ICF-Based simple scale for children with cerebral palsy: Application of Mokken scale analysis and Rasch modeling

ABSTRACT

Children with cerebral palsy (CP) are faced with long-term dysfunction. The International Classification of Functioning, Disability and Health for Children and Youth (ICF-CY) has been proposed but the complicated procedure limits the feasibility of clinical application and the exploration of health degrees. This study was aimed to establish a Mokken scale based on the ICF-CY for CP, and then to estimate psychometric properties through the derived Rasch model. 150 children with CP were assessed by the categories of “b” and “d” components in the core set. The binarized data was screened by the Mokken scale analysis and utilized for generating a reliable Rasch model. The validity of the final model was checked by the correlation between person ability, Gross Motor Function Classification System (GMFCS) and total scores. Using the Mokken scale to guide Rasch modeling, we can parameterize the properties of ICF-CY and realize the simple assessment of person abilities for children with CP.

KEYWORDS:

• International Classification of Functioning, Health and Disability (ICF)
• cerebral palsy (CP)
• Mokken scale analysis (MSA)
• Rasch modeling
• item response theory (IRT)

Introduction

Cerebral palsy (CP) is usually caused by non-progressive damage to the fetus or infant brain during development, which is manifested as a developmental disorder of movement and posture, as well as limited activity caused by developmental impairment.^1–3 Although the brain injury of CP ought to be static, patients are faced with long-term disability and may even develop progressive dysfunction.⁴ In addition to mobility disorders, patients also have complex problems at biological, psychological, and social levels, including impairment of higher brain functions such as cognition and language, and secondary impairment of musculoskeletal system functions, as well as multiple factors such as upbringing and schooling.^5,6 As the growth, development, and living conditions of children with CP change, new health problems and activity limitations, such as fatigue, pain, or employment problems, may also occur.⁷ There are dozens of evaluation methods and evident variations in etiology, comorbidities, and response to treatment.⁸ Therefore, the need for rehabilitation treatment for children with cerebral palsy is clear, while how to recognize the integral function level and how to analyze the intervenable and favorable items are inevitable but still unresolved.¹ Currently, specialized scales are mostly developed for specific diseases, making it difficult to obtain comprehensive and standard-based assessments for patients with multiple comorbidities or spectrum diseases.

The activities of daily living (ADL) are widely evaluated, but the simple content of the Barthel Index and the time-consuming property of the 36-Item Short-Form health survey (SF-36) limit the feasibility in the clinical application.⁹ The Gross Motor Function Classification System (GMFCS) is one of the most common means of motor function assessment in children with CP.^10,11 However, abilities and disabilities are assessed from a single functional level in GMFCS, ignoring the integrity of the individual and the attributes of the environment. It is difficult to guide the rehabilitation objectives and procedures in this approach. On the other hand, children with CP have certain adaptability and compensatory ability during growth and development. Rehabilitation should focus not only on the disorders and disabilities but also on the abilities and activities to assess the overall health condition. As a result, a comprehensive scale for rapid assessment of the health level is urgently needed in the clinic.

The World Health Organization’s International Classification of Functioning, Health and Disability (ICF) and the Child and Adolescent edition (ICF-CY) use uniform terminology to describe the basic elements of health, which are divided into four components (body structure, body function, activity and participation, and environmental factors), equipped with appropriate combinations of terms for a variety of diseases. A hierarchical domain-category-item description system is formed by a qualitative framework and a defined value ranging from 0 (no impairment) to 4 (complete impairment). There are some difficulties and controversies about how to implement such assessments. Two points are particularly prominent: (1) It is hard to unify the recognized concept and grading standards of items, especially in the determination of the qualification value, which always raise various disputes; (2) The number of items is too large to be used clinically, which means it is necessary to simplify the set such as using the Delphi method to determine the alternative items of the combination.¹²

It has been proposed that a core set of ICF items can describe the disease-related health status.^13,14 The core set for children with CP was developed including a comprehensive core set (0 ~ 18 years old, 135 items), a general concise core set (0 ~ 18 years old, 25 items), and a concise core set for three age groups (0 ~ 6 years old, 31 items; 6 ~ 14 years old, 35 items; 14 ~ 18 years old, 37 items).¹⁵ Using convenience sampling of interview data, ICF item information can be considered health-related functional variables, providing a basis for possible rehabilitation intervention targets.¹⁶ However, the ICF scoring system essentially focuses on disability. The higher the disability level is, the higher the score is. Thus, how to assess the health status of children with CP rather than disease status become an urgent problem to be solved.

By using health-oriented scoring strategies such as 1 for function items and 0 for dysfunction items, models of item response theory (IRT) can measure levels of person abilities rather than degrees of patient disabilities.^17–23 There are two approaches of item response modeling. Mokken scale analysis (MSA) is the non-parametric method.^24–26 The parametric approach involves a family of models in which the Rasch model is prominent. The primary difference between MSA and Rasch modeling is that the Mokken scale uses the sum of raw scores to compare person abilities, while the Rasch model estimates person abilities and item difficulties in the same unit (logit). Therefore, the Rasch model enables the comparison of individual abilities with populational item difficulties, and thus it offers more information for finding possible rehabilitation goals, such as the items with difficulties close to the individual’s ability. Recent developments in IRT modeling prefer integration of MSA and Rasch modeling into one pipeline, rather than selecting one over the other.^17,18 The reason is that MSA can act as a tool for shaping and testing the data, according to the four hypotheses for further Rasch modeling, including unidimensionality (the questionnaire only measures one latent trait/person ability), local independence (the items associate with each other only because of the latent trait), monotonicity (the scoring possibility of each item always raises with increasing levels of person ability), and invariant item ordering (IIO, the rank of item difficulties is fixed for persons with same abilities).

The MSA-Rasch pipeline removes the items that do not contribute to differentiating persons with different abilities. The pipeline with the health-oriented scoring strategies can generate a concise scale for measuring a person's ability and comparing the ability with item difficulties. The present study was designed based on this approach. The ICF 0–4 qualifiers were converted to a dichotomous scoring system that assigning score 1 to functioning and score 0 to dysfunction. The existing ICF core sets of CP were integrated and screened for extracting an new set with the IRT parameters. This report also discussed the perspective of utilizing this set and its Rasch model for selecting rehabilitation targets.

Method

Subjects

A convenience sample of 150 children with CP received three assessments: (1) Gross Motor Function Classification System (GMFCS); (2) manual ability classification system (MACS); (3) ICF-CY questionnaire following the existing ICF study enrollment criteria for CP according to Maximum Variation Sampling Strategy for convenient sampling requirements.^2,27,28 The inclusion criteria were as follows: (1) CP was diagnosed by a pediatric neurologist conforming to the diagnostic criteria of the Chinese guidelines for CP rehabilitation; (2) the age was under 16 years; (3) the informed consent of the guardian was obtained. Exclusion criteria were: (1) CP was accompanied by uncontrolled epilepsy, genetic metabolic diseases, trauma, or unhealed surgical wound; (2) there were any other factors affecting information collection. The study was approved by the ethics committee of Sir Run Run Hospital, Nanjing Medical University (IRB# 2018-SR-017).

