Rasch Analysis of the Barthel Index in the Assessment of Hospitalized Older Patients After Admission for an Acute Medical Condition

Participants 

Barthel Index data for Rasch analysis were obtained from participants who were enrolled in the exercise intervention studies reported by de Morton13 and Jones14 and colleagues. Data were collected at 2 acute care public hospitals in Melbourne, Australia. Participants were eligible for inclusion if they were a general medical patient, were 65 years or older, and were assessed within 48 hours of hospital admission. Patients were excluded if they were admitted to the hospital from a nursing home, were nursing home level of care, required palliative care, had suffered a stroke, had a condition for which mobilization was contraindicated, or were readmitted during the data-collection period and had previously participated in the study. Data were collected from 236 and 160 consecutive older acute medical patients admitted to the 2 hospitals. Ethics approval to perform deidentified secondary analyses was obtained from the Monash University Ethics Committee and relevant Hospital Ethics Committees.

Procedure 

The Barthel Index was administered by using patient self-report in response to a face-to-face interview with a physiotherapist within 48 hours of hospital admission and again within 48 hours of hospital discharge. Where there was uncertainty about the cognitive ability of the patient, the Barthel Index was administered by asking nursing staff or family.

Outcome Measures 

The original Barthel Index,1 which is comprised of two 2-point dichotomous, six 3-point, and two 4-point response option items, was administered at 1 hospital. At the other hospital, a modified version of the Barthel Index15 was used (ten 5-point response option items). The response options for these differing versions of the Barthel Index are shown in table 1.

Table 1. Response Options for the Original and Modified Versions of the Barthel Index

	Original Barthel Index1†	Unable	With Help	Independent
	1. Feeding	0	5	10
	2. Chair/bed transfers	0	5–10	15
	3. Grooming	0	0	5
	4. Toilet	0	5	10
	5. Bathing	0	0	5
	6. Walking	0	5–10⁎	15
	7. Stairs	0	5	10
	8. Dressing	0	5	10
	9. Bowels	0	5	10
	10. Bladder	0	5	10

	MBI15‡	Unable	Attempts But Unsafe	Moderate Help	Minimal Help	Fully Independent
	1. Feeding	0	2	5	8	10
	2. Chair/bed transfers	0	3	8	12	15
	3. Grooming	0	1	3	4	5
	4. Toilet	0	2	5	8	10
	5. Bathing	0	1	3	4	5
	6. Walking	0	3	8	12	15
	or wheelchair	0	1	3	4	5
	7. Stairs	0	2	5	8	10
	8. Dressing	0	2	5	8	10
	9. Bowels	0	2	5	8	10
	10. Bladder	0	2	5	8	10

⁎ Propel wheelchair. † Data from Mahoney and Barthel.1 ‡ Data from Shah et al.15 Reprinted with permission.

Rasch Analysis 

The Rasch model is a probabilistic model that asserts that an item response is a result of an interaction between person ability (ß) and item difficulty (θ).10 This model assumes that the probability that a person of a particular ability will successfully complete an item is a logistic function of the difference between person ability (eg, level of ADL ability) and item difficulty (eg, difficulty of ADL challenge). If ß equals θ, the probability of success is 0.5. As ß (person ability) increases and exceeds θ (item difficulty), the probability of success increases. If data fit the Rasch model, the person responses are expected to be consistent with the order of item difficulty because they are measuring 1 construct,10 and this consistency is indicated by a total-item chi-square probability greater than .05.

The Rasch model has 2 assumptions. The first requires that items measure a single underlying construct, thereby forming a unidimensional scale. The second assumption is that items have local independence. This requires that responses to 1 item are not dependent on the responses to another item or that “after controlling for the underlying trait, item responses are independent.”16(p147) Residuals from Rasch analysis were examined to investigate these assumptions. A finding of no association between residuals for individual items has been argued as evidence of local item independence.17 High positive correlation between residuals provides evidence of local item dependence, and high negative correlations is thought to indicate multidimensionality.

