Probit structural equation regression model: general depressive
symptoms predicted post-myocardial infarction mortality
after controlling for somatic symptoms of depression
Brett D. Thombsa,*, Roy c. Ziegelsteinb, Kapil Parakhb, Donna E. Stewartc,d,
Susan E. Abbeyc,d, Sherry L. Gracec,d,e
Objective: Reported links between depression and post-acute myocardial infarction (AMI) mortality may be due to confounding be-
tween somatic symptoms ofdepression and symptoms related to the AMI. The objective ofthis study was to assess the relationship between
depressive symptoms and 12-month post-AMI mortality after removing potential bias from somatic symptoms of depression.
Study Design and Setting: Four hundred seventy-seven hospitalized AMI patients from 12 cardiac care units. The relationship of
a General Depression factor with mortality was assessed using a probit structural equation regression model, controlling for an uncorrelated
somatic symptom factor, age, Killip class, previous AMI, and other potential confounders.
Results: Mortality was significantly predicted by the General Depression factor (P =0.009), controlling for age (P = 0.128), Killip
class (P = 0.210), history of AMI (P = 0.001), and other predictors in a structural equation model that removed variance related to somatic
factors, but unrelated to the General Depression factor.
Conclusion: This study demonstrated that the use of structural equation modeling presents a viable mechanism to test links between
symptoms of depression and health outcomes among patients with AMI after explicitly removing variance due to somatic symptoms that is
unrelated to the General Depression factor.
Keywords: Myocardial infarction; Mortality; Depression; Assessment; Beck Depression Inventory; Confirmatory factor analysis
Numerous studies have found that symptoms of depres-
sion are related to increasedriskofmortality following acute
myocardial infarction (AMI) after controlling for demo-
graphic and disease severity variables [1-4], although not
all studies have reported a significant association [5,6].
Several recent systematic reviews or meta-analyses of the
independent association between post-AMI depression and
mortality have concluded that unambiguous conclusions
could not be reached because ofincomplete control for con-
founding [7-9]. The authors of one of the reviews  and
others [3,10-12] have argued that existing studies linking
depression to cardiac and all-cause mortality post-AMI have
not adequately controlled for confounding in measurement
of depressive symptoms related to overlap between somatic
toms characteristically associated with depression, such as
fatigue, anhedonia, changesin sleeppatterns,changes inappe-
tite, or poorconcentration, for instance, could occur as anor-
mal reaction to the AMI, from side effects ofits treatment, or
from the hospitalization itself [13,14]. The BD! is the most
commonly used method to screen for symptoms of depres-
sion among post-AMI patients , and specific concerns
have been raised about its validity in medical patients
because six of2l items assess somatic symptoms [16-20].
Itis importantto be able to accurately distinguish somatic
symptoms related to depression from nondepressive somatic
symptoms. Clinically, bias in the assessment of depressive
symptoms could result in the overidentification of patients
with the most severe AMIs as depressed. In outcomes
What is New?
• Structural equation modeling (SEM) methods can
be used to model a General Depression factor free
of variance from somatic symptoms that are unre-
lated to depression, but including variance from
somatic symptoms that are related to depression.
• This methodology is useful to assess the independent
contribution of depressive symptoms to important
outcomes free ofbias from somaticsymptom overlap.
• In a sampleof477 post-acute myocardial infarction
(AMI) patients, the General Depression factor pre-
dicted mortality 12 months post-AMI, controlling
for somatic symptoms unrelatedtodepressionperse.
• Future studies should incorporate SEM methods to
assess the independent association of depressive
symptoms with important outcomes and should in-
clude greater coverage ofcardiac risk variables than
were available in this study.
research, bias could lead to artifactuallinks between symp-
toms of depression and post-AMI morbidity and mortality.
