Field-test and Psychometric Validation of the Pectus Excavatum Evaluation Questionnaire in the Dutch Pectus Excavatum Population

A Kaiser-Meyer-Olkin (KMO) test and Bartlett's test of sphericity are performed to assess the adequacy of patient sampling before performing further structural tests. Threshold values of ≥ 0.70 in KMO test and p < 0.05 in Bartlett's test of sphericity indicate the suitability of the collected data for factor analysis (6,7). Exploratory factor analysis (EFA), using principal axis factoring and a promax rotation method, will be conducted to identify the underlying factor structure for both the child and parent sections (8,9). These factor structures will later be subjected to confirmatory factor analysis (CFA), using polychoric correlations and robust maximum likelihood estimation, to evaluate the validity of the structures derived from EFA (8,10). Within EFA, the Kaiser criterion (eigenvalue > 1), explained variance (≥50%), and interpretability principle will be applied to determine the number of factors to be retained. Squared multiple correlations are used to compute the communality

Cronbach's alpha coefficient, a measure of internal consistency, will be calculated for each subscale. A value > .70 indicates sufficient reliability of the questionnaire for application at the group level, while a value > .90 implies suitability for individual assessment

Test-retest reliability for each subscale will be evaluated using a two-way mixed-effects model for the intraclass correlation coefficient (ICC), type (3.1), with 95% confidence intervals reported (CI) (15). The strength of agreement will be interpreted following the guideline provided by Cicchetti (1994) (16): < 0.40 = poor, 0.40-0.59 = fair, 0.60-0.74 = good, 0.75-1.00 = excellent. For individual items, quadratic weighted Cohen's kappa will be calculated along with its 95% to identify problematic items, with interpretation based on the standards proposed by Landis and Koch (1977) (17): <0 = poor, 0.01-0.20 = slight, 0.21-0.40 = fair, 0.41-0.60 = moderate, 0.61-0.80 = substantial, and 0.81-.001 = almost perfect.

The responsiveness of the questionnaire will be determined using the construct approach in which preoperative and postoperative scores are compared using a paired t-test or Wilcoxon signed-rank test for skewed data. The effect size will be expressed in Cohen's d and is calculated as the mean difference divided by the standard deviation of the difference. We hypothesize that the total score on the PEEQ and mean scores per subscale improve after surgical correction of the pectus excavatum deformity as demonstrated by the original questionnaire (2,3). Responsiveness of individual items will be evaluated using a paired t-test or Wilcoxon signed-rank test, as appropriate, to guide further item refinement.

The standard error of measurement (SEM) quantifies the precision of the scores across different time points and is calculated as (18):

SEM = squareroot of MSE

Where:

· Mean square error (MSE) is the error term obtained from repeated measures ANOVA

The SDC represents the minimum change in points a patient must score on the questionnaire over time to ensure the observed change reflects a real change and not a measurement error. The SDC is expressed in points on the PEEQ and will be calculated for the mean scores per subscale, and the total scores of the child's section, parent's section and entire questionnaire. The SDC at a 95% confidence level will be calculated as (18):

SDC = 1.96 x square root of 2 x SEM

Where:

• 1.96 is the z-score corresponding to a 95% confidence level
• square root of 2 x SEM accounts for the error variance from both time points

The floor and ceiling effects will be assessed by calculating the proportion of participants scoring the lowest or highest possible scores. Effects are considered substantial if > 15% of the participants score at the extremes for a specific item or subscale (18).