Pre-process

ICF-CY core set for CP contains a total of 135 items, including 34 items from the body function (b), 7 items from the body structure (s), 58 items from the activity and participation (d), and 36 items from the environmental factors (e). Domains b and d were selected in this study, excluding s and e to lessen the bias as much as possible. A total of 92 items were selected in domains b and d. The final scores were determined by a three-person inspection team (including a CP rehabilitation therapist, a rehabilitation therapist with ICF assessment certificate and a senior rehabilitation physician) after reaching a consensus on the disputed items. Each item was rated by the 5-point qualifier system: 0 = no impairment; 1 = mild impairment; 2 = moderate impairment; 3 = severe impairment; 4 = complete impairment. For 8 (not specified) and 9 (not applicable) in the original scoring system, both were recorded as missing value (NA). Information for rating came from medical histories, clinical examinations and observations, and descriptions from caregivers and health professionals.

Mokken Scale Analysis

Mokken scale analysis (MSA) was divided into three steps: (1) data examination, (2) scale identification, and (3) scale properties estimation.²⁹ The tools were embedded in the “mokken” (3.0.6) package of R software.^29,30

(1) Data examination

The item with a missing value ≥5% in the sample population would be removed.²¹ The censored data in the remaining items were completed by k-nearest neighbor imputation with k = 5 by using the “VIM” package of R. The imputed data was then binarized using the following criteria: 0 (no impairment) as 1 (healthy), and 1 to 4 (mild, moderate, severe, or complete impairment) as 0 (disabled). That was, the original 5-point impairment-scoring system was converted to a dichotomous functioning-scoring system. A form of binary data was constructed to obtain the total score of the scale to reflect the health degree of the patients. The data frame conformed to a matrix with observations in rows and ICF items in columns. There were no categories completely healthy or disabled in the shaped data set. The numbers of Gutman errors were calculated, and the correlation between the scores of subjects and the numbers of Gutman errors were analyzed. Participants were identified as outliers if they exceeded the upper limit of the Gutman errors cutoff value by adjusted boxplot.^29,31

(2) Scale identification

The Automatic Item Selection Procedure (AISP) embedded in the “mokken” package of R was applied based on the genetic algorithms.^32–34 The global scalability coefficient (denoted as H) of the items was calculated. The boundary-value of the H set by the screening process started from .30 and ended at .54, and each step was .03. H < .30 would be taken as a violation of the Mokken principle, or unscalable.²⁹ After checking the results of different thresholds, an optimal value was selected, and a set with most or all items in one scale was extracted for further hypothesis testing. The pairwise scalability coefficient between items i and j was calculated as well (denoted as H_ij). Item pairs with H_ij<0 were concerned especially, as the pair relationship violated the Mokken model.

The local dependency testing algorithm of the Mokken package was used to test the scale.^29,35 The algorithm calculated the W index based on conditional association, indicating the degree to which an item was suspected to be local dependence. W was classified into W1, W2, and W3. The larger the value of W1 was, the more likely the two items i and j were to be a pair of positive-locally dependent items. The larger the value of W2 was, the more likely the item i was to be in a positive-locally dependent item pair. The larger the value of W3 was, the more likely the items i and j were to be negative-locally dependent pairs. The Tukey fence algorithm was used to define the extreme value: W>Q3 + 3*(Q3-M), in which M was the median and Q3 was the 3rd percentile. All W values beyond this limit are defined as extreme values, which determined whether items remained in the scale.

The monotonicity was tested by the “check.monotonicity” function from the “Mokken” package of R.²⁹ The parameter set the minimum sample size as 50 and the minimum size of a violation as .03.²⁴ Four indiceswould be reported for this test: (1) #ac: the number of possible violations; (2) #vi: the actual number of violations; (3) #zsig: number of statistically significant violations; (4) Crit: the critical value with weighted sum of other indices.³⁰ The larger the statistic was, the less monotonous the item was.

The invariant item ordering (IIO) assumed that the order of item difficulty was constant in any location of the trait continuum, which was also embedded in the “check.iio” algorithm of the “mokken” package.²⁴ The function was set as a manifest invariant item ordering (MIIO) by conducting a backward item selection procedure to make the final decision.

The items violating one of the three hypotheses were removed. The remained items entered the reliability testing step.

(3) Scale properties

Four reliability coefficients were calculated: Cronbach’s alpha, Guttman’s lambda-2, the Molenaar Sijtsma (MS) statistic, and the latent class reliability coefficient (LCRC), all ranging from 0 to 1.³⁶ A larger value indicated the stronger internal consistency. In comparison with the traditional Cronbach’s alpha and Guttman’s lambda-2, MS statistic and LCRC could afford an unbiased estimation of the reliability.³⁰ To be more precise, LCRC was more superior to MS statistic for multiple-scale analysis.

Rasch Modeling

The reason for Rasch modeling on the basis of the Mokken scale was that the Mokken scale could only rank the ability of the subjects but could not give the estimated values of the person ability level. The Rasch model provided an estimate of the individual’s level of competence. The Mokken scale provided a set of items for further Rasch modeling. The Rasch algorithms were embedded in the “ltm” (1.1–1) package of R, including 3 steps: (1) screening loop, (2) model checking, (3) parameter estimation.

(1) Screening loop

The point biserial correlation between each item and the total score was examined. The flagged items were summarized in X1. Then, an optimal model was selected from the constrained (discrimination = 1) and unconstrained (discrimination ≠ 1) Rasch models based on the likelihood ratio test. The model with the lower value of Akaike Information Criterion (AIC) was preferred. The item goodness-of-fit test was performed based on Chi-square statistics, and the items with p < .05 were recorded in the list of X2. If the aggregation of X1 and X2 was non-empty, the therein items would be removed and the next circle would start. Otherwise, the loop would stop. The last candidate set was fed into the next stage.

(2) Model checking

The goodness-of-fit test of the model was carried out by Pearson chi-square statistic with the “GoF.Rasch” algorithm of “ltm” package. The null hypothesis stated that the observed data had been generated under the Rasch model.³⁷ A p > .05 suggested that the parameters of the selected model were not significantly different from the simulated Rasch model. The unidimensionality was examined with 100 uni-dimensional models by the Monte Carlo simulation method.³⁸ A p > .05 indicated the candidate model was not significantly different from the simulated unidimensional models. If the candidate model passed both tests, it would become the final Rasch model for further parameter estimating.

