Rasch Analysis of Combining Two Indices to Assess

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Rasch Analysis of Combining Two Indices to Assess
Comprehensive ADL Function in Stroke Patients
I-Ping Hsueh, MA; Wen-Chung Wang, PhD; Ching-Fan Sheu, PhD; Ching-Lin Hsieh, PhD
Background and Purpose—To justify the summation of scores representing comprehensive activities of daily living
(ADL) function, a Rasch analysis was performed to examine whether items of the Barthel Index (BI), assessing ADL,
and items of the Frenchay Activities Index (FAI), assessing instrumental ADL, contribute jointly to a single,
unidimensional construct in stroke patients living in the community. The number of scoring points of both indices was
examined for their usefulness in discerning the various ability levels of ADL in these patients.
Methods—A total of 245 patients at 1 year after stroke participated in this study. The BI and FAI were administered to
the patient and/or the patient’s main caregiver by interview.
Results—The initial Rasch analysis indicated that the middle scoring points for many items of the BI and FAI could be
collapsed to allow only dichotomous response categories. All but 2 items of the FAI, social occasions and walking
outside, fitted the model’s expectations rather well. These 2 items were excluded from further analysis. A factor analysis
performed on the residuals of the Rasch-transformed scores recovered no dominant component. These results indicate
that the combined 23 dichotomous items of the BI and FAI assess a single unidimensional ADL function.
Conclusions—A clinically useful assessment of the comprehensive ADL function of patients at or later than 1 year after
stroke can be obtained by combining the items of the BI and FAI (excluding 2 FAI items) and simplifying the responses
into dichotomous categories. It is also demonstrated that the items of the new scale measure comprehensive ADL
function as a single unidimensional construct when assessed at 1 year after stroke. (Stroke. 2004;35:721-726.)
Key Words: activities of daily living 䡲 cerebrovascular accident 䡲 disability evaluation
S
troke is the most common cause of dependence in
activities of daily living (ADL) among the elderly.1 ADL
generally refers to basic or personal ADL, which has been
widely used as a main outcome measure after stroke.2
However, basic ADL does not capture significant losses in
higher levels of physical function or activities that are
necessary for independence in the home and community (ie,
Instrumental ADL [IADL]).2 Both the basic ADL and IADL
are recommended as the primary outcome measures after
stroke.3 Several authors4,5 have recommended combining the
basic ADL and the IADL to comprehensively measure ADL
function. Such a combined scale is expected to be more
responsive and have a wider range than either of the individual measurements.6,7
Previous studies using factor analysis found that the
Barthel Index (BI) (measuring basic ADL) and the Frenchay
Activities Index (FAI) (measuring IADL) assessed different
constructs in patients with stroke.4,5 Because the BI and FAI
supplemented each other with a minimum of overlap in
content, it was proposed that they be combined to assess
comprehensive ADL function.4,5 However, the main question
in combining items of ADL and IADL indices is whether
these items together contribute to a unidimensional construct,
which is necessary to justify the summation of scores.8
Furthermore, factor analysis operates on interval scale
scores,9 whereas the BI and FAI scores are ordinal by nature.
Thus, the results of studies using factor analysis to examine
whether items of both indices could be combined to measure
a single construct were inconclusive.
Rasch analysis transforms ordinal scores to the logit scale
and thus to an interval-level measurement.10,11 Furthermore,
the Rasch model can examine whether items from a scale
measure a unidimensional construct.10,11 If items do not fit the
model’s expectation, unidimensionality is not preserved.10,11
Therefore, Rasch analysis is a useful method to validate the
unidimensional construct of all the items of the BI and FAI
and to obtain an objective, interval scale.10,11 Appropriateness
of scoring points refers to whether or not participants can be
differentiated by their responses as clearly as the points
allow.12 The items of the BI are either dichotomous or on a 3or 4-point scale; those of the FAI are on a 4-point scale.
Recent studies13,14 have shown that a higher number of
scoring points may not lead to finer differentiation of the
participants. Given that the BI has been found to have a
Received August 12, 2003; final revision received November 23, 2003; accepted December 2, 2003.
From the School of Occupational Therapy, College of Medicine, National Taiwan University, Taipei (I-P.H., C-L.H.); Department of Psychology,
National Chung Cheng University (W-C.W.), Chia-Yi, Taiwan; and Department of Psychology, DePaul University, Chicago, Ill (C-F.S.).
