Psychometric Properties of the China Developmental Scale of Children in Infant Aged 0-1 Years old with developmental delay: A Rasch Analysis

DOI: https://doi.org/10.21203/rs.3.rs-2188811/v1

Abstract

Background: Children development is a multidimensional construct encompassing gross motor, fine motor, adaptive behavior, speech and language, and social behavior. The China Developmental Scale of Children (CDSC) has been tested using traditional methods. This study aimed to make amendment to previous evidence by using Rasch Model and elaborate the psychometric properties of the CDSC in a new perspective. 

Methods: 200 children and infants were recruited and finished the CDSC. Data were collected and used for the analysis. Rasch Model was adopted to test the psychometric properties of the CDSC regard the fitness to the prediction of the Model. Unidimensionality was tested using principal component analysis. Differential item functioning (DIF) analysis was performed across gender and age group (older or younger than 6.5 months old). 

Result: Data from 200 children with developmental delays were obtained. The result showed that the items from the CDSC presented acceptable fitness to the Rasch Model(Person Infit MNSQ:0.83~0.9;Item Infit MNSQ:0.9~0.93). Besides, 11 unfitting(misfitting or overfitting) items were found. The impact of the unfitting items on the average fit statistics was evaluate by reanalysis, and the result showed that the person reliability and separation were lower while the infit MNSQ got higher. The unidimensionality was supported by the result of the principal component analysis(Measures explained variance:79.6%~87.8%). Further, the reliability and the separation index of the item and person indicated that the assumption of the internal consistency was confirmed (Person.Reliability:0.91~0.96; Person.Separation:4.27~3.5; Item.Reliablity:0.99~1; Item.Separation:13.39~19.28). 

Conclusion: Our study found that the CDSC had shown reasonable fitness to the Rasch Model. The result support that the CDSC was established based on a unidimensional structure with good internal consistency. The misfitting items still required reformulation to demonstrate corresponding content more clearly.

Background

Developmental Delay has been introduced by the International Classification of Function, Disability and Health for Children and Youth(ICF-CY), this diagnosis describes those children who exhibits significant variation in achieving developmental milestones(Warren et al., 2016).Previous studies suggested that efforts needs to be made when we designing tools for monitoring developmental trajectory, lags in the emergence of developmental milestones may be found in various domain(e.g. motor, cognition, speech and language, communication and mobility)(Marlow, Servili, & Tomlinson, 2019).

The China Developmental Scale for Children(CDSC) is a comprehensive scale developed for assessing children with developmental disability or delay(Chun-hua et al., 2014; Zhang et al., 1997). The CDSC contains items originate from a longitude and cross-section study on children under 42 months old in 1980.Theses items were categorized into 5 developmental domain including gross motor function, fine motor function, speech and language, adaptive ability, social interaction. Based on Classical Testing Theory, previous studies have examined the psychometric properties of the CDSC, these findings suggested that CDSC exhibited good reliability in children under 6 years old, while the gross motor function domain of CDSC shown a reasonable correlation with Alberta Infant Motor Scale in children under 12 months old(Chun-hua et al., 2015; Li-li et al., 2015; Rui-li et al., 2015; Zhao-fang et al., 2013).

Rasch Model is generally accepted as an augment to Classical Testing Theory. Rasch Model converts the raw score summary to its natural logarithm, constructing an interval scale from dichotomous-level observation. Classical Testing Theory defines the total score of a set of items as the latent traits of a person, while Rasch Model utilized the score of items as the Sufficient Statistic for estimating person ability (the latent traits of a person) and items difficulty independently. The Rasch Model related the probability of a successful(unsuccessful) responses \({x}_{\upsilon \iota }\) to the difference between person ability \({\beta }_{\upsilon }\)and item difficulty \({\delta }_{\iota }\), it allows us to estimate \({\beta }_{\upsilon }\)and \({\delta }_{\iota }\) independently from available data, then we can examine the way these data fit with prediction calculated from the model. The equation is shown below:

$$P\left\{{x}_{\upsilon \iota }=1|{\beta }_{\upsilon },{\delta }_{\iota }\right\}=\frac{exp\left({\beta }_{\upsilon }-{\delta }_{\iota }\right)}{\left[1+exp\left({\beta }_{\upsilon }-{\delta }_{\iota }\right)\right]}$$

