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Latent variable approach to the measurement of physical disability in rheumatoid arthritis.

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Arthritis & Rheumatism (Arthritis Care & Research)
Vol. 51, No. 3, June 15, 2004, pp 399 – 407
DOI 10.1002/art.20404
© 2004, American College of Rheumatology
ORIGINAL ARTICLE
Latent Variable Approach to the Measurement of
Physical Disability in Rheumatoid Arthritis
AGUSTÍN ESCALANTE,1 INMACULADA DEL RINCÓN,1
AND
JOHN E. CORNELL2
Objective. To measure physical disability in rheumatoid arthritis (RA) using a latent variable derived from a generic and
a disease-specific self-reported disability instrument and an observer-assessed functional status scale.
Methods. Consecutive patients with RA completed the modified Health Assessment Questionnaire (M-HAQ) and the
Short Form 36 (SF-36) physical function scale. An observer assigned a Steinbrocker functional classification. We used
principal component factor analysis to extract a latent variable from the 3 scales. We used the Bayesian Information
Criterion to compare how well the new latent variable and the 3 primary scales fit the criterion standards of current work
status; vital status at 6 years; grip strength; walking velocity; the timed-button test; pain; and joint tenderness, swelling,
and deformity.
Results. Complete data were available for 776 RA patients. The extracted latent variable explained 75% of the variance
in the 3 primary scales. On a scale of 0 –100, higher scores representing less disability, its mean ⴞ SD was 56.4 ⴞ 22.5.
Correlation between the latent variable and the M-HAQ was ⴚ0.87; between the latent variable and SF-36 physical
function scale was 0.89, and between the latent variable and Steinbrocker class was ⴚ0.85. Multivariate models that
included the latent variable had superior fit than did models containing the primary scales for the criteria of current
working; death by 6 years; pain; joint tenderness, swelling, or deformity; grip strength; walking velocity; and timed button
test.
Conclusion. A latent variable derived from the M-HAQ, the SF-36 physical function scale, and the Steinbrocker
functional class provides a parsimonious scale to measure physical disability in RA. The fit of the latent variable to
comparison standards is equivalent or superior to that of the primary scales.
KEY WORDS. Physical disability; Rheumatoid arthritis; Disease-specific health measures; Generic health measures;
Outcome assessment; Factor analysis.
INTRODUCTION
The rheumatic disease process frequently leads to physical
disability (1). Researchers aiming for a better understanding of rheumatoid arthritis (RA) outcome must first quantify it in a meaningful and reliable way. However, physical
disability is a hypothetical construct, i.e., it was put to-
Supported by an Arthritis Investigator Award and a Clinical Science Grant from the Arthritis Foundation; NIH
grants RO1-HD37151, K23-HL004481, K24-AR47530; and
grant M01-RR01346 for the Frederic C. Bartter General Clinical Research Center.
1
Agustı́n Escalante, MD, Inmaculada del Rincón, MD: The
University of Texas Health Science Center at San Antonio;
2
John E. Cornell, PhD: The University of Texas Health Science Center at San Antonio and the South Texas Veterans
Administration Health System, San Antonio, Texas.
Address correspondence to Agustı́n Escalante, MD, University of Texas Health Science Center at San Antonio, 7703
Floyd Curl Drive, San Antonio, Texas 78229-3900.
Submitted for publication October 5, 2002; accepted in
revised form August 1, 2003.
gether by scientists to explain the decline in the ability to
perform physical activities that can occur in RA and other
diseases (2). This implies that physical disability cannot
be directly observed or measured, and as such, it can be
considered a latent variable (3). Available measurement
tools to assess physical disability in RA indirectly tap into
the underlying construct (3).
To measure disability in RA, researchers have a variety
of instruments and scales from which to choose (4). Some
of these are considered arthritis-specific because they center on outcomes more immediately relevant to arthritis
(5–7). Generic scales, on the other hand, measure more
global outcomes and are suitable for studying a diversity of
diseases (8). Each has its own set of advantages (9 –12).
