Data from the Paediatric Multi-Instrument Comparison (P-MIC) study (data cut 2, dated 10 August 2022) were used [19]. Data cut 2 includes approximately 94% of the total planned P-MIC participants. This study is part of the wider Quality of Life in Kids: Key Evidence for Decision Makers in Australia (QUOKKA) research programme in Australia. A detailed summary of the P-MIC data collection is available from Jones et al. [20, 21]. This study focused on 5- to 18-year-olds in the sample, as the instruments for use in children aged 2–4 years of age are experimental. Children and adolescents aged 7–18 years were invited to self-report their own HRQoL. Proxies were used if the child was not able to report their health themselves, either due to younger age (< 7 years) or health problems. In the current paper, ‘child’ refers to both children and adolescents.

The P-MIC study included a number of different generic and condition-specific instruments. The instruments that have been used in this study are the EQ-5D-Y-5L, PedsQL, CHU-9D and HUI3 (hereafter HUI). The EQ-5D-Y-5L, PedsQL and CHU-9D were administered to the whole sample as these instruments were part of the P-MIC core instrument set [20]. HUI, PROMIS-25 and AQoL6D each were administered to a subset (approximately one-third) of the online panel to minimize respondent burden [20]. As this paper aimed to explore relationships among commonly used instruments, and given that HUI is the most frequently used instrument among the three subset instruments, it was also selected for inclusion in this study.

EQ-5D-Y-5L: The EQ-5D-Y instruments, both the 3L and 5L, have shown validity and reliability in measuring HRQoL in children and adolescents [22]. Despite the P-MIC dataset including the EQ-5D-Y-5L and EQ-5D-Y-3L, this analysis opted to use only one of the EQ-5D-Y instruments, as both versions share the same dimensions. The decision to include EQ-5D-Y-5L over EQ-5D-Y-3L was supported by evidence indicating its psychometric advantages [23]. With the EQ-5D-Y-5L being the newer instrument, there is a need for evidence about how it relates to other generic instruments. The EQ-5D-Y-5L measures five dimensions of health using single items: ‘able to walk around’, ‘looking after myself’, ‘doing usual activities’, ‘having pain or discomfort’, and ‘feeling worried, sad, or unhappy’. Each dimension assesses severity across five severity response levels ranging from no problems to unable to/extreme problems [4]. Proxy- and self-report versions of the EQ-5D-Y-5L have been developed and were used according to instrument age recommendations for self-report above age 7 years.

CHU-9D: The CHU-9D is designed for measuring HRQoL [24] in children aged 7–11 years. It was developed with and for children as a de novo measure. The CHU-9D has nine dimensions and each dimension has five severity response categories (from ‘no’ (don’t feel) to ‘very’ in five items, and ‘no problem’ to ‘can’t do’ in four items). The dimensions are ‘worry’, ‘sadness’, ‘pain’, ‘tiredness’, ‘annoyed’, ‘school’, ‘sleep’, ‘daily routine’ and ‘joining in with activities’ [13, 25].

PedsQL: The PedsQL Generic Core 4.0 has been widely used to assess HRQoL in children and adolescents [26]. It includes versions for different age groups: 5–7, 8–12, and 13–18 years. Proxy versions are available for children aged 2–4, 5–7, 8–12, and 13–18. The instrument was designed to measure core health dimensions and is based on guidelines from the World Health Organization (WHO) [26]. The PedsQL is composed of 23 items that measure four broad domains, defined as ‘physical’, ‘emotional’, ‘social’ and ‘school’ functioning. Each item has five frequency levels (from never to almost always) [26]. PedsQL was included in the study even though it was not designed to be preference weighted, because it is the most comprehensive instrument in terms of scope of items, validation across all child ages, and potentially the most used generic paediatric QoL instrument [27].