Hence, Rasch Model is widely used to investigate the properties of each items in scale, and the properties of items include item difficulties, discrimination and fitness to hypothetic theoretical model, etc. Previous studies have utilized this method to validate conventional assessment including the Test of Infant Motor Development, Gross Motor Function Measure, Motor Proficiency 2nd Edition, etc.(Campbell, Swanlund, Smith, Liao, & Zawacki, 2008; Dallmeijer, Scholtes, Becher, & Roorda, 2011; Huang et al., 2018; Wilson et al., 2011).

It is critical to emphasize that the applications of clinical assessments are based on rigorous scientific evidence, hence the psychometric properties of assessment tools ought to be tested constantly. To date, the CDSC has been validated using Classical Testing Theory, hence, we conducted this study to augment the existing evidence. Based on Rasch Model, we attempt to evaluate the consistencies among the items and latent traits through calibrating items difficulties, calculating items fitness to the theoretical model, verifying the unidimensionality.

The aim of this study was to explore more about the psychometric properties of the CDSC by applying an analysis based on Rasch Model. The following questions would be addressed:

  1. Do the response pattern of participants to the items demonstrate acceptable fitness to the Rasch Model

    2.

  2. Is most of the latent traits explained by a single underlying construct

    3.

  3. Does the CDSC differentiate the sample into a reasonable number of ranks of developmental status.

    4.

Therefore, the goal was to provide supplemental information about the psychometric properties of the CDSC and to support its clinical application.

Methods

This was a retrospective study approved by the Research and Ethics Committee of Shenzhen Children’s Hospital. Infant aged under 12 months old diagnosed with developmental delay were recruited from Shenzhen Children’s Hospital following the inclusion criteria:1)Aged under 12 months old; 2)Diagnosed as developmental delay according to DSM5 diagnostic criteria; 3)Had signed an informed consent form. Participants were excluded by the exclusion criteria:1)Diagnosed as neurological disease (e.g. Cerebral Palsy, Traumatic Brain Injuries, Seizure); 2)Cardiopulmonary dysfunction; Prior to administration, written consents were obtained from parents.

All informed consents were obtained from all subjects and/or their legal guardian(s) before administration.

Data collection

Demographics Data were attained before administrated to CDSC assessment. The CDSC consist of 6 domains, and each domain contains 1 or 2 items per month that required Infant to finish given tasks. Our researcher assigned the score according to the performance of Infant with 1 point for task finish or 0 point for task fail.

The CDSC contain five developmental domains, each domain consists of 12 sets of items corresponding to 12 developmental milestones, and each set of item consists of one or two testing items. The sum of scores attained from each domain would be utilized to calculate the corresponding developmental level and quotation.

Statistical Analysis

The Rasch Model

This study utilized Dichotomous Model for examining CDSC data. Data were analyzed using the WINSTEPS software package. Prior to the analysis, persons with extreme scores(> 95%maximum score/<5%mimmum score) as well as items with unacceptable correct rate(> 95%/<5%) were removed, since these items and persons with extreme measurement were representing infinite or indefinite measures on latent traits that are not directly estimable(Wæhrens, Kottorp, & Nielsen, 2021). For our analysis, developmental levels were considered as the latent variable.

Reliability and separation

Item/Person separation index was used to present the internal consistency of the CDSC through Cronbach’s alpha, and the bivariate data metric was transformed to logit scores instead of the raw score. An acceptable separation should lager than 2.0 (Stolt, Kottorp, & Suhonen, 2021; Sung et al., 2021). Reliability index was recommended to larger than 0.8 (Ogawa, Shirai, Nishida, & Tanimukai, 2021; Sung et al., 2021).