(3) Parameter estimation

The position of the item, i.e., item difficulties, with standard error, and standardized score (z score) of the Rasch model were estimated. The chi-square test was performed to test the goodness of item fit, and the Bonferroni method was used to calibrate the p value. Items with an adjusted p > .05 fit good to the model. The Wright map was plotted to assess the compatibility between personal ability and item information.¹⁹ The item characteristic curve (ICC) checked the shape and described the relationship between the latent trait of the subjects and the probability of scoring. The monotonicity and IIO could be represented as parallel increasing ICCs. The differential item functioning (DIF) of the model was analyzed using Lord’s Chi-square analysis embedded in the “difR” package of R.³⁹ The purpose of DIF analysis was to prevent bias in the application of the same scale to different populations and thus avoid unfair evaluation for a certain population. Spearman correlation coefficient between the GMFCS and personability was estimated to analyze the validity of the estimated person ability and justification the Rasch model to measure health levels.

Results

Demographics

150 children with CP (84 males and 66 females) were recruited in this research. The distribution of demographic data was shown in Table 1, to show that the convenience sample conformed to the principle of maximum variation sampling, that was, to cover the whole range. There was no difference among different levels.

Table 1. The distribution of demographic data.

	0–5 years	6–13 years	14–18 years	p	statistics
n	63	81	6
Gender = male (%)	34 (54.0)	48 (59.3)	2 (33.3)	0.426	χ^2 = 1.7058
Diagnosis type (%)				0.360	χ^2 = 8.7896
ataxia	4 (6.3)	4 (4.9)	1 (16.7)
dyskinetic	10 (15.9)	13 (16.0)	0 (0.0)
hypotonic	0 (0.0)	4 (4.9)	0 (0.0)
spastic	34 (54.0)	50 (61.7)	4 (66.7)
mixed	15 (23.8)	10 (12.3)	1 (16.7)
GMFCS (%)				0.068	χ^2 = 14.564
I	18 (28.6)	10 (12.3)	0 (0.0)
II	15 (23.8)	20 (24.7)	3 (50.0)
III	10 (15.9)	9 (11.1)	0 (0.0)
IV	8 (12.7)	13 (16.0)	0 (0.0)
V	12 (19.0)	29 (35.8)	3 (50.0)
MACS (%)				0.369	χ^2 = 8.6913
I	5 (11.6)	6 (9.5)	0 (0.0)
II	15 (34.9)	12 (19.0)	0 (0.0)
III	10 (23.3)	17 (27.0)	2 (40.0)
IV	9 (20.9)	15 (23.8)	1 (20.0)
V	4 (9.3)	13 (20.6)	2 (40.0)

Pre-process

According to the standard that missing value should <5%, 24 items were eliminated. A total of 68 items were further analyzed by Mokken, including 33 items b and 35 items d.

Mokken Scale Analysis

(a) Data examination

Item b730 (Muscle power functions) handicap rate was 100% in the binarized data set, therefore excluded. The remaining 67 items were further analyzed as shown in Table 2.

Table 2. The remaining items in data examination during MSA.

No.	Code	Category title	Domain	No.	Code	Category title	Domain
1	b117	Intellectual functions	b	33	d110	Watching	d
2	b126	Temperament and personality functions	b	34	d115	Listening	d
3	b1301	Motivation	b	35	d120	Other purposeful sensing	d
4	b134	Sleep functions	b	36	d130	Copying	d
5	b140	Attention functions	b	37	d131	Learning through actions with objects	d
6	b152	Emotional functions	b	38	d133	Acquiring language	d
7	b156	Perceptual functions	b	39	d137	Acquiring concepts	d
8	b163	Basic cognitive functions	b	40	d140	Learning to read	d
9	b167	Mental functions of language	b	41	d160	Focusing attention	d
10	b210	Seeing functions	b	42	d220	Undertaking multiple tasks	d
11	b2152	Functions of external muscles of the eye	b	43	d230	Carrying out daily routine	d
12	b230	Hearing functions	b	44	d250	Managing one’s own behaviour	d
13	b260	Proprioceptive function	b	45	d310	Communicating with – receiving – spoken messages	d
14	b280	Sensation of pain	b	46	d330	Speaking	d
15	b320	Articulation functions	b	47	d331	Pre-talking	d
16	b440	Respiration functions	b	48	d335	Producing nonverbal messages	d
17	b445	Respiratory muscle functions	b	49	d350	Conversation	d
18	b4501	Transportation of airways mucus	b	50	d410	Changing basic body position	d
19	b455	Exercise tolerance functions	b	51	d415	Maintaining a body position	d
20	b510	Ingestion functions	b	52	d420	Transferring oneself	d
21	b525	Defecation functions	b	53	d430	Lifting and carrying objects	d
22	b530	Weight maintenance functions	b	54	d435	Moving objects with lower extremities	d
23	b620	Urination functions	b	55	d440	Fine hand use	d
24	b710	Mobility of joint functions	b	56	d445	Hand and arm use	d
25	b715	Stability of joint functions	b	57	d450	Walking	d
26	b735	Muscle tone functions	b	58	d455	Moving around	d
27	b740	Muscle endurance functions	b	59	d460	Moving around in different locations	d
28	b755	Involuntary movement reaction functions	b	60	d465	Moving around using equipment	d
29	b760	Control of voluntary movement functions	b	61	d530	Toileting	d
30	b765	Involuntary movement functions	b	62	d540	Dressing	d
31	b770	Gait pattern functions	b	63	d550	Eating	d
32	b810	Protective functions of the skin	b	64	d560	Drinking	d
				65	d710	Basic interpersonal interactions	d
				66	d760	Family relationships	d
				67	d880	Engagement in play	d

As a significant correlation existed between the Guttman error number of each subject and the total score of the questionnaire as shown in Figure 1 (p < .001), Pearson’s correlation coefficient indicated a positive correlation and the effect reached .61, which was considered to be a moderate correlation.⁴⁰

Figure 1. The correlation between the Guttman error number of each subject and the total score of the questionnaire.

The distribution of the Guttman error number was skewed, and the upper bound of the adjusted boxplot was 455.04. In this study, no extreme value beyond the upper bound was found as shown in Figure 2. Therefore, all subjects entered the next analysis.

Figure 2. The distribution of Guttman error.

(b) Scale identification

The overall homogeneity coefficient of the 67 items was .5235, which could be judged that the items constituted a strong scale.²⁹ The items needed to be furtherly filtered to conform to the MSA. The calculation results of AISP were illustrated in Table 3.

Table 3. The calculation results of AISP.

lower bound	max scale	unscalable items (%)	items in scale 1 (%)
0.30	3	7.46	80.60
0.33	2	10.45	82.09
0.36	2	8.96	76.12
0.39	1	16.42	83.58
0.42	2	14.93	82.09
0.45	2	16.42	80.60
0.48	2	16.42	76.12
0.51	2	22.39	68.66
0.54	2	28.36	65.67

According to the report of the sample size required for MSA, the results of automated item filtering were examined around a threshold of .42.³⁴ There was 10 unscalable items (scale = 0), 2 minority dimension items (scale = 2) and 55 1-scale items (scale = 1). The remaining 1-scale items were concluded in Table 4.