Correspondence to Ching-Lin Hsieh, PhD, School of Occupational Therapy, College of Medicine, National Taiwan University, 7 Chung-Shan S Rd,
Taipei 100, Taiwan. E-mail [email protected]
© 2004 American Heart Association, Inc.
Stroke is available at http://www.strokeaha.org
DOI: 10.1161/01.STR.0000117569.34232.76
721
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Stroke
March 2004
TABLE 1.
Characteristics of the Patients With Stroke (nⴝ245)
Characteristics
Basic characteristics
Sex
Male/female
130/115
Age
Mean year (SD)
65.4 (11.2)
Diagnosis
Side of hemiplegia
Canadian Neurological score at admission
Cerebral hemorrhage
68 (28%)
Cerebral infarction
177 (72%)
Right/left
101/144
Median (interquartile range)
7 (4–9)
At 1 year after stroke
BI
Median (interquartile range)
90 (65–100)
FAI
Median (interquartile range)
6 (0–13)
Combined ADL raw score
Median (interquartile range)
9 (5–13)
Combined ADL Rasch-transformed score
notable ceiling effect4,5 and that the FAI demonstrated a floor
effect,4,5 it is of interest to examine whether or not the scoring
points of these 2 indices are appropriate. Such an investigation can also be conducted by performing a Rasch analysis on
the scores of these indices.12 This study used Rasch analysis
to (1) investigate the appropriateness of the scoring points of
the BI and FAI and (2) examine whether all the items of the
BI and FAI contribute to a unidimensional construct in
patients with stroke living in the community.
Subjects and Methods
Subjects
The study sample was recruited from the registry of the Quality of
Life After Stroke Study in Taiwan between December 1, 1999, and
December 31, 2001. Patients were included in the study if they met
the following criteria15: (1) diagnosis of cerebral hemorrhage or
cerebral infarction; (2) first onset of cerebrovascular accident,
without other major diseases; (3) stroke onset within 14 days before
hospital admission; and (4) informed consent given personally or by
proxy. Further selection and exclusion criteria can be found
elsewhere.15
Procedure
Data were collected at 1 year after stroke. An occupational therapist
administered the BI and FAI to the patient and/or the patient’s main
caregiver by face-to-face or telephone interview. The therapist tried
to obtain the actual performance of the patients in daily life from all
the informants available.
Measures
Two dichotomous, six 3-point, and two 4-point items constitute the
BI.16 The FAI, which was developed to assess social activities or
lifestyle after stroke,17 consists of fifteen 4-point items. Stroke
severity at admission to the hospital was determined by the Canadian
Neurological Scale.18 All 3 scales have been shown to be valid and
reliable.18 –22
Data Analysis
The analysis consisted of 2 parts. First, the appropriateness of the
scoring points in each item of the BI and FAI was investigated with
the use of the Rasch partial credit model.10 The scoring points of the
items of both indices were reorganized if they were found to be
inappropriate. Second, the unidimensionality of the combined BI and
FAI scale with appropriate categories was examined by Rasch
analysis. The WINSTEPS computer program23 was used to perform
the Rasch analysis.
Mean (SD)
⫺1.17 (3.94)
The partial credit model can be used for polytomous items such as
those of the BI and FAI. We examined the order of the step
difficulties of each item of both indices to see whether their scoring
points could be simplified.
To examine unidimensionality of the combined scale, infit and
outfit statistics were used to examine whether the data fit the model’s
expectation. The infit mean square (MNSQ) is sensitive to unexpected behavior affecting responses to items near the person’s
proficiency measure; the outfit MNSQ is sensitive to unexpected
behavior by persons on items far from the person’s proficiency
level.10,24 MNSQ can be transformed to a t statistic, termed the
standardized Z value (ZSTD), which follows approximately the t or
standard normal distribution when the items fit the model’s expectation. In this study items with both infit and outfit ZSTD beyond ⫾2
were considered poor fitting.
When items fit the model’s expectation, the residuals (observed
scores minus expected scores) should be randomly distributed. A
factor analysis was conducted to verify whether any dominant
component existed among the residuals. The unidimensionality
assumption held if no dominant component was found.25
The sufficiency of the BI and FAI combined was verified by
examining whether there were substantial gaps between the item
difficulties along the item hierarchy.
