Abstract
Objectives
Various scales exist to assess different domains of functioning in knee osteoarthritis (OA). This study aimed to explore whether it is possible to develop a common metric (CM) from the frequently used scales to assess functioning in knee OA.
Patients and methods
The methodological study evaluated 411 patients (81 males, 330 females; mean age: 61.8±10.5 years; range, 41 to 88 years) with knee OA. Data from the Health Assessment Questionnaire, Oxford Knee Score, Medical Outcomes Study Short Form 36, Knee Injury and Osteoarthritis Outcome Score, Western Ontario and McMaster Universities Arthritis Index, and the Nottingham Health Profile were used, and the items focusing on self-care, mobility, and domestic activity domains based on the activities and participation component of the International Classification of Functioning, Disability, and Health were included. Concurrent calibration was performed to combine the items of the scales. The CM parameters were estimated using the Rasch measurement model. Reliability was assessed using the person separation index. The CM was utilized to generate a transformation table to convert the scale scores to each other based on the reference metric score.
Results
Each scale fitted the Rasch model. Item invariance was achieved for the CM (p=0.775). The CM had a person separation index of 0.827. Age, sex, and disease duration did not cause difference in item functions. The CM satisfied the assumptions of unidimensionality and local independence.
Conclusion
A reliable CM was created from the commonly used scales to measure functioning in individuals with knee OA. Thus, clinicians and researchers can refer to the transformation table to directly compare scores of those scales and use them interchangeably.
Keywords: Common metric, concurrent calibration, functioning, knee osteoarthritis, Rasch model.
Introduction
Musculoskeletal disorders are common in the general population and constitute a heavy burden to society. They affect the quality of life negatively, particularly in terms of pain and physical function (PF).[1] Osteoarthritis (OA) is a musculoskeletal disorder that causes pain and restriction of joint movement, which leads to disability.[2] Therefore, it is important to assess the functioning of patients with OA. The International Classification of Functioning, Disability, and Health (ICF) published by the World Health Organization defines functioning as an umbrella term encompassing body functions and structures, as well as activities and participation.[3] Functional assessment generally addresses the measurement of an individual’s abilities in performing tasks necessary to daily living, leisure activities, vocational pursuits, social interactions, and other required behaviors.[4]
Generic or disease-specific scales are used to assess functioning in patients with OA. There are more than 90 generic or disease-specific instruments used to assess various domains of functioning (e.g., pain, PF, work, and general health status) in OA.[5,6] The heterogeneity of the scales used in different studies makes it hard to compare the results of those studies. In addition, most of those scales are ordinal-level scales, limiting their usability in monitoring change over time. Lack of comparable and interval-level scales might hinder clinicians and researchers in using clinical data for different goals, such as patient registries, hospital statistics, benchmarking, and research purposes, including meta-analyses.[7,8] Therefore, in such cases, a scale/metric to directly compare the results of two or more scales would be helpful.[9,10] Test equating methods are used to that end. Test equating can be conducted using different data collection designs. One can perform test equating either separately or concurrently.[11] Rasch measurement model allows conversion of ordinal scales to interval-level measures and thus performs concurrent calibration of various scales on the same common metric (CM).[12]
Prodinger et al.[7] used the Rasch measurement model to create a CM from four scales commonly used to assess functioning in OA and developed an easy-to-use transformation table. Oude Voshaar et al.[13] calibrated PF results from different scales to a single metric in inflammatory rheumatic diseases. They developed a standardized PF score metric based on item response theory for 10 scale items. Prodinger et al.[8] used data from four countries to compare different scales measuring functioning in rheumatoid arthritis. These researchers noted that using different patient-reported outcome measures made it difficult to compare scale outcomes. Therefore, they developed CMs based on item response theory. To our knowledge, no studies have ever developed a CM to assess functioning in patients with knee OA. Hence, this study aimed to develop a CM from frequently used scales to assess functioning in patients with knee OA and to use the CM to compare the results of different scales. The CM will allow us to determine what score of one scale corresponds to on the other scales and thus to directly compare functioning of patients who have been evaluated by different scales.
Patients and Methods
The methodological study was conducted with 411 patients (81 males, 330 females; mean age: 61.8±10.5 years; range, 41 to 88 years) with knee OA. The data set was composed of recently and previously collected data. The previously collected data for secondary analysis was obtained from the responses of 284 patients who filled the scales Health Assessment Questionnaire (HAQ), Western Ontario and McMaster Universities Arthritis Index (WOMAC)-PF, and Nottingham Health Profile (NHP)-physical mobility (PM).[14] The newly collected data consisted of the responses of 127 patients with knee OA treated at the Department of Physical Medicine and Rehabilitation at Ankara University Faculty of Medicine; these patients filled the HAQ, the Medical Outcomes Study Short Form 36 (SF36)-PF, the Knee Injury and Osteoarthritis Outcome Score (KOOS)-PF, and the Oxford Knee Score (OKS). The inclusion criteria were (i) having been diagnosed with knee OA according to the American College of Rheumatology knee OA diagnostic criteria,[15] (ii) being over 40 years of age, (iii) speaking Turkish, and (iv) being literate. The exclusion criteria were (i) having comorbidities affecting functioning and (ii) having knee arthroplasty surgery in the past.
Scales should be conceptually equivalent to develop a CM.[16] Therefore, this study considered the conceptual definition of the contents of the scales depending on the ICF categories. We reviewed common scales for assessing patients with knee OA and decided to use three disease-specific and three generic patient-reported outcome measures.[5,6] These scales were the HAQ,[17,18] SF36,[19,20] NHP,[21,22] KOOS,[23,24] OKS,[25,26] and WOMAC[27,28] (Table 1).