Some empirical studies, however, have not found major
differences in performance between the 2 types of scales
(13,14). The choice between one type over the other not
being clear cut, some authorities reasonably advocate including both an arthritis-specific and a generic outcome
measure in RA trials (9,15). This recommendation has the
added benefit that 2 or more measurement tools will pro399
400
vide a more reliable representation of the underlying construct (16).
However, not much attention has been given to how to
report the results of studies that include 2 or more outcome measures of the same construct. The option of describing results on both scales separately in the same, or
different, reports has certain disadvantages, including the
need to conduct separate, parallel analyses; a greater potential for type I errors due to multiple comparisons; the
added space needed to show results fully; enticement to
duplicate publication; and problems of interpretation if
results on the different scales diverge. When the last of
these occurs, investigators may be lured into simply omitting results on the scale that do not fit their hypotheses.
These potential problems, theoretical or real, can be
averted by a data-reduction process aimed at estimating
the underlying latent variable, conserving or enhancing
information provided by the various scales.
We have confronted some of the above dilemmas during
an ongoing study of the disablement process in RA. We
selected 2 self-report scales, one generic and the other
disease-specific, and an observer-derived classification
system to assess the extent of physical disability in RA. In
this article, we describe the data-reduction process we
utilized to derive a parsimonious, single variable representing the construct of physical disability. We also show
evidence of its equivalence, or superiority, to the 3 primary scales.
PATIENTS AND METHODS
Patients. From 1996 to 2000 we enrolled patients meeting the 1987 American College of Rheumatology (formerly
American Rheumatism Association) RA criteria (17) into a
study of the disablement process in RA (18). We have
described our sample in previous publications (18 –21).
The study’s acronym, ÓRALE (Outcome of Rheumatoid
Arthritis Longitudinal Evaluation), matches a Mexican
American idiom for “Lets go!” Here we will show crosssectional results obtained during the recruitment evaluation of each participant.
Data collection procedures. Our study was approved by
the Institutional Review Board of each of the recruitment
centers and all patients gave written, informed consent. A
physician or a research nurse, assisted by a trained research associate, conducted evaluations at the clinic
where the patient was recruited. The evaluation lasted
⬃90 minutes and consisted of a comprehensive interview,
physical examination, review of available medical records,
laboratory tests, and radiographs. Interviews were conducted in either English or Spanish, as preferred by patients.
Demographics. We ascertained age, sex, and race/ethnicity by self report, as described previously (20).
Musculoskeletal examination. A physician or research
nurse, trained in joint examination techniques, assessed
Escalante et al
48 joints in each patient for the presence or absence of
tenderness or pain on motion, swelling, or deformity, as
described elsewhere (22).
Pain. We asked patients to rate the amount of pain they
experienced due to their arthritis during the past week on
a graded, horizontal 10-point scale that has been validated
in our patient population (23).
Performance-based functional measures. We measured
grip strength with a hand-held JAMAR dynamometer
(Sammons Preston, Bolingbrook, IL). In a sitting position,
with the elbow held at 90° and the forearm supported on a
flat horizontal surface, patients were asked to squeeze the
handle with as much as strength as possible. Three repetitions from each hand were recorded in kilograms. The
mean value of all repetitions for both hands is shown.
Walking velocity was measured with patients starting in
a standing position. They were asked to walk at their usual
pace for a distance of 50 feet, or 25 feet if they had difficulty covering the full distance. No effort was made to
conceal the stopwatch used to time the patients. Results
are expressed in feet per second. Patients unable to walk
were assigned a velocity of 0 feet per second.
Patients were timed as they donned and fastened the
front buttons in a standard 8-button shirt (Wal-Mart, San
Antonio, TX). Results are expressed as buttons per second.
Patient unable to don the shirt were assigned a value of 0
buttons per second.
