
0.0%
17
1
0.0%
18
7
0.0%
19
6
0.0%
20
38
0.1%
21
28
0.1%
22
551
1.8%
23
795
2.6%
24
27,502
91.0%
25
693
2.3%
26
595
2.0%
S1.2 Per-variable missingness across the joined cohort
Supplementary Figure 1: Missingness across baseline metadata variables. Computed on the inner-joined cohort (n = 30,218) prior to quality-control exclusions.
S1.3 Predictor collinearity
Supplementary Figure 2: Pairwise Pearson correlations between continuous metadata predictors. Body mass, BMI, and body-fat percentage cluster tightly, motivating the multivariable adjusted regression design of Methods §2.8.2 rather than relying on bivariate associations.
S1.4 Descriptor collinearity
Supplementary Figure 3: Pairwise Pearson correlations between per-rib shape descriptors. Computed on participant-level per-rib means. Voxel volume was dropped at the analysis stage (Methods §2.6) due to conceptual identity (and perfect collinearity) with mesh volume.
S1.5 Distribution and normality of shape descriptors
Supplementary Figure 4: Per-descriptor histograms with Q-Q overlays. Q-Q axes are z-standardised so that the y = x reference line denotes exact normality.
Supplementary Figure 5: Shapiro–Wilk normality summary across shape descriptors.
S1.6 Predictor distributions by sex
Supplementary Figure 6: Distribution of each continuous metadata predictor stratified by biological sex. Companion view to Table 1.
Supplementary Figure 7: Smoking-status composition stratified by biological sex. Companion view to Table 1.
S2 Shape-model variance and convergence
S2.1 Scree plot
Supplementary Figure 8: Per-mode and cumulative explained variance. Variance retained at the truncation threshold (95%) is annotated; 28 modes were carried forward into all downstream PC-score analyses.
S2.2 Generalized Procrustes Analysis convergence
Supplementary Figure 9: GPA convergence trace. Mean-shape change per iteration of the Generalized Procrustes Analysis described in Methods §2.7.3, with the convergence threshold marked.
S3 Descriptor-level associations
S3.1 Adjusted OLS effect maps
(a) Panel A – standardised β.
(b) Panel B – Frisch–Waugh–Lovell partial R².
Supplementary Figure 10: Adjusted (multivariable) OLS effect maps.(A) Standardised β and (B) Frisch–Waugh–Lovell partial R² per (shape descriptor × predictor) pair from the single adjusted model (Methods §2.8.2) – the mutually-adjusted counterpart to the main-text targeted maps. FDR-masked at q ≥ 0.05; cluster-robust standard errors at the participant level.
S3.2 Adjusted OLS standardised β forest plot
Supplementary Figure 11: Adjusted OLS standardised β forest plot. 95% confidence intervals on the standardised slope per (predictor, descriptor) pair from the adjusted model.
S3.3 Unadjusted (marginal) standardised β heatmap
Supplementary Figure 12: Unadjusted (marginal) standardised β heatmap. Per-predictor marginal slope for each (shape descriptor × predictor) pair, including BMI (unadjusted layer only) – the total-association counterpart to the adjusted and targeted maps.
S3.4 Per-descriptor rib-position maps
Supplementary Figure 13: Mean rib length by anatomical level and side.
S4 PC score associations
S4.1 Adjusted PC association map
Supplementary Figure 14: Adjusted (multivariable) associations with the leading PC scores. Standardised β from the per-PC adjusted (HC3) OLS against the seven covariates – the mutually-adjusted counterpart to the main-text targeted map.
S4.2 PC β-vector field
Supplementary Figure 15: Per-PC β-vector field. Each predictor’s standardised β as an arrow in PC space; solid arrows are the unadjusted (marginal) effect, dashed arrows the adjusted effect. Complements the magnitude ranking of the heatmaps with effect direction.
S4.3 Marginal and adjusted PC sex pair-plots
Supplementary Figure 16: PC score pair-plot by sex (marginal). The unadjusted by-sex pair-plot; companion to the targeted view in the main text.
Supplementary Figure 17: PC score pair-plot by sex (adjusted). PC scores residualised on all covariates except sex; the PC1 separation shrinks relative to the marginal and targeted views, visualising the body-composition mediation of the sex difference.
S4.4 PC scores pair-plot by body fat
Supplementary Figure 18: PC score pair-plot coloured by body-fat percentage. Off-diagonal bins coloured by mean body-fat percentage, showing the body-composition gradient aligning with the leading modes.
S4.5 Per-rib PC loadings
Supplementary Figure 19: Per-rib loadings of the leading principal components. Loadings of each PC onto each of the 24 rib positions.
S4.6 PC scores pair-plot by smoking status
Supplementary Figure 20: PC score pair-plot stratified by smoking status. Companion view to the by-sex pair-plot in the main text. Smoking is shown here as the descriptive three-level variable (Never / Ex-smoker / Current); the association models use the binary ever-smoker contrast. Marginal density panels show the per-PC distribution per smoking-status group.
S5 Anatomical interpretation of principal modes
S5.1 PC-anchored anatomical maps (PC4 onwards)
Supplementary Figure 21: Per-PC anatomical cross-walk (PC4 onwards). Standardised slope of every (rib position × shape descriptor) pair on each PC score (cohort-z-scored), rendered as 24-row × 14-column heatmaps. Print shows PC4–PC7; the interactive supplement browses all 28 modes. PC1–PC3 are in the main-text anatomical maps.
S5.2 Descriptor-anchored anatomical maps
Supplementary Figure 22: Per-descriptor anatomical cross-walk. Standardised slope of one shape descriptor at every rib position on each PC score, one panel per descriptor. Print shows all 14 descriptors; the interactive supplement browses the same set.