Table 1. Properties of the outcome measures used in this study.
| Scale name | Type-Aim | The number of items and the subscales* | Scoring items | The score range of the PF/PM domain! | Abbreviation | |
| The Health Assessment | G - Assessing the difficulties | Items | 20 | 0: Without any | 0-24 | HAQ |
| Questionnaire (HAQ) | in performing activities of | Dressing | 2 | difficulty- | ||
| daily living | Arising | 2 | 3: Unable to do | |||
| Eating | 3 | |||||
| Walking | 2 | |||||
| Hygiene | 3 | |||||
| Reach | 2 | |||||
| Grip | 3 | |||||
| Activities | 3 | |||||
| The Medical Outcomes | G - Allows for the evaluation | Items | 36 | In different types as | 0-20 | SF36-PF |
| Study Short Form 36 (SF36) | of one’s health status | Physical functioning | 10 | 3-5-6 point Likert, | ||
| Role limitations due to physical problems | 4 | yes-no. | ||||
| Role limitations due to emotional problems | 3 | re-coded as | ||||
| Pain | 2 | 0: No, not limited at | ||||
| Social functioning | 2 | all-2: | ||||
| Mental health | 5 | Yes, limited a lot. | ||||
| Energy/fatigue | 4 | |||||
| General health perceptions | 5 | |||||
| Change in health | 1 | |||||
| The Knee Injury and | DS - Evaluates functional | Items | 42 | 0: No problem- | 0-68 | KOOS-PF |
| Osteoarthritis Outcome | status due to knee OA | Symptoms | 7 | 4: Severe problem | ||
| Score (KOOS) | Pain | 9 | ||||
| Function-activities of daily living | 17 | |||||
| Sports and recreational activities | 5 | |||||
| Knee related quality of life | 4 | |||||
| Oxford Knee Score (OKS) | DS - The patient with knee | Items | 12 | 0: Easily/no pain/ | 0-48 | OKS |
| OA evaluates herself or | Physical function & pain during activities | difficulty- | ||||
| himself | 4: Impossible/severe pain/ | |||||
| difficulty | ||||||
| The Western Ontario and | DS - Specific scale for hip | Items | 24 | 0: No difficulty/ | 0-68 | WOMAC-PF |
| McMaster Universities | and/or knee OA | Pain | 5 | pain-4: Extreme | ||
| Arthritis Index (WOMAC) | Stiffness | 2 | difficulty/pain | |||
| Physical function | 17 | |||||
| The Nottingham Health | G - Aims to measure the | Part 1: items | 38 | No: 0-yes: Percentage | 0-8 | NHP-PM |
| Profile (NHP) | self-perceived health status of | Sleep | 5 | no: 0-yes: 1 | ||
| the person in terms of | Energy | 3 | ||||
| physical, emotional, | Emotional reaction | 9 | ||||
| and social aspects | Social isolation | 5 | ||||
| Physical mobility | 8 | |||||
| Pain | 8 | |||||
| PF: Physical function; PM: Physical mobility; DS: Disease specific; G: Generic; OA: Osteoarthritis; * The items/domains used in the study are shown in bold; † A higher score indicates poor functioning. | ||||||
Subscales focusing on PF of the SF36, KOOS, WOMAC, and NHP, as well as all items of the HAQ and the OKS, were included in this study. The items were selected such that they would measure “self-care,” “mobility,” and “domestic activity” categories based on the activities and participation component of the ICF. Higher HAQ, KOOS-PF, OKS, WOMAC-PF, and NHP-PM scores indicate worse PF, while higher SF36-PF scores indicate better PF. Therefore, SF36-PF items were recorded such that high scores indicated worse functioning, similar to the other five scales. The total score for each scale was created by summing the responses to respective items.
Statistical analysis
A power analysis was performed to determine the sample size. The results showed that a sample of 384 patients would be large enough to detect significant differences (an effect size of ±0.20 logit in item difficulty estimation with 95% reliability).[29]
The data were analyzed using IBM SPSS version 21.0 (IBM Corp., Armonk, NY, USA) at a significance level of 0.05. Psychometric properties were examined using RUMM2020 (RUMM Laboratory, Perth, Australia).[30] Reference metrics were developed using Microsoft Office Excel 2016 (Microsoft Corp., Redmond, WA, USA). Descriptive statistics [mean ± standard deviation, median, minimum, maximum, and frequency (percentage)] were used for demographic statistics. Initially, the assumptions of the Rasch measurement model were tested in each scale or subscale. A binary Rasch model was used to examine the psychometric properties of the NHP-PM with two response categories,[31] whereas for scales with more than two response categories, the partial credit model was used according to the likelihood ratio test result.[32] The concurrent calibration method based on the internal-anchor design and item response theory was used to develop a CM.[33] The difficulty level of items (β) and the level of the examined characteristic of the individual (θ) were estimated by concurrent calibration. The partial credit model was used to obtain parameter estimates since the distance between the number of response categories and threshold values of the items in the CM was not equal. Reliability was assessed using the person separation index. The protocol followed to examine the Rasch model assumptions for CM was described in the following paragraph.[34]
First, the threshold ordering of polytomous items was performed. The category probability curves were examined to determine whether the thresholds of consecutive response categories were sequential. Second, local independence was assessed. An item residual correlation of 0.2 and above was considered local dependence. Third, data were tested for fit to the model. The Bonferroni-corrected chi-square test (item trait interaction statistics) showed that the p-value was above 0.05, indicating that the dataset fit the model and that invariance across the trait was satisfied. The model fit was also evaluated to determine whether the standardized fit residuals were within ±2.5. Fourth, residual principal components analysis was performed on the residuals to assess unidimensionality, resulting in two subscales with at least 12 thresholds. There was no difference between the means of the θ estimates obtained from the two subscales (items with positive and negative factor loadings), indicating that unidimensionality was achieved. Unidimensionality is ensured if the 95% confidence interval obtained for the percentages of subjects with differences between subscales includes 5% or its lower bound is less than 5%.
Finally, differential item functioning was evaluated. Two-way analysis of variance was used to test whether the probabilities of the response categories given to an item by individuals in different groups with similar θ levels were different. Bonferroni correction was applied for multiple testing.[35] Differential item functioning was analyzed for groups defined by the median for age (<62 years vs. ≥62 years), disease duration (<5 years vs. ≥5 years), and sex (female vs. male).
The compliance of the metric with the assumptions showed that the internal validity of the scale was ensured. Thus, ordinal raw scores (RS) could be transformed into logit scores (LS).
Creating common metric scores and a transformation table
Each scale combined with concurrent calibration over the response matrix was taken as a single item or subtest to develop the CM. The RS and LS were calculated for each scale or subscale. The RS is the original ordinal score of the scale. The logit is the mathematical interval unit estimated by the Rasch measurement model. First, the LS, estimated by the Rasch model, corresponding to all possible RS for CM obtained from the total number of scales of subtests (items), was recorded. Afterward, reference metric score (RMS) in the range of 0 to 100 was defined with the help of CM LS obtained by concurrent analysis. The RMS equivalents of other scale RS were calculated. A transformation table with the CM and the corresponding RS, LS, and RMS for each scale was created.
