For
the analysis, correlation matrix calculated with list-wise case deletion were
used. Maximum likelihood method was used for the estimation of parameters.
We decide a possible
model according to the following criteria: 1) The model can be reasonably
explained, 2) The model fits the data by statistically as goodness-of-fit index
(GFI) of 0.90 or greater, comparative goodness-of-fit index (CFI) of 0.90 or greater,
root-mean square error of the approximation (RMSEA) less than 0.05, and a
chi-square is not significant (p>0.05) [6]. Although standardized root mean
square error (SRMSE) was also presented to demonstrate a multivariate
normality, SEM is not so sensitive for multivariate normality rather than
factor analysis. When two or more models were met above criteria, the final
model was selected based on Akaike’s information criterion (AIC), a statistic
of goodness-of-fit adjusting number of estimated parameters. (See appendix).
Results and Discussion
Structural Equation Modeling of HRQOL of Cancer Patients
Assuming that HRQOL of patients consists
of four latent variables (EWB, FWB, SWB and PWB domains) as reported in the
literature [17], an initial model was constructed by exploratory factor
analysis. Then, the model was modified to make better fit between the model and
data by trial and error approach.
Table 4 shows
the correlation matrix of variables used in the final model. Because of little
contribution to the model, other variables were removed during optimization of
the model. The final model is shown in
Fig. 1 with path diagram (model 1) in
which circles (or ellipses) represent unobserved latent variables, squares (or
rectangles) represent observed variables and single arrows represent the impact
of one variable on another. e1 to e12 and d1 to d3 enclosed in a circle
indicate error representing measurement error. The single-headed arrows represent
linear dependencies. The numeric values located with single-arrows is an
estimate of standardized regression weight (standardized maximum likelihood
parameter). The estimates of standardized regression weight from errors to
variables (e1 to e12 and d1 to d3) were removed in the path diagram in order to
clear the relationship among variables.
Figure 1. SEM model of HRQOL of cancer patients with standardized regression weights (model 1).
The final model
suggests that HRQOL in cancer patients consists of three latent variables. From
the observed variables in three latent variables, the latent variables were regarded
to be physical, emotional and functional elements, respectively. Although there
are a little conflict in signal of standardized regression weight among
variables, overall, this model would be acceptable from empirically,
and statistics of goodness-of-fit between the model and data were very good to
be GFI=0.952, CFI=1.000, RMSEA=0.000, SRMSE=0.0615 and chi-square=8.285 (df=14,
p=0.874).
This result positively
supports the previous finding that the HRQOL of the patients consists of four
ideal domains (EWB, FWB, SWB and PWB) reported the results by Ward et al., [17],
even though lack of SWB domain in our model. This result also indicates that
data collected in this study contain information explaining HRQOL of patients.
From the magnitude
of estimates of standardized regression weight, physical and emotional domains
were predominant elements in HRQOL of cancer patients rather than functional
domain indicating that experiences of nausea and vomiting were mainly decreased
HRQOL of patients. We further examined the model taking into account relationship
between of HRQOL estimated by model 1 and subjected QOL in patients in Q.18.
The final model is shown in
Figure 2 (model 2). A double arrow between
estimated HRQOL (latent variable) and subjected QOL (observed variable)
represents the correlation coefficient between two variables.
Figure 2. SEM Model of correlation between estimated HRQOL and
subjected QOL in patients with standardized regression weights (model 2).
We did not further modify the relationship among the variables to
improve the fit, because a purpose was to investigate the relation between estimated
HRQOL in model 1 and subjected QOL answered by patients. Model 2 also satisfied
all statistical criteria (GFI=0.937, CFI=1.000, RMSEA=0.000, SRMSE=0.0688 and
chi-square=12.396 (df=21, p=0.928)).
As shown in
Figure 2, a correlation coefficient between estimated HRQOL by model 1 and subjected
QOL in patients was weak to be 0.23 (not significant). This would be result
that since the patients in this study were in the hospital and received
appropriate cares from pain care team; their pain was well controlled by taking
appropriate amount of opioid analgestics. This result also suggest that a
meaningful part of subjected QOL in patients would be influenced by other
parameters (latent or observed variables), such as qualification and/or intervention
of medical professionals.
SEM Modeling of subjected QOL in patients and qualification
of pharmacists
We postulated that a weak correlation
between modeled HRQOL and subjected QOL in patients would result that subjected
QOL is influenced by qualification and/or intervention of other medical professionals.
Then, the relationship between qualification of pharmacists and subjected QOL in
patients was modeled by SEM.
