Pharmacology & Pharmacy, 2011, 2, 226-232
doi:10.4236/pp.2011.23031 Published Online July 2011 (http://www.scirp.org/journal/pp)
A Structural Equation Model (SEM) for
Pharmacist Competencies in Improving Quality of
Life of Cancer Patients: Effect of Missing Values
on the SEM
Rieko Takehira1, Keiko Murakami2, Sirou Katayama2, Kenji Nishizawa3, Shigeo Yamamura1
1Faculty of Pharmaceutical Sciences, Josai International University, Chiba, Japan; 2Department of Pharmacy, Nippon Medical Uni-
versity Hospital, Tokyo, Japan; 3Department of Pharmacy, Omori Medical Center, Toho University, Tokyo, Japan.
Received April 1st, 2011; revised May 20th, 2011; accepted June 22nd, 2011.
ABSTRACT
Objective: With the goal of improving health-related quality of life (HRQOL) in cancer patients, we previously reported
a structural equation model (SEM) of subjected QOL and qualificatio ns of pharmacists, based on a series of question-
naires completed by patients and pharmacists. However, several patients and pharmacists were excluded from the pre-
vious study because it was not always possible to obtain all the data intended for collection. In order to reveal the effect
of missing data on the SEM, we established SEMs of HRQOL and the competency of pharmacists, using correlation
matrices derived by two different statistical methods for handling missing data. Method: Fifteen can cer patients hospi-
talized for cancer and were receiving opioid analgesics for pain control, and eight pharmacists were enrolled in this
study. Each subject was asked four times weekly to answer questions presented in a questionnaire. SEMs were explored
using two correlation matrices derived with pair-wise deletion (PD matrix) and list-wise deletio n (LD matrix). The final
models were statistically evaluated with certain goodness-of-fit criteria. Results: Data were intended to be collected
four times weekly for each patient, but there were some missing values. The same SEMs for HRQOL were optimized
using both the LD and PD matrices. Although the path d iagrams of the SEMs were not identical in the “competency of
pharmacists,” the two models suggested that a higher competency of a pharmacist lowered the “severity” of condition
and increased the “comfort” of patients, resulting in an increase in the subjected QOL. Conclusions: In collecting data
for clinical research , missing values are unavoidable. When the structure of the model was robust enough, the missing
data had a minor effect on our SEM of QOL. In QOL research, the LD matrix as well as the PD matrix would be effec-
tive, provided the model is sufficiently robust.
Keywords: QO L, Cancer Patients, Structural Equation Model, Pharmacists, Missing Data
1. Introduction
Pharmaceutical care is defined as the responsible provi-
sion of drug therapy for achieving specific outcomes that
improve a patient’s quality of life (QOL) [1]. Typically,
this improved QOL would be achieved in collaboration
with other healthcare professionals. Intervention of
pharmacists in patient care has been reported to improve
patients’ QOL in various diseases [2,3]. Gilbar reported
that pharmacists play an important role in executing ap-
propriate patient care in palliative care settings [4]. Can-
cer patients tend to experience increasing pain with pro-
gressing stages of the cancer. Opioid preparations have
been used to relieve the pain of cancer patients, accord-
ing to the three-step analgesic ladder established by the
WHO [5]. Relief from pain together with the manage-
ment of adverse events with analgesics is essential in
palliative care for cancer patients. By minimizing suffer-
ing with drug therapy, health-related QOL (HRQOL) of
patients can be improved.
HRQOL of patients is a concept that consists of vari-
ous elements, including emotional well-being (EWB),
functional well-being (FWB), social well-being (SWB)
and physical well-being (PWB), as suggested by Schip-

A Structural Equation Model (SEM) for Pharmacist Competencies in Improving Quality of Life of Cancer Patients: Effect
of Missing Values on the SEM 227
per [6]. Religious spirituality should also be considered
as an important element for terminally ill patients [7].
Accordingly, to enhance patient care, it is important to
take into accoun t the improvements in patients’ HRQOL
and evaluations of subjected QOL by patients. There are
some tools to evaluate patients’ QOL or HRQOL, in-
cluding SF-36, FLIC, and FACT [8-11]. A support team
assessment schedule (STAS) for evaluating the relevance
between patients’ objective outcome and support team
assessment in a palliative care setting is also reported.