Results
The median age of the participants was 62 years, and the mean of disease duration was 7.2±7.7 (median: 5; range, 0.5 to 40) years. The median of missing responses per item value for the six scales ranged from 0.0 to 3.4%.
The results of the Rasch analyses of each scale are presented in Table 2. All scales except KOOS-PF satisfied the assumption of local independence. Subtests were created for the KOOS-PF analysis to overcome this problem. All scales met the assumption of unidimensionality and fit the model. Differential item functioning was not observed in the scale items according to age, sex, and disease duration.
Table 2. Results of Rasch analyses for HAQ, SF36-PF, KOOS-PF, OKS, WOMAC-PF, NHP-PM scales, and CM*.
| HAQ | SF36-PF | KOOS-PF | OKS | WOMAC-PF | NHP-PM | Common metric | |
| Item location | 0.000±0.865 | 0.000±1.183 | 0.000±0.530 | 0.000±1.018 | 0.000±0.603 | 0.000±3.766 | 0.000±0.201 |
| Person location | -1.134±1.945 | 1.063±1.384 | 0.147±1.530 | 0.195±1.475 | 0.412±1.467 | -0.073±2.318 | 0.006±0.618 |
| Item fit residuals | 0.176±0.746 | -0.011±0.929 | 0.156±1.213 | 0.215±1.344 | -0.140±1.468 | -0.082±1.543 | -0.103±2.539 |
| Person fit residuals | -0.316±0.958 | -0.202±0.956 | -0.386±1.649 | -0.277±1.347 | -0.291±1.267 | -0.275±0.227 | 0.681±1.134 |
| Item trait interaction (χ2 (df); p‡) | 35.638 (35); 0.438 | 33.451 (14); 0.003 | 39.756 (28); 0.070 | 31.986 (24); 0.127 | 100.605 (75); 0.026 | 96.875 (32); <0.001 | 23.935 (30); 0.775 |
| Person separation index | 0.849 | 0.822 | 0.945 | 0.899 | 0.912 | 0.715 | 0.827 |
| Tests of unidimensionality | |||||||
| Number of sample | 399 | 124 | 126 | 127 | 279 | 276 | 395 |
| n (%) of significant t-test | 24 (6.0) | 6 (4.8) | 12 (9.5) | 11 (8.7) | 18 (6.5) | 5 (1.8) | 9 (2.3) |
| 95% CI† | 3.7-8.3 | 1.1-8.6 | 4.4-14.6 | 3.8-13.6 | 3.6-9.3 | 0.2-3.4 | 0.8-3.8 |
| Local dependency | ✓ | ✓ | X | ✓ | ✓ | ✓ | ✓ |
| DIF | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
| HAQ: Health Assessment Questionnaire; SF36: Short Form-36; KOOS: The Knee Injury and Osteoarthritis Outcome Score; PF: Physical function; OKS: The Oxford Knee Score; WOMAC: Western Ontario and McMaster Universities Osteoarthritis Index; NHP: Nottingham Health Profile; PM: Physical mobility; CM: Common metric; df: Degrees of freedom; CI: Confidence interval; DIF: Differential item functioning (was examined for age, sex, and disease duration); * The results of the final analysis, in which the Rasch model assumptions were met; ✓ Assumption was satisfied; c: Assumption was not satisfied; ‡ If it is higher than 0.05/number of items, it indicates model fit; † If this value is lower than or equal to 5% then the unidimensionality is acceptable; The mean ± standard error was used as descriptive statistics unless indicated otherwise. | |||||||
After the scales were shown to fit the model, item invariance was ensured for the CM obtained by concurrent equating (p=0.775, Table 2). Therefore, the CM included the items of all scales with 84 items. The CM had a person separation index of 0.827, indicating high reliability. Differential item functioning was not determined according to age, sex, and disease duration in the CM. The residual principal component analysis revealed no statistically significant differences between the subsets [number of significant test results was nine (2.3%)], indicating that unidimensionality was achieved. The local independence assumption was satisfied. The β for CM items ranged from -3.544 to 3.600 logits. The θ ranged from -2.583 to 2.850 logits. Thus, the CM contained a sufficient number of items for all levels of functioning (Figure 1).
Figure 1. Person and item threshold distribution for common metric.
The HAQ, SF36-PF, KOOS-PF, OKS, WOMAC-PF, and NHP-PM had a maximum RS of 24, 20, 68, 48, 68, and 8, respectively. The CM had a maximum RS of 236. The RMS values between 0 and 100 from the CM and the CM equivalents of other scale RS are presented in Table 3. The Figure 2 shows the operational ranges of the scales in logits along with the interval-level CM. The HAQ, SF36-PF, and KOOS-PF better identify those with RMS values above 30, while the WOMAC-PF better identifies those with RMS values below 70.
Table 3. The transformation table between outcome scales commonly used in knee OA*.
