**3. Results**

For normal scapulae, simple linear regressions showed that AAx was the acromion landmark coordinate most strongly and significantly associated with the GRA (R<sup>2</sup> = 0.480, *p* < 0.0001), followed by ACx (R<sup>2</sup> = 0.310, *p* < 0.0001) (Table 1). Stepwise multiple linear

regressions between the six acromion landmark coordinates examined here (AAx, AAy, AAz; and ACx, ACy ACz) and the GRA confirmed the importance of AAx, and the slight improvement in the model by combining AAx with AAz and ACx (R<sup>2</sup> = 0.530, *p* < 0.0001). Using this existing correlation, we were able to predict the measured GRA with an error (RMSE) of 3.6 degrees.

**Table 1.** Root mean square errors (RMSE), coefficients of determination (R2), and *p*-values of simple and stepwise multiple linear regressions between several acromion landmark coordinates and angles and the glenoid retroversion angle (GRA), for normal scapulae.


Of the four acromion angles examined here (APA, ATA, ALA, and AXA in Figure 1), the APA was the most strongly and significantly associated with the GRA (R<sup>2</sup> = 0.482, *p* < 0.0001). Combining the APA with the ALA and ATA helped slightly improve the correlation, while adding the AXA did not. The APA was very strongly and significantly correlated with AAx (R<sup>2</sup> = 1.00, *p* < 0.0001) (Supplementary Material). Because of this, among the 10 morphological acromion parameters (6 landmark coordinates and 4 angles), we then focused the analysis between the acromion morphology and glenoid retroversion to the APA versus GRA (Figure 2), which can be written as follows: GRA = 1.9 × APA − 25.2 (with GRA and APA in degrees). A 1-degree increase in the APA corresponded approximately to a 2-degree increase in the GRA.

For osteoarthritic scapulae, we also observed a significant positive correlation between the APA and GRA (R<sup>2</sup> = 0.197, *p* < 0.0001), suggesting that a higher APA was associated with an increased GRA (Figure 2). While both the GRA and APA increased with the (alphabetical) progression of the updated Walch class, the increase in APA was not proportional to that of the GRA (Table 2, Figure 3). The ROC curve analysis predicted a critical GRA value of 8 degrees (AUC = 0.78) and a critical APA value of 15 degrees to best identify high GRA (>8 degrees) from low GRA ( ≤8 degrees).

**Figure 2.** Measured acromion posterior angle (APA, *x* axis) vs. glenoid retroversion angle (GRA, *y* axis) for normal scapulae (black dots) and primary osteoarthritic scapulae (white dots). The continuous line represents the linear regression between the APA and GRA for normal scapulae, with its 95% confidence interval (dotted lines). The grey-shaded area (top right corner) shows the number of osteoarthritic scapulae with critical angle values (dashed lines) of APA > 15 degrees and GRA > 8 degrees.

**Table 2.** Glenoid retroversion angle (GRA; mean ± SD) and acromion posterior angle (APA; mean ± SD) for normal and osteoarthritic scapulae, subclassified according to the updated Walch classification.


Data for the six acromion landmarks, four acromion angles, and the GRA all followed a normal distribution. Of the six acromion landmarks, AAx, AAy, ACx, and ACy differed significantly between normal and osteoarthritic scapulae (*p* ≤ 0.03), but with a moderateto-small effect size (Cohen's d ≤ 0.64). Among the four acromion angles, only APA and ALA were significantly different between normal and osteoarthritic scapulae (*p* ≤ 0.04), but again with a moderate to small effect size (d ≤ 0.43). GRA was significantly more retroverted in osteoarthritic (11.1 degrees) than in normal scapulae (3.0 degrees) (*p* < 0.001). There were no significant differences in age between osteoarthritic scapulae having an APA above or below 15 degrees (*p* = 0.38). Regressions between GRA and APA were slightly different between males and females but remained within the 95% confidence intervals (CIs) of the entire datasets.

**Figure 3.** Measured acromion posterior angle (APA, *x* axis) vs. glenoid retroversion angle (GRA, *y* axis) for normal scapulae (black dots) and primary osteoarthritic scapulae subclassified according to the updated Walch classification (yellow, orange, red, and purple dots). The continuous line represents the linear regression between the APA and GRA for normal scapulae, with its 95% confidence interval (dotted lines). The grey-shaded area (top right corner) shows the number of osteoarthritic scapulae with critical angle values (dashed lines) of APA > 15 degrees and GRA > 8 degrees.
