A retrospective study was conducted at Motol University Hospital, Czechia, involving patients who had previously undergone total glenoid arthroplasty. The analysis focused exclusively on the SMR Reverse Shoulder System implants (Lima Corporate, San Daniele del Friuli, Italy; [6]). The study inclusion criteria encompassed the following parameters: unilateral RTSA, documented information regarding implant size and type, recorded patient height and weight, availability of digital anteroposterior (AP) radiographs of the shoulder in a neutral position from the hospital archives, and clear visibility of the humeral and glenoid components of the RTSA. A total of 98 digital AP radiographs from a consecutive cohort of 98 patients, taken during the first follow-up after glenoid arthroplasty, were obtained as DICOM files. Three patients were excluded from the study due to evident arm rotation in the radiographic images, and one patient was excluded due to missing information on the radiographic setup in the DICOM file. The final cohort comprised 94 patients, including 62 female and 32 male patients. The average age of patients at the time of surgery was 69.4 years (±8.7 years, ranging from 38 to 85 years). The data were collected during the period 2014–2017, with the actual study being conducted in April 2023. This noninterventional retrospective study based on an anonymized dataset was approved by the ethics committee of Motol University Hospital (reference no. EK-1204/18). The authors did not have access to any information that could potentially identify individual participants either during or after the process of data collection.

For reference, the diameter of the proximal part of the reverse humeral body (component no. 1352.20.010) was used (Fig. 1). This component possesses a cylindrical shape, and its diameter remains consistent regardless of internal or external rotation. The cylindrical geometry was confirmed by fitting a cylinder to a 3D scan of a nonimplanted specimen using an optical coordinate measuring system (Omnilux, RedLux Ltd., Romsey, UK). The physical diameter of 36.6 mm was obtained from the cylindrical fit and verified by measuring the component using a digital caliper (Mahr GmbH, Göttingen, Germany). The component dimension on the radiographs was estimated from the DICOM files using the Fiji platform for biological-image analysis [12]. Specifically, two points on each side of the cylindrical portion of the component were defined and used to construct the lateral and medial edges of the component. A custom MATLAB script (MATLAB R2020b, The MathWorks, Inc., Natick, MA, USA) was developed to calculate the diameter of the component as the mean perpendicular distance between the lines measured at the defined points (Fig. 1). A single observer (A. K.) analyzed all radiographs. To assess the reliability of the method for estimating radiographic magnification, five independent and blinded observers (postgraduate students of biomechanics at CTU in Prague) analyzed a set of 20 randomly selected radiographs.

Estimation of reverse humeral body dimension from standard anteroposterior radiograph of the shoulder. The lateral edge (red line) and the medial edge (yellow line) of the component were defined. The transverse size of the humeral body was determined as the mean perpendicular distance between the edges

The radiographic magnification (M) of the implants was calculated as

$$M\mathrm}=\left(\frac}}-1\right)\times 100\mathrm},$$

where 0% magnification correspond to exact match between the image size and implant size.

Data analysis was performed utilizing R (version 4.1.2; R Foundation for Statistical Computing, Vienna, Austria). To assess interobserver variability, the intraclass correlation coefficient (ICC) was calculated using model 2.1 as described by Shrout and Fleiss [13]. The Shapiro–Wilk test was employed to assess the normal distribution of radiographic magnification. The analysis was conducted for the entire cohort as well as separately for male and female patients. An unpaired Welch t test was used to compare radiographic magnification between male and female patients. Multiple linear regression was employed to investigate whether patient weight and height significantly predicted magnification [14]. The computation of 95% confidence intervals (Cis) and p values was carried out using the Wald approximation. An alpha value of 0.05 was applied to evaluate the statistical significance. In the post hoc power analysis, based on the sample size for the primary outcome, the power was determined to be 0.99 for a two-tailed comparison, with an effect size of 0.5 and an alpha error of 0.05.