| Common metric | HAQ | SF36-PF | KOOS-PF | OKS | WOMAC-PF | NHP-PM | ||||||||||||||
| Raw score (RS) | Logit score (LS) | Reference metric score (RMS) | RS | LS | RMS | RS | LS | RMS | RS | LS | RMS | RS | LS | RMS | RS | LS | RMS | RS | LS | RMS |
| 0 | -3.544 | 0.00 | 0 | -1.143 | 33.61 | 0 | -1.272 | 31.80 | 0 | -1.350 | 30.71 | 0 | -1.865 | 23.50 | 0 | -2.315 | 17.20 | 0 | -2.380 | 16.29 |
| 1 | -2.889 | 9.17 | 1 | -0.834 | 37.93 | 1 | -1.013 | 35.43 | 1 | -1.132 | 33.76 | 1 | -1.538 | 28.08 | 1 | -2.004 | 21.56 | 1 | -1.817 | 24.17 |
| 2 | -2.489 | 14.77 | 2 | -0.622 | 40.90 | 2 | -0.844 | 37.79 | 2 | -0.989 | 35.76 | 2 | -1.316 | 31.19 | 2 | -1.788 | 24.58 | 2 | -1.313 | 31.23 |
| 3 | -2.246 | 18.17 | 3 | -0.477 | 42.93 | 3 | -0.735 | 39.32 | 3 | -0.895 | 37.08 | 3 | -1.164 | 33.31 | 3 | -1.639 | 26.67 | 3 | -0.823 | 38.09 |
| 4 | -2.075 | 20.56 | 4 | -0.363 | 44.53 | 4 | -0.648 | 40.54 | 4 | -0.825 | 38.06 | 4 | -1.044 | 34.99 | 4 | -1.522 | 28.30 | 4 | -0.228 | 46.42 |
| 5 | -1.944 | 22.40 | 5 | -0.264 | 45.91 | 5 | -0.575 | 41.56 | 5 | -0.765 | 38.90 | 5 | -0.942 | 36.42 | 5 | -1.418 | 29.76 | 5 | 0.441 | 55.78 |
| 6 | -1.839 | 23.87 | 6 | -0.173 | 47.19 | 6 | -0.51 | 42.47 | 6 | -0.715 | 39.60 | 6 | -0.851 | 37.70 | 6 | -1.325 | 31.06 | 6 | 1.070 | 64.59 |
| 7 | -1.750 | 25.11 | 7 | -0.087 | 48.39 | 7 | -0.451 | 43.30 | 7 | -0.669 | 40.24 | 7 | -0.769 | 38.84 | 7 | -1.239 | 32.26 | 7 | 1.713 | 73.59 |
| 8 | -1.673 | 26.19 | 8 | -0.003 | 49.57 | 8 | -0.391 | 44.13 | 8 | -0.628 | 40.82 | 8 | -0.693 | 39.91 | 8 | -1.157 | 33.41 | 8 | 2.421 | 83.50 |
| 9 | -1.606 | 27.13 | 9 | 0.078 | 50.70 | 9 | -0.332 | 44.96 | 9 | -0.589 | 41.36 | 9 | -0.623 | 40.89 | 9 | -1.078 | 34.52 | |||
| 10 | -1.545 | 27.98 | 10 | 0.160 | 51.85 | 10 | -0.268 | 45.86 | 10 | -0.553 | 41.87 | 10 | -0.559 | 41.78 | 10 | -1.002 | 35.58 | |||
| 11 | -1.489 | 28.77 | 11 | 0.243 | 53.01 | 11 | -0.201 | 46.79 | 11 | -0.518 | 42.36 | 11 | -0.500 | 42.61 | 11 | -0.930 | 36.59 | |||
| 12 | -1.438 | 29.48 | 12 | 0.326 | 54.17 | 12 | -0.128 | 47.82 | 12 | -0.485 | 42.82 | 12 | -0.446 | 43.37 | 12 | -0.862 | 37.54 | |||
| 13 | -1.391 | 30.14 | 13 | 0.411 | 55.36 | 13 | -0.047 | 48.95 | 13 | -0.454 | 43.25 | 13 | -0.396 | 44.06 | 13 | -0.797 | 38.45 | |||
| 14 | -1.347 | 30.75 | 14 | 0.498 | 56.58 | 14 | 0.047 | 50.27 | 14 | -0.423 | 43.69 | 14 | -0.351 | 44.69 | 14 | -0.736 | 39.31 | |||
| 15 | -1.305 | 31.34 | 15 | 0.588 | 57.84 | 15 | 0.157 | 51.81 | 15 | -0.394 | 44.09 | 15 | -0.31 | 45.27 | 15 | -0.678 | 40.12 | |||
| 16 | -1.266 | 31.89 | 16 | 0.681 | 59.14 | 16 | 0.285 | 53.60 | 16 | -0.365 | 44.50 | 16 | -0.271 | 45.81 | 16 | -0.623 | 40.89 | |||
| 17 | -1.229 | 32.40 | 17 | 0.777 | 60.48 | 17 | 0.440 | 55.77 | 17 | -0.338 | 44.88 | 17 | -0.234 | 46.33 | 17 | -0.571 | 41.62 | |||
| 18 | -1.194 | 32.89 | 18 | 0.878 | 61.90 | 18 | 0.637 | 58.52 | 18 | -0.312 | 45.24 | 18 | -0.200 | 46.81 | 18 | -0.523 | 42.29 | |||
| 19 | -1.161 | 33.36 | 19 | 0.986 | 63.41 | 19 | 0.923 | 62.53 | 19 | -0.286 | 45.60 | 19 | -0.168 | 47.26 | 19 | -0.477 | 42.93 | |||
| 20 | -1.129 | 33.80 | 20 | 1.104 | 65.06 | 20 | 1.340 | 68.37 | 20 | -0.261 | 45.95 | 20 | -0.137 | 47.69 | 20 | -0.434 | 43.53 | |||
| 21 | -1.099 | 34.22 | 21 | 1.239 | 66.95 | 21 | -0.237 | 46.29 | 21 | -0.107 | 48.11 | 21 | -0.394 | 44.09 | ||||||
| 22 | -1.070 | 34.63 | 22 | 1.409 | 69.33 | 22 | -0.214 | 46.61 | 22 | -0.078 | 48.52 | 22 | -0.356 | 44.62 | ||||||
| 23 | -1.043 | 35.01 | 23 | 1.651 | 72.72 | 23 | -0.192 | 46.92 | 23 | -0.049 | 48.92 | 23 | -0.321 | 45.11 | ||||||
| 24 | -1.016 | 35.39 | 24 | 1.997 | 77.56 | 24 | -0.170 | 47.23 | 24 | -0.019 | 49.34 | 24 | -0.288 | 45.58 | ||||||
| 25 | -0.991 | 35.74 | 25 | -0.148 | 47.54 | 25 | 0.009 | 49.73 | 25 | -0.257 | 46.01 | |||||||||
| 26 | -0.967 | 36.07 | 26 | -0.127 | 47.83 | 26 | 0.039 | 50.15 | 26 | -0.228 | 46.42 | |||||||||
| 27 | -0.944 | 36.39 | 27 | -0.106 | 48.12 | 27 | 0.070 | 50.59 | 27 | -0.201 | 46.79 | |||||||||