Structural equation modeling (SEM) techniques present an
alternative to traditional regression models that allows for
the possibility of explicitly separating variance related to
depression per se and variance related to extraneous somatic
factors through the use of latent variables. Ward  recently
published a confirmatory factor analysis (CFA) model for the
Beck Depression Inventory (BDI)-ll that explicitly separated
variance from a General Depression factor from variance
from unrelated somatic symptoms. Ward demonstrated in five
different samples that a BDI-ll model with orthogonal
General Depression, Somatic, and Cognitive factors (G-
S-C) fit as well or better than previously published corre-
lated-factor models. In Ward's model, all BDI-ll item scores
are indicators of the General Depression factor, and some
items also load on Somatic or Cognitive factors that are or-
thogonal to the General Depression factor and each other.
Although Ward's model is a promising alternative, most
post-AMI research continues to use the original BDI rather
than the revised BDI-ll. Many items on the BDI and BDI-II
are equivalent, but six of 21 items are not. Thus, the objec-
tives of this study were (l) to develop a G-S-C model for
the BDI in post-AMI patients and (2) to use the model to
assess the relationship between the General Depression
latent factor and mortality 12 months post-AMI after re-
moving potential bias from somatic symptoms on the BDI.
2.1. Patients and procedures
Data were collected as part of a longitudinal study of
depression after acute coronary syndromes (ACS). The
methods of the study have been described previously
. Adult patients (18 years and older) who were diag-
nosed with a confirmed AMI or unstable angina (UA) were
recruited in the coronary care unit (CCU) by a research
nurse on the 2nd to 5th day of the acute hospitalization. Pa-
tients were recruited from 12 CCUs in both large urban
teaching hospitals and community hospitals in small- and
medium-sized cities across Southcentral Ontario, Canada.
Patients were excluded if they were medically unstable or
unable to read or speak English. Patients who met study cri-
teria and agreed to participate signed a consent form and
were provided with a self-report questionnaire, which in-
cluded the BDI. Questionnaires were also administered
via mail at 6 months and 12 months post-AMI. All patients
received standard aftercare for their ACS. The original
study protocol was approved by the Research Ethics Boards
of the University of Toronto and University Health Net-
work. In-hospital data from AMI patients, but not UA
patients, were included in the present analyses.
2.2.1. Symptoms ofdepression
The BDI  is a 2l-item measure of depressive symp-
toms. Each item consists of four statements, scored 0-3,
indicating increasing symptom severity, and total scores
range from 0 to 63. Respondents are instructed to describe
the way they have been feeling during the past week. The
authors of the BDI recommend cutoff scores of ~ 10 for
at least mild symptoms of depression , and this cutoff
is typically used in studies of patients with AMI .
2.2.2. Medical variables
Killip class, measured on a four-point scale, was used to
indicate the severity of the AMI by assessing the presence
of heart failure at the time of the AMI. Killip class and his-
tory ofprevious AMI were determined from the medical re-
cord. Other health status variables, such as comorbidities
and smoking status were determined from the patient health
2.2.3. Mortality status
The primary outcome variable was all-cause mortality
within 12 months of discharge from the hospital. For
patients who did not return l2-month follow-up question-
naires, vital status was determined by contacting by tele-
phone, in sequence as necessary, patients, patients' family
members or contacts listed in the initial data collection
form, patients' general practitioners, and patients' specialist
2.3. Data analyses
Patient demographic and medical data were compared
between patients who were alive 12 months post-AMI
and patients who died during this period. Differences
between the groups on categorical variables were assessed
using the X2statistic and on continuous variables with
two-tailed t-tests. Comparisons were conducted with SPSS
version 15.0 (Chicago, IL, USA) with a significance level
of P < 0.05.
2.3.1. CFA models
Two CFA models were fit to the BDI data following the
procedure used by Ward with the BDI-II . First, the
data were fit to the most commonly used BDI factor model,
the three-factor Negative Attitudes-Performance Impair-
ment-Somatic Disturbance model (NA-PI-SD) . In
the NA-PI-SD model, the items sadness, pessimism, past
failure, guilty feelings, punishment feelings, self-dislike,
self-blame, suicide ideation, and physical appearance load
on the NA factor; the items loss ofpleasure, irritability, loss
of interest, indecisiveness, ability to work, fatigue, and
health concerns load on the PI factor; and the items sleep
problems, appetite, weight loss, and sexual disinterest load
onto the SD factor. For the NA-PI-SD model, modifica-
tion indices were used to identify pairs of items within fac-
tors for which model fit would improve if error estimates
were freed to correlate, and for which there appeared to
be theoretically justifiable shared method effects .