Table 4. The remaining 1-scale items in the Mokken scale identification.

Code	Category Title	Code	Category Title
b117	Intellectual functions	d110	Watching
b126	Temperament and personality functions	d115	Listening
b1301	Motivation	d120	Other purposeful sensing
b134	Sleep functions	d130	Copying
b140	Attention functions	d131	Learning through actions with objects
b152	Emotional functions	d133	Acquiring language
b156	Perceptual functions	d137	Acquiring concepts
b163	Basic cognitive functions	d140	Learning to read
b167	Mental functions of language	d160	Focusing attention
b2152	Functions of external muscles of the eye	d220	Undertaking multiple tasks
b230	Hearing functions	d230	Carrying out daily routine
b280	Sensation of pain	d250	Managing one’s own behaviour
b320	Articulation functions	d310	Communicating with – receiving – spoken messages
b440	Respiration functions	d330	Speaking
b445	Respiratory muscle functions	d331	Pre-talking
b4501	Transportation of airways mucus	d335	Producing nonverbal messages
b455	Exercise tolerance functions	d410	Changing basic body position
b510	Ingestion functions	d420	Transferring oneself
b525	Defecation functions	d430	Lifting and carrying objects
b530	Weight maintenance functions	d435	Moving objects with lower extremities
b620	Urination functions	d440	Fine hand use
b715	Stability of joint functions	d445	Hand and arm use
b765	Involuntary movement functions	d450	Walking
b770	Gait pattern functions	d460	Moving around in different locations
b810	Protective functions of the skin	d465	Moving around using equipment
		d530	Toileting
		d540	Dressing
		d550	Eating
		d560	Drinking
		d710	Basic interpersonal interactions

Based on the reserved 55 items, a new scale was constructed again, and the homogeneity coefficients of the whole and each item were calculated. The global homogeneity coefficient of the scale H = .5761 and the standard error (SE) = .0352 were concluded in Table 5. The H_i of every items was > .42, suggesting that the current sample size was suitable for the Mokken analysis of this item set. The standard error of b770 (Gait pattern functions) and d435 (Moving objects with lower extremities) was > .10, suggesting that more attention should be paid to future analysis and clinical evaluation.

Table 5. The global homogeneity coefficient and standard error of the reserved items.

Code	Category Title	Hi	SE
b117	Intellectual functions	0.4434	0.0600
b126	Temperament and personality functions	0.5648	0.0519
b1301	Motivation	0.4972	0.0564
b134	Sleep functions	0.6234	0.0646
b140	Attention functions	0.4896	0.0758
b152	Emotional functions	0.4938	0.0564
b156	Perceptual functions	0.5533	0.0542
b163	Basic cognitive functions	0.5093	0.0532
b167	Mental functions of language	0.6399	0.0441
b2152	Functions of external muscles of the eye	0.4337	0.0742
b230	Hearing functions	0.6766	0.0673
b280	Sensation of pain	0.5317	0.0737
b320	Articulation functions	0.5762	0.0492
b440	Respiration functions	0.5992	0.0567
b445	Respiratory muscle functions	0.6176	0.0553
b4501	Transportation of airways mucus	0.7475	0.0529
b455	Exercise tolerance functions	0.4863	0.0593
b510	Ingestion functions	0.6786	0.0418
b525	Defecation functions	0.7164	0.0445
b530	Weight maintenance functions	0.5953	0.0619
b620	Urination functions	0.6824	0.0576
b715	Stability of joint functions	0.4243	0.0979
b765	Involuntary movement functions	0.4492	0.0558
b770	Gait pattern functions	0.6025	0.2028
b810	Protective functions of the skin	0.6223	0.0530
d110	Watching	0.5349	0.0835
d115	Listening	0.7102	0.0614
d120	Other purposeful sensing	0.5395	0.0605
d130	Copying	0.6126	0.0451
d131	Learning through actions with objects	0.6114	0.0461
d133	Acquiring language	0.5997	0.0456
d137	Acquiring concepts	0.6315	0.0485
d140	Learning to read	0.6230	0.0549
d160	Focusing attention	0.5008	0.0881
d220	Undertaking multiple tasks	0.7150	0.0523
d230	Carrying out daily routine	0.5552	0.0761
d250	Managing one’s own behaviour	0.5831	0.0480
d310	Communicating with – receiving – spoken messages	0.5715	0.0484
d330	Speaking	0.6020	0.0447
d331	Pre-talking	0.6026	0.0446
d335	Producing nonverbal messages	0.5856	0.0481
d410	Changing basic body position	0.5234	0.0673
d420	Transferring oneself	0.5228	0.0573
d430	Lifting and carrying objects	0.6051	0.0812
d435	Moving objects with lower extremities	0.4758	0.1109
d440	Fine hand use	0.5978	0.0741
d445	Hand and arm use	0.4725	0.0627
d450	Walking	0.4204	0.0945
d460	Moving around in different locations	0.5030	0.0672
d465	Moving around using equipment	0.5603	0.0522
d530	Toileting	0.5434	0.0553
d540	Dressing	0.5685	0.0550
d550	Eating	0.6513	0.0398
d560	Drinking	0.6751	0.0366
d710	Basic interpersonal interactions	0.6195	0.0484
All items		0.5761	0.0352

The homogeneity coefficient H_ij was visualized in the form of a thermal diagram Figure 3. The color of the origin was related to the value of H_ij. The darker the blue, the larger H_ij was; the darker the red, the smaller H_ij was. A grid with a red box meant H_ij < 0. By analyzing the figure, it was found that most of the absolute values of H_ij violating the model were < .10: b770 and b715 (−.07), b770 and d430 (−.06), b770 and d440 (−.06) as well as d115 and d435 (−.05).

Figure 3. Local dependence based on the homogeneity coefficient H_ij.

No items were eliminated through the local dependency algorithm embedded in the “check.ca” function. The 55 items were retained in the scale.

The indices of the monotonicity test were shown in Table 6. There were no significant violations , that was, #zsig was equal to 0. The item response function (IRF) of all items was of ascending type as shown in Appendix A.

Table 6. The indices of the monotonicity test.