Results
A total of 311 patients were registered in the Quality of
Life After Stroke Study during the study period. Eight of
the 311 patients declined to participate in the study, and 58
patients either did not survive another stroke or could not
be contacted for follow-up. A total of 245 patients were
included in this study. The Canadian Neurological Scale
scores showed that the patients had a broad range of
severity at admission. The characteristics of the study
sample are shown in Table 1.
Appropriateness of Level of Scaling
All but 2 items (social occasions and walking outside) fitted
the model’s expectation fairly well, indicating that these
items measured a single construct for patients at or after 1
year after stroke. Table 2 shows that all but 2 of the 23
polytomous items of both indices exhibited disordering of the
step difficulty (ie, that the difficulty of a higher step was
lower than that of its adjacent lower step), indicating that the
middle categories were never the most likely responses of any
patient and were thus redundant. Accordingly, the response
Hsueh et al
TABLE 2.
Step Difficulties Under the Partial Credit Model
Item
Step 1
Logit
BI1: feeding
⫺1.53
BI2: bathing
0.47
BI3: grooming
BI4: dressing
BI5: bowel control
Step 2
Logit
Step 3
Logit
Rasch Analysis of Combining 2 ADL Indices
TABLE 3. Difficulty, Standard Error, and Outfit Statistics When
the 2 Poor-Fitting Items of the FAI Were Excluded
Item*
⫺6.93*
723
FAI13: household/car maintenance
Difficulty
Logit
4.72
SE
Logit
Outfit
ZSTD
Infit
ZSTD
0.31
⫺0.1
0.3
⫺3.68
FAI14: reading books
4.72
0.31
0.0
⫺0.6
⫺0.19
⫺1.00*
FAI15: gainful work
4.01
0.26
⫺0.1
0.8
⫺5.25*
FAI12: gardening
3.75
0.25
0.0
1.0
3.52
0.24
0.9
0.6
⫺2.23
BI6: bladder control
⫺1.07
⫺5.82*
FAI9: actively pursuing hobbies
BI7: toileting
⫺0.82
⫺2.57*
FAI11: travel outings/car rides
3.52
0.24
1.1
3.5
FAI1: preparing main meals
3.24
0.23
⫺0.1
⫺0.6
BI8: transfer
⫺4.40
⫺2.24
BI9: mobility
⫺4.05
⫺1.43
FAI3: washing clothes
3.19
0.23
⫺0.2
⫺2.5
⫺0.38
FAI2: washing up
3.09
0.22
⫺0.2
⫺2.1
⫺1.09*
FAI5: heavy housework
2.75
0.22
⫺0.2
⫺2.2
0.03
FAI4: light housework
1.95
0.21
⫺0.3
⫺2.6
FAI10: driving a car/bus travel
1.83
0.20
⫺0.2
⫺0.8
0.59
0.21
⫺0.2
⫺0.6
BI10: stairs
FAI1: preparing main meals
FAI2: washing up
FAI3: washing clothes
⫺2.59
3.94
5.67
4.66
2.36*
⫺0.72*
⫺2.35*
⫺1.12*
FAI4: light housework
4.57
1.02*
⫺2.05*
FAI6: local shopping
FAI5: heavy housework
4.47
0.66*
⫺0.55*
BI2: bathing
0.55
0.21
⫺0.2
0.5
⫺0.72
0.22
⫺1.0
⫺1.6
FAI6: local shopping
3.91
⫺0.78*
⫺1.09*
BI10: stairs
FAI7: social occasions
3.90
0.35*
⫺0.50*
BI4: dressing
⫺0.77
0.22
⫺0.6
⫺1.1
⫺2.85
0.26
⫺0.6
⫺1.6
FAI8: walking outside
1.80
⫺1.74*
⫺3.23*
BI9: mobility
FAI9: actively pursuing hobbies
5.79
⫺0.79*
0.56
BI7: toileting
⫺3.48
0.27
⫺1.0
⫺3.4
⫺0.55*
BI8: transfer
⫺3.99
0.27
⫺0.9
⫺4.8
2.00
BI3: grooming
⫺6.77
0.32
0.2
0.9
0.94*
BI6: bladder control
⫺7.09
0.34
0.6
0.3
FAI10: driving a car/bus travel
FAI11: travel outings/car rides
3.63
0.56*
4.03
0.43*
FAI12: gardening
3.41
2.27*
FAI13: household/car maintenance
3.61
2.94*
BI5: bowel control
⫺7.33
0.35
⫺0.1
⫺0.7
0.63*
BI1: feeding
⫺8.41
0.44
⫺0.1
⫺0.1
Mean
0.00
0.26
⫺0.1
⫺0.8
SD
4.19
0.06
0.5
1.7
FAI14: reading books
FAI15: gainful work
4.95
5.94
2.16*
⫺1.71*
*Disordering of the step difficulties.