Physical disability measures. We used 3 instruments to
measure physical disability. The disability index of the
modified Health Assessment Questionnaire (M-HAQ) is a
self-administered, arthritis-specific instrument that asks
respondents to rate the amount of difficulty they have
performing 8 activities (dressing, getting out of bed, lifting
a cup, walking, bathing, bending, turning faucets, and
getting in and out of a car) on a scale ranging from 1 to 4
(without difficulty, with some, with much, and unable)
(24). We used a cross-culturally equivalent Spanish version for our Spanish-speaking patients (23). The Short
Form 36 (SF-36) physical functioning scale (SF-36PF) is an
interviewer-administered generic instrument (8). The SF36PF asks respondents to rate the amount of limitation
caused by health on 10 physical activities (vigorous activities; moderate activities; carrying groceries; climbing several or 1 flight of stairs; bending; kneeling or stooping;
walking more than a mile; walking several blocks or 1
block; bathing; and dressing). Respondents rate each activity on a 3-level scale (a lot of difficulty, a little, no difficulty). Individual responses were summed, and the sum
was rescaled to range. The Steinbrocker functional classification was used by the physician or research nurse, who
were trained in physical function assessment, to rate the
extent of physical disability on a 4-level scale, ranging
from class I, “complete functional capacity to carry out all
usual duties without handicaps,” to class IV, “largely or
wholly incapacitated with (the person) bedridden or confined to wheelchair” (25). We used each of these 3 scales as
Latent Variable Measuring Disability in RA
intended when they were originally developed, scoring
them as recommended by their original authors.
Work status. We asked patients to describe their current
work status from among the following answers: working
full or part time, retired, student, housewife, unemployed/
laid off, or disabled/unable to work. We used these responses for 2 sets of analyses: For the first, we classified
patients as working (full or part time) versus not working
(all others); for the second, we classified patients as disabled/unable to work versus all others.
Vital status. We have recontacted the patients at yearly
intervals since their initial evaluation. For patients with
whom we were not able to establish contact, even through
family members, we searched publicly available death registries. We obtained a death certificate for all patients who
died.
Statistical analysis. We performed a principal component factor analysis using the composite summary scores
of the M-HAQ, SF-36PF, and the Steinbrocker functional
class, and then extracted the first principal component
from the unrotated factor loadings using the least squares
regression method (26). We rescaled the extracted factor to
range from 0 to 100 with a positive valence, higher values
representing less disability. To evaluate the degree of bivariate association between the new latent variable and
other study variables with interval or ratio distributions,
we used Pearson product moment correlation coefficients
(27). For the Steinbrocker functional class, a 4-level ordinal scale, we used the square root of the multiple R2 from
a regression model that included dummy variables for
each Steinbrocker level instead of the Pearson coefficient.
Differences between the coefficients were tested after
Fisher z-transformation (28) using the procedure provided
by Goldstein (29). Because this required us to perform a
total of 21 correlation coefficient comparisons, we only
considered coefficients to be significantly different if the
comparison P value was ⱕ 0.002, adjusted according to the
Bonferroni technique (the conventional ␣ ⫽ 0.05 ⫼ number of comparisons ⫽ 21). To evaluate the latent variable’s
association with categorical criterion variables, we divided the latent variable into ordinal categories and used
chi-square to test the strength of association (27). We then
evaluated the fit of multivariate models that included the
new latent variable compared with models that included
the primary variables. We asked the question: Does a multivariate model that includes the new latent variable fit the
criterion standards better than models that include any of
the primary variables? We included age and sex as covariates in all these multivariate models because they can have
a strong influence on any of the criterion measures we
used. The general form of the models we compared was
y ⫽ a ⫹ b ⫹ pd
where y could be any of the criterion standards (working
status, vital status, grip strength, etc.), a was age, b was sex,
and pd was 1 of the 4 physical disability scales (M-HAQ,
SF-36PF, Steinbrocker class, or the new latent variable).
401
When y was a categorical variable, the model was a logistic
regression; and when y was an interval or ratio variable,
the model was ordinary least squares regression. We expected that the fit of a multivariate model including the
new latent variable on any of the criterion standards
would be equivalent or superior to the fit of models that
include any of the 3 primary variables. We used the Bayesian Information Criterion (BIC) to confirm this expectation
(30). The BIC varies inversely with a model’s fit, and given
2 models, the one with the smaller or more negative BIC
has better fit (30). We used Raftery’s guidelines to interpret
BIC differences between 2 models: A BIC difference ⬎10 is
considered “very strong” evidence in favor to the model
with the smaller BIC; a difference of 6 –10 is “strong;” 2– 6
is “positive,” and 0 –2 is “weak” evidence (30). We performed all analyses on a desktop personal computer, using
the Stata 7.0 software package (College Station, TX).