Fit statistics

Rasch Model was applied to examine the item properties of the CDSC. The overall fit of observed data to the expectations of the Rasch Model was presented using fit statistic through outfit mean square and outfit Zstd, besides infit mean square and infit Zstd were calculated based on the weighed residual to neutralized the impact of unreasonable response away from expectation. An acceptable INFIT/OUTFIT Mean square can range from 0.75 to 1.33, and an acceptable INFIT/OUTFIT Zstd can fall within − 2 to 2(Ogawa et al., 2021; Stolt et al., 2021; Sung et al., 2021). Additionally, individual item fit was evaluated through this method as well.

Unidimensionality

Unidimensionality of the CDSC was examined by running a principal component analysis(PCA) on the residual. PCA of residuals was used to examine whether a substantial factor existed in the residuals after the primary measurement dimension has been estimated. This allowed determination of whether the set of items represented a single construct(McCreary et al., 2013). If the items measure a single latent dimension as estimated by the Rasch Model, then the remaining residual variance should reflect random variation. Previous studies recommended 4 criteria to evaluate unidimensionality:1)the variance explained by the measurement dimension should greater than 40%,2)the variance explained by the first principal component of the residuals be less than 15%,3)the ratio of the variance in the measurement dimension to the variance in the first principal component of residuals should be greater than 3:1,4)eigenvalue < 2.0(McCreary et al., 2013; Stolt et al., 2021; Sung et al., 2021).

Differential item functioning

Previous studies proposed a formal definition of DIF, and it written as:

$$\mathcal{f}\left(\mathcal{Y}|\theta ,\mathcal{G}=\mathcal{R}\right)\ne \mathcal{f}\left(\mathcal{Y}|\theta ,\mathcal{G}=\mathcal{F}\right)$$

Here, \(\mathcal{G}\) denotes the group variable, and \(\mathcal{R}\) stands for the reference subsample with \(\mathcal{F}\) representing the reference subsample. \(\mathcal{Y}\mathcal{ }\)denotes the response to a test item, and \(\theta\)represents the tested latent traits. Conventionally, the reference subsample refers to most of the total sample, while the focal subsample indicates the minorities or those individuals who are at risk of being disadvantaged by the test. Therefore, the statistics methods utilized to detect the DIF in assessment tool are mostly based on the null hypothesis of no DIF, which can be written as:

$$\mathcal{f}\left(\mathcal{Y}|\theta ,\mathcal{G}=\mathcal{R}\right)=\mathcal{f}\left(\mathcal{Y}|\theta ,\mathcal{G}=\mathcal{F}\right)$$

Welch’s refinement of Student’s t-test for possibly unequal variances is adopted by the compare statistics between the focal subsample and the reference subsample. When p-value < 0.05, the result indicates that there exists significant difference between the focal subsample and the reference subsample.

According to previous study, a potential DIF item is confirmed when the DIF contrast > 0.64(moderate to large DIF) and the Welch’s p-value < 0.05.

Sample size consideration

Previous studies considered that the Rasch Model for dichotomous data recommend recruiting up to 1600 individuals, and fit statistics remained constant in the number of items whether identified as fitting or misfitting (unfit or overfit)(Smith, Rush, Fallowfield, Velikova, & Sharpe, 2008).Therefore, a sample size set at 200 would be an acceptable choice(Smith et al., 2008).

Result

Descriptive statistics

To examine the psychometric properties of the CDSC, 200 Infant with developmental delay were recruited. All the Infant had completed the test. The demographic characteristics of 200 Developmental delay Infant are shown in Table.1. The mean age was 6.37±2.73 months. Most participants were male (n=124, 62%). 

Wright Person-item Map

Figure.1 and Figure.2 shows the Wright person-item map of the items from 5 domains. The ordering of the test items indicates that the items representing fundamental developmental level were the easier test task. Those items serve as the milestone in the Infant advanced growth trajectory were the more challenging ones (Figure.1,2). The map shows that the items were spread out averagely, representing the developmental level from low (bottom) to high (top). Therefore, individuals with higher level of development tended to score higher on more items instead of certain specific items.