Code	Category Title	#ac	#vi	#zsig	Crit
b117	Intellectual functions	1	0	0	0
b126	Temperament and personality functions	1	0	0	0
b1301	Motivation	1	0	0	0
b134	Sleep functions	1	0	0	0
b140	Attention functions	0	0	0	0
b152	Emotional functions	1	0	0	0
b156	Perceptual functions	1	0	0	0
b163	Basic cognitive functions	1	0	0	0
b167	Mental functions of language	0	0	0	0
b2152	Functions of external muscles of the eye	1	0	0	0
b230	Hearing functions	1	0	0	0
b280	Sensation of pain	1	0	0	0
b320	Articulation functions	1	0	0	0
b440	Respiration functions	1	0	0	0
b445	Respiratory muscle functions	1	0	0	0
b4501	Transportation of airways mucus	1	0	0	0
b455	Exercise tolerance functions	0	0	0	0
b510	Ingestion functions	1	0	0	0
b525	Defecation functions	1	0	0	0
b530	Weight maintenance functions	1	0	0	0
b620	Urination functions	1	0	0	0
b715	Stability of joint functions	0	0	0	0
b765	Involuntary movement functions	0	0	0	0
b770	Gait pattern functions	0	0	0	0
b810	Protective functions of the skin	1	0	0	0
d110	Watching	1	0	0	0
d115	Listening	1	0	0	0
d120	Other purposeful sensing	1	0	0	0
d130	Copying	1	0	0	0
d131	Learning through actions with objects	0	0	0	0
d133	Acquiring language	0	0	0	0
d137	Acquiring concepts	0	0	0	0
d140	Learning to read	0	0	0	0
d160	Focusing attention	0	0	0	0
d220	Undertaking multiple tasks	0	0	0	0
d230	Carrying out daily routine	0	0	0	0
d250	Managing one’s own behaviour	0	0	0	0
d310	Communicating with – receiving – spoken messages	0	0	0	0
d330	Speaking	0	0	0	0
d331	Pre-talking	0	0	0	0
d335	Producing nonverbal messages	0	0	0	0
d410	Changing basic body position	0	0	0	0
d420	Transferring oneself	0	0	0	0
d430	Lifting and carrying objects	0	0	0	0
d435	Moving objects with lower extremities	1	0	0	0
d440	Fine hand use	0	0	0	0
d445	Hand and arm use	0	0	0	0
d450	Walking	0	0	0	0
d460	Moving around in different locations	0	0	0	0
d465	Moving around using equipment	1	0	0	0
d530	Toileting	0	0	0	0
d540	Dressing	0	0	0	0
d550	Eating	1	0	0	0
d560	Drinking	0	0	0	0
d710	Basic interpersonal interactions	1	0	0	0

#ac: the number of possible violations; #vi: the actual number of violations; #zsig: number of statistically significant violations; Crit: the weighted sum of other indices.

There were four items defined with a significant violation number #zsig of 1 in the invariant item ordering (IIO) test. Among the four items, the corresponding Crit < 40, and the actual number of violations was 2 or 3. The b1301 had the highest Crit value and the highest number of possible violations. The b152 ranked second in the number of possible violations, but the number of actual violations was the largest. After Mokken’s IIO algorithm deleted these two items in sequence, the remaining items could be invariantly ordered. There were 53 items left as shown in Table 7 till now.

Table 7. The remaining items after Mokken’s IIO algorithm (manifest invariant item ordering, MIIO).

Code	Category Title	#ac	#vi	#zsig	Crit
b117	Intellectual functions	56	0	0	0
b126	Temperament and personality functions	56	0	0	0
b1301	Motivation	57	2	1	39
b134	Sleep functions	54	3	0	7
b140	Attention functions	54	0	0	0
b152	Emotional functions	56	3	1	30
b156	Perceptual functions	56	1	0	1
b163	Basic cognitive functions	56	1	0	5
b167	Mental functions of language	54	0	0	0
b2152	Functions of external muscles of the eye	55	6	0	38
b230	Hearing functions	54	1	0	−4
b280	Sensation of pain	54	1	0	11
b320	Articulation functions	55	0	0	0
b440	Respiration functions	58	1	0	2
b445	Respiratory muscle functions	55	1	0	−1
b4501	Transportation of airways mucus	54	1	0	−7
b455	Exercise tolerance functions	55	0	0	0
b510	Ingestion functions	54	1	0	3
b525	Defecation functions	54	0	0	0
b530	Weight maintenance functions	54	1	0	4
b620	Urination functions	54	0	0	0
b715	Stability of joint functions	54	0	0	0
b765	Involuntary movement functions	54	0	0	0
b770	Gait pattern functions	54	0	0	0
b810	Protective functions of the skin	55	1	0	7
d110	Watching	54	0	0	0
d115	Listening	54	1	0	−6
d120	Other purposeful sensing	54	1	0	1
d130	Copying	54	0	0	0
d131	Learning through actions with objects	54	0	0	0
d133	Acquiring language	54	0	0	0
d137	Acquiring concepts	54	0	0	0
d140	Learning to read	54	0	0	0
d160	Focusing attention	54	0	0	0
d220	Undertaking multiple tasks	54	0	0	0
d230	Carrying out daily routine	54	0	0	0
d250	Managing one’s own behaviour	55	0	0	0
d310	Communicating with – receiving – spoken messages	54	0	0	0
d330	Speaking	54	0	0	0
d331	Pre-talking	54	0	0	0
d335	Producing nonverbal messages	54	0	0	0
d410	Changing basic body position	54	0	0	0
d420	Transferring oneself	54	0	0	0
d430	Lifting and carrying objects	54	0	0	0
d435	Moving objects with lower extremities	54	0	0	0
d440	Fine hand use	54	0	0	0
d445	Hand and arm use	54	0	0	0
d450	Walking	54	0	0	0
d460	Moving around in different locations	54	0	0	0
d465	Moving around using equipment	54	0	0	0
d530	Toileting	54	0	0	0
d540	Dressing	54	0	0	0
d550	Eating	55	2	1	32
d560	Drinking	54	2	1	17
d710	Basic interpersonal interactions	54	0	0	0

#ac: the number of possible violations; #vi: the actual number of violations; #zsig: number of statistically significant violations; Crit: the weighted sum of other indices.

(c) Scale properties

The reliability test results showed that the Cronbach’s alpha = .9621, lambda-2 = .9653, MS statistic = .9705, LCRC = .9811, which indicated good reliability of the 53-item Mokken scale.⁴¹

Rasch Modeling

(a) Screening loop

There were two loops in this study, and all the excluded items were generated from the goodness-of-fit test of items in the first loop, including b2152 (Functions of external muscles of the eye), b280 (Sensation of pain), d110 (Watching) and d435 (Moving objects with lower extremities). The list of all deleted items was concluded in Appendix B.

The Rasch model constructed by the remaining 49 items was compared. The p = 1 indicated no significant difference between the restricted model and the unrestricted model. However, the AIC (5250.53) and BIC (5398.05) of the restricted Rasch model were lower than the unrestricted Rasch model (7019.16 and 7169.69 respectively), while the logLik was higher (−2576.27 v.s. −3459.58) as displayed in Table 8. Therefore, the restricted Rasch model was selected. This constrained Rasch model comprising 49 items moved on to the next stage.

Table 8. The comparison of the restricted Rasch model and the unrestricted model.

Rasch model	AIC	BIC	log.Lik	LRT	DF	p.value
restricted	5250.53	5398.05	−2576.27
unrestricted	7019.16	7169.69	−3459.58	−1766.63	1	1

AIC: Akaike information criterion; BIC: Bayesian Information Criterion; log.Lik: log-likelihood; LRT: the value of the Likelihood Ratio Test statistic; DF: the degree of freedom.