RESULTS
As expected for a group of people with established RA
visiting a rheumatologist, most were women, median disease duration was 8 years, and rheumatoid factor was
present in the majority (Table 1). The median number of 8
deformed joints indicates a substantial amount of joint
damage (22). In accord with this finding, only 21% of the
patients were working full or part time, and 27% stated
they were unable to work. Of the 756 patients on whom we
had followup information up to 6 years later, 71 were
known to have died (9%).
Figure 1 is a diagram of the factor analysis we used to
derive the physical disability latent variable. The 3 primary variables, M-HAQ, SF-36PF, and Steinbrocker class,
loaded strongly on a single factor, with loadings ⱖ0.8. This
factor explained ⱖ75% of the primary variables’ combined
variance. Uniqueness values were ⬍0.3 for each of the
primary variables, indicating that these share more than
two-thirds of their combined variance. We extracted the
single factor without rotation, using linear regression scoring. Figure 2 shows probability distributions for the 3
primary scales and the latent variable.
The Pearson correlation coefficients between the extracted latent variable and the primary variables, as expected, was also strong, with r values ⱖ0.8. Figure 3 shows
scatterplots of the bivariate distribution of these variables.
The correlations between the latent variable and the criterion variables (pain, joint tenderness, swelling or deformity, grip strength, walking velocity, and the timed button
test) are shown in Table 2, contrasted with the correlation
coefficients between the primary scales and the same criterion standards. The latent variable had a significantly
stronger correlation with most of the criterion standards
than did the primary variables M-HAQ, SF-36PF, and
Steinbrocker class. Notable exceptions were the correlation with the pain and articular examination variables, for
which there was no significant difference between the
M-HAQ and the latent variable. Also interestingly, the
number of deformed joints correlated more strongly with
Steinbrocker class that with any of the other physical
disability scales.
402
Escalante et al
Table 1. Clinical characteristics of the 776 RA patients studied*
Characteristic
Age, median (range), years
Male, no. (%)
Ethnic group, no. (%)
White
Black
Asian
Hispanic
Other
Education, median (range), years
Currently working, no. (%)
Disabled for work, no. (%)
Time from disease onset, median (range), years
Tender joint count, no. (%)
Swollen joint count, no. (%)
Deformed joint count, no. (%)
Nodules, no. (%)
Rheumatoid factor positive, no. (%)
Walking velocity, mean ⫾ SD, meters/minute
Grip strength, mean ⫾ SD, lbs
Button test, mean ⫾ SD, buttons/minute
MHAQ, mean ⫾ SD
SF-36, mean ⫾ SD
Steinbrocker functional class, mean ⫾ SD
I
II
III
IV
Latent Disability Scale, mean ⫾ SD, lbs
Deaths as of March 2002, no. (%)
No. with data
available
776
776
776
772
776
776
776
776
776
776
776
770
775
776
769
776
776
776
776
756
Distribution
57 (19–90)
229 (30)
272 (35)
53 (7)
14 (2)
431 (56)
6 (1)
12 (0–17)
166 (21)
213 (27)
8 (0–52)
15 (13)
7 (7)
10 (11)
233 (30)
682 (89)
59 ⫾ 25
14 ⫾ 10
7.1 ⫾ 3.8
1.89 ⫾ 0.70
35.6 ⫾ 27.87
163 ⫾ 21
383 ⫾ 49
190 ⫾ 24
40 ⫾ 5
56 ⫾ 23
71 (9)
* RA ⫽ rheumatoid arthritis; MHAQ ⫽ Modified Health Assessment Questionnaire; SF-36 ⫽ Short Form
36.
Figure 4 shows the relationship between the latent variable and selected comparison criteria. These graphs show
the association between higher values in the latent variable and graded decreases in the number of deformed
joints, the proportion of disabled patients, and the proportion of those who died within 6 years. Conversely, performance-based functional measures (grip strength, timed
button test, and walking velocity) displayed a proportional
rise with increasing values on the latent scale, as did the
probability of working full or part time.