The model was
established on three hypothesis: 1) As described before, the estimated HRQOL was
strongly related with the physical element such as nausea and vomiting,
suggesting that severity of side effects of opioid would be one of predominant
factors to describe HRQOL of patients; 2) If the “severity” of side effects is controlled
to be low, this would lead comfortable life of patients in hospital and HRQOL score
in patients would increase; 3) If pharmacists can restrain side effects of patients,
subjected QOL in patients would increase.
We
explored the reasonable model to express the relationship among subjected QOL in
patients, qualification of pharmacists and severity of symptoms by SEM.
The final model
and correlation matrix are shown in
Figure 3 (model 3) and
Table 5,
respectively. In the model 3, one calculated parameter was introduced to make reasonable
model, that is, absolute value of difference of pain scores answered by
patients and assessed by pharmacists. This parameter would express a level of pharmacists’
skill to assess pain level of patients, because when the parameter is 0, the
pharmacist can assess the patients’ pain exactly. The statistics of
goodness-of-fit parameters of model 3 were all satisfactory to be GFI=0.907,
CFI=0.958, RMSEA=0.039, SRMSE=0.1192 and chi-square=16.957 (df=22, p=0.388).
The final model
consists of 4 latent variables, expressing “qualification of pharmacists”, “skill
of assessment” of pain level in patients, “severity” of side effect” and “comfort”
level, respectively. From the magnitude of estimates of standardized regression
weight between variables, the model can be explained as follows: when
pharmacists have high ability with skill to assess patients’ pain level, they
can work to restrain unpleasant symptoms such as pain and constipation. If “severity”
of side effects can be reduced by intervention by pharmacists, “comfort” level of
patients would be increased with decreasing uneasiness and increasing of
subjected QOL. Thus, subjected QOL in patients was considered to be one of factor
describing “comfort” level of patients in the SEM model.
The “qualification
of pharmacists” consists of skill to assess the pain level of patients and
experience in pain control team. The former was found to be predominant factor
in “qualification of pharmacists”. When pharmacists who have excellent skill to
assess the pain level of patients would intervene in pain control setting, they
can restrain the unpleasant symptoms of patients as pain and constipation. As a
result, subjected QOL in patients will be improved.
Figure 3 SEM model of subjected QOL in patients taking into
account intervention of pharmacists with standardized regression weights (model
3).
Gammaitoni et
al. reported that the palliative-trained pharmacist can play an important role
in managing chronic pain [18]. On the other hand, Malone et al. indicated that
clinical pharmacists had no significant impact on HRQOL as measured by SF-36 at
high risk patients [19]. These reports suggest that a professional of
pharmacists to improve QOL of cancer patients have not been evident. Our
research indicates that pharmacists with good skills and qualification to
assess patients’ pain can improve QOL of patients.
This model is a
quite simple model to express the relation between HRQOL of patients and qualification
of pharmacists to evaluate pain of patients. Because the number of questions to
patients was limited to be 18 according to the suggestion by a local research committee,
items of questionnaire were not sufficient to make sophisticated model to
evaluate HRQOL. Furthermore, sample size was also insufficient to make rigid
model.
Using SEM
modeling, the relationship between subjected QOL in patients and qualification of
pharmacists can be expressed by path diagram being easy to understanding. SEM model
would be a useful statistical technique to express the relationship between
latent variable such as patients’ QOL and intervention by health care stuffs.
We
will investigate effective interventions of pharmacists to improve QOL of
cancer patients by multi-institutional setting in future.
Appendix
Index of overall model fit used in SEM [5, 6]
Goodness-fit-index (GFI) indexes
the relative amount of the observed variances and covariance’s accounted for by
a model. GFI varies from 0 to 1 and a model with GFI close to 1 indicates a
very good fit.
Comparative goodness-of-fit
index (CFI) indexes the relative reduction in lack of fit as estimated by non-central
chi-square of a target model vs. a baseline model. CFI varies from 0
to 1. CFI close to 1 indicates a very good fit.
Root-mean
square error of the approximation (RMSEA) residuals are the coefficients which
result from taking the square root of the mean of the squared residuals, which
are the amounts by which the sample variances and covariance’s differ from the
corresponding estimated variances and covariance’s. The closer the RMR to 0 for
a model being tested, the better the model fit.
Chi-square
test is the statistical test of the lack of fit resulting from over-identifying
restrictions placed on the model. If chi-square difference shows no significant
difference between the unconstrained original model and the nested, constrained
modified model, then the modification is accepted.
Akaike
Information Criterion (AIC) is a goodness-of-fit measure that adjusts model
chi-square to penalize for model complexity. AIC reflects the discrepancy
between model-implied and observed covariance matrices. AIC close to zero
reflects good fit and between two AIC measures, the lower one reflects the
model with the better fit.
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