*The items are arranged in descending order of difficulty.
categories were collapsed into a dichotomy. The highest score
category of the items in the BI was rescored as 1, indicating
full independence in the activity. The rest of the categories
were rescored as 0, indicating dependence in the activity. For
the FAI, all but the lowest score category (0) of the items
were collapsed into a category and rescored as 1, indicating
participation in the activity. The lowest score category of the
items in the FAI remained 0, indicating no participation in the
activity.
Unidimensionality of Simplified Scale
When the Rasch dichotomous model was applied to examine the
25 dichotomous items together, 2 misfit items (social occasions
and walking outside) had outfit ZSTD statistics of 2.9
(MNSQ⫽9.90 and 4.76, respectively) and infit ZSTD statistics
of 3.4 (MNSQ⫽1.37) and 5.3 (MNSQ⫽1.86), respectively,
which were statistically significant at the 0.05 level. These 2
items were excluded from the rest of the analyses. Table 3 shows
that none of the outfit ZSTD was statistically significant for the
remaining 23 items. The infit ZSTD had slightly more variations
(SD⫽1.7) than the outfit ZSTD (SD⫽0.5), indicating that there
was some degree of unexpected behavior affecting responses to
items near the person’s ability measure. However, because they
were not very far away from the critical point ⫾2 or ⫾3 (more
liberal) and their corresponding outfit ZSTD statistics were not
significant, those items with slightly extreme infit ZSTD were
not treated as poor-fitting items. A factor analysis on the
residuals of Rasch-transformed scores showed no dominant
factors. The first and second factors accounted for only 12.3%
and 8.3% of the residual variance, respectively. These results
indicated that there was a good model-data fit and that the
assumption of unidimensionality held for these 23 dichotomous
items when assessed at 1 year after stroke.
We further examined the psychometric properties of the
23-item scale. The person measures (ranging from ⫺9.46
to 6.04) had a mean of ⫺1.17 and a SD of 3.94. The person
reliability was 0.94 (which can be similarly interpreted as
Cronbach’s ␣), indicating that these items yielded very
precise estimates for the patients. The person reliability
was practically identical to that under the partial credit
modeling (0.93), ie, collapsing categories did not reduce
the person reliability. The person measures under the
Rasch dichotomous model were also highly correlated with
those under the partial credit model (r⫽0.97), indicating that
collapsing the categories did not substantially alter ADL score in
the patients.
The Figure shows the map of persons and items along the
continuum. The item difficulties were spread out across the
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Stroke
March 2004
Item and person map
under the Rasch model.
patients, indicating that these items could well differentiate
these patients. The Figure also shows that there were obvious
gaps between items BI3 (grooming) and BI8 (transfer),
between BI9 (mobility) and BI4 (dressing), between BI2
(bathing) and BI10 (stairs), and between FAI6 (local shopping) and FAI10 (driving a car/bus travel).
A conversion table showing combined BI and FAI raw
scores (23 items) and their Rasch-transformed scores (ie,
person measure in logit) is shown in Table 4. It allows
prospective users to easily derive the Rasch-transformed
scores from the raw scores.
Discussion
Combining ADL and IADL indices can provide a measurement tool with an enhanced range and sensitivity for
assessing comprehensive ADL function,6,7 which is especially useful when applied to patients with stroke who are
living in the community. Using Rasch analysis, this study
found that such a measurement tool can be created by
combining all but 2 items of the BI and FAI and simplifying the polytomous responses into dichotomous categories. Because the items of the new scale have been shown
to measure comprehensive ADL function as a single,
unidimensional construct for patients at 1 year after stroke,
it is valid to sum the item scores of the combined scale.