HUI: The HUI Mark 2 and 3 (HUI2/3) can be used to assess a child’s HRQoL. The HUI2 was developed to address the global morbidity burden of childhood cancer, while the HUI3 was developed to resolve certain issues related to the definitions of HUI2, ensuring applicability in both clinical and general population studies, and was therefore selected for inclusion in this study. The HUI3 [15] has eight domains measured across 15 items, each with five or six response levels. The domains are ‘vision’ (2 items), ‘hearing’ (2 items), ‘speech’ (2 items), ‘ambulation’ (2 items), ‘dexterity’ (1 item), ‘emotion’ (2 items), ‘cognition’ (2 items) and ‘pain’ (2 items) [28, 29]. HUI measures typically are designed for people aged 5 years and older.

As the HUI was administered to one-third of the online panel, fewer data are available for exploring dimensionality between the HUI and the other instruments.

Correlation among variables was used in factor analysis to model latent factors. To provide a basis for the dimensionality assessment, the convergence and divergence between the items and dimensions were assessed using Spearman’s correlations (that assumes a non-normal distribution). We prespecified that correlation scores < 0.3 were considered weak, scores between 0.3 and < 0.5 were considered moderate, and scores of ≥ 0.5 indicated a strong correlation [30]. The correlation was assessed to see if the instruments were measuring the same construct and for the presence of outliers.

Choice of Factor Analysis Approach Common methods to detect the dimensionality in variables include principal components analysis (PCA) and exploratory factor analysis (EFA). The main aim of each method is slightly different; PCA is a technique for reducing the dimensionality of the data, whereas EFA is a method for identifying and measuring latent variables or factors, which cannot be measured directly. As we aimed to investigate the dimensionality of the item pool, without imposing a pre-existing model framework, EFA was used. To assess the overall dimensionality, the items from the four instruments were pooled for the self- and proxy-reported data separately. The Stata default EFA method, principal factor, was used for the estimation method. As children were aged 5–18 years in the proxy-completed data and 7–18 years in the self-reported data, the EFA was also applied for proxy-reported data for children aged 7–18 years to see if the results differed.

Data Check for Suitability Kaiser–Meyer–Olkin (KMO) and Bartlett's test of sphericity were used to assess the suitability of the data for EFA. KMO examines the strength of the partial correlation between variables, and ranges between 0 and 1; a value close to 1 suggests that the sum of the partial correlations is relatively small in comparison with the sum of the correlations. This indicates that the correlations tend to be concentrated and cluster among a few variables, which is advantageous for factor analysis. A rule of thumb for interpreting the KMO is that values between 0.8 and 1 indicate the sample is adequate to run a factor analysis. The significance level for Bartlett's test should be below 0.05. A p-value < 0.05 on Bartlett’s test indicates that individual variables are sufficiently correlated for a factor analysis to be accomplished.

Choosing Factors and Items When using EFA, a range of indicators could inform the identification of the most appropriate domain structure. The structure can be decided based on the number of factors included in the model, items representing each factor, and the correlation between items.

The number of factors in EFA can be decided using the number of eigenvalues. The eigenvalue shows the variance explained by factors. The rule of thumb for choosing factors is based on eigenvalues > 1, but factor structures can be forced to extract a certain number of factors. This choice can be supported by scree plots (that plot the eigenvalues) and parallel analysis (determines the number of factors based on eigenvalues). To check a range of possible factor structures, 6, 7, 8, 9, 10, and 11 factor models were identified and assessed for interpretation. Hereafter, factors resulting from EFA will be referred to as domains.

Each factor consists of items; to choose the items presenting each factor, loadings were used. Loadings are the correlation between item and factor and uniqueness is the variance that is unique to that item in the model, represented as (1- loading^2). Items were kept when loadings were more than 0.32 [31, 32] for each factor. Factor loadings < 0.32 usually indicate a poor correlation between the items and the factor [33]. If there was cross-loading, i.e., if an item had a loading > 0.32 on two factors, we chose the factor with the higher loading. Due to the assumption of correlation between factors, the oblique method of rotation (Promax) was used. Factor correlation was confirmed using a correlation matrix. All analyses were performed using Stata software version 17.0 (StataCorp LLC., College Station, TX, USA) [34].