Relative Contributions of Alpha and Beta Angles to Age-Specific Graf Classification in Infant Hip Ultrasonography: A...

Because the age-specific Graf endpoint is itself defined by the alpha and beta angles, angle-based discrimination is inherently classification-internal rather than a measure of independent diagnostic accuracy. Within this framework, the relative contribution of alpha and beta angles to the classification was quantified.

This single-center retrospective study included 313 infants examined from May 2025 to May 2026. The endpoint was Graf IIa or higher in infants younger than 3 months and Graf IIb or higher in infants aged 3 months or older. Logistic regression, receiver operating characteristic analysis, paired DeLong tests, bootstrap validation, side-level generalized estimating equations, an age interaction analysis, and bootstrap estimation of calibration slope and intercept were used.

The endpoint was positive in 140 infants (44.7%). Worst alpha angle had an area under the curve of 0.904 (95% confidence interval, 0.867-0.940), versus 0.666 (95% confidence interval, 0.606-0.726) for worst beta angle and 0.903 for the multivariable model. Each 1° increase in worst alpha angle was associated with lower odds of endpoint positivity (odds ratio, 0.495; 95% confidence interval, 0.417-0.574; p < 0.001). Worst beta angle and sex were not independently associated. In a post hoc age interaction analysis, adding an age-by-worst-alpha term improved model fit (likelihood ratio test p = 0.026; Akaike information criterion 261.7-248.7), with an interaction odds ratio of 1.132 (95% confidence interval, 1.015-1.270; p = 0.030). Bootstrap calibration of the primary model showed an optimism-corrected slope of 0.976 (95% confidence interval, 0.706-1.251) and intercept of 0.009 (95% confidence interval, -0.274 to 0.326).

Within the age-specific Graf framework, the worst alpha angle captured most of the classification-internal statistical information, whereas beta angle and sex added little discrimination, and model calibration was adequate. Because the endpoint is defined by the angles themselves, these findings describe the internal structure of the classification and do not establish diagnostic accuracy against an independent reference standard or justify omitting beta angle from a complete clinical Graf examination.