Rasch analysis was conducted with 167 to 203 subjects in the derivation sample (out of 266) and with 90 to 105 subjects in the validation sample (out of 132), due to extreme scores or missing data per item.
Choice Of The Rasch Model
The likelihood ratio tests conducted with a derivation subsample on four dimensions were significant (p < .001), which rejected the rating scale model and indicated the appropriateness of the partial credit Rasch model for the current analysis.
The initial Rasch analysis indicated satisfactory reliability person separation index for all dimensions (> .70). But the overall initial model fit was poor for three dimensions (p < .01), and 16 items displayed disordered thresholds. The stiffness dimension was the only one that showed no need for recoding (p = 0.45). A recoding procedure was applied to all items of the other dimensions.
Item Rescoring
The items showed disordered thresholds with different patterns. Optimal ordering of thresholds was achieved through non-uniform rescoring of all 11-point scale responses through collapsing response categories to a shorter-point scale. Figure 1 provide an example of a typical item category probability curve, displaying a disordered threshold (left) and threshold ordered (rigth) after final rescoring, respectively.
Item Fit Statistics
Item 11 (I felt more restricted or impaired in my movements) in dimension Consequence of symptoms, presented misfit (fit residual=-2.583; p = 0.0055), as well as item 15 (I felt frustrated because I was limited in my daily activities) in dimension Psychological aspects (fit residual=-2.473; p = 0.0041) which led to discarding these items.
Unidimensionality
We observed that less than 5% of the t-tests were significant, confirming the unidimensionality of scale in four dimensions.
Local Dependency
The residual correlation matrix indicated local dependency between item 1 (My pain felt more severe compared to my usual pain) and item 3 (My pain was more persistent than usual), which was solved by creating a super item score combining response modalities of both items into one scale. Good model fit was found on re-evaluation and no further local dependency was confirmed.
Differential Item Functioning
A uniform DIF was detected for joint in Item 4 (My pain disrupted my sleep more than usual) in dimension Pain (Fig. 2, on the top). As the observed DIF was clinically consistent with clinical difference between knee and hip symptoms, we decided to retain the item in its dimension and solved DIF problem by splitting Item 4 across joint.
Item 9 (I needed to put ice or something cold on my joint more than usual) presented a non-uniform DIF according to the age (Fig. 2, on the left) and the country (Fig. 2, on the right) and was excluded from its dimension Consequence of symptoms.
Person-item Threshold Distribution
The person-item threshold distribution of the rescored Flare-OA-16 Questionnaire is shown in Fig. 3 for both the derivation and validation samples.
Overall, there was a good match between location of items and of persons over each dimension trait in derivation and validation samples, with a regular spread of thresholds despite some gaps inside trait. In addition, the mean location for persons was close to 0 (from − 0.478 to 0.416), and dimensions of Flare-OA-16 were well focused, i.e. not too easy and not too hard for the targeted population.
Final Model
A new round of analysis was performed in the derivation sample and in the validation sample. Modifications decided at previous steps allowed improvement of the overall fit model for four dimensions (p > 0.05, Table 1) in both samples, with acceptable reliability in three dimensions (PSI > 0.7) and minimal reliability in the Pain dimension (PSI = 0.62 and 0.64) (Table 1).
Table 1
Summary test-of-fit statistics for last rescored items and after items deleted with derivation sample and validation sample.