Reliability

The average person reliabilities for the 5 subscales were high, ranging from 0.91-0.96. That indicated the invariant of person ordering along the ability continuum could be expected if this sample were given another set of items measuring the same latent traits (developmental level). The average item reliabilities ranged from 0.99-1, indicating that the replicability of the ordering of the items along the scale could be assure when another subsample of the target population was given the test (Table.2,3).

Overall fit to the Rasch Model

The average infit mean square of the items from each domain are all within 0.75 to 1.33 recommended range in the person fit statistics and the item fit statistics(Table.2,3). 

Item fit to the Rasch Model

The fit statistics result shows that fitness of the items to the Rasch Model. The unfitting items are found according to the judging criteria (Table.4).

To Check for the potential impact of the unfitting items on the overall fit statistics, the analysis was done after the unfitting items were excluded (Table.5). The results show that person reliability is lower in gross motor, adaptive ability, speech and language, social behavior, while the person reliability remains the same in fine motor. The person separation is lower in gross motor, adaptive ability, speech and language, social behavior, while the person separation remains the same in fine motor.

Unidimensionality

The PCA of the residuals demonstrate that the variance explained by the measures ranges from 79.6% to 87.8%, the variance explained by the first contrast was range from 1.4% to 2.5%, and variance ratio of measures dimension to 1st contrast variance was all greater than 3:1. The eigenvalue of 1st contrast variance was range from 2 to 2.3. Hence, 5 test domains from CDSC all fulfilled criteria for unidimensionality (Table.6).

The PCA was executed again after removing those unfitting items (Table.7). The result shows that the variance explain by the Rasch Model is slightly higher in fine motor, speech and language, social behavior, while the ratio drops a little in gross motor, adaptive ability. The removal of the unfitting items brings a slight change in 1st contrast.

Differential item functioning

DIF was tested for each of the items in all 5 subscales in Table.8. Our study aimed to identify items with DIF across age groups and gender (Table.8).

Gender Specific analysis of variance of the standardized residuals at the sample size of 200 participants showed that item 82 (“Using motion or gesture to express”) is the item with the largest magnitude of gender specific DIF. All items with DIF displayed nonuniform difference of response patterns between male and female. That indicates these items did not always advantage one group over the other along the whole ability scale. Our result finds that item 82 advantages female with high ability. For item 41 (“Staring at mirror image”), with the same location on the ability continuum, female with low ability get higher scores than the male.

Age specific DIF analysis shows that item 3 (“Making fist when palm is touched”) is the item with the largest magnitude of DIF. For items with uniform DIF, the older participants are scoring higher value than the younger with the same developmental level in fine motor. For items with nonuniform DIF, item 25 (“Hold handbell for 30 seconds”) and item 66 (“Sit straight up”) advantage the older participants with low ability. In contrast, item 3 and item 5 (“Follow red ball across midline”) disadvantage old participants with lower developmental level in fine motor and adaptive ability respectively. Item 90 (“play handbell”) and item 100 (“imitating voice”) advantage the younger participants over the older with the same developmental level in adaptive ability and speech and language correspondingly.

Discussion

This study presents a comprehensive assessment tool CDSC developed for Chinese infant, which is a multidisciplinary observation scale to assess different developmental domains in infants. an assessment tool should provide rigorous result to precisely capture or depict a significant alternation of developmental domains in infants as they grow rapidly. It is changeling to precisely portray the developmental trajectory of infants within one year. Since the reliability of the CDSC was examined by the Classical Testing Theory in the previous studies, this study attempted to provide the complementary evidence to promote the clinical application of the CDSC based on the Rasch Model. The overall evidence suggests that the CDSC items present acceptable fitness to the Rasch Model, and the items also construct a unidimensional testing structure that demonstrate powerful differential function to evaluate the developmental level of Chinese Infant. Besides, several items showed the unfitness to the Rasch Model, the infants’ response patterns were found to deviate from the prediction model. However, our study found that the removal of these unfitting items would jeopardize the integrity of the instrument structure. Certain items are identified as items with DIF across age groups and gender. Therefore, our study finding supported that the CDSC can be applied in clinical practice with excellent psychometric properties to measure the developmental level of infant under 12 months old with developmental delay.