| 28 | -0.922 | 36.70 | 28 | -0.086 | 48.40 | 28 | 0.101 | 51.02 | 28 | -0.175 | 47.16 | |||||||||
| 29 | -0.900 | 37.01 | 29 | -0.065 | 48.70 | 29 | 0.135 | 51.50 | 29 | -0.150 | 47.51 | |||||||||
| 30 | -0.880 | 37.29 | 30 | -0.045 | 48.98 | 30 | 0.170 | 51.99 | 30 | -0.127 | 47.83 | |||||||||
| 31 | -0.860 | 37.57 | 31 | -0.026 | 49.24 | 31 | 0.208 | 52.52 | 31 | -0.105 | 48.14 | |||||||||
| 32 | -0.840 | 37.85 | 32 | -0.006 | 49.52 | 32 | 0.248 | 53.08 | 32 | -0.084 | 48.43 | |||||||||
| 33 | -0.822 | 38.10 | 33 | 0.014 | 49.80 | 33 | 0.292 | 53.70 | 33 | -0.063 | 48.73 | |||||||||
| 34 | -0.804 | 38.35 | 34 | 0.034 | 50.08 | 34 | 0.339 | 54.35 | 34 | -0.042 | 49.02 | |||||||||
| 35 | -0.787 | 38.59 | 35 | 0.054 | 50.36 | 35 | 0.392 | 55.10 | 35 | -0.022 | 49.30 | |||||||||
| 36 | -0.770 | 38.83 | 36 | 0.075 | 50.66 | 36 | 0.449 | 55.89 | 36 | -0.004 | 49.55 | |||||||||
| 37 | -0.753 | 39.07 | 37 | 0.096 | 50.95 | 37 | 0.511 | 56.76 | 37 | 0.015 | 49.82 | |||||||||
| 38 | -0.737 | 39.29 | 38 | 0.117 | 51.25 | 38 | 0.580 | 57.73 | 38 | 0.034 | 50.08 | |||||||||
| 39 | -0.722 | 39.50 | 39 | 0.138 | 51.54 | 39 | 0.654 | 58.76 | 39 | 0.052 | 50.34 | |||||||||
| 40 | -0.707 | 39.71 | 40 | 0.160 | 51.85 | 40 | 0.734 | 59.88 | 40 | 0.072 | 50.62 | |||||||||
| 41 | -0.692 | 39.92 | 41 | 0.183 | 52.17 | 41 | 0.821 | 61.10 | 41 | 0.091 | 50.88 | |||||||||
| 42 | -0.677 | 40.13 | 42 | 0.206 | 52.49 | 42 | 0.914 | 62.40 | 42 | 0.110 | 51.15 | |||||||||
| 43 | -0.663 | 40.33 | 43 | 0.230 | 52.83 | 43 | 1.016 | 63.83 | 43 | 0.130 | 51.43 | |||||||||
| 44 | -0.650 | 40.51 | 44 | 0.255 | 53.18 | 44 | 1.129 | 65.41 | 44 | 0.150 | 51.71 | |||||||||
| 45 | -0.636 | 40.71 | 45 | 0.281 | 53.54 | 45 | 1.261 | 67.26 | 45 | 0.171 | 52.00 | |||||||||
| 46 | -0.623 | 40.89 | 46 | 0.307 | 53.91 | 46 | 1.425 | 69.55 | 46 | 0.192 | 52.30 | |||||||||
| 47 | -0.610 | 41.07 | 47 | 0.335 | 54.30 | 47 | 1.663 | 72.89 | 47 | 0.214 | 52.60 | |||||||||
| 48 | -0.597 | 41.25 | 48 | 0.364 | 54.70 | 48 | 2.009 | 77.73 | 48 | 0.237 | 52.93 | |||||||||
| 49 | -0.585 | 41.42 | 49 | 0.394 | 55.12 | 49 | 0.262 | 53.28 | ||||||||||||
| 50 | -0.573 | 41.59 | 50 | 0.425 | 55.56 | 50 | 0.288 | 53.64 | ||||||||||||
| 51 | -0.561 | 41.76 | 51 | 0.458 | 56.02 | 51 | 0.315 | 54.02 | ||||||||||||
| 52 | -0.549 | 41.92 | 52 | 0.492 | 56.49 | 52 | 0.344 | 54.42 | ||||||||||||
| 53 | -0.537 | 42.09 | 53 | 0.527 | 56.98 | 53 | 0.375 | 54.86 | ||||||||||||
| 54 | -0.526 | 42.25 | 54 | 0.564 | 57.50 | 54 | 0.407 | 55.31 | ||||||||||||
| 55 | -0.515 | 42.40 | 55 | 0.602 | 58.03 | 55 | 0.442 | 55.80 | ||||||||||||
| 56 | -0.504 | 42.55 | 56 | 0.642 | 58.59 | 56 | 0.479 | 56.31 | ||||||||||||
| 57 | -0.493 | 42.71 | 57 | 0.683 | 59.17 | 57 | 0.518 | 56.86 | ||||||||||||
| 58 | -0.482 | 42.86 | 58 | 0.726 | 59.77 | 58 | 0.560 | 57.45 | ||||||||||||
| 59 | -0.472 | 43.00 | 59 | 0.771 | 60.40 | 59 | 0.604 | 58.06 | ||||||||||||
| 60 | -0.461 | 43.16 | 60 | 0.818 | 61.06 | 60 | 0.652 | 58.73 | ||||||||||||
| 61 | -0.451 | 43.30 | 61 | 0.868 | 61.76 | 61 | 0.702 | 59.43 | ||||||||||||
| 62 | -0.441 | 43.44 | 62 | 0.922 | 62.51 | 62 | 0.758 | 60.22 | ||||||||||||
| 63 | -0.431 | 43.58 | 63 | 0.981 | 63.34 | 63 | 0.820 | 61.09 | ||||||||||||
| 64 | -0.421 | 43.72 | 64 | 1.049 | 64.29 | 64 | 0.890 | 62.07 | ||||||||||||
| 65 | -0.411 | 43.85 | 65 | 1.131 | 65.44 | 65 | 0.975 | 63.26 | ||||||||||||
| 66 | -0.401 | 43.99 | 66 | 1.237 | 66.92 | 66 | 1.086 | 64.81 | ||||||||||||
| 67 | -0.392 | 44.12 | 67 | 1.397 | 69.16 | 67 | 1.253 | 67.15 | ||||||||||||
| 68 | -0.382 | 44.26 | 68 | 1.637 | 72.52 | 68 | 1.504 | 70.66 | ||||||||||||
| 69 | -0.373 | 44.39 | ||||||||||||||||||
| 70 | -0,364 | 44,51 | ||||||||||||||||||
| 71 | -0,355 | 44,64 | ||||||||||||||||||
| 72 | -0,346 | 44,76 | ||||||||||||||||||
| 73 | -0,337 | 44,89 | ||||||||||||||||||
| 74 | -0,328 | 45,02 | ||||||||||||||||||
| 75 | -0,319 | 45,14 | ||||||||||||||||||
| 76 | -0,311 | 45,25 | ||||||||||||||||||