Table 3 shows the BICs of models that contained age,
sex, and each of the 4 disability scales (the M-HAQ, SF36PF, Steinbrocker class, and the latent variable) as independent variables for each of the criterion standards. For
most of the criterion standards, the BIC was smaller, indicating better fit, in the models that included the latent
variable (Table 3). Notable exceptions, again, included the
Steinbrocker class, whose model had a better fit versus the
deformed joint count than did any of the other physical
disability scales. Likewise, there was positive evidence
that the SF-36PF fit better in a model for disabled work
status, than did any of the other physical disability scales.
DISCUSSION
Figure 1. Diagram of the factor analysis we conducted to extract
the latent variable measuring physical disability. The 3 primary
variables are represented by squares and the circles represent
information outside the latent variable. M.H.A.Q. ⫽ modified
Health Assessment Questionnaire; SF-36 ⫽ Short Form 36.
One desirable characteristic of research data is parsimony,
or simplicity of explanation (31). Under this principle, one
variable is preferable to 2 or more, providing that the
single variable is as informative as the 2 or more. We have
shown evidence that a single latent variable derived from
principal component factor analysis of 3 scales, the MHAQ, the SF-36PF, and the Steinbrocker functional class,
has equal or superior performance to the primary scales, as
Latent Variable Measuring Disability in RA
403
Figure 2. Frequency distributions of the disability scales employed. Disability level decreases from left to right. A large proportion of
patients had a score of 1 on the modified Health Assessment Questionnaire (M.H.A.Q.), indicating low disability levels on this scale (top
left). However, the opposite is true for the Short Form 36 physical function (SF36PF) scale, in which the largest category is made up of
patients with low scores, indicating high disability levels (top right). The Steinbrocker functional class provides only 4 levels to classify
physical disability (lower left). The distribution of scores on the latent disability scale approached normality (lower right).
manifested by an equal or stronger degree of association
with the criterion standards we selected. We used the
disablement process as a theoretical framework to inform
our selection of criterion standards (18,32,33), aiming to
test the underlying physical disability construct from as
many perspectives as possible. Thus, our comparison criteria included key RA impairments, such as the amount of
pain and the number of tender, swollen, and deformed
joints (33). We also used measures of functional limitation,
occupational status, and death within 6 years as criteria.
The correlation between the joint impairments and the
latent variable was nearly always stronger than that between the same impairments and the primary disability
scales (Table 2). This likely is due to the superior reliability of the latent variable, which is a composite of the 3
primary disability scales. This approach has been referred
to as incomplete principal component regression because
the variable of interest is provided by the first principal
component in a factor analysis (34). The composite measure’s stronger correlation with most criterion standards
conforms to a fundamental theorem of measurement theory
Corr(x,y) ⱕ
冑rel共 x 兲 ⫻ rel共 y兲
according to which the correlation between 2 variables, x
and y is limited by the square root of the product of each
variable’s reliability (16). However, there were 2 comparisons that did not follow this rule: The M-HAQ correlated
equally strongly as the latent variable with the impairments; and the Steinbrocker class correlated more strongly
with the number of deformities than did any of the other
disability scales, including the latent variable. The reason
for this may be that examiners may have incorporated
findings from the joint exam into their judgment of the
Steinbrocker class. In contrast, the M-HAQ and the SF-36
are self-reported scales that patients answer according
their own perceived condition.
We also used 3 performance-based measures of functional limitation: grip strength, walking velocity, and
timed button test. Within the disablement process framework, these measurements are closer to the physical disability construct than are the joint impairments (18,32,33)
and, consequently, their degree of correlation with the
disability scales was stronger. Here, even more so than
with the impairments, the latent variable’s association
with the performance-based measures was stronger than
that of any of the 3 primary physical disability scales
considered individually.
Work loss is one of the main adverse consequences of
RA (35). We found that work status was strongly associated with the 4 physical disability scales with a tendency
for the association to be stronger for the latent variable.