(b) Model checking

In this study, the GoF.Rasch algorithm of “ltm” package was applied and the resulted p value was .02. The selected Rasch model was considered to be not far from the simulated Rasch models based on the same parameters. The unidimensional test revealed that the measured second eigenvalue was 4.7482, while the average second eigenvalue of the Monte Carlo simulation model was 5.1080. The p value was .5545, which indicated there was no significant difference between the selected model and the simulated unidimensional models. In addition, a significant correlation between the total score of the scale and the individual ability level estimated by the Rasch model was shown in Figure 4. The p value of the correlation test was 4 × 10⁻¹²⁴, the effect value was .99, which meant a strong correlation.⁴⁰

Figure 4. The correlation between the total score of the scale and the individual ability level estimated by the Rasch model.

(c) Parameter estimation

The parameters of 49 items in the final Rasch model were displayed in Table 9, including item difficulty (also known as position), standard error (SE), and normalized value (z-score). It could be found that the Bonferroni adjusted p value of each item was greater than .05, suggesting that all items fit well.

Table 9. The parameters of 49 items in the final Rasch model.

Code	Category title	Difficulty	SE	z-score	χ^2	p	p.adj
b770	Gait pattern functions	5.7215	0.7433	7.698	6.6316	0.6754	1
d430	Lifting and carrying objects	4.1077	0.4125	9.9583	2.8107	0.9713	1
d440	Fine hand use	3.9616	0.395	10.0297	4.9357	0.8399	1
b715	Stability of joint functions	3.8146	0.3788	10.0708	7.6167	0.5732	1
d220	Undertaking multiple tasks	3.8144	0.3788	10.0709	7.779	0.5566	1
d450	Walking	3.5685	0.3545	10.0675	13.1569	0.1556	1
d230	Carrying out daily routine	3.3493	0.3354	9.9851	5.7367	0.7659	1
d540	Dressing	3.2465	0.3273	9.9202	8.1583	0.5183	1
d160	Focusing attention	3.0613	0.3137	9.7598	11.5827	0.2379	1
d445	Hand and arm use	2.9739	0.3077	9.6647	10.1327	0.3399	1
d410	Changing basic body position	2.9739	0.3077	9.6646	5.9193	0.748	1
d460	Moving around in different locations	2.9739	0.3077	9.6646	4.9799	0.8361	1
d530	Toileting	2.8885	0.3022	9.5597	7.5025	0.585	1
b140	Attention functions	2.8885	0.3022	9.5596	3.5543	0.9382	1
d140	Learning to read	2.5806	0.2842	9.0814	7.617	0.5732	1
d420	Transferring oneself	2.4394	0.2769	8.8101	6.0561	0.7343	1
d137	Acquiring concepts	2.3059	0.2705	8.5238	13.0732	0.1593	1
b167	Mental functions of language	2.1804	0.265	8.2288	10.8414	0.2867	1
b765	Involuntary movement functions	2.1193	0.2624	8.0761	17.0075	0.0486	1
d250	Managing one’s own behaviour	2.0589	0.26	7.9195	14.7179	0.099	1
b455	Respiratory muscle functions	1.9415	0.2555	7.5989	12.0265	0.2118	1
d465	Moving around using equipment	1.885	0.2535	7.4372	7.6743	0.5673	1
d710	Basic interpersonal interactions	1.8299	0.2515	7.275	20.4178	0.0155	0.7596
b117	Intellectual functions	1.8299	0.2515	7.275	8.5719	0.4777	1
d310	Communicating with – receiving – spoken messages	1.7758	0.2497	7.1111	13.2254	0.1527	1
d131	Learning through actions with objects	1.7757	0.2497	7.1109	17.2694	0.0447	1
d335	Producing nonverbal messages	1.722	0.248	6.9442	11.9954	0.2136	1
d133	Acquiring language	1.6155	0.2447	6.6018	9.9976	0.3507	1
d330	Speaking	1.5633	0.2432	6.428	14.1423	0.1174	1
d331	Pre-talking	1.4618	0.2404	6.0799	12.3533	0.1941	1
b163	Basic cognitive functions	1.3636	0.238	5.7304	6.7956	0.6584	1
b320	Articulation functions	1.3151	0.2368	5.5535	8.4983	0.4848	1
d130	Copying	1.2198	0.2347	5.1976	13.1636	0.1553	1
d550	Eating	0.8526	0.2281	3.7371	14.6817	0.1001	1
d560	Drinking	0.8083	0.2275	3.5525	16.8803	0.0506	1
b156	Perceptual functions	0.7648	0.227	3.3698	15.3849	0.0809	1
d120	Other purposeful sensing	0.5468	0.2246	2.4345	11.8228	0.2235	1
b126	Temperament and personality functions	0.5034	0.2242	2.245	13.2679	0.1509	1
b445	Respiratory muscle functions	−0.3435	0.2234	−1.5379	15.1472	0.087	1
b510	Ingestion functions	−0.4714	0.2242	−2.1021	12.5052	0.1863	1
b440	Respiration functions	−0.5153	0.2246	−2.2945	11.9638	0.2154	1
b810	Protective functions of the skin	−0.7317	0.2267	−3.227	3.6414	0.9334	1
b530	Weight maintenance functions	−0.8209	0.2278	−3.6032	18.149	0.0335	1
b525	Defecation functions	−1.1884	0.2336	−5.0871	11.5399	0.2405	1
b620	Urination functions	−1.2356	0.2345	−5.2691	12.7609	0.1737	1
b134	Sleep functions	−1.3316	0.2364	−5.632	11.0591	0.2717	1
b230	Hearing functions	−1.3316	0.2364	−5.632	22.3831	0.0077	0.3793
d115	Listening	−1.4295	0.2386	−5.9917	9.6832	0.3767	1
b4501	Transportation of airways mucus	−1.53	0.2409	−6.3498	17.1129	0.047	1

SE: standard error; p.adj: the Bonferroni adjusted p value.

The Wright map of the relationship between individual capabilities and items was shown in Figure 5, which suggested the items were fairly distributed across the range of individual abilities, and most items had proper difficulties. There was no obvious skewness in the distribution of individual ability.

Figure 5. The Wright map of the relationship between individual capabilities and item difficulties.

The ICCs indicated that the distribution of the items at different positions was s-shaped as shown in Figure 6, and most item difficulties were in the range of 0–1. The slopes of curves were not far apart from each other. The parallelly increasing curves also supported the monotonicity and IIO.

Figure 6. The item characteristic curves in Rasch modeling.

The item information curves indicated that each item had a relatively balanced amount of information at different levels of individual ability as displayed in Figure 7. That was, although the bell-shaped curve moved along the horizontal axis, there was no significant difference in the highest point and the shape along the vertical axis.

Figure 7. The item information curves in Rasch modeling.