[12,13] Even with these tools, it is difficult to model the
causal relationship between patients’ HRQOL and the
intervention of pharmacists in patients’ care.
A SEM is known to model the dir ect and indirect rela-
tionships among the latent variables and is used to quan-
tify explained and unexplained variance [14,15]. Because
SEM can deal with the abstraction of psychological ef-
fects as latent variables, it has been applied to measure
the HRQOL of patients in nursing care [16-18].
For various reasons related to patient care, investiga-
tors are not always successful in obtaining all the in-
tended data in a clinical study. Although “missing data”
can cause difficulties for statistical analysis, it is often
unavoidable in a clinical setting. Shimozuma reported
that issues based on missing data tend to increase when
researching QOL i n pr og ressive cancer patients [19 ] .
In our previous report, we established a SEM of sub-
jected QOL in cancer patients, wherein we accounted for
the competency of pharmacists using a matrix derived
with list-wise deletion (LD matrix) [20]. However, in
that report, only completed forms containing all the va-
lues collected from patients and pharmacists were used
in the analysis, and all incomplete forms containing mis-
sing values were excluded. In QOL research in cancer
patients, missing values were unavoidable in some cases,
depending on the condition of the patient. In the present
report, we established SEMs using the LD matrix and a
matrix derived with pair-wise deletion (PD matrix), a
method designed to handle missing data. We investigated
the effect of missing data on the SEM of HRQOL of
cancer patients and competency of pharmacists to im-
prove patients’ QOL.
2. Methods
2.1. Participants
Patients: Eighteen cancer patients hospitalized in Nippon
Medical University Hospital (Sendagi, Tokyo Japan)
were included in this study. All patients received opioid
analgesics for pain control and appropriate care with a
pain control team organized by physicians, pharmacists,
and nurses in the hospital. Patients who started chemo-
Table 1. Questionnaire for patients.
No.Questions
1 Did you sleep well?
2 Do you have uneasiness about your pain and/or nausea?
3 Have you felt uneasy?
4 Have you felt depressed?
5 Have you felt unable to concentrate?
6 Did you experience nausea?
7 Did you vomit?
8 Did you have constipation?
9 Did you have diarrhea?
10Rate of your pain.
11Were you able to move freely without pain?
12Did you enjoy a book or radio or television program?
13 Were you able to move fr ee ly t o a rest r oom without assis-
tance?
14Were you able to tell a family member about your concerns?
15 Do you need more explanation about the effects and side ef-
fects of the analgesics?
16Were you able to tel l t he pharmacist about your pain?
17Were you able to tell the nurse abou t your pain?
18Please rate your overall quality of li f e .
Q1 - Q5, EWB; Q6 - Q10, PWB; Q11 - Q13, FWB; Q14, SWB. Q15 - Q18
was to explore the relationship among patients and other health profession-
als. Answers were scores ranging in 1 to 5 except for Q10. Answers of Q10
were rated on a score ranging from 0 to 10. (Adapted from Yamamura, et al.
(20))
therapy during this research or who did not complete the
answer form due to severe illness were excluded. After
obtaining their consent for participation, fifteen patients
were enrolled in this study. A questionnaire designed to
assess the HRQOL of patients consisted of four impor-
tant domains: EWB, FWB, SWB, and PWB. The number
of questions in the questionnaire was limited to eighteen
in order to avoid unnecessary burden on the patients, as
suggested by a local research committee.
Pharmacists: Eight pharmacists providing pharmaceu-
tical care in a pain control team were included in this
study. Many of them had experience in pain management
as members of the pain control team in the hospital.
Pharmacists scored patients’ status simply, and not in a
structured manner, by answering seven questions based
on bedside interviews with the patients.
The study design and questionnaires were reviewed by
a local research committee. The background of patients
and questionnaires to patients and pharmacists are the
same as described in our previous paper [20]. Question-
naires to patients and pharmacists are listed in Tables 1
and 2. Patients and pharmacists were asked four times
weekly to answer the questionnaire.