Likewise, death displayed a similar pattern of association.
One of the main uses of these comparison standards, occupational and vital status, is as anchors that researchers
or clinicians can use to interpret the values along the latent
variable scale. As shown in Figure 4, there are strong
adverse outcomes associated with lower values for the
latent variable.
The physical disability scales we used in the present
404
Escalante et al
Figure 3. Matrix plot showing the bivariate distribution of the 3 primary variables and the latent variable. The Pearson correlation
coefficient between the latent variable and the modified Health Assessment Questionnaire was ⫺0.87; between the latent variable and
Short Form 36 physical function scale (SF-36PF) was 0.89; and between the latent variable and the Steinbrocker class was ⫺0.85. All
coefficients were significant at P ⱕ 0.0001.
analyses, including the latent variable we developed, often
find use in multivariate models, either as outcomes or
predictors. We thus compared the fit of models that included the different physical disability scales as independent variables and each of the different criterion variables
as outcomes. Because each of the criteria we used can be
heavily influenced by age and sex, we included these 2
variables as covariates in all of the multivariate models.
We chose the BIC as a comparative measure because it is a
tool used often for model selection (30,36). We expected
that the models that included the new latent variable
Table 2. Correlation between physical disability scales
and variables measured as criterion standards*
Pain
Tender
Swollen
Deformity
Grip
Velocity
Button
MHAQ
SF-36PF
Steinbrocker
class
Latent
variable
0.59
0.49
0.24
0.20†
⫺0.54†
⫺0.61†
⫺0.54†
⫺0.53†
⫺0.43
⫺0.22
⫺0.25†
0.52†
0.65†
0.55†
0.41†
0.33†
0.22
0.52†
0.48†
0.67†
0.60
⫺0.59
⫺0.47
⫺0.24
⫺0.35
0.59
0.72
0.64
* Pearson correlation coefficients were compared after Fischer ztransformation, after equalizing coefficient signs (28,29). MHAQ ⫽
Modified Health Assessment Questionnaire; SF-36PF ⫽ short form
36 physical functioning scale.
† Significance of comparisons versus latent variable was set at P ⱕ
0.002.
would have smaller BICs, indicating better fit. Indeed this
was the case with nearly all of the criterion variables.
The latent disability variable has distributional advantages over the 3 primary scales. Both the M-HAQ and the
SF-36PF display skewed distributions (Figure 2), the
former displaying a ceiling effect, the latter, a floor effect
(37). The latent scale lacks skewness in either direction,
more closely approximating normality than any of the
primary scales. Moreover, the latent variable displays an
interval or near-interval distribution, as suggested by the
monotonic rise in criterion variables as the scale increases
(Figure 4).
The latent variable has theoretical advantages as well:
Physical disability is a hypothetical construct and claims
that any one disability measurement scale is superior to
others are debatable. Using more than one measurement
tool may be a more accurate way to get at the underlying
construct because it enables the unmeasured construct to
be assessed from a variety of angles. For this same reason,
the idea of using both a scale intended specifically for
arthritis and one intended for unselected populations
(9,15) is quite attractive, because the arthritis-specific
scale, the M-HAQ in our study, will capture the arthritisrelevant outcomes whereas the generic scale, here provided by the SF-36PF, will capture an overall nonspecific
disease impact.
We acknowledge some limitations of our analysis. Factor analysis assumes that data are distributed on interval,
multivariate normal scales, an assumption that may not be
stringently met by the 3 disability scales we entered into
Latent Variable Measuring Disability in RA
405
Figure 4. Relationship between the latent variable measuring physical disability and the criterion measures deformed joint count (top left;
trend P ⱕ 0.001); walking velocity, grip strength, and timed button test (top right; trend P ⱕ 0.001 for each variable); work disability and
death within 6 years (bottom left; trend P ⱕ 0.001 for each); and currently working (bottom right; trend P ⱕ 0.001). Error bars represent
standard error.