The CDSC subscales are established based on the item banks collected by different members based on their expertise before, and the subscales targeted different developmental domains can be used independently from one another. Therefore, the clinician can select those subscales essential for the needs of infants.

The primary result has distinguished serval misfitting items, and reanalysis is done to evaluate the impact of these misfitting items on the instrument psychometric properties. These misfitting items with abnormal MNSQ and ZSTD value indicate the unexpected respond pattern when participants encountered these items, and more analysis is needed to evaluate the impact of these misfitting items. Our result shows that the misfitting items did not jeopardized the instrument structure, and these items have made contribution to maintain the integrity of the test framework. The responds of the participants to these items seem to be deviate from the Rasch Model prediction, they still function as mile stones in corresponding domain. We suggest that the misfitting items representing a dimension partially belong to the concept of corresponding developmental domains, and they also contain other irrelevant information representing another dimension. As previous studies recommend, the misfitting items that do not jeopardize the psychometric quality of the instrument should be reformulated to reflect the intent content more clearly and precisely, for example action speed, attention, engagement, etc.(Wæhrens et al., 2021; Wilson et al., 2011).

It is well known that the cause of DIF is the manifestation of multidimensionality in a test(Erhart, Ravens-Sieberer, Dickinson, & Colver, 2009). The PCA of residual shows that the items in the testing domains fulfills the judge criteria for the unidimensionality assumption. These findings support that the subscales are measuring single latent traits respectively. However, the identification of items with DIF indicated that certain items may be influenced by secondary dimensions. The test of the unidimensionality did not deny the existence of secondary dimensions, and the result showed that these secondary dimensions only explained 1.4%-2.5% of the measurement variance.

Our finding identified 2 items with gender specific DIF, and this result denotes that participants with the same developmental level in corresponding domains responds differently to the items of the CDSC dependent on gender. Generally, these two items seem to advantage the female than the male with the same ability. The number of items that presented DIF corresponding to less than 5% of the total items evaluated in corresponding subscale. For items with age groups DIF (older or younger than 6.5 months), most of these items advantage the older infants. This is not surprising that aging is associated with more access to more sensory input or living experience that allows individuals to learn more skills. Therefore, DIF for age may be explained by the living experience difference that exists among growing infants. Our hypothesis concurred with related studies(Gorton et al., 2011; Morales-Murillo, García-Grau, McWilliam, & Grau Sevilla, 2021). Hence, further efforts are needed to explore this relation, and to determine the influence of living experience and personal factors on child developmental level in different domains.

The results of the Rasch analysis of the SCDC presents the hierarchy order of item difficulty. The item difficulty was corresponding with the developmental trajectory of Infant. Floor and ceiling effects were defined as the proportion of response that scored either higher than 95%(ceiling) or lower than 5%(floor) possible score for that domain(Park, Hong, & Park, 2021). This study report 0.5% (Gross motor), 2% (Fine motor), 0.5% (Adaptive behavior), 1.5% (Speech and language), 1% (Social behavior) ceiling effect, indicating less than 5 persons (200-person total) obtain high score in each domain. However, our sample was collected from inpatient infants with developmental delay or certain risk factors, hence those participants with maximum score may still display important developmental lag in emerge of the milestone that were not detected by the CDSC. Therefore, the clinician my possible observe poor movement quality or abnormal movement strategies in infants with high CDSC scores. Future application of the CDSC should focus more on its utilization in treatment planning based on the observation rather than simply the measurement outcome.

This study also reported 6% (Gross motor), 1.5% (Fine motor), 11% (Adaptive ability), 3.5% (Speech and language), 5.5% (Social behavior) in floor effect, indicating 11 persons in average obtain low score in each domain. As the Rasch model assume, Infant with lower developmental level tend to achieve less growth milestones. This can be explained that infant with developmental delay caused by various factors (Extremely preterm, extremely low birthweight) present much lower developmental level than those born at term in gross motor, fine motor, cognition, and language domains(Kwong et al., 2022).