Dimension
|
Item fit residual
|
|
Person fit residual
|
|
Goodness of fit
|
|
Pearson
Separation
Item (PSI)
|
|
Independent t-test
|
Value
|
SD
|
|
Value
|
SD
|
|
chi square (df)
|
p
|
|
|
|
%
|
95% CI
|
Derivation sample
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Pain
|
0.267
|
1.613
|
|
-0.397
|
1.249
|
|
19.747
|
0.072
|
|
0.62
|
|
NA**
|
0.267
|
Stiffness
|
-0.255
|
0.494
|
|
-0.592
|
0.897
|
|
8.245
|
0.221
|
|
0.80
|
|
1.13
|
-0.255
|
Consequences of symptoms
|
0.013
|
0.826
|
|
-0.288
|
0.842
|
|
25.100
|
0.014*
|
|
0.74
|
|
1.17
|
0.013
|
Psychological aspects
|
-0.176
|
1.389
|
|
-0.252
|
0.808
|
|
21.677
|
0.117
|
|
0.75
|
|
1.57
|
-0.176
|
Learning sample
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Pain
|
0.234
|
1.180
|
|
-0.326
|
1.026
|
|
4.163
|
0.842
|
|
0.64
|
|
NA**
|
0.234
|
Stiffness
|
0.028
|
0.467
|
|
-0.767
|
1.259
|
|
4.311
|
0.366
|
|
0.73
|
|
1.53
|
0.028
|
Consequences of symptoms
|
0.093
|
0.613
|
|
-0.300
|
0.847
|
|
10.232
|
0.249
|
|
0.77
|
|
1.56
|
0.093
|
Psychological aspects
|
0.030
|
1.173
|
|
-0.270
|
0.921
|
|
10.138
|
0.428
|
|
0.78
|
|
0.00
|
0.030
|
* p ajustement de Bonferroni = 0,05/4 items final model = 0,0125 |
** Not Applicable (split of item 4) |
The threshold map for all dimensions of the resulting 16-item Flare-OA questionnaire (Flare-OA-16) is shown in Fig. 4 for derivation and validation samples.
In CFA (maximum likelihood method), factors with at least two items were entered and showed good fit indicators: CFI = .97; RMSEA = .05 with LLCI90% = .047 until ULCI90% = .068). Considering the convergent validity analysis (Table 2), the results found for the Flare-OA-16 were similar to those found for the full version (22).
Table 2
Pearson correlation between Flare-OA score and scores for functional limitations on the HOOS, KOOS and Mini-OAKHQOL (n in parentheses indicates the number of respondents)
Validity
|
Mean (SD)
|
Correlation (r)
|
HOOS
|
|
|
Pain (n = 46)
|
61.30 (23.53)
|
-0.86
|
Symptoms (n = 46)
|
61.52 (20.97)
|
-0.70
|
Function in daily living (ADL) (n = 44)
|
65.61 (23.04)
|
-0.81
|
Function in sport and recreation (Sport/Rec) (n = 44)
|
50.99 (28.88)
|
-0.69
|
Quality of life (QoL) (n = 44)
|
46.31 (26.04)
|
-0.71
|
KOOS
|
|
|
Pain (n = 333)
|
57.57 (19.33)
|
-0.73
|
Symptoms (n = 333)
|
54.56 (20.05)
|
-0.61
|
Function in daily living (ADL) (n = 328)
|
62.86 (21.13)
|
-0.68
|
Function in sport and recreation (Sport/Rec) (n = 328)
|
31.53 (26.07)
|
-0.52
|
Quality of life (QoL) (n = 328)
|
39.83 (22.94)
|
-0.64
|
Mini-OAKHQOL
|
|
|
Pain (n = 368)
|
53.66 (25.87)
|
-0.75
|
Physical activities (n = 368)
|
56.25 (27.58)
|
-0.73
|
Mental health (n = 368)
|
73.97 (27.19)
|
-0.69
|
Other domains
|
|
|
Social support (n = 367)
|
56.10 (28.20)
|
-0.12
|
Social activities (n = 368)
|
67.73 (28.73)
|
-0.31
|
Professional activity (n = 365)
|
72.71 (31.54)
|
-0.55
|
Fear of dependent (n = 367)
|
66.05 (37.73)
|
-0.63
|
Sexual relation (n = 367)
|
76.59 (33.89)
|
-0.40
|
HOOS = Hip osteoarthritis outcome score, KOOS = Knee osteoarthritis outcome score, Mini-OAKHQOL = Osteoarthritis Knee and quality of life, SD = standard deviation.
Coefficients were from 0.61 to 0.86 for the Flare-OA score correlated with scores for pain, symptoms, and ADL domains of the HOOS and KOOS and pain, physical activities and mental health domains of the Mini-OAKHQOL. For the other domains of the HOOS and KOOS, coefficients ranged from 0.52 to 0.69. For the other domains of the Mini-OAKHQOL, coefficients ranged from 0.12 to 0.63.