The Lord’s Chi-square limit was 3.84, but no items were identified as DIF items after Holm adjustment for multiple comparisonsas shown in Table 10. It was suggested that the Rasch model with 49 ICF items established had no significant gender bias in the estimation of individual ability level.

Table 10. The output of Lord’s Chi-square test.

Code	Category Title	χ^2	p	Holm adj.p
b117	Intellectual functions	0.5808	0.446	1
b126	Temperament and personality functions	0	0.9953	1
b134	Sleep functions	0.1528	0.6959	1
b140	Attention functions	0.8335	0.3613	1
b156	Perceptual functions	0.1119	0.738	1
b163	Basic cognitive functions	0.1811	0.6704	1
b167	Mental functions of language	1.891	0.1691	1
b230	Hearing functions	0.0007	0.979	1
b320	Articulation functions	0.4087	0.5226	1
b440	Respiration functions	0.1863	0.666	1
b445	Respiratory muscle functions	0.0741	0.7854	1
b4501	Transportation of airways mucus	0.1081	0.7423	1
b455	Exercise tolerance functions	0.3016	0.5829	1
b510	Ingestion functions	0.8225	0.3645	1
b525	Defecation functions	0.8392	0.3596	1
b530	Weight maintenance functions	0.0882	0.7665	1
b620	Urination functions	0.1093	0.741	1
b715	Stability of joint functions	1.3564	0.2442	1
b765	Involuntary movement functions	4.5526	0.0329	1
b770	Gait pattern functions	0.03	0.8626	1
b810	Protective functions of the skin	0.4162	0.5188	1
d115	Listening	0.2075	0.6487	1
d120	Other purposeful sensing	1.8321	0.1759	1
d130	Copying	0.9491	0.33	1
d131	Learning through actions with objects	0.1266	0.722	1
d133	Acquiring language	0.472	0.4921	1
d137	Acquiring concepts	0	0.9964	1
d140	Learning to read	0.0064	0.9362	1
d160	Focusing attention	0.1031	0.7482	1
d220	Undertaking multiple tasks	0.9241	0.3364	1
d230	Carrying out daily routine	1.6981	0.1925	1
d250	Managing one’s own behaviour	0.9817	0.3218	1
d310	Communicating with – receiving – spoken messages	0.2731	0.6013	1
d330	Speaking	0.2096	0.6471	1
d331	Pre-talking	0.7187	0.3966	1
d335	Producing nonverbal messages	0.0219	0.8825	1
d410	Changing basic body position	0.0039	0.9505	1
d420	Transferring oneself	0.0012	0.972	1
d430	Lifting and carrying objects	1.3128	0.2519	1
d440	Fine hand use	0.0037	0.9514	1
d445	Hand and arm use	1.1333	0.2871	1
d450	Walking	0.6609	0.4162	1
d460	Moving around in different locations	1.1336	0.287	1
d465	Moving around using equipment	1.0138	0.314	1
d530	Toileting	0.0353	0.8511	1
d540	Dressing	0.0736	0.7862	1
d550	Eating	5.1692	0.023	1
d560	Drinking	4.3362	0.0373	1
d710	Basic interpersonal interactions	0.3204	0.5713	1

There was a significant correlation between the individual ability level of each participant in the Rasch model and the GMFCS score (p = .006 < .05). The correlation coefficient was Spearman r = −.28 with 95%CI [−.42, −.12]. However, there was no significant correlation between individual ability level and MACS score (p = .192, Spearman r = −.19, 95%CI [−.37, −.00387]).

Discussion

The present study employed MSA based on the ICF-CY and estimated psychometric properties of children with CP through the Rasch model derived from the Mokken scale. The results confirmed the unidimensionality of the instrument and realized a simple assessment of ICF-based personability estimation for children with CP.

It is necessary to build a scale based on ICF to measure individual competence from the healthy level instead of the disabled degree. IRT is a theoretical system developed from the examination method to solve this requirement. As one of the best-known IRT models, the Rasch model has been applied to several ICF studies with the ICF brief core set, the rehabilitation set and the spinal cord injury set.^17–23 To describe the relationship between person ability and the scale score, the parametric IRT models set a variety of parameters including discrimination, difficulty, pseudo-guessing parameter, and careless responding. In recent years, the nonparametric IRT models based on the Mokken hypothesis have raised attention in medical research, which can simplify the procedure of item screening for further Rasch modeling.^24–26 Mokken proposes that high-ability subjects are more likely to score on low-difficulty tasks. Thus, MSA has been developed for the calculation of the total score, and the Mokken scale becomes the simplest form of clinical quantitative evaluation.^24,35 On the one hand, MSA can rank the personal abilities by sorting total scores rather than by estimating parameters. The unidimensional Rasch model can help obtain the individual ability estimation of the subjects. In addition, the general ICF assessment takes a long time to complete the five-level score of each item, which limits the clinical application. By changing the graded method, a binary data series (0 means disabled, 1 means healthy) can be constructed, so that the total score can reflect the health level of patients.

This study excluded 24 items at the pre-processing phase. The great number of missing values in these items could be due to inapplicability to all age groups. For example, d815 (Preschool education) and d820 (School education) were not suitable for certain age groups. Also, b164 (Higher-level cognitive functions), d145 (Learning to write), d510 (Washing oneself), d520 (Caring for body parts), d845 (Acquiring, keeping, and terminating a job) were unfit for younger children. Item b730 (Muscle power functions) was eliminated in the data examination step of the MSA stage because of the 100% dysfunction rate. To apply Rasch modeling in the follow-up stage, it was necessary to build unidimensional data instead of multidimensional data. According to the recommendation criteria of the Mokken analysis, the threshold filtering requirements of a one-dimensional data set are as follows: A) most or all of the items are located in the same scale; B) there is a secondary scale less than the primary scale; C) one or above smaller scales are with some non-scalable entries.²⁹ If the screening scheme meets these three requirements, the item contained in A will be selected as the final item. As such, the AISP eliminated 12 items with a boundary of .42. The eliminated 0-scale item included b210 (Seeing functions), b260 (Proprioceptive function), b710 (Mobility of joint functions), b735 (Muscle tone functions), b740 (Muscle endurance functions), b755 (Involuntary movement reaction functions), b760 (Control of voluntary movement functions), d415 (Maintaining a body position), d455 (Moving around), d880 (Engagement in play), and the eliminated 2-scale items were d350 (Conversation) and d760 (Family relationships). During the invariant item ordering test of the MAS stage, b152 (Emotional functions) and b1301 (Motivation) were excluded. The former ranked second in the number of possible violations, but the number of actual violations was the largest. The latter got the highest Crit value and the highest number of possible violations. During item screening looping of the Rasch stage, four items failed to pass the goodness-of-fit test in the first loop, including b2152 (Functions of external muscles of the eye), b280 (Sensation of pain), d110 (Watching) and d435 (Moving objects with lower extremities). To sum up, a total of 19 items were excluded in MSA and Rasch modeling stages. Considering that the research population was children with CP, one possible reason for these exclusions could be that the content of the item was a favored and valued issue for diagnosis rather than for functioning level evaluation, such as b735 (Muscle tone functions), b755 (Involuntary movement reaction functions), b760 (Control of voluntary movement functions) and so on. Another potential reason may be that the items were assessed without sufficient consistency and precision. Some functions were more likely to vary in children than in adults. Some conditions may not be expressed clearly by children. For example, b1301 (Motivation), b152 (Emotional functions), b280 (Sensation of pain). One highly important reason that should be emphasized was that IRT modeling filterd out all items that did not contribute to differentiating person abilities. That was, although the removed items seemed valuable for CP children, they could not constitute a scale for ranking functioning abilities.