Unidimensionality was formally tested by examining the principal component loadings of the residuals.17, 18 Items were identified that loaded either positively or negatively on the first residual component after Rasch analysis (correlated at >0.3), and 2 item subsets were created. Person-location estimates were obtained by using the differing item subsets, and a series of independent t tests were conducted to compare person-location estimates obtained by using the differing item subsets. The percentage of t tests outside the acceptable range of 2 standard deviations (SDs) was then calculated with an accompanying binomial proportions 95% confidence interval (CI).19 A result of less than 5% is reported as the most robust method for confirming scale unidimensionality.17, 18

Rasch analysis was performed in this study by using RUMM2020 softwarea and SPSS software.b The unrestricted Rasch partial credit model was used to investigate overall model fit, item misfit, differential item functioning (DIF), and item thresholds. Participants were divided into 3 class intervals (ie, 3 groups of patients at different levels of ADL ability). Item misfit was considered if the chi-square or F statistic probability value was less than the Bonferroni-adjusted α value for multiple testing or the fit residuals were greater than ±2. DIF was investigated to identify items that operated differently for people of the same level of ability (ie, have the same amount of the underlying trait of interest) who share another feature (variable). DIF by age (65–70y, 80–86y, >87y) and sex were investigated and considered significant if the chi-square probability value was lower than the Bonferroni-adjusted P value. For both versions of the Barthel Index, item thresholds were also studied to investigate the existence of disordered thresholds (ie, response patterns for item categories that are not in the expected order).

The person separation index was reported to provide an indication of the internal consistency (reliability) of the scale by examining the ability of the scale construct to discriminate among respondents.

Sample-Size Calculations 

Linacre20 proposed that for most purposes a sample size of 150 (n range, 108–243) will provide 99% confidence of item calibration ±0.5 logits and a sample size of 100 (n range, 64–144) will provide 95% confidence within ±0.5 logits. However, the adequacy of test targeting influences sample-size requirements for Rasch analysis. For well-targeted tests, a sample size of 108 is likely to provide 99% confidence within ±0.5 logits.20 Conversely, for tests that are not well targeted, a larger sample size (eg, n=243) is required for similar item location precision.20

In this study, hospital admission data were planned for analysis for the original (n=236) and MBI (n=160). However, hospital discharge assessments were also planned for analysis to validate findings on an independent dataset.

Preliminary examination of the range of participant scores in this study indicated that more than 10% of both samples would score within the minimal detectable change (≈10 points on the Barthel Index) of the highest possible Barthel Index score (ie, ≥90 points).12, 13, 14 However, in this study, the relationship under investigation was the proportion of persons that were unable to be located on the Barthel Index continuum after Rasch analysis. Each item location has an error estimate and surrounding 95% CI on the Rasch converted logit scale. A ceiling effect was therefore considered to exist if more than 10% of persons had a logit location higher than the upper band of the 95% CI of the standard error (SE) of measurement for the most difficult item.

Rasch Analysis of the Original and Modified Barthel Index 

For the original Barthel Index, there were 236 admission assessments performed, and there were 40 extreme-person responses. These persons scored either the lowest (n=2) or highest (n=38) possible score on the Barthel Index and, therefore, have a theoretical ability to represent either −∞ or ∞ on the Rasch logit scale. A total-item chi-square test for item-trait interaction indicated that original Barthel Index data did not fit the Rasch model (χ202=94.17, P=.00).

For the MBI, there were 160 admission assessments performed, and there were 3 extreme-person responses. A total-item chi-square test for item-trait interaction indicated that the MBI data did not fit the Rasch model (χ202=153.21, P=.00). A significant likelihood ratio test (χ262=199.15, P=.00) combined with visual inspection of the item-threshold categories justified the use of the unrestricted Rasch partial credit model for the MBI.

The person separation index for both versions of the Barthel Index was high, .91 for the original Barthel Index and .94 for the MBI. This indicates a high ability of the Barthel Index to discriminate among respondents. Both versions of the Barthel Index showed evidence of multidimensionality. For the original version of the Barthel Index, the percentage of individual t tests outside the acceptable range was 12.24% (95% CI, 9–15), and for the modified version, it was 29.94% (95% CI, 27–33).

Item Misfit 

Many items for both versions of the Barthel Index showed misfit to the Rasch model. Table 2 summarizes the results of Rasch analysis in this study. The bladder item for the original Barthel Index and the bladder and bowel items for the MBI had fit residuals of greater than 2, indicating the likely measurement of another construct. Multiple items for each version of the Barthel Index had fit residuals that exceeded −2, indicating item redundancy and that these items over discriminate. Items in both versions of the Barthel Index also had a significant chi-square and/or F statistic probability value that indicated that the observed proportions deviated significantly from the Rasch model on the basis of person scores and/or class intervals.