Based on modification indices, correlated errors were
permitted between two items: ability to work and fatigue.
After fitting the NA-PI-SD model, an orthogonal
G-S-C factor model similar to Ward's G-S-C model
for the BDI-II was developed for the BDI. Consistent with
Ward's procedure, all 21 items were specified to load on the
General factor. In addition, six items were specified to load
on the Somatic factor (ability to work, sleep problems, fa-
tigue, appetite, weight loss, health concerns), eight items
on the Cognitive factor (pessimism, pastfailure, guiltyfeel-
ings, punishment feelings, self-dislike, self-blame, suicidal
thoughts, physical appearance), two items on a minor
Self-Criticalness factor (self-dislike, self-blame), and two
items on a minor Anhedonia factor (loss ofpleasure, loss
ofinterest). Thepairsofitems thatloadedon each ofthelatter
two factors wereconstrainedto equality for model identifica-
tion purposes. It is important to note that all items thatloaded
on the Somatic, Cognitive, Anhedonia, or Self-Criticalness
factors also loaded on the General Depression factor. This
is because the G-S-C model estimates the proportion of
variancefrom a single item, such as fatigue, for example, that
is related to depression and the proportion ofvariance in that
item due to somatic factors unrelated to depression. For
model identification purposes, each of the latent factors
was specified to have a mean of 0 and a variance of I.
In addition to the main G-S-C model, a simplified
G-S-C model that would allow for easier implementation
in outcomes research was tested. This model did not in-
clude the minor Self-Criticalness and Anhedonia factors.
For the G-S-C and simplified G-S-C models, item com-
munalities (h2s) that represented the percent of variance in
each item predicted by the factors were calculated from
standardized factor loadings.
All CFA models were conducted with Mplus (version
3.11) , explicitly modeling the BDI items as ordinal
data. A robust least square estimator was used to accommo-
date the ordinal BDI item data and the binary mortality out-
come variable. Mplus provides adjusted mean and mean
and variance-adjusted x2-values and goodness-of-fit statis-
tics. A chi-square goodness-of-fit test and four fit indices
were used to assess model fit, including the Tucker-Lewis
Index (TU) , the comparative fit index (CH) , the
root mean square error of approximation (RMSEA) ,
and the standardized root mean square residual (SRMR)
. Because the chi-square test is highly sensitive to sam-
ple size and can lead to the rejection of well-fitting models,
practical fit indices were emphasized . Guidelines pro-
posed by Hu and Bentler  suggest that models with TU
and CH close to 0.95 or higher, RMSEA close to 0.06 or
lower, and SRMR close to 0.08 or lower are representative
of good-fitting models. A CH of 0.90 or above  and an
RMSEA of 0.08 or less , however, are also considered
to represent reasonably acceptable model fit.
2.3.2. Mortality prediction
To assess the independent relationship between the Gen-
eral Depression factor and all-cause mortality 12 months
post-AMI, regression models were carried out using Mplus.
The G-S-C model was extended, and mortality status was
regressed on the General Depression factor, controlling for
known predictors of mortality (age, Killip class, and history
of AMI). Regressing mortality status on the General
Depression factor was done to estimate the association
between depressive symptoms and mortality after removing
variance from somatic and cognitive factors unrelated to
depression. Only three covariates were used to avoid over-
fitting the prediction model because there were only 25
deaths in the first 12 months post-AMI . Post hoc test-
ing of additional variables was done by adding each addi-
tional predictor variable (sex, marital status, history of
angina, diabetes, smoking) one at a time to the initially
specified model to determine if the inclusion of these vari-
ables affected the relationship between mortality and the
General Depression factor.