| 77 | -0,302 | 45,38 | ||||||||||||||||||
| 78 | -0,294 | 45,49 | ||||||||||||||||||
| 79 | -0,285 | 45,62 | ||||||||||||||||||
| 80 | -0,277 | 45,73 | ||||||||||||||||||
| 81 | -0,269 | 45,84 | ||||||||||||||||||
| 82 | -0,261 | 45,95 | ||||||||||||||||||
| 83 | -0,253 | 46,07 | ||||||||||||||||||
| 84 | -0,245 | 46,18 | ||||||||||||||||||
| 85 | -0,237 | 46,29 | ||||||||||||||||||
| 86 | -0,229 | 46,4 | ||||||||||||||||||
| 87 | -0,221 | 46,51 | ||||||||||||||||||
| 88 | -0,214 | 46,61 | ||||||||||||||||||
| 89 | -0,206 | 46,72 | ||||||||||||||||||
| 90 | -0,198 | 46,84 | ||||||||||||||||||
| 91 | -0,191 | 46,93 | ||||||||||||||||||
| 92 | -0,183 | 47,05 | ||||||||||||||||||
| 93 | -0,176 | 47,14 | ||||||||||||||||||
| 94 | -0,169 | 47,24 | ||||||||||||||||||
| 95 | -0,161 | 47,35 | ||||||||||||||||||
| 96 | -0,154 | 47,45 | ||||||||||||||||||
| 97 | -0,147 | 47,55 | ||||||||||||||||||
| 98 | -0,14 | 47,65 | ||||||||||||||||||
| 99 | -0,133 | 47,75 | ||||||||||||||||||
| 100 | -0,126 | 47,84 | ||||||||||||||||||
| 101 | -0,119 | 47,94 | ||||||||||||||||||
| 102 | -0,112 | 48,04 | ||||||||||||||||||
| 103 | -0,105 | 48,14 | ||||||||||||||||||
| 104 | -0,098 | 48,24 | ||||||||||||||||||
| 105 | -0,091 | 48,33 | ||||||||||||||||||
| 106 | -0,084 | 48,43 | ||||||||||||||||||
| 107 | -0,078 | 48,52 | ||||||||||||||||||
| 108 | -0,071 | 48,61 | ||||||||||||||||||
| 109 | -0,064 | 48,71 | ||||||||||||||||||
| 110 | -0,057 | 48,81 | ||||||||||||||||||
| 111 | -0,051 | 48,89 | ||||||||||||||||||
| 112 | -0,044 | 48,99 | ||||||||||||||||||
| 113 | -0,037 | 49,09 | ||||||||||||||||||
| 114 | -0,031 | 49,17 | ||||||||||||||||||
| 115 | -0,024 | 49,27 | ||||||||||||||||||
| 116 | -0,017 | 49,37 | ||||||||||||||||||
| 117 | -0,010 | 49,47 | ||||||||||||||||||
| 118 | -0,004 | 49,55 | ||||||||||||||||||
| 119 | 0,003 | 49,65 | ||||||||||||||||||
| 120 | 0,009 | 49,73 | ||||||||||||||||||
| 121 | 0,016 | 49,83 | ||||||||||||||||||
| 122 | 0,023 | 49,93 | ||||||||||||||||||
| 123 | 0,029 | 50,01 | ||||||||||||||||||
| 124 | 0,036 | 50,11 | ||||||||||||||||||
| 125 | 0,043 | 50,21 | ||||||||||||||||||
| 126 | 0,049 | 50,29 | ||||||||||||||||||
| 127 | 0,056 | 50,39 | ||||||||||||||||||
| 128 | 0,063 | 50,49 | ||||||||||||||||||
| 129 | 0,070 | 50,59 | ||||||||||||||||||
| 130 | 0,076 | 50,67 | ||||||||||||||||||
| 131 | 0,083 | 50,77 | ||||||||||||||||||
| 132 | 0,090 | 50,87 | ||||||||||||||||||
| 133 | 0,097 | 50,97 | ||||||||||||||||||
| 134 | 0,104 | 51,06 | ||||||||||||||||||
| 135 | 0,111 | 51,16 | ||||||||||||||||||
| 136 | 0,118 | 51,26 | ||||||||||||||||||
| 137 | 0,125 | 51,36 | ||||||||||||||||||
| 138 | 0,132 | 51,46 | ||||||||||||||||||
| 139 | 0,139 | 51,55 | ||||||||||||||||||
| 140 | 0,146 | 51,65 | ||||||||||||||||||
| 141 | 0,153 | 51,75 | ||||||||||||||||||
| 142 | 0,160 | 51,85 | ||||||||||||||||||
| 143 | 0,168 | 51,96 | ||||||||||||||||||
| 144 | 0,175 | 52,06 | ||||||||||||||||||
| 145 | 0,182 | 52,16 | ||||||||||||||||||
| 146 | 0,190 | 52,27 | ||||||||||||||||||
| 147 | 0,198 | 52,38 | ||||||||||||||||||
| 148 | 0,205 | 52,48 | ||||||||||||||||||
| 149 | 0,213 | 52,59 | ||||||||||||||||||
| 150 | 0,221 | 52,70 | ||||||||||||||||||
| 151 | 0,229 | 52,81 | ||||||||||||||||||
| 152 | 0,237 | 52,93 | ||||||||||||||||||
| 153 | 0,245 | 53,04 | ||||||||||||||||||
| 154 | 0,253 | 53,15 | ||||||||||||||||||
| 155 | 0,261 | 53,26 | ||||||||||||||||||
| 156 | 0,269 | 53,37 | ||||||||||||||||||
| 157 | 0,278 | 53,50 | ||||||||||||||||||
| 158 | 0,286 | 53,61 | ||||||||||||||||||
| 159 | 0,295 | 53,74 | ||||||||||||||||||
| 160 | 0,304 | 53,86 | ||||||||||||||||||
| 161 | 0,312 | 53,98 | ||||||||||||||||||
| 162 | 0,321 | 54,10 | ||||||||||||||||||
| 163 | 0,330 | 54,23 | ||||||||||||||||||
| 164 | 0,340 | 54,37 | ||||||||||||||||||
| 165 | 0,349 | 54,49 | ||||||||||||||||||
| 166 | 0,358 | 54,62 | ||||||||||||||||||
| 167 | 0,368 | 54,76 | ||||||||||||||||||
| 168 | 0,377 | 54,89 | ||||||||||||||||||
| 169 | 0,387 | 55,03 | ||||||||||||||||||
