Score derivation and validation

Logit coefficient values of parameters remaining after selection were used to construct the score-based prediction model. The sum of the total score for each patient was used to assess the model’s ability to predict CBD stone status. The model performance was evaluated by discriminative ability in terms of the area under the receiver operating characteristic curve (AUC) (concordance index) and classification measures (e.g., sensitivity and specificity). Calibration (i.e., the relationship between predicted and observed risk) was performed by Hosmer-Lemeshow goodness-of-fit statistics and construction of a calibration plot. The ability to predict clinical outcomes was assessed using decision curve analysis [23]. In addition, an internal validation with bootstrap resampling procedures was performed to quantify the optimism and over-fitting of the derived model.

For clinical applications, cut-off considerations were intended to guide clinicians in the selection of investigations and treatments. Currently, there is no optimal CBD stone threshold probability to suggest treatment modalities [5]. We created a cut-off point by conducting a short survey and analyzing the classification properties for 10% increments of the model-predicted CBD stone probability.

The TRIPOD statement [16] suggests comparisons to existing models. However, to our knowledge, acceptable CBD stone scoring models are unavailable. Thus, we compared the proposed model with two widely used guidelines: the American Society of Gastrointestinal Endoscopy (ASGE) 2019 (revised version) guidelines [9] and the European Society of Gastrointestinal Endoscopy (ESGE) guidelines [5]. The guidelines-predicted CBD stone probabilities were calculated using logistic regression analysis to compare AUC and decision curves.

Finally, sensitivity analysis was conducted to investigate outcome variability according to alteration of determinants. Statistical significance was set at P < 0.05. All statistical analyses were conducted using STATA software, version 17 (StataCorp, College Station, TX, USA).

This study used the same data as a previously published study [15]. However, both studies have different research questions, theories, unique analyses, and clinical implications. Technical descriptions of backward stepwise method, score derivation, and decision curve analysis are provided here (Supplementary Material 1, www.gastrores.org).