## Materials and Methods
### Study Design
#### 2.1.2 Second Stage  
The modified PSQ, with the 15 added items, was administered via digital form (Google form) so it could be widely and easily distributed in the COVID-19 pandemic period.  
The administration of the new questionnaire was, therefore, conducted from 16 to 30 June 2020 among a population of children, aged between 3 and 13 years, from four public schools located in the province of Palermo (Sicily, Italy). Informed consent for data processing was obtained in advance from the parents of the children through the school Dean. More specifically, an information letter and the entire questionnaire was sent to the school Deans in order to obtain the consent to proceed. The Deans then sent the digital questionnaire to the parents by e-mail or mobile phone. Before filling out the questionnaire, each parent had to give consent for data processing in compliance with Italian and European Union policies on the management of sensitive data.  
Male or female children not presenting syndromic disorders (i.e., achordrolasia; [PERSON] syndrome; [PERSON] syndrome; [PERSON] syndrome; Ellis-van Creveld syndrome; [PERSON] syndrome; Pierre Robin sequence/complex; [PERSON] syndrome; sickle cell diseases) were considered eligible for inclusion. In the case of more than one eligible child within the same family unit, the parents were asked to complete the questionnaire for each of their children.  
The validation of the 15 added items was conducted through the following statistical analysis. Demographic characteristics of patients were summarised through counts and percentages for categorical variables and mean \(\pm\) standard deviation (SD) for quantitative variables. For the diagnosis of OSAS, the optimal cut-off of 0.33 was used, as suggested by [PERSON] et al. 2000 [6]. For each item, sensitivity and specificity, positive and negative predictive values and positive and negative likelihood ratios were calculated and expressed as percentages and 95% exact confidence intervals. The difference between these measures of accuracy was judged to be statistically significant in the case of non-overlapping confidence intervals. In the first stage of the analysis, multiple correspondence analysis (MCA) was applied to find the similarity among items in terms of their profiles in a subspace of low dimensionality [24]. The aim of MCA is to reduce data dimensionality with the minimum loss of information. Both the quality of approximation and the loss of information were measured in terms of percentage of total inertia; they add up to 100% [25; 26]. Internalreliability of items was assessed through the Cronbach's alpha, and alpha \(\geq\)0.7 was considered acceptable. Finally, logistic regression was used to assess the predictive ability of the items to predict OSAS (presence or absence). Data sparseness was taken into account through Firth penalisation. Results were shown as adjusted odds ratios (ORs) and the triplet of Wald, score and gradient \(p\)-values. Statistical analysis was performed using Stata IC/SE 15.1 (Stata Corporation, College Station, TX, USA) and R software (version 4.0.2), limited to logistic regression with Firth penalisation. An alpha value of 0.05 was considered significant.