Ultimately, the number of preserved ICF items was reduced to 49, which would help to shorten the interview elapsed time visibly. The difficulty ranking of the items showed that among the top 10 items, 2 items were in the b domain and 8 items were in the d domain. Among them, b770 (Gait pattern functions) was the most difficult item, suggesting that children with CP were most prone to gait disorders. Most d domain items involved upper limb and hand mobility, indicating that most children with CP had dysfunction of upper limbs and hands. A distinct proportion of items 11 to 40 were related to cognitive and verbal functions, while the last 9 items were more related to basic functions such as b440 (Respiration functions), b134 (Sleep functions), b525 (Defecation functions), b620 (Urination functions) and so on. The score conversion table could be found in Appendix C.

The significant correlation between person ability and GMFCS revealed that the scale generated in this study can be used to reflect the gross exercise level of children. The lower the GMFCS score is, the lower the handicap level is, the higher the health level is.⁴⁰ In addition, the individual ability level calculated by the model can aid in the diagnosis and treatment of CP. However, the fine motor level (MACS) cannot be obtained by the conversion of score alone and may need to be combined with the special evaluation.

This study has certain clinical value. First, the binarization of the data offers a clinically friendly scoring system. The assessment can be done via a quick yes-or-no questionnaire. Second, the strategy of assigning impairment/dysfunction as 0 and independent/functioning as 1 makes the latent trait estimated by the IRT model to be level of person abilities rather than degree of person disabilities. Third, based on the “assigning by functioning” strategy, the difficulty estimated by the IRT model gets its clinical meaning of “how difficult is it to let this item get score 1, be independent, or maintain healthy.” Putting the three points together, for a specific person, their personal health level estimated through the IRT model and the specific dysfunction items in their response records can be embedded into a background of the populational distribution of person abilities and item difficulties. Figure 5 shows that the J.H. had personal ability value of 2.8612 logit. The d420 (Transferring oneself) was easier than her ability. From a populational perspective, J.H. should be capable of d420. However, her d420 was dependent. Therefore, we can propose the d420 as the preferred rehabilitation target. Among the categories more difficult than J.H.’s ability, the d410 (Changing basic body position), d445 (Hand and arm use), d460 (Moving around in different locations), and d530 (Toileting) were the four dependent items closest to her ability level. If we want to discuss with the caregiver/child about which item should be the optimal rehabilitation goal, the relationships between individual ability and populational item difficulty distribution can offer more solid evidence for the conversation. If we want to study the dependent items in more details, the rank of item difficulty may provide directions for assessments utilizing other comprehensive scales. To sum up, the primary purpose of this study is to provide a convenient ICF-based tool for children with CP at the level of functioning, independent, and health. Additionally, it can also provide a reference for the selection of therapeutic target items in clinical application.

Some limitations should be acknowledged in this study. First, the subjects of this study were children with CP, who may lack sufficient judgment, execution, and cooperation. Thus, a portion of the ICF assessments was completed by the guardians, which differs from the original design of IRT. This cohort of children will continue to be followed up in the future to determine if the model of this study reflects the actual health status in this age group. Second, the sample size needed to be expanded in order to help address the above issues and to provide the indicator as accurate as possible. We will continue to include subjects of different ages and educational levels, as the unscalable items in this study may be scalable well across populations with different age ranges and educational levels.

Conclusion

This study has confirmed the ICF clinical application through the Rasch model based on MSA, which focused on the healthy level rather than the disabled condition. With relatively fewer but more specific items, it can guide the grading of individual functioning degrees in the assessment and treatment for children with CP.

Acknowledgments

The study was approved by the ethics committee of TheSir Run Run Hospital, Nanjing Medical University (IRB# 2018-SR-017). We are grateful to all the participants and therapists for data collection.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Supplementary Material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/17518423.2023.2166614

Additional information

Funding

This work was supported by the Key Disciplines Construction Project of Suzhou under Grant Szxk201811 and the Introduction Project of Yue Shouwei Rehabilitation Medicine Team of Qilu Hospital of Shandong University under Grant SZYJTD201808.

Appendix A.

The item response function (IRF) of items

Appendix B.

All deleted items in this study

Table

Code	Category title	Domain
b1301	Motivation	b
b152	Emotional functions	b
b210	Seeing functions	b
b2152	Functions of external muscles of the eye	b
b260	Proprioceptive function	b
b280	Sensation of pain	b
b710	Mobility of joint functions	b
b730	Muscle power functions	b
b735	Muscle tone functions	b
b740	Muscle endurance functions	b
b755	Involuntary movement reaction functions	b
b760	Control of voluntary movement functions	b
d110	Watching	d
d350	Conversation	d
d415	Maintaining a body position	d
d435	Moving objects with lower extremities	d
d455	Moving around	d
d760	Family relationships	d
d880	Engagement in play	d

Appendix C.

The score conversion table for children with CP

Table

sum score	person ability (logit)	personal ability (percentage)	sum score	person ability (logit)	personal ability (percentage)
0	−2.362	0	25	1.6426	65
1	−2.1675	3	26	1.7657	67
2	−1.976	6	27	1.8859	69
3	−1.7872	9	28	2.0033	71
4	−1.6014	12	29	2.1178	73
5	−1.4183	15	30	2.2294	74
6	−1.2382	18	31	2.3382	76
7	−1.0609	21	32	2.4442	78
8	−0.8864	24	33	2.5473	80
9	−0.7148	27	34	2.6475	81
10	−0.5461	29	35	2.7449	83
11	−0.3802	32	36	2.8394	84
12	−0.2171	35	37	2.9311	86
13	−0.057	37	38	3.0199	87
14	0.1004	40	39	3.1059	89
15	0.2548	42	40	3.189	90
16	0.4065	45	41	3.2693	91
17	0.5552	47	42	3.3467	93
18	0.7011	50	43	3.4212	94
19	0.8442	52	44	3.4929	95
20	0.9844	54	45	3.5618	96
21	1.1217	56	46	3.6278	97
22	1.2562	59	47	3.6909	98
23	1.3879	61	48	3.7512	99
24	1.5167	63	49	3.8086	100