2.2. Covariance Matrix for SEM Analysis
Although it was intended that sixty answers would be
collected in the research, some answer forms from the
patients or pharmacists were not completed, resulting in
missing values. The number of completed paired (patient

A Structural Equation Model (SEM) for Pharmacist Competencies in Improving Quality of Life of Cancer Patients: Effect
of Missing Values on the SEM
228
Table 2. Questionnaire for pharmacists.
No. Questions
1 Do you think that the patient understands the medication?
2 Do you think that the patient could communicate about his
or her pain with the physician?
3 Do you think that the patient could communicate about his
or her pain with the nurse?
4 Do you think that you can g rasp the patient’s pain?
5 How would you rate the overall QOL of the patient?
6 How would you rate the pain scale of the patient?
7 How much experience do yo u ha ve in p ai n co nt rol?
Answers were noted as scores ranging from 1 to 5, except for Q6. Answers
to Q6 were rated on a score ranging from 0 to 10. (Adapted from Yamamura,
et al. (20))
and pharmacist) answers was forty and the remaining
twenty answers were removed to build the covariance
coefficient matrix. This handling of missing data is
known as list-wise deletion (a covariate matrix derived
with list-wise deletion is called an LD matrix) [15]. An
entire record is excluded from an analysis if a single
value is missing. The other method for handing missing
data is known as a pair-wise deletion. All answers are
included and each covariance between variables is com-
puted solely on the basis of available pairs of observa-
tions (a covariate matrix derived with pair-wise deletion
is called a PD matrix). SEM using the PD matrix is con-
sidered suitable for confirmatory analysis and unsuitable
for exploratory analysis.
2.3. Structural Equation Modeling (SEM)
SEM is a comprehensive statistical approach to test hy-
potheses about the relation among latent and/or observed
variables. Possible models including latent and observed
variables were built with AMOS 18J (SPSS Japan, To-
kyo, Japan). We developed a possible model using the
following criteria: 1) The model could be reasonably
explained, and 2) The fitting between the model and the
data could be evaluated statistically by certain goodness-
of-fit (GOF) parameters: goodness-of-fit index (GFI) or
adjusted goodness o f fit index (AGFI) of 0.90 or gr eater,
comparative goodness-of -fit index (CFI) of 0.90 or grea-
ter, and root-mean square error of the approximation
(RMSEA) less than 0.05 [15]. Akaike’s information cri-
terion (AIC), a measure of GOF criteria adjusting for the
number of estimated parameters, was also used to evalu-
ate GOF. Owing to the use of different sample sizes for
computing covariance terms in the model with the PD
matrix, AIC would not be a good GOF criteria, but it was
indicated for reference. Robustness of the model was
investigated by a leave-one-out cross validation (LOOV).
In the LOOV procedure, the model was established using
covariance matrices derived from the data sets after re-
moval of 1 observation, and this procedure was repeated
Figure 1. SEM for HRQOL of cancer patients optimized
with the PD matrix EWB, emotional well-being; FWB,
functional well-being and PWB, phy sic al well-being.
for the number of data.
3. Results and Discussion
3.1. SEMs for HRQOL
Table 3 shows the covariance coefficients derived with
PD and LD. The effect of missing data was minimal,
depending on the handling of the missing data. Figure 1
shows a SEM for HRQOL established with a PD matrix
with some stati stical GOF parameters. The model showed
the same path diagram as the model established with LD
matrix described in our previou s report[20], and fulfilled
nearly all GOF criteria: GFI = 0.958, AGFI = 0.892, CFI
= 1.000, RMSEA = 0.000, and AIC = 53.633, indicating
that that the mod el with the PD matrix can be considered
a reasonable statistical model. The SEM for HRQOL of
cancer patients was optimized to have three elements
(PWB, EWB, and FWB) in four main elements of QOL
reported in the literatu re [6,20], regardless of the LD and
PD matrices. Table 4 summarizes the standardized esti-
mates of regression weights among variables optimized
with the LD and PD matrices. In the model with the PD
matrix, mean and standard deviation (SD) evaluated by
LOOV are also shown in Table 4 to reveal the robust-
ness of the model. Some of the standardized regression
weights between variables established with LD and PD
matrices were close to each other, and others were
slightly different, such as the weights between HRQOL
o PWB, EWB and FWB. This can be considered as fol- t
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A Structural Equation Model (SEM) for Pharmacist Competencies in Improving Quality of Life of Cancer Patients: Effect
of Missing Values on the SEM
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Table 3. Covariance matrix for HRQOL derived with pairwise deletion and listwise deletion.
