A 54-mm acetabular cup (Trilogy, Zimmer, Indiana, USA) was attached to a custom-made bi-planar anteversion measurement model that enabled control of inclination and anteversion (Figure 1). The model had two axes that represented inclination and anteversion, respectively, and a goniometer was attached to each axis for precise control of changes in both inclination and anteversion. The cup was fixed to the plexiglass plate at a 10-cm height to represent the normal height of the hip joint in the supine position (Model A). Another model with the same cup and design was manufactured (Model B) and was fixed to the plexiglass plate 9.9 cm lateral and 4.9 cm distal to the Model A (Figure 2). The distance between the two models represented the distance from the center of the triangle formed by the anterior superior iliac spine (ASIS) and symphysis pubis, which is typically used for conventional pelvis AP radiographs, and the hip joint. Thus, an X-ray beam directed toward Model A represented the simple X-ray in hip-centered AP radiographs, while the image in Model B represented the acetabular cup in conventional pelvis AP radiographs. The radiographs were acquired with both models’ inclinations changing from 10° to 70° at 10° increments; for each inclination angle, the anteversion was changed from 0° to 30° at 5° increments. Therefore, X-rays of the two models were acquired in 49 scenarios.
All images were digitally acquired using a Picture Archiving and Communication System (INFINITT PACS system, Seoul, South Korea), and all measurements on radiographs were subsequently conducted using PACS software. The measurements were conducted independently by two orthopedic surgeons blinded from each other using six methods described by Pradhan et al. , Lewinnek et al. , Widmer et al. , Liaw et al. . Hassan et al. , and Ackland et al. , respectively. Before measuring anteversion, the two evaluators held a consensus-building session and clarified the definitions for each measurement method. All measurements were blinded from each other, and the measurements were repeated after 2 months to calculate intra-observer correlations.
Anteversion measurement methods (Figure 3)
1) Pradhan et al.’s method  = arcsin (p/0.4D) (Figure 3a)
In which D is the maximum distance across the long axis of the ellipse of the component. A line is drawn perpendicular to the long axis and intersecting the rim of the component beginning at a point one-fifth of the total distance of the longitudinal line, and p is the distance along this perpendicular line from the longitudinal line to the rim.
2) Lewinnek et al.’s method  = arcsin (D1/D2) (Figure 3b)
In which D1 is the distance across the short axis of an ellipse drawn perpendicular to the long axis of the acetabular component and D2 is the distance of the long axis, which is considered the maximal diameter of the implant.
3) Widmer et al.’s method  = arcsin ([S]/[TL]) (Figure 3c)
In which S is the short axis of the ellipse and TL is the total length of the projected cross-section of the component along the short axis. This method shows a linear correlation for values of S/TL between 0.2 and 0.6.
4) Liaw et al.’s method  = sin-1 tan β (Figure 3d)
In which β is the angle formed by the long axis of the component (the line from point A to B), line connecting the top point of the ellipse, and endpoint of the long axis (the line from point A to C).
5) Hassan et al.’s method  = [arcsin [(h/D) / √([m/D] – [m2/D2])] (Figure 3e)
In which D represents the maximum diameter of the acetabular component, m is the distance along D that is not obscured by the femoral head, and h is the length of the perpendicular line dropped from the endpoint of the distance m to the acetabular rim.
6) Ackland et al.’s method  = arcsin [2y / 2√(2Dx – x2)] (Figure 3f)
In which D is the distance of the long axis of the acetabular component and x is the distance along the line AB. An arbitrary tangent is drawn at a right angle to the diameter, and y is the distance from the two-cup rims along this tangent.
Reliability was defined as the consistency in the measurements, while accuracy was defined as the proximity to the reference anteversion angle. The reference anteversion was defined as the anteversion measured by the protractor of the custom-made bi-plane anteversion measurement model. The statistical analysis was performed using SPSS for Windows version 22.0 software (SPSS Inc., Chicago, Illinois). For the assessment of reliability based on inter- and intra-observer measurements, the intraclass correlation coefficient (ICC) and 95% confidence interval were calculated using the two-way random effects model assuming a single measurement and absolute agreement. ICC values were characterized as slight (0.00 to 0.20), fair (0.21 to 0.40), moderate (0.41 to 0.60), substantial (0.61 to 0.80), and almost perfect (>0.80). For the assessment of accuracy, mean differences from the anteversion measurements of each method and reference anteversion were calculated and presented as mean ± standard deviation. The paired T-test and Pearson’s correlation coefficients were used with 0.00 to 0.20 representing poor, 0.21 to 0.40 representing fair, 0.41 to 0.60 representing moderate, 0.61 to 0.80 representing good, and 0.81 to 1.00 representing excellent. Statistical significance was set at p < 0.05. Bland–Altman plots were utilized to show differences between the measurements obtained using pelvis AP and hip-centered AP radiographs.
To assess the bias resulting from including outliers in the data, subset analysis for the accuracy of anteversion was performed for anteversion within a safe inclination zone (30° to 50°).