the factor analysis. However, this assumption is a strict
requirement only if statistical inference is used to determine the number of factors and can be relaxed when factor
analysis is used descriptively (26,38). The least squares
factor extraction method we used is also robust to devia-
tions from normality (39). The M-HAQ and SF-36PF scales
we used were developed using sound psychometric theory
to produce results on interval or near-interval scales, and
they have each been used as such in numerous studies
over many years. We used the composite scores of both
Table 3. Bayesian information criterion of multivariate models, according to physical
disability scale used as independent variable*
Physical disability scale included as independent variable in
multivariate model†
Dependent variable
MHAQ
SF-36PF
Steinbrocker class
Latent variable‡
Currently working
Currently disabled
Death within 6 years
Pain
Tender joint count
Swollen joint count
Deformed joint count
Grip strength
Walking velocity
Timed button test
⫺4,429§
⫺4,288§
⫺4,782#
⫺1,588§
809#
⫺8¶
662§
248§
1,654§
⫺7,501§
⫺4,447¶
⫺4,308
⫺4,780§
⫺1,531§
855§
⫺5¶
661§
261§
1,609§
⫺7,465§
⫺4,432§
⫺4,266§
⫺4,775§
⫺1,414§
933§
7§
519
306§
1,660§
⫺7,478§
⫺4,451
⫺4,303
⫺4,791
⫺1,602
818
⫺14
607
170
1,466
⫺7,597
* Values shown are Bayesian information criteria. MHAQ ⫽ Modified Health Assessment Questionnaire;
SF-36PF ⫽ Short Form 36 physical functioning scale.
† Model’s form was y ⫽ age ⫹ sex ⫹ physical disability scale, where y ⫽ dependent variable. For current
working, currently disabled, and death by 6 years, the model was logistic; for other variables, model was
ordinary least squares.
‡ Extracted from a principal component factor analysis of MHAQ, SF-36PF and Steinbrocker class (Figure
1).
§ Very strong support for model that includes the latent variable.
¶ Positive support for model that includes the latent variable.
# Strong support for model that includes the latent variable.
406
these scales, scored as originally intended. It is possible,
however, to select items from each of these scales and
calibrate their weights so that they more closely approximate a true interval or ratio scale by using item response
theory or Rasch analysis (40,41). This may represent an
alternative method to accomplish the aims we pursued
here.
Data parsimony is a desirable feature in a research study;
among other reasons, because it avoids the problems we
mentioned in the beginning of this article. In the present
analysis, we have reduced the original 3 scales into 1
single variable that in many respects outperforms the individual primary scales. A similar data reduction strategy
could be used for other RA processes, such as inflammatory disease activity, disease damage, joint impairment,
and functional limitation (32,33). For example, a latent
variable extracted from the disease activity measures recommended for RA clinical trials (42) could potentially
lead to more efficient trials if the latent variable outperforms the primary scales, as was the case for disability
measures in the present analysis.
It is important to point out that ours is a data-driven
approach, and that the latent variable cannot be fully specified as an outcome measure in advance of a study. We do
not advise investigators to attempt to directly apply the
factor loadings we estimated here to develop a latent disability variable for use in their own studies, because data
from another patient sample could be quite different.
Moreover, investigators may have reasons to choose a different set of primary disability scales from those used here.
We do believe, however, that researchers can apply a principal component factor analysis, similar to that shown
here to their own data, to extract a latent variable that will
likely exceed the primary scales in reliability.
In conclusion, we have used factor analysis to derive a
latent variable that measures physical disability in RA.
The new variable outperforms the primary scales in a
number of tests of association with comparison criterion
standards. This approach may be used to develop latent
variables measuring other RA disease components, such as
disease activity, damage, and functional limitation.
ACKNOWLEDGMENT
We acknowledge the invaluable assistance of Florencia
Salazar and Samvel Pogosian, MD, in the conduct of the
ÓRALE study. We also thank Drs. Ramon Arroyo, Daniel
Battafarano, Rita Cuevas, Alex de Jesus, Michael Fischbach, John Huff, Rodolfo Molina, Mathew Mosbacker,
Frederick Murphy, Carlos Orces, Christopher Parker,
Thomas Rennie, Jon Russell, Joel Rutstein, and James Wild
for giving us permission to study their patients and for
contributing to this study.
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