Table 2. Results of Rasch Analysis of the Original and Modified Barthel Index

		Admission Data		Admission Data After Rescoring Disordered Thresholds
		Original Barthel Index	MBI	Original Barthel Index	MBI
	n	236	160	236	160
	Extreme persons	40	3	44	3
	Fit to the Rasch model (df=20)	χ2=94.17, P=.00	χ2=153.21, P=.00	χ2=53.06, P=.00	χ2=161.06, P=.00
	Misfitting items
	High positive fit residual	Bladder (2.01) Bowel (2.63)	>Bladder (4.28)	>None	>Bladder (4.14)
	High negative fit residuals	Transfers (−3.21) Toilet use (−2.01)	Toilet use (−3.92) Bathing (−3.13) Dressing (−2.63) Walking (−2.01)	Toilet use (−2.81) Dressing (−2.22) Transfers (−2.13)	Toilet use (−3.85) Bathing (−3.04) Dressing (2.52)
	Significant χ2P	Bowels (P=.02) Transfers (P=.00) Bladder (P=.00) Walking (P=.00)	Toilet use (P=.00) Bladder (P=.00)	Bladder (P=.00)	Toilet use (P=.00) Bladder (P=.00)
	Significant F statistic P	Transfers (P=.00) Toilet use (P=.00) Walking (P=.00)	Toilet use (P=.00) Bathing (P=.00) Dressing (P=.00) Walking (P=.00) Transfers (P=.00) Bladder (P=.00)	Toilet use (P=.00)	Toilet use (P=.00) Bathing (P=.00) Dressing (P=.00) Bladder (P=.00)
	Disordered thresholds	Feeding, stairs, bowels, walking	Stairs, bowels	None	None
	DIF	None	Toilet use: uniform DIF by age (F=10.57, P=.00)	None	Toilet use: uniform DIF by age (F=10.32, P=.00)
	Unidimensionality (independent t test) (%)	12.24 (9–15)	29.94 (27–33)	6.25 (3–9)	15.29 (12–19)

No DIF was identified for the original version of the Barthel Index. The toilet-use item showed significant uniform DIF by age for the MBI (F=10.57, P=.00). Persons in the youngest category (range, 65–79y) had a significantly higher probability of independence for this item compared with those in the middle age group (range, 80–86y).

Exploratory Rasch analysis showed that original Barthel Index data did not fit the Rasch model after the misfitting bladder item had been removed (χ182=69.66, P=.00) or the modified version of the Barthel Index after the bladder and bowel items had been removed (χ162=32.4, P=.01). However, removal of these continence items reduced the item-trait chi-square value for both versions of the Barthel Index and indicated improvement in the fit of the data to the Rasch model.

Disordered Thresholds 

Items from both versions of the Barthel Index had disordered thresholds. For the original version, these items were feeding, stairs, bowels, and walking. There was no person ability level at which it was most likely that assistance was required for feeding, stairs, and bowels. For walking, there was no person ability level at which the most likely response was to be independent with a wheelchair. Therefore, these items were rescored to remove disordered thresholds. There were no persons who were “independent with their wheelchair mobility,” so this category was combined with “unable to walk.” “Assistance with” feeding, stairs, and bowels was combined with “unable” to perform these items.

For the MBI, 2 items, stairs and bowel control, had disordered thresholds. There was no person ability level at which it was most likely that “substantial assistance” is required for ascending and descending stairs. Similarly, there was no person ability level at which the most likely response was to require “moderate help” with bowel continence. To remove disordered thresholds, the stairs and bowel items were rescored by combining the 3 assistance response options.

Rasch Analysis After Rescoring Disordered Thresholds 

Fit of the data to the Rasch model was not achieved by rescoring disordered thresholds for the original (χ202=161.06, P=.00) or modified (χ202=74.95, P=.00) versions of the Barthel Index. The item-trait interaction chi-square value for the original version of the Barthel Index was reduced by rescoring disordered thresholds and indicated an improvement in the fit of the data to the Rasch model. In contrast, the chi-square value for the modified version of the Barthel Index increased and indicated poorer fit of the data to the Rasch model after the rescoring of disordered thresholds.

After rescoring disordered thresholds, the bladder item continued to display a high positive fit residual for the MBI but not for the original Barthel Index. No items had fit residuals greater than 2 for the original version of the Barthel Index. Many items continued to show misfit to the Rasch model for both versions of the Barthel Index with high negative fit residuals (indicating item redundancy) and significant chi-square and/or F statistic probability values (see table 2). The same item, toilet use, continued to show uniform DIF by age for the MBI.

Rescoring the disordered thresholds resulted in a reduction in the percentage of individual t tests outside the acceptable range (see table 2). This indicates an improvement in the unidimensionality of both versions of the Barthel Index after the rescoring of the disordered thresholds. Nevertheless, the percentage of individual t tests remained greater than 5% for both versions.