Q1 Q2 Q5 Q6 Q7 Q10 Q12 Q13 Q18
Q1 (Sleep) 1.000
Q2
(Uneasiness) 0.203 (0.165) 1.000
Q5 (Concentration) 0.318
(0.294) 0.237 (0.234) 1.000
Q6 (Nausea) 0.173
(0.158) 0.355 (0.340) 0.298 (0.312) 1.000
Q7 (Vomiting) 0.052
(0.006) 0.273 (0.290) 0.205 (0.160) 0.706 (0.665) 1.000
Q10 (Pain) 0.034
(0.042) 0.004 (–0.019) 0.156 (0.158) 0.184 (0.188) 0.149 (0.178) 1.000
Q12 (Enjoys
books/radio/TV) –0.148 (–0.175) –0.450 (–0.476) –0.446 (–0.451) –0.292 (–0.343) –0.288 (–0.359) –0.079 (–0.087) 1.000
Q13 (Moveme nt) 0.009
(0.007) 0.087 (0.012) –0.279 (–0.259) –0.143 (–0.251) –0.255 (–0.273) 0.075 (–0.60) 0.226 (0.213) 1.000
Q18 (QOL) –0.051
(–0.032) –0.167 (–0.171) –0.191 (–0.228) 0.000 (–0.010) –0.066 (–0.068) –0.095 (–0.054) 0.268 (0.217 –0.046 (–0.081) 1.000
SD *1 0.976
(0.975) 1.380 (1.377) 1.277 (1.310) 1.580 (1.509) 1.203 (1.148) 1.874 (1.757) 1.337 (1.377) 1.900 (1.945) 0.791 (0.816)
*1 SD is the standard deviation of answers to each question. Please refer to questions in Table 1.
Table 4. Standardized estimates of SEM for HRQOL with PD and LD matrices.
PD LD
Cross-validation
Standardized regression weights Estimate Mean SD
Estimate
PWB <---HRQOL –0.916 –0.896 0.061 –0.808
EWB <---HRQOL –0.684 –0.685 0.040 –0.791
FWB <---HRQOL 0.459 0.462 0.059 0.686
Q6 (Nausea) <---PWB 0.773 0.782 0.066 0.838
Q7 (Vomiting) <---PWB 0.566 0.568 0.059 0.630
Q10 (Pain) <---PWB 0.239 0.237 0.018 0.231
Q1 (Sleep) <---EWB 0.436 0.441 0.034 0.361
Q2 (Uneasiness) <---EWB 0.519 0.516 0.049 0.523
Q5 (Concentration) <---EWB 0.355 0.362 0.048 0.209
Q5 (Concentration) <---FWB –0.532 –0.530 0.034 –0.520
Q12 (Enjoys book/radio/TV) <---FWB 0.703 0.703 0.030 0.712
Q13 (Movement) <---FWB 0.420 0.419 0.022 0.385
PD: Pair-wise deletion, LD: List-wise deletion. Est imates wer e calcul ated fro m the o ptimized SEM. The val ues of cr oss-v alidati on were obtained by the leave-
one-out cross-validation.
lows: the data from the patients who did not answer the
questions due to th e severity of illness were not included
in the LD matrix. The relationship between HRQOL to
PWB consisting of the scores of nausea, vomiting, and
pain, would be strong in the PD matrix. Therefore, the
regression weight from HRQOL to PWB in the LD ma-
trix would become larger than that in the PD matrix.
According to be strength of the relation between
HRQOL to PWB, regression weights between HRQOL
to EWB and QOL to FWB would be relatively smaller.
The SD of estimates evaluated by LOOV was reasonably
narrow, suggesting that the optimized SEM was robust
and not affected strong ly by ou tlier(s).
