Whether the joint-pain comorbidities can simply be summed up was evaluated using Rasch analysis. A feature of the Rasch model is that it assumes all items to be equally discriminating . As a result, a good fit between the Rasch model and the data indicates that individual joint scores can be summed up to obtain a total score of joint-pain comorbidities during the past month .
In order to perform Rasch analysis, the data must conform to a number of underlying assumptions of the Rasch model [8–10] including unidimensionality, model fit, and local independence.
The first assumption, unidimensionality, was tested with a principal component analysis of the tetrachoric correlation matrix in SPSS Statistics 18.0, using oblimin rotation. The scale was assumed to be sufficiently unidimensional (i.e. there is one dominant underlying factor) if the ratio of the first and second eigenvalue was >3 : 1 .
The second assumption concerns the model’s ability to reflect the true relationship among the underlying construct and the item responses [8–10]. This was tested by evaluation of the mean square Infit (Infit MNSQ) and mean square Outfit (Outfit MNSQ) fit statistics. Mean square values show the ratio between the observed and predicted variance, with an expected value of 1.0 . Corrected for the sample size of 401 patients, the Infit and Outfit ranges required for a good fit are 0.90-1.10 and 0.70-1.30 respectively . Higher values show unexpected responses (noise) or might point to multidimensionality. Lower values point to item redundancy, meaning that the information provided by the item overlaps with the information provided by other items [12, 14, 15].
The final assumption assumes that the items are not further associated with each other once the Rasch factor is taken into account. Violation of this assumption might point to response dependency (e.g. overlapping items in the scale) or to multidimensionality of the scale [9, 12]. Items were assumed to be locally dependent if the residual correlation between two items was >0.5 .
In case the Rasch assumptions were satisfied, joints were checked for differential item functioning (DIF). DIF is present when subgroups of patients with similar levels of the measured underlying construct (i.e. the degree of joint-pain comorbidity as measured by summing the number of painful joints) give different responses (i.e. painful or not painful) to a specific joint [9, 10]. DIF was tested for age, gender, BMI, disease duration, and patient group. Subgroups of age (≤58 and >58) and disease duration (≤10 years and >10 years) were created by splitting the group at the median. BMI subgroups were created by splitting the group at the BMI cut-off point for overweight (BMI≥25). Patient groups were formed by separating the knee OA patients from the hip OA patients. In case a patient experienced both knee as well as hip pain, the patient was classified based on their primary complaint.
Finally, the performance of the sum score was examined by evaluating its test information function with associated reliability levels; showing whether precise and reliable joint-pain comorbidity scores can be obtained across the range of joint pain comorbidity severity. Reliabilities >0.7 were deemed acceptable for group use . In addition, the higher the test information, the better the test will be able to discriminate among individuals .
Rasch analyses were performed using Winsteps, version 3.65 (Winsteps, Chicago, IL, USA).