The person and item separation index were within the recommended range (> 2), hence we suggest that the CDSC items were enough to differentiate person into at least 12 distinct development level. Further, the person and item reliability were within satisfactory range as well(> 0.8), and the result supports that the CDSC is reliable enough if the same testing items were applied on different sample with the same participants characteristic or our study sample received another item set that belongs to the CDSC test structure.

In brief, the CDSC has demonstrated good psychometric properties in our Rasch Model analysis. Based on the previous psychometric properties’ studies of the CDSC, we believe that the CDSC is a reliable tool to describe the developmental trajectory of Infant under 12 months old, the testing items have demonstrated promising unidimensionality and reasonable fitness to Rasch Model. Further, the items content still required further calibration and redefinition to reflect the testing content more clearly. The future study also needs to examine the differential item functioning of the CDSC items on sample with different characteristics (preterm/term, low weigh born/extremely low weigh born, etc.).

Implications For Clinical Practice

Our results provide preliminary evidence for the psychometric properties of the CDSC and indicate that the clinician should be confident with the assessment results. However, our study also identified certain short comings that may jeopardize the accuracy of the assessment outcomes. Certain items may provide misinformation to the real growth trajectory of the infants. Further, the clinicians should also pay special attention to the potential bias caused by gender or age groups that infants with the same developmental level may respond to certain items differently dependent on their age groups.

Study Limitation

Three limitations should be noted in this study. Firstly, the sample recruited in our study was mainly from those with developmental delay, but the developmental level varies from person to person due to different causal factors(extremely low birth weight, extremely preterm, e.g.). Our result is limited to this population. Secondly, the ceiling and floor effect of the CDSC indicate that the items still need more calibration to improves the precision and efficiency of the existing version. Therefore, future studies may adopt our research results to revise the CDSC based on data from different samples, because the developmental trajectory may vary in children with developmental delay caused by various factors. Thirdly, our result cannot be related to the previous studies statistically due to the different testing theories and software. In brief, our studies achieved the similar psychometric quality of the CDSC as previous studies reported by using different mathematically methods, and we also proposed a way to revise the current version to achieve better construct validity based on the Rasch Model.

Conclusion

Our study support that the CDSC was established based on a unidimensional structure with reasonable difficulty hierarchy. The CDSC items can describe the developmental trajectory of the gross motor, fine motor, adaptive ability, speech and language, social behavior. Future study is recommended to examine the items invariant properties across sample with different characteristics, the clinical application of the CDSC still need more comprehensive evidence so that the early screening of the developmental delay individual is applicable in the very early stage of Infant growth.

Abbreviations

CDSC

The China Developmental Scale of Children

MNSQ

Mean Square

ICF-CY

International Classification of Function, Disability and Health for Children and Youth

Declarations

Ethics approval and consent to participate

All methods conducted in our study were carried out accordance with relevant guidelines and regulations by qualified clinicians. Our study had achieved the ethics approval from Ethics Committee of Shenzhen Children’s Hospital. 

All informed consents were obtained before the administration of the participants from individuals or their legal guardian(s).

Consent for publication

Not applicable.

Availability of data and materials

All authors agree to share our raw data if anyone is interested on our study. The dataset used and analyzed during the current study available from the corresponding author on reasonable request. All original data can be access by sending email to contact the corresponding author.

Competing interests

All authors declared no conflict of interest related to this study.

Funding

Our study was supported by Sanming Project of Medicine in Shenzhen “The ADHD research group from Peking University Sixth hospital, SZSM201612036

Authors' contributions

All the authors listed above contributed equally to this paper.

Acknowledgements

Give special credit to the parents’ generosity to provide the assessment results of their children.

Author information

Kanglong Peng1*, Master of science,

Jinggang Wang1, Master of Medicine,

Guixiang Liu1, Undergraduate,

Zhujiang Tan1, Undergraduate,

*Correspondence:[email protected]

1Affiliation: Department of Children’s Rehabilitation, Shenzhen Children’s Hospital, Shenzhen, Guangdong, China

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Tables

Tables 1 to 8 are available in the Supplementary Files section.