3.1. Sample characteristics
A total of477 AMI patients consented to participate, and
417 completed the BDI during their acute hospitalization
with no missing items. As shown in Table I, of the 417 pa-
tients included in the study, vital status was available for
416, and 25 (6.0%) died by 12 months post-AMI. Patients
who died were significantly older (P = 0.016), more likely
to have had a previous AMI (P = 0.002), and more likely to
Patient demographic and medical characteristics (N = 417)
Number* Percent Mean SD
Age in yr (mean ± SD)
Family income> $50,000
Education high school or less
Killip class> I
History of angina
Systolic blood pressure> 130 mm Hg 238/405
Smoked in last 2 yr
Symptoms of depression
BDI score (mean ± SD)
Abbreviation: MI, myocardial infarction.
* For some variables, the total N is < 417 due to missing data.
have a history of angina (p.s; 0.001). A higher percentage
of patients who died within 12 months of the AMI had
Killip class > I, although this was not statistically signifi-
cant (P = 0.158)..Mean total BDI scores were significantly
higher for patients who died (P = 0.031), and there was a
higher percentage, although nonsignificantly so (P = 0.077),
ofpatients with BD! ;;;. 10 among patients who died (44.0%
Model fit statistics for each of the two models tested are
shown in Table 2. The three-factor NA-PI-SD fit reason-
ably well based on fit indices. All factor loadings for the
model were statistically significant with standardized load-
ings of 0.51 or higher for all items except item 19 (weight
loss), for which the factor loading was 0.27. The fit of the
G-S-C model and the simplified G-S-C model was sim-
ilar to that of the NA-PI-SD based on the fit indices, sug-
gesting that the G-S-C model is a reasonable alternative
to standard models. The total communalities attributable
to the Anhedonia and Self-Criticalness factors were negli-
gible «0.01% each) in the initial G-S-C model, and fac-
tor loadings were not statistically significant. There was no
Summary of results from CFA
Abbreviations: CFl, comparative fit index; TU, Tucker-Lewis Index;
RMSEA, root mean square error of approximation; SRMR, standardized
root mean square residual; NA-PI-SD, Negative Attitude-Performance
Difficulty-Somatic Elements; G-S-C, General-Somatic-Cognitive;
CFA, confirmatory factor analyses.
appreciable difference between the G-S-C model and the
simplified G-S-C model in overall fit. Thus, results are
presented here only for the simplified version. All factor
loadings from the simplified G-S-C model were signifi-
cant with the exception of the hypothesized loading of item
14 (physical appearance) on the Cognitive factor, so this
item was removed from that factor. Item-factor specifica-
tions for the simplified G-S-C model are shown in the
measurement model portion of Fig. 1. On the General De-
pression factor, loadings ranged from 0.45 (sexual disinter-
est) to 0.81 (past failure). The most salient factor loading
on the Somatic factor was fatigue (0.61), with other factor
loadings ranging from 0.22 (weight loss) to 0.50 (ability to
work). Loadings on the Cognitive factor ranged from 0.21
(pessimism) to 0.53 (self-dislike). Item communalities were
calculated for each item along with communality estimates
for each factor that represented the proportion of total com-
munality attributable to that factor (Table 3). As in Ward's
results for the BDI-I1, the General factor explained the high-
est proportion of total covariance (communality = 81%)
with the Somatic and Cognitive factors contributing modest
amounts (9% each). Item-factor loadings and other model
data are available upon request from the corresponding
3.3. Mortality prediction
Fig. 1 shows the regression model in which 12-month
mortality status is regressed on the General Depression fac-
tor, age, Killip class, and history of myocardial infarction.
Path coefficients and the R2-value from the model are
provided in Table 4. The General Depression factor
significantly predicted mortality at 12 months post-AMI
(P = 0.009), controlling for age, Killip class, and history
of AMI. History of AMI and history of angina were the
only other variables that were significantly associated with
death at 12 months. The fit indices indicated a reasonably
good fit for the model: TU = 0.94, CFt = 0.91, and
RMSEA = 0.07. The inclusion/exclusion of predictors not
in the initially specified model (history of angina, sex, mar-
ital status, smoking) did not meaningfully alter the relation-
ship between the General Depression factor and mortality.
When the Somatic and Cognitive factors were similarly
included as predictors of mortality post hoc, neither was
significant. The Somatic factor was positively associated
with mortality risk (P = 0.204) whereas the Cognitive
factor was negatively related to mortality risk (P = 0.269).