| 170 | 0,397 | 55,17 | ||||||||||||||||||
| 171 | 0,407 | 55,31 | ||||||||||||||||||
| 172 | 0,417 | 55,45 | ||||||||||||||||||
| 173 | 0,428 | 55,60 | ||||||||||||||||||
| 174 | 0,438 | 55,74 | ||||||||||||||||||
| 175 | 0,449 | 55,89 | ||||||||||||||||||
| 176 | 0,460 | 56,05 | ||||||||||||||||||
| 177 | 0,470 | 56,19 | ||||||||||||||||||
| 178 | 0,482 | 56,35 | ||||||||||||||||||
| 179 | 0,493 | 56,51 | ||||||||||||||||||
| 180 | 0,504 | 56,66 | ||||||||||||||||||
| 181 | 0,516 | 56,83 | ||||||||||||||||||
| 182 | 0,527 | 56,98 | ||||||||||||||||||
| 183 | 0,539 | 57,15 | ||||||||||||||||||
| 184 | 0,551 | 57,32 | ||||||||||||||||||
| 185 | 0,564 | 57,50 | ||||||||||||||||||
| 186 | 0,576 | 57,67 | ||||||||||||||||||
| 187 | 0,589 | 57,85 | ||||||||||||||||||
| 188 | 0,601 | 58,02 | ||||||||||||||||||
| 189 | 0,614 | 58,20 | ||||||||||||||||||
| 190 | 0,628 | 58,40 | ||||||||||||||||||
| 191 | 0,641 | 58,58 | ||||||||||||||||||
| 192 | 0,655 | 58,78 | ||||||||||||||||||
| 193 | 0,669 | 58,97 | ||||||||||||||||||
| 194 | 0,683 | 59,17 | ||||||||||||||||||
| 195 | 0,697 | 59,36 | ||||||||||||||||||
| 196 | 0,712 | 59,57 | ||||||||||||||||||
| 197 | 0,726 | 59,77 | ||||||||||||||||||
| 198 | 0,742 | 59,99 | ||||||||||||||||||
| 199 | 0,757 | 60,20 | ||||||||||||||||||
| 200 | 0,773 | 60,43 | ||||||||||||||||||
| 201 | 0,789 | 60,65 | ||||||||||||||||||
| 202 | 0,805 | 60,88 | ||||||||||||||||||
| 203 | 0,822 | 61,11 | ||||||||||||||||||
| 204 | 0,840 | 61,37 | ||||||||||||||||||
| 205 | 0,857 | 61,60 | ||||||||||||||||||
| 206 | 0,876 | 61,87 | ||||||||||||||||||
| 207 | 0,894 | 62,12 | ||||||||||||||||||
| 208 | 0,914 | 62,40 | ||||||||||||||||||
| 209 | 0,933 | 62,67 | ||||||||||||||||||
| 210 | 0,954 | 62,96 | ||||||||||||||||||
| 211 | 0,975 | 63,26 | ||||||||||||||||||
| 212 | 0,997 | 63,56 | ||||||||||||||||||
| 213 | 1,020 | 63,89 | ||||||||||||||||||
| 214 | 1,044 | 64,22 | ||||||||||||||||||
| 215 | 1,069 | 64,57 | ||||||||||||||||||
| 216 | 1,095 | 64,94 | ||||||||||||||||||
| 217 | 1,123 | 65,33 | ||||||||||||||||||
| 218 | 1,152 | 65,73 | ||||||||||||||||||
| 219 | 1,183 | 66,17 | ||||||||||||||||||
| 220 | 1,216 | 66,63 | ||||||||||||||||||
| 221 | 1,251 | 67,12 | ||||||||||||||||||
| 222 | 1,289 | 67,65 | ||||||||||||||||||
| 223 | 1,329 | 68,21 | ||||||||||||||||||
| 224 | 1,374 | 68,84 | ||||||||||||||||||
| 225 | 1,423 | 69,53 | ||||||||||||||||||
| 226 | 1,477 | 70,28 | ||||||||||||||||||
| 227 | 1,537 | 71,12 | ||||||||||||||||||
| 228 | 1,606 | 72,09 | ||||||||||||||||||
| 229 | 1,686 | 73,21 | ||||||||||||||||||
| 230 | 1,779 | 74,51 | ||||||||||||||||||
| 231 | 1,892 | 76,09 | ||||||||||||||||||
| 232 | 2,035 | 78,09 | ||||||||||||||||||
| 233 | 2,220 | 80,68 | ||||||||||||||||||
| 234 | 2,488 | 84,43 | ||||||||||||||||||
| 235 | 2,916 | 90,43 | ||||||||||||||||||
| 236 | 3,600 | 100,00 | ||||||||||||||||||
| OA: Osteoarthritis; HAQ: Health Assessment Questionnaire; SF36: Short Form-36; KOOS: The Knee Injury and Osteoarthritis Outcome Score; PF: Physical function; OKS: The Oxford Knee Score; WOMAC: Western Ontario and McMaster Universities Osteoarthritis Index; NHP: Nottingham health profile; PM: Physical mobility; * Logit score (LS), Raw score (RS), Reference metric score (RMS)- ranging from 0 to 100 based on the com- mon metric (0: no problems - 100: severe problems). A higher score indicates poor functioning. | ||||||||||||||||||||
Figure 2. (a, b) The widths of each scale along the reference metric ranging from 0 to 100 (from -3.5 to 3.6 logits) based on the CM. (Dashed line shows the expected raw scores of an individual with a raw score of 16 on the HAQ scale in other scales). NHP: Nottingham health profile; PM: Physical mobility; WOMAC: Western Ontario and McMaster Universities Osteoarthritis Index; PF: Physical function; OKS: The Oxford Knee Score; KOOS: The Knee Injury and Osteoarthritis Outcome Score; SF36: Short Form-36; HAQ: Health Assessment Questionnaire; CM: Common metric.