Figure 2 shows the model indicating the relationship
between the HRQOL modeled with PD matrix and sub-
jected QOL (Q18 QOL in Figure 2) answered by the
patients. The GOF criteria of the model were calculated
to be GFI = 0.942, AGFI = 0.876, CFI = 1.000, RMSEA
= 0.000, and AIC = 63.524. The correlation coefficient
between HRQOL and subjected QOL was poor, calcu-
lated to be 0.22. The correlation coefficient in the model
with LD matrix was also poor, calcu lated to b e 0.23 [20 ].
These results suggest that a meaningful part of subjected
QOL in patients is influenced by other elements not in-
cluded in the model. Table 5 summarizes the standard-
ized regression weights between variables. Similar to
Table 4, the regression weight from HRQOL to PWB in
he model with PD matrix was larger than that with LD t

A Structural Equation Model (SEM) for Pharmacist Competencies in Improving Quality of Life of Cancer Patients: Effect
of Missing Values on the SEM
230
Table 5. Standardized estimates of SEM for Competencies optimized with PD and LD matrices.
PD LD
Cross-validation Estimate
Standardized regression weights Estimate Mean SD
PWB <--- HRQOL –0.799 –0.794 0.062 –0.727
EWB <--- HRQOL –0.772 –0.767 0.049 –0.845
FWB <--- HRQOL 0.589 0.591 0.068 0.799
Q6 (Nausea) <--- PWB 0.686 0.694 0.074 0.761
Q7 (Vomiting) <--- PWB 0.532 0.539 0.050 0.600
Q10 (Pain) <--- PWB 0.270 0.269 0.039 0.255
Q1 (Sleep) <--- EWB 0.459 0.458 0.029 0.380
Q2 (Uneasiness) <--- EWB 0.475 0.478 0.041 0.479
Q5 (Concentration) <--- EWB 0.389 0.388 0.039 0.274
Q5 (Concentration) <--- FWB –0.483 –0.481 0.041 –0.471
Q12 (Enjoys book/radio/TV) <--- FWB 0.708 0.711 0.027 0.714
Q13 (Movement) <--- FWB 0.406 0.405 0.025 0.360
PD: Pair-wise deletion, LD: List-wise deletion. Est imates wer e calcul ated fro m the o ptimized SEM. The val ues of cr oss-v alidati on were obtained by the leave-
one-out cross-validation.
Figure 2. SEM of correlation between HRQOL and sub-
jected QOL in patients optimized with the PD matrix EWB,
emotional well-being; FWB, functional well-being and PWB,
physical well-being.
matrix, resulting in similar effects described before. The
SD of the estimates evaluated by LOOV was reasonably
narrow suggesting that the optimized SEM was not af-
fected strongly by outlier(s). These results indicate that
the HRQOL model with a path diagram described in
Figures 1 and 2 would be robust enough against missing
values and outliers. The SEM analysis with both LD and
PD matrices would have advantages with regard to the
effect of missing data.
3.2. SEM of Pharmacist Competency in
Improving QOL of Patients
We previously reported the SEM for the competency of
pharmacists to improve subjected QOL of patients [20].
The model consisted of four latent variables, expressing
“ability of pharmacists,” “skill of assessment” of pain
level in patients, “severity” of side effect and “comfort”
level, respectively. The model suggested that the compe-
tency of pharmacists can improve subjected QOL in
cancer patients. Table 6 shows the covariance coeffi-
cients used for SEM analysis of competency of pharma-
cists to improve patients’ subjected QOL calculated with
the PD and LD. Some coefficients were found to be af-
fected by missing data, in contrast to the model of
HRQOL. To establish the SEM, we introduced another
parameter, i.e., the absolute value of difference of pain
scores answered by patients and evaluated by pharma-
cists. This variable would indicate the pharmacists’ com-
petency to understand the patients’ condition. A smaller
value for this variable would indicate the pharmacist’s
ability to evaluate the patients’ pain more accurately. The
optimized model established with the PD matrix is
shown in Figure 3, and GOF criteria of the model were
almost satisfactory: GFI = 0.932, AGFI = 0.856, CFI =
1.000, RMSEA = 0.000 and AIC = 63.124.