The examination of the residual correlation matrix indicated negative correlations of greater than 0.3 between the bowel and stairs items (r=−.31) for the original Barthel Index and the bladder control item with bathing (r=−.36), toilet (r=−.44), stairs (r=.33), dressing (r=−.45), and walking (r=−.36) items for the MBI. For the MBI, these findings support the high positive fit residual identified for the bladder item (ie, the likely measurement of another construct). A positive correlation of greater than 0.3 was only identified between the walking and transfers (r=.36) items for the MBI and indicates response dependency between these mobility-assessment tasks (ie, violation of the assumption of local dependence).

The removal of the misfitting bladder item from the MBI (after rescoring disordered thresholds) did not result in the data fitting the Rasch model (χ182=49.8, P=.00), and the percentage of t tests outside the acceptable range also remained greater than 5% (12.74%; 95% CI, 9–16). However, the reduced item-trait chi-square value indicated improved fit of the data to the Rasch model.

Person-Item Threshold Map After Rescoring Disordered Thresholds 

Person ability and item thresholds are shown on the same logit scale in the person-threshold map for the original Barthel Index and the MBI in Fig 1, Fig 2, respectively. Higher person ability and higher item difficulty are located to the right of 0. Person ability is spread above and below the range of measurement captured by both versions of the scale. At hospital admission, there were 16.1% of persons who scored above the upper band of the 95% CI for the SE of measurement for the most difficult item, stairs, on the original version of the Barthel Index and 5.6% for the MBI. For both versions of the Barthel Index, only a small number of persons were unable to complete an item, and, therefore, a floor effect was not identified. After item rescoring, the person separation index was .92 and .94 for the original version and the MBI, respectively.

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Fig 1. Person-item threshold distribution for the original Barthel Index after rescoring disordered thresholds.

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Fig 2. Person-item threshold distribution for the MBI after rescoring disordered thresholds.

Validation in the Discharge Dataset 

The examination of the discharge dataset for the original (n=167) and modified (n=126) Barthel Index validated the findings from the analysis of the hospital admission dataset. Barthel Index data did not fit the Rasch model for the original (χ202=37.56, P=.01, n=119) or modified version of the Barthel Index (χ202=78.61, P=.00, n=112). However, the bladder item only showed misfit for the MBI with a high positive fit residual of 3.93. The walking and stairs items had disordered thresholds for the original and MBI, respectively.

After rescoring disordered thresholds in the discharge dataset, the original Barthel Index data demonstrated fit to the Rasch model (χ202=27.14, P=.13), and for the percentage of individual t tests outside the acceptable range, the lower band of the 95% CI overlapped 5% (5.04%; 95% CI, 1–9). Despite the original Barthel Index satisfying these strict unidimensionality requirements, 2 items showed mild misfit to the model. The toilet use (−2.3) and dressing (−2.16) items had high negative fit residuals, indicating item redundancy. However, had a cut point of 2.5 been selected for item fit residuals in this study (instead of 2), these items would not have been identified as misfitting. Fit to the model was also identified in this dataset in the item (mean ± SD, −0.4±1.25) and person (mean, −.30±.58) fit residual statistics.

After rescoring disordered thresholds, the MBI data did not fit the Rasch model in the discharge dataset (χ202=76.36, P=.00), and the bladder item continued to show misfit with a high positive fit residual (+3.56). The percentage of individual t tests outside the acceptable range was greater than 5% (18.85%; 95% CI, 15–23). The proportion of patients scoring above the SE of measurement for the most difficult item was 45.9% and 13.5% at hospital discharge for the original and modified versions, respectively.

Item Hierarchy for the Original Compared With the MBI 

Figure 3 compares the item hierarchy for the original and modified versions of the Barthel Index based on hospital admission data after rescoring disordered item thresholds.

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Fig 3. Scatterplot of item logit locations (95% CI) for the original and Modified Barthel Index (BI) at hospital admission after rescoring disordered thresholds.

Study Limitations 

A limitation of this study was that the proportion of patients for whom the Barthel Index was completed by others (ie, nurse or family member) was not recorded. Another possible limitation is that there was a greater than 15% loss to follow-up for discharge destination data for the original and Modified Barthel Index. Therefore, a smaller sample size was available for Rasch analysis in the discharge compared with the admission dataset for both the original and Modified Barthel Index. The influence of these factors on the results of Rasch analysis in this study is not known.