The main findings ofthis study were that (1) Ward's 
G-S-C model for the BDI-I1 was successfully adapted for
the original BDI and fit as well as or slightly better than
a widely published, correlated three-factor model in a sam-
ple of patients hospitalized with AMI, and (2) the General
Fig. I. Mortality status at 12 months regressed on the General Depression factor, age, Killip class, and history of myocardial infarction. In the G-S-C
model, factors are uncorrelated, and item error variances are not shown.
Depression factor of the G-S-C model was a significant
predictor of 12-month all-cause mortality in multivariate
models even after potential measurement bias from somatic
symptoms unrelated to depression was removed. The Gen-
eral factor ofthe G-S-C model accounted for 81%oftotal
explained variance, which is within the range of 71-82%
reported by Ward across five nonmedical samples. The So-
matic and Cognitive factors each accounted for 9% of total
explained variance, within the ranges of 6-11% (Somatic)
and 8-14% (Cognitive) reported by Ward. The finding that
9% of explained variance in BDI scores was accounted for
by somatic factors unrelated to depression indicates that, as
suggested by several authors [3,7,10-12], measurement of
depressive symptoms with the BDI does pick up some
variance related to somatic experience, but not depression.
The amount of potential bias due to somatic symptoms,
however, was small, and measurement bias did not explain
the relationship between depressive symptoms and mortality.
When variance from the Somatic symptom factor was re-
moved from the measurement model with SEM techniques,
symptoms of depression continued to predict mortality.
The Somatic symptom factor was positively related to
mortality risk, whereas the Cognitive symptom factors were
negatively related. These findings may be related to the
likely meaning of the Somatic and Cognitive factors in
the context ofpost-AMI hospitalization. The Somatic factor
a Comrnunality (h2) for each factor is the proportion of total commu-
nality that is attributable to the factor.
Standardized factor loadings and communalities
from the G-S-C model
was dominated by items related to fatigue and loss of en-
ergy, both of which are commonly experienced during hos-
pitalization for AMI and which mayor may not be related
to depression. Variance from items on the Cognitive factor
may take on special meaning in the context of an AMI
given the predominance of self-blame on the Cognitive
factor. Cognitive theories of depression  associate
self-blame with poor adjustment. On the other hand, studies
of the consequences of illness attributions among patients
with medical illness  suggest that self-blame or attribu-
tion of consequences to one's own behavior may be related
to more positive coping and better subsequent outcomes
. These two theoretical models may be addressing
two distinct constructs, characterological and behavioral
self-blame, however. Whereas characterological or person-
ality-related self-blame would be expected to be maladap-
tive, behavioral self-blame may be a useful coping
strategy after an acute medical event that provides a sense
of controllability of the future and over one's own health
and a motivation to behavior change .
As reviewed by Ward , in addition to essentially
equal fit to the data, the orthogonal G-S-C model for
the BDI has several advantages over correlated-factor
models. Many different correlated-factor models for the
BDI have been reported. Correlated models tend to produce
highly correlated factors that provide only limited discrimi-
nant validity. Because ofthe high factor correlations, item-
factor allocations often vary substantially across samples,
which limits their substantive interpretability [21,39]. In
addition, the NA-PI-SD model for the BD! does not
provide clear theoretical coherence, and several items are
not easily described as either purely somatic or performance
related. The G-S-C model, on the other hand, has been
shown to provide a stable fit that is as good or better than
the correlated-factor models across several different sam-
ples, including the sample ofAMI patients in this study us-
ing an adapted version for the BDI. Interpretation of the
G-S-C is also consistent with the use of a single summary
score to estimate the severity ofdepressive symptoms as de-
scribed by Beck et al. . On the other hand, one potential
advantage of a correlated-factor model is that the degree of
relationship between somatic and nonsomatic elements is
built into the model.
In the context of post-AMI depression, the most impor-
tant advantage of the G-S-C is that it allows for predic-
tion of outcomes, such as mortality, free from bias from
somatic symptoms that are unrelated to depression per se.
