### I. Introduction

### II. Methods

_{mod}’ and Wall Hyperaemia (absent, present), ‘X

_{wall}’. Secondary sonographic signs included Mesentery Appearance (echogenic, normal), ‘X

_{mes}’ and Appendicolith (present, absent) , ‘X

_{lith}’.

_{anor}’, Nausea (present/absent), Pain Migration to the right iliac fossa (present/absent), ‘X

_{migr}’; and Duration of Symptoms, which was a continuous variable (hours), ‘X

_{dur}’. The Physical Assessment sub-model included a patient's temperature with a binary febrile threshold of 38℃ (normal/elevated), ‘X

_{feb}’ and rebound tenderness (absent/present), ‘X

_{tend}’. The Diagnostic Tests sub-model included neutrophil count with a threshold of 7.5 × 10

^{9}/L (normal/elevated), ‘X

_{neut}’, white cell count with a threshold of 10 × 10

^{9}/L (normal /elevated), ‘X

_{wcc}’, and C-reactive protein with a threshold of 3 mg/L (normal/elevated), ‘X

_{crp}’ [19,20,21,22].

_{wcc}, X

_{neut}, and X

_{crp}). Categorical principal components analyses (CATPCA) were conducted for the remaining submodels [23,24]. The CPT of the target acute appendicitis node was calculated by allocating equal importance to each of the four parent nodes and a 90% diagnostic accuracy considering a possible 5% false-positive and false-negative error rate [25]. GeNIe Modeler version 2.2 software (Bayes-Fusion LLC, Pittsburgh, PA, USA) was used to create a DAG that visually represents the BN. All statistical analysis was performed with IBM SPSS Statistics version 22 (IBM Corp., Armonk, NY, USA).

### III. Results

_{mod}) was discretised from a continuous variable into five categories: <2.5 mm, 2.7–5.0 mm, 5.2–7.4 mm, 7.5–10 mm, and 10.4–19.0 mm. To improve the face and content validity of the discretisation, these were rounded to the nearest millimetre to reflect empirical values in the BN node (<3 mm, 3–6 mm, 6–8 mm, 8–10 mm, >10 mm). Component loadings from the two CATPCA components were used to calculate the CPT values for the Ultrasound Index sub-model = 0.74 (0.820X

_{wall}+ 0.940X

_{mes}+ 0.555X

_{lith}+ 0.864X

_{mod}) + 0.26 (−0.230X

_{wall}− 0.203X

_{mes}+ 0.892X

_{lith}− 0.131X

_{mod}).

_{dur}) was considered a binary variable using a cut-off at 36 hours, with the relatively brief timeframe of appendicitis pathogenesis in children and the risk of perforation increasing after that time period [19,27,28,29,30]. Other nodes were informed through the PAS scoring system [19]. They included anorexia (present/absent), ‘X

_{anor}’, nausea (present/absent), ‘X

_{naus}’, and pain migration to the right iliac fossa (present/absent), ‘Xmig’ [25]. Their respective positive and negative predictive values (PPV and NPV) from the literature were used to determine the latent probability of each variable to calculate CPT for the sub-model = log[CHppv(0.94X

_{naus}+ 0.69X

_{dur}+ 0.70X

_{migr}+ 0.88X

_{anor}) − CHnpv(0.73X

_{naus}+ 0.13X

_{dur}+ 0.97X

_{migr}+ 0.89X

_{anor}) + 4].

_{tend}and X

_{feb}. The first component of the two-dimensional model had an internal consistency coefficient (Cronbach's alpha) of 0.324 and yielded an eigenvalue of 1.046, indicating that 52.30% of the variance was accounted for by this component. The second component had an internal consistency coefficient of 0.095 and an eigenvalue of 0.954, accounting for 47.70% of variance. Component loadings from the two CATPCA components were used to calculate the CPT values for the sub-model = 0.52 (1.092X

_{feb}− 0.019X

_{tender}) + 0.48 (0.018X

_{feb}+ 1.024X

_{tender}).

*p*< 0.001), indicating that the data was likely factorizable. PCA revealed that the components explained 75.43% (X

_{wcc}), 23.41% (X

_{neut}), and 1.16% (X

_{crp}) of the total variance respectively, and cumulatively explained 100% of the total variance. Component loadings were used to calculate CPT values for the sub-model = 0.959X

_{wcc}+ 0.955X

_{neut}+ 0.657X

_{crp}.

### IV. Discussion

_{mes}and X

_{lith}. Changing the state of these nodes would then influence the Ultrasound Index CPT accordingly. The latent probabilities of X

_{mod}and X

_{wall}would not change their influence on the Ultrasound Index CPT would remain unchanged and based on the prior probabilities that determined their weighting.