## 2 Materials and Methods
### Statistical Analysis  
In the present analysis, the significance level was set at \(\alpha\) = 0.05. Descriptive statistics were employed to summarize the data. For continuous variables, the median (Mdn) served as the central tendency measure due to its robustness against outliers and distributional skewness. Furthermore, the first (Q1) and third (Q3) quartiles were reported to delineate the central 50% range of the data. Additionally, the inclusion of minimum (Min) and maximum (Max) values offers a complete view of the data's range, highlighting the extremes. Categorical variables were quantified by counts (n) and the proportion of each category. The relationship between two numerical variables was investigated using Pearson correlation. The 95% confidence intervals (CI 95%) and \(p\)-values were computed through the asymptotic approximation of the \(t\)-test statistic. The predictive performance of the BiomedCLIP model was evaluated by determining the optimal cutpoints for dichotomous outcomes (positive class--incidence of the event, negative class--absence of the event) through a method that maximizes the sum of specificity and sensitivity. The model's discriminative ability was further assessed by estimating metrics such as accuracy, sensitivity, specificity, and the Area Under the Curve (AUC) with results visualized via Receiver Operating Characteristic (ROC) curves. To ascertain the model's predictive capability beyond mere guessing, the 95% confidence intervals for the AUC metrics were estimated employing the DeLong test [13]. A high level of sensitivity was defined as achieving a result \(>\)90%, reflecting optimal performance for early detection and classification tasks. Specificity requires a proper equation to connect ROC, AUC, and CI calculations for single- and double-curve scoliosis. \[Sensitivity=\frac{TP}{TP+FN}\]\[Specificity=\frac{TN}{TN+FP}\,\]  
where _TP_--true positive values; _FN_--false negative values; _TN_--true negative values; _FP_--false positive value. \[AUC=\int_{0}^{1}Sensitivity\ d(1-Specificity),\]  
where \(d\) is the difference in scores or ranks between the positive and negative classes. Variance of AUC is defined as:  
\[Var\ (AUC)=\frac{1}{n_{1}n_{2}}\sum_{i=1}^{n1}\sum_{j=1}^{n2}{(V_{ij}-AUC)^{2}},\]  
where \(V_{ij}\) is a weight assigned to each pair of observations; \(n_{1}\)--number of positive instances, \(n_{2}\)--number of negative instances, \(i\)--index of positive instances, \(j\)--index of negative instances. \[CI=[AUC-z\cdot SE,\ AUC+z\cdot SE],\]  
where _CI_--confidence interval for AUC; \(z\)--is the critical value from the standard normal distribution (\(z=1.96\) for 95% confidence); \(SE\)--standard error, defined as:  
\[SE=\sqrt{Var(AUC)}\]  
Characteristics of the applied statistical tool and external packages  
Analyses were conducted using the R Statistical language (version 4.3.3; [14]) on Windows 11 Pro 64 bit (build 22631), using the packages see (version 0.9.0; [15]), report (version 0.5.8; [16]), correlation (version 0.8.5; [17; 18]), patchwork (version 1.2.0; [19]), pROC (version 1.18.5; [20]), gtsumumary (version 1.7.2; [21]), cutpointr (version 1.1.2; [22]), ggplot2 (version 3.5.0; [23]), readxl (version 1.4.3; [24]), dplyr (version 1.1.4; [25]), and psych (version 2.4.6.26; [26]). Characteristics of the observed data  
An analysis was conducted on 262 radiographic images all identified with scoliosis. These images were assessed by two independent neurosurgical experts who evaluated the Cobb angles, scoliosis type, and its stage. The results of these assessments are presented in Table 2 and will be treated as observed data in further analyses. The examination of the data demonstrated that the median Cobb angle was 42.0 degrees, with observed values ranging from 12 to 115 degrees. The first and third quartiles were noted at 25.0 and 66.8 degrees, respectively, reflecting a significant variability in the