The final model consists of three latent variables, ex-
pressing “competency of pharmacists,” “severity” of side
effect, and “comfort” level. From the magnitude of esti-
mates of standardized weight between variables, the
model can be explained as follows: when pharmacists are
highly competency to assess patients’ pain level based on
experiences from previous association with a pain con-
rol team, they can work to restrain unpleasant symptoms t
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A Structural Equation Model (SEM) for Pharmacist Competencies in Improving Quality of Life of Cancer Patients: Effect
of Missing Values on the SEM 231
Table 6. Covariance matrix for competency of pharmacists derived by Pair-wise deletion and List-wise deletion.
Pt-Q2 Pt-Q5 Pt-Q8 Pt-Q10 Pt-Q18 Ph-Q4 Ph-Q7 Difference
Pt-Q2 (Uneasiness) 1.000
Pt-Q5 (Concentration) 0.237
(0.234) 1.000
Pt-Q8 (Constipation) 0.299
(0.222) 0.137 (0.203) 1.000
Pt-Q10 (Pain) 0.184
(0.205) 0.099 (0.141) 0.457 (0.568) 1.000
Pt-Q18 (QOL) –0.167
(–0.171) –0.191 (–0.228) –0.256 (–0.354) –0.173 (–0.137) 1.000
Ph-Q4 (Grasp pain) 0.052
(0.086) 0.047 (0.221) –0.024 (–0.087) 0.020 (–0.060) –0.158 (–0.090) 1.000
Ph-Q7 (Experience) 0.027
(0.019) –0.001 (–0.028) –0.101 (–0.158) –0.049 (–0.006) 0.215 (0.233) –0.212 (–0.291) 1.000
Difference
Pain score *1 –0.164
(–0.116) –0.085 (–0.104) 0.157 0.183 0.305 (0.294) 0.114 (0.202) –0.011 (–0.107) 0.220 (0.310) 1.000
SD *2 1.380
(1.377) 1.277 1.310 1.645 1.641 1.895 1.836 0.791 (0.816) 0.592 0.526 0.298 (0.607) 1.163 (1.091)
Pt and Ph indicate the questions for patients and pharmacist, respectively. Upper and lower values were obtained with pairwise deletion and listwise deletion,
respectively. *1 Difference of pain score between by Pt and Ph. *2 SD is the s tand ard devi ation o f the ans wer to e ach qu estion . Please r efer t o ques tions in Ta-
bles 1 and 2.
Figure 3. SEM of competency of pharmacists to improve
subjected QOL of cancer patients optimized with the PD
matrix.
such as pain and constipation. If “severity” of side ef-
fects can be reduced by competency of pharmacists,
“comfort” level of patients would be increased with de-
creasing uneasiness and increasing of subjected QOL.
Because the covariate coefficients with the PD matrix
were a little different from those with the LD matrix, the
optimized path diagrams were slightly different from
each other. However, the most important factor of com-
petency of pharmacists in improving subjected QOL of
patients was to assess the pain level of patients in both
models. The models suggest that pharmacists with prior
experience in a pain control team and are competent to
assess patients’ pain level can restrain the unpleasant
symptoms of patients. As a result, subjected QOL in pa-
tients will improve.
4. Conclusions
The models for HRQOL of cancer patients and for
pharmacists’ competency to improve the subjected QOL
could be established using the SEM. If there was little
effect of missing values and outliers on the SEM, similar
SEMs were optimized with both the LD and the PD ma-
trices. When using the PD matrix, AIC was not a good
criterion because the sample sizes for computing covari-
ance terms were different with each other. Therefore,
SEM with the PD matrix should be used for confirmatory
analysis after the model has been fixed using the LD
matrix. In this study, we found that if the model is suffi-
ciently robust and if there is little effect of missing val-
ues and outliers, the PD matrix could be also effective to
establish the models for HRQOL and competency of
pharmacists by SEM. The two models established with
LD and PD matrices str ongly suggest that competency of
pharmacists can improve subjected QOL of patients.
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