The total score represents a stroke patient’s ADL function
on a single continuum encompassing the entire range of
ADL. A higher score indicates higher independence in
living in the community.
There are some advantages to using the combined scale.
The items of the BI are located in the lower part of item
difficulty, indicating easier activities, and those of the FAI
are located in the upper part, indicating more difficult
activities. The total score of the combined scale is useful in
showing whether the subject has basic ADL problems or
IADL problems. A conversion table was compiled showing
combined BI and FAI raw scores (0 to 23) and their
Rasch-transformed scores. The Rasch-transformed scores
can be viewed as interval-level measurements,24 whereas
the combined BI and FAI raw scores are ordinal data.
Since most statistical techniques assume that the data are at
least on an interval scale, the Rasch-transformed scores of
the combined scale are recommended for future applications. In addition, both the original BI and FAI and their
scoring guidelines19,22 as used in this study can be employed as usual. To use the new scale proposed in this
article, the users can first obtain the combined ADL score
for a patient by adding the dichotomized scores of all but
the 2 poor-fitting items and then use the conversion table
to look up the corresponding Rasch-transformed interval
score.
There have been few empirical investigations of the
appropriateness of scoring points of the BI and FAI. The
items in both indices contain 2 to 4 scoring points. We
found that the middle categories of both indices provide
little information about the patients and are redundant.
Thus, the response categories of all the items were recoded
as dichotomous in this study. Given that the psychometric
Hsueh et al
TABLE 4. Raw Score, Rasch-Transformed Score, and Standard
Error of the Combined and Dichotomized BI and FAI (23 items)
Rasch-Transformed
Score
SE
0
⫺9.46
1.52
1
⫺8.56
1.18
2
⫺7.40
1.01
3
⫺6.38
1.04
4
⫺5.23
1.11
5
⫺4.05
1.05
6
⫺3.01
1.00
7
⫺2.03
0.98
8
⫺1.14
0.91
9
Raw Score
⫺0.37
0.84
10
0.29
0.79
11
0.87
0.74
12
1.38
0.70
13
1.85
0.66
14
2.27
0.64
15
2.66
0.62
16
3.03
0.61
17
3.40
0.61
18
3.77
0.62
19
4.18
0.65
20
4.63
0.70
21
5.19
0.80
22
6.04
1.06
23
6.80
1.45
properties of the dichotomous items were equivalent to
those of the polytomous items and that a scale with only
dichotomous items is much more convenient and efficient
to administer, the dichotomous categories are recommended for use in both indices for patients at or after 1
year after stroke.
Tennant et al26 also used Rasch analysis to examine the
dimensionality of the BI and found that the item “bladder
control” did not fit the model’s expectation. The discrepancy between their findings and our findings may be
explained by the different scoring guidelines of the BI used
in the respective studies. We adopted the scoring guidelines suggested by Wade and Collin,22 whereas they used
those from Shah et al.27 Therefore, the results from this
study should be interpreted with caution when other
scoring guidelines are used.
Cultural or environmental factors may explain why the
items “social occasions” and “walking outside” did not fit
the model well.28,29 In addition, all the patients were
assessed at 1 year after stroke and had been discharged
from the hospital ⬎6 months previously. Our results may
not be broadly applicable to patients with different characteristics (eg, patients at a subacute stage or those who
have just been discharged from the hospital).
The combined scale can be further improved by generating items to fill the gaps among pairs of current items
Rasch Analysis of Combining 2 ADL Indices
725
(eg, grooming and transfer). These new items will be able
to differentiate the ability levels of patients falling in the
gaps of the current scale. Future studies to examine utility
and other psychometric properties (eg, interrater reliability
and responsiveness) of the combined scale in stroke
patients are needed. Furthermore, it may be promising to
extend the BI and FAI into an item bank and to use
computerized adaptive testing to further elaborate ADL
measurement.
In summary, this study provides good evidence for a
unidimensional construct of the dichotomized and combined BI and FAI, with the exclusion of 2 FAI items. The
results imply that these 2 indices can be combined to
assess comprehensive ADL function in patients after 1
year after stroke.
Acknowledgments
This study was supported by research grants from the National
Science Council (NSC 89-2320-B-002-069, NSC 90-2320-B-002033, and NSC 91-2320-B-002-008) and the National Health Research Institute (HNRI-EX92-9204PP).
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