The equivalent of an RS from one scale in other scales can be obtained using the corresponding RMS on the reference metric scale (Figure 2a), which is defined in the CM in the range of 0 to 100. It can also be obtained with the help of the corresponding LS on the logit scale (Figure 2b), which is defined in the logit range of -3.544 to 3.600. An RMS or LS equivalent to the RS of one scale was determined for the other scales, and the closest value was taken in the absence of the same value. Some examples of the interpretation of the transformation table (Table 3) are given below for clarity and comprehensibility.
An individual with 16 RS (or 0.681 LS) on the HAQ scale has an RMS of 59.14 on the CM (Figure 2a). The RS values corresponding to an RMS of approximately 59.14 in the CM for the SF36-PF, KOOS-PF, OKS, WOMAC-PF, and NHP-PM are 18, 57, 39, 61, and 5, respectively. The RMS equivalent of 57 RS from the KOOS-PF scale is 59.17 in the CM. The RS values corresponding to an approximate RMS value of 59.17 in the CM for the HAQ, SF36-PF, OKS, WOMAC-PF, and NHP-PM are 16, 18, 39, 61, and 5, respectively. The RMS equivalent of 7 RS from the OKS scale is 38.84 in the CM. The RS values corresponding to approximately 38.84 RMS in the CM for the HAQ, SF36-PF, KOOS-PF, WOMAC-PF, and NHP-PM are 1, 3, 5, 13, and 3, respectively. The RMS equivalent of 3 RS from the SF36-PF scale is 39.32 in the CM. The RS values corresponding to approximately 39.32 RMS value in the CM for the HAQ, KOOS-PF, OKS, WOMAC-PF, and NHP-PM are 1, 5, 7, 14, and 3, respectively. The RMS equivalent of 38 RS from the WOMAC-PF scale is 50.08 in the CM. The RS values corresponding to an RMS of approximately 50.08 in the CM for the HAQ, SF36-PF, KOOS-PF, OKS, and NHP-PM are 8, 14, 34, 26, and 4, respectively. The RMS equivalent of 8 RS from the NHP-PM scale is 83.50 in the CM. The RS values corresponding to an RMS value of approximately 83.50 in the CM for the HAQ, SF36-PF, KOOS-PF, OKS, and WOMAC-PF are 24, 20, 68, 48, and 68, respectively.
Discussion
In the present study, we developed a reliable CM based on the Rasch model containing sufficient items from the six common scales that assess PF in terms of self-care, mobility, and domestic activities in patients with knee OA. We also created an easyto-use standardized transformation table to ensure direct comparability of the scores. Thus, clinicians and researchers can directly compare their data and levels of functioning by the scales used in this study through the transformation table. In addition, this CM will enable the transformation of patient scores evaluated at different settings with different scales and therefore help with follow-up of the individual patient in terms of functioning.
The CM had an item difficulty estimates of -3.5 to 3.6 logits, while it had a person ability estimate of -2.6 to 2.9 logits. These results showed that the CM developed in this study covered a greater location of functioning compared to each scale. The range of variation over both the logit scale and reference metric scale for other scales showed that the diseasespecific scales (WOMAC-PF, KOOS-PF, and OKS) provided a wider range of prediction and more precise measurements than the generic scales (HAQ, SF36-PF, and NHP-PM).
Lundgren-Nilsson et al.[6] conducted a systematic review of the use and psychometric properties of 78 patient-reported scales in OA. It is important to make a transformation of the scale scores to provide standardization in patient follow-up and to compare results without changing the measurement tools used in daily practice and research. The CM developed in this study ensures that the original RS of the ordinal scales are sufficient to estimate patients' level of functioning[36] as we can make comparisons among converted scales. The commonly used scales in OA were reported to be WOMAC, SF36, KOOS, and OKS.[6] As all these scales are included in our study, the transformation table we created can have a potential for widespread use in clinical practice and research.
Meta-analyses integrate the results of several independent studies and are considered to provide the top level of evidence in scientific research. However, researchers conducting a meta-analysis may encounter different scale scores used for the same purpose in different studies. de Rooij et al.[37] conducted a systematic review and meta-analysis on functioning and pain in patients with knee OA. They reported that despite the large number of studies identified, few studies were included in the meta-analyses because different scales and metrics were used to assess the outcome. Similarly, Raposo et al.[38] showed that different scales were used by studies in their review. These studies address that the effect size of some interventions was unavailable due to the variety of scales used to assess the same construct in the same group of patients. Thus, if we want to perform a systematic review of functioning in patients with knee OA, a direct comparison of results may not be possible since different researchers use different scales. In that case, the CM and the transformation table created in this study for the relevant scales can be used to convert the scale scores.
One limitation of the study is that the scales except the HAQ were not answered by all patients. However, the use of Rasch model eliminates this problem. Another limitation is that this study was conducted in a single center. Therefore, future multicenter studies are needed to confirm our results. Finally, the differential item functioning assessment for sex was not adequate due to the unbalanced distribution (80.3% of the participants were female). The strength of the study is that the content of the CM is based on the ICF and includes PF in terms of self-care, mobility, and domestic activities. Additionally, the distribution of the patients’ functioning levels was well calibrated on the CM, which means that the CM is able to measure a wider range of the patients’ ability levels compared to each scale.
In conclusion, we created a CM including six common scales/subscales for assessing functioning in terms of self-care, mobility, and domestic activities in patients with knee OA. This CM covers a greater location of functioning compared to each scale assessed in the study, and together with the transformation table, it allows interchangeability of those scale scores. Thus, clinicians and researchers can refer to the transformation table to directly compare scores of those scales and use them interchangeably.
Footnotes
Ethics Committee Approval: The study was conducted according to the guidelines of the Declaration of Helsinki and approved by the clinical research ethics committee of Ankara University Faculty of Medicine (date: 25.09.2017, no: 15-952-17). The approval no for the previously collected data is 138-3999 (Project no: BAP 0809241).
Conflict of Interest: The authors declared no conflicts of interest with respect to the authorship and/or publication of this article.
Author Contributions: Had access to all data, literature review: P.D.; Study design, data collection, writing the article, and interpretation of results: P.D., A.A.K., Ş.K., A.H.E.; All authors critically evaluated the manuscript and approved the final version to be submitted for publication.
Financial Disclosure: The authors received no financial support for the research and/or authorship of this article.
Patient Consent for Publication: A written informed consent was obtained from each patient.<br><br><b>Data Sharing Statement:</b><br> The data that support the findings of this study are available from the corresponding author upon reasonable request.
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