Confirmatory factor analysis of the thyroid-related quality of life questionnaire ThyPRO

The current 85-item version of ThyPRO measures quality of life in 13 scales, covering physical (4 scales) and mental (2 scales) symptoms, function and well-being (3 scales) and participation/social function (4 scales) and one single item about overall quality of life. Content and scale structure were derived from a literature search [8] and from expert and patient interviews [10] and the development was conducted within a classical health-related quality of life theoretical framework [22]-[25]. Items are rated on a five-point scale from 0 = not at all to 4 = very much, with a reference period of 4 weeks. Thirteen scales are scored by reverting positively worded items and rescaling item scores from 0 (best QoL - absence of symptoms) to 100 (worst QoL – maximum level of symptoms) and taking the average across the items in the scale – i.e., standard summation and linear transformation.

The patient population comprised a cross-sectional sample of 907 patients attending two university hospital endocrine outpatient clinics during 2007 (Table 1 (For further details, see reference [13])). At one center, all consecutive patients newly referred to the clinic were invited to participate; at the other center, all patients attending the clinic during a specified period of time were invited, regardless of their referral time. Thus, patients from the former were mainly newly diagnosed whereas from the latter most were already receiving treatment. All common benign thyroid diagnoses were represented, as were various stages of disease and treatment. Clinical description of the patients included physical examination, ultrasonographic imaging and biochemical testing. The overall response rate was 69%. The project was approved by the local ethical committee (KF01 2006–1579) and the Danish Data Protection Agency and was registered at ClinicalTrials.gov (NCT00150033).

Prior to any of the statistical analyses mentioned below, a content analysis of each scale was performed to identify items which might be less associated with the remaining items in the same scale, and item pairs which might be closely related to one another after being accounted for by the scale (local item dependence). This was done to provide a content-based guidance to model fitting.

Then a one-factor confirmatory model for ordinal data was fitted to each individual scale [26],[27], using Mplus (version 7.11) [28]. The ordinal items were regressed on the scale-factor by probit regressions estimated by a robust weighted least squares estimator with mean and variance adjustment (WLSMV) [28],[29]. Appropriateness of the initial one-factor model for each scale was assessed by: 1) overall goodness-of-fit statistics including the comparative fit index (CFI) and the root mean square error of approximation (RMSEA), where CFI >0.95 and RMSEA < 0.08 were regarded as appropriate fit [30]-[34]; 2) magnitude of factor loadings; 3) model residual correlations (RC) and 4) modification indices (MI) [28],[35]. For the latter three criteria, their magnitude was evaluated in comparison to other items in the scale and in an integrative manner, taking all three under consideration at once, so no strict thresholds were applied for each criterion. In general though, modification indices >100 and residual correlations >|.10| were taken as indices of lack of fit (local dependence or lack of convergent validity), but smaller values could also give rise to model revision considerations, if several indices pointed in the same direction; e.g., if an item had a modification index of 40 for a specific residual correlation (a "WITH"-statement in Mplus) and also had residual model correlations with several items. Revisions to improve model fit were based on both confirmatory factor modeling and content analysis, including specification of residual correlations among items, omission of poorly associated items from the models, and specification of sub-factors (for example among positively worded items in a scale). For scales where secondary factors seem plausible, a bifactor model was fitted to evaluate the dominance of the primary factor when secondary factors were modeled. A bifactor model specifies that each item is regressed on both a general and a group (secondary) factor, and the general and group factors are uncorrelated with each other [34],[36]-[39]. The magnitude of loadings on the general and group factors were compared. The two-item scale on impaired sex life was not examined in this step, since a separate factor analysis of a two-item scale is not useful.

In an attempt to understand any possible item misfit identified through individual scale analyses, hypotheses which could explain the misfit were sought. These hypotheses were evaluated in a combined, investigational multidimensional model, where the individual scale factors were allowed to correlate freely. Also items were cross-loaded on multiple scale factors when necessary to explore a better understanding of item misfit. For example, if an item in a physical symptoms scale, e.g., "Palpitations", had low own-factor loadings, it could be hypothesized that this was due to palpitations being influenced by mental health, e.g., as part of anxiety. Then cross-loading of this item on the mental symptoms scales would be specified and evaluated in the combined model.

In order to examine the stability of the model across various estimation techniques, the overall final model was compared with graded response multidimensional IRT models [40], fitted with the Mplus program [28]. For computational reasons, a 13-dimensional IRT model could not be estimated, so the model was broken down to four separate models, each containing scales with cross-loadings across scales. Stability was examined by comparing the estimated factor scores for each patient from the SEM vs. the IRT-model using intra-class correlations.

Table 2 shows the results of the content analyses and the confirmatory factor analyses of the ThyPRO scales in their current version. In general, loadings were high in all scales and CFI was also high for the vast majority of scales. In contrast, for most scales, RMSEA was not below the 0.08 threshold for appropriate fit. Model parameters indicative of item misfit are presented to the right in Table 2. The consequential remodeling resulted in the revised scales presented in Figure 1 and the remodeling as well as the overall goodness-of-fit statistics are described separately for each scale in the following text.

This investigative model is presented in Table 3. The hypotheses concerning the reason for misfit of the omitted items are presented in the second column of the table. In these models, the possible sub-factors tested in bifactor models (Figure 2) were specified as residual correlations among the involved items. In the third column of Table 3, it is specified how these hypotheses were modeled in the combined multidimensional model, where all the factors were evaluated simultaneously and were allowed to correlate freely. The results of this investigative modeling are described in the rightmost column of Table 3. Generally, a closer association was found between items and their own scale for the items in the multidimensional model (e.g. items 2e, 2 t and 10e), than in the unidimensional model for each scale. For most items, the hypothesized explanations for the apparent misfit were confirmed. Thus, 2b Visible swelling on neck was indeed associated with Cosmetic Complaints (–0.23). Item 2l Hoarseness did load also on the Hypothyroid Symptoms scale (0.22), 2t Loose stools was negatively associated with particularly Hypothyroid Symptoms (–0.55), and a negative association between 6d Afraid of being seriously ill and time since diagnosis was found. In contrast, no relationship between item 10e Other people lack understanding and mental health scales was found. Item13g Feeling too fat was associated with both Hypothyroid Symptoms (–0.16), Anxiety (–0.22) and Depressivity (0.15), and had low loading on its own factor (0.53).

In analyses of concordance of results from SEM and the IRT-model, high intra-class correlation coefficients (0.94-0.99) were found for all 13 scales, when comparing factor scores derived by the SEM with IRT score estimates (Table 4).