Mortality prediction with SEM of the G-S-C has impor-
tant advantages over the approaches used in the two previ-
ous studies that have addressed this issue. Irvine et al. 
used cognitive symptoms alone to predict mortality. That
approach, however, may be overly restrictive and may in
some cases fail to detect valid depression-mortality links
because it removes all somatic items, and somatic symp-
toms are central to the experience of depression for many
patients, regardless of medical illness [41,42]. The G-S-C
approach used in this study, on the other hand, allows var-
iance from the somatic items to load on the General De-
pression factor and, thus, includes them in the latent
predictor variable, excluding only systematic variance from
the somatic items that is unrelated to the General Depres-
sion factor. de Jonge et al.  used exploratory factor
analysis techniques to assess whether measurement bias in-
fluences the relationship between symptoms of depression
as measured by the BDI and cardiac outcomes. They re-
gressed the cardiac outcomes variable on both the cognitive
and the somatic factors of a traditional two-factor corre-
lated model. This method, however, would not be expected
to differentiate well between cognitive and somatic factors
because several items loaded on both factors and the high
correlation between the factors (>0.70) may lead to prob-
lems with multicollinearity in regression models [43,44].
Although many items in the present study loaded on two
factors, the factors were uncorrelated, which allowed for
explicit isolation of variance on somatic items that were
not related to the General Depression factor.
There are limitations in our study that should be ac-
knowledged. The study had a moderate-sized patient popu-
lation and a relatively small number of total mortalities.
Mortality data did not include whether or not death was car-
diac related and were collected via report of patients' fam-
ily members, general practitioners, or specialist physicians,
the accuracy of which has not been demonstrated. Adjust-
ment for confounders only included age, Killip class, and
a history of AMI. Other potentially important confounders,
such as sociodemographic factors, indicators of AMI
Loss of pleasure
Ability to work
Concerns about health
Path coefficients and R2-value for structural equation model regression
of 12-month mortality on the General Depression factor and covariates
VariablePath coefficient P-value
12-month mortality status
General Depression factor
History of MI
Killip class > I
History of angina"
Smoked in last 2 yr"
" Each variable added to core predictors (General Depression factor,
age, history of MI, Killip class) individually.
severity (e.g., left-ventricular ejection fraction), comorbid
conditions, and hospital course were not measured, but
should be included in future studies that use these methods.
In addition, we used a probit structural equation model
rather than a survival model, because time to death was
not available and because this is not an option in SEM ofla-
tent variables with programs such as Mplus. On the other
hand, SEM paradigms allow for much greater sophistication
in modeling sources ofvariance within and across items that
cannot be implemented with traditional survival models.
It is not clear how the findings of this study would apply
to other widely used depression symptom assessment in-
struments, such as the Center for Epidemiological Studies
Depression Scale (CES-D) , the Hamilton Rating
Scales for Depression (HRSD) , or the Patient Health
Questionnaire-9 (PHQ-9) . Although the CES-D,
HRSD, and PHQ-9 have generally similar emphases on
somatic or vegetative symptoms (seven of 20 items
on the CES-D, four of 14 on the HRSD, and four of nine
on the PHQ-9) , a similar exercise would need to be
conducted for each instrument to determine the degree to
which findings from this study would replicate.
In summary, the G-S-C model provides a reasonably
good-fitting explanation ofBDI data from patients hospital-
ized with AMI that is as good as orbetter than model fit with
an alternative three-factor model. The G-S-C model has
important theoretical and practical advantages, including
the ability to model the relationship ofa General Depression
factor with mortality afterexplicitly removing variance from
somatic factors unrelated to the General Depression factor.
When this model was implemented, controlling for impor-
tant demographic and medical variables, the General De-
pression factor significantly predicted 12-month all-cause
mortality in a sample of417 post-AMI patients.
This research was conducted with funds from the Heart
and Stroke Foundation of Ontario and the Samuel
Lunenfeld Foundation of Toronto, Ontario awarded to Dr.
Stewart and Dr. Abbey. Dr. Grace receives funding from
the Canadian Institutes of Health Research, and Dr. Ziegel-
stein is supported by NIH/NINDS R21 NS048593. We also
are grateful to Linda Green for her diligence in study
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