Patients and setting
Our data was collected from 389 outpatients with
rheumatoid arthritis (RA) (n=174) and osteoarthritis
(OA) (n=215) who had participated in previous
studies performed at the Department of Physical
Medicine and Rehabilitation, Ankara University,
Faculty of Medicine between 2002 and 2011.
13-15
Out of the 389 patients, 385 (171 with RA and 214
with OA) had completed all of the items on the
HAQ-DI, There were 309 females (80%) and 76
males (20%) in the study and the mean age and
disease duration were 55±12 years (range; 18 to 84)
and 8.5±8.3 years (range; 0 to 60), respectively. We
used the responses of the 385 patients who had no
missing item scores, and this led to a data set that
had a complete set of answers for each respondent.
After imposing missingness, multiple imputation
and all analyses were performed using the scores
of the eight sections of the HAQ-DI. All patients
gave their informed consent to take part in this
study, which was carried out in compliance with the
Helsinki Declaration.
Selected scale
The HAQ-DI is the most widely utilized self-report
questionnaire to assess the functional status of patients
with a variety of rheumatic diseases. After it was
introduced in the 1980s for RA,16 it is then applied
to other diseases such as OA, juvenile RA, systemic
lupus erythematosus (SLE), scleroderma, ankylosing
spondylitis (AS), fibromyalgia, and psoriatic arthritis.17
The HAQ-DI assessment instrument includes the eight
domains of dressing and grooming, arising, eating,
walking, hygiene, reach, grip, and common daily
activities. For these eight domains, there are 20 questions
with four possible responses (without any difficulty:
0, with some difficulty: 1, with much difficulty: 2,
unable to do: 3). The highest score reported by the
patient across any component question of the eight
domains is recorded as the score of that domain unless
aids or devices are required. In that case, the score is
automatically raised to 2 when it is rated as 0 or 1. The
HAQ-DI score is then calculated as the average of the
eight domains (items) with scores ranging between 0
and 3, with a higher score representing more disability.
The Turkish adaptation was used in the study.18
Missing data simulation
Data sets with the missing item responses were
created to evaluate the performance of the RF
imputation technique with regard to patient disability
level estimates. Item responses were deleted from
the full data set (n=385) with respect to the MCAR
mechanism, and the missing data was generated
through simple random selection from among all
respondents with three missingness proportions (0.10,
0.30, and 0.50).
Multiple imputation and Rasch model estimates
Multiple imputation was carried out separately
for each of the three newly created data sets. In the
imputation phase, the missing responses were imputed
five times with different plausible values using the RF
method. Then in the analysis phase, a Rasch model was
used, and the patient disability levels were estimated
for each of the completed data sets. In the pooling
phase, the patient disability estimates and standard
errors were combined into a single set of results for
each of the three data sets (Figure 1).
Click Here to Zoom |
Figure 1: Graphic representation of the multiple imputation process for each of the newly
created three data sets with missing values. θ: a vector of the 385 patient disability estimates
and standard errors. |
Imputation method
The RF imputation method was first proposed
by Sijtsma and Van der Ark2 for data related to test
or scale. In the Rasch model, for a patient with a
latent trait level, the probability of having a score x
on item j is called the item response function, shown
as, P(Xj=x|θ). The RF imputation uses the estimated
item response function to impute item scores, and
it has been proven to be an efficient imputation
method for unidimensional scales in simulation
studies.2-4
The classical test theory and item response theory
The item response theory (IRT) is a modern test
theory used for the design, analysis, and scoring of
scales that are utilized to measure latent traits. It is
generally considered to be superior to the classical
test theory (CTT) due to its more cogent theoretical
justifiability. In the IRT, the true score is defined by
the latent trait level of interest (θ) rather than the
ordinal raw score used in the CTT. The Rasch model,
a one-parameter IRT model, helps to measure the latent trait levels of patients using the categorical
response data collected to assess them.19 Therefore,
it has a specific property that provides a criterion for
objective and successful measurement. Because the
polytomous nature of the responses and the distance
between thresholds across items were not similar,
Master's partial credit model (PCM),20 one of the
Rasch models, was used to analyze the HAQ-DI data
in this study.
To evaluate the similarity between the disability
estimates from the original data and those from the
multiple imputed data, a scatter plot and an ICC
were used. We also evaluated the similarity between
the disability estimates from the original data and
those from the data with missing values. We found
that the bias increased as the similarity between the
two disability estimates was impaired. The same ICC
calculations were also performed for the standard
errors of disability estimates, and they were used for
calculating between the items both before and after
imputation.
The missing data simulation, multiple imputation
with the RF method, pooling of the disability
estimates and their standard errors, and scatter plots
were performed using functions written in the R
software package version 2.13.0 (The R Foundation
for Statistical Computing).21 Readily available
functions in the extended Rasch modeling package
(eRm) of R were used for PCM fit and the patient
disability estimates.22 The Statistical Package for
the Social Sciences (SPSS Inc., Chicago, Illinois,
USA) for Windows version 15.0 was used to calculate
the ICC and its 95% confidence interval (CI). The
R codes used in this study will be provided by the
authors upon request with no expiration date (the
RF imputation used in this study is also available as
SPSS syntax that is freely downloadable from [http://
spitswww.uvt.nl/~avdrark/research/research.htm]).23
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