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Prediction of coronary events following myocardial infarction using a discriminant function analysis
J ChronDii Vol. 39,No. 7,pp. 543-552,1986 Printedin GreatBritain
0021-9681/86 $3.00+0.00 Pergamon JournalsLtd
PREDICTION OF CORONARY EVENTS FOLLOWING MYOCARDIAL INFARCTION USING A DISCRIMINANT FUNCTION ANALYSIS LIANG Hsu,
MANOHARA
P. J. SENARATNE, SANGADASA DE-SILVA,
RICHARD E. ROSSALL
and
TISSA KAPPAGODA*
Division of Cardiology, Department of Medicine, 8-104 Clinical Sciences Building, University of
Alberta, Edmonton, Alberta, Canada T6G 2E3 (Received in revised form 6 November 1985)
Abstract-This study was undertaken to derive an index for predicting coronary events in the first year after a myocardial infarction in “low-risk” patients enrolling in a Cardiac Rehabilitation Program. Data from 145 consecutive patients were analysed. The events were classified as follows: angina requiring further therapy, re-infarction and coronary death. Seventy patients had events: Angina-52, Re-infarction-S, Coronary Death-IO. A discriminant function analysis was performed to predict such events using data available at the time of discharge from hospital. The following were significant predictors: (1) previous infarction/angina, (2) radiological evidence of cardiomegaly or lung congestion in the Coronary Care Unit, (3) Non-Q wave infarction and (4, 5 and 6) angina, atria1 arrhythmias and a decrease in R wave amplitude in V, during a pre-discharge exercise test. The jack-knife method classified correctly 71.2% of those with events and 72.6% of those without events. In patients with discriminant scores > +0.2, 82% developed events.
INTRODUCTION
THE MAJORITY of patients who recover from an episode of myocardial infarction embark upon a life of chronic ill health. It is evident that Cardiac Rehabilitation Programs should not be viewed as exercise training programs per se. They have the added responsibility of providing long term clinical surveillance for such patients [l]. Since the provision of such “after care” is a relatively expensive process, in terms of both personnel and equipment, it would be useful to identify individuals who are likely to encounter clinically significant events amongst those enrolling in such programs. Although there are many reports of prognostic indices developed for post-infarction patients [e.g. 2-4 (review)] they cannot be adapted readily for the needs of clients who traditionally enroll in Cardiac Rehabilitation Programs, for two main reasons. The first relates to the population under scrutiny. The majority of such programs emphasise the value of exercise training as a therapeutic modality [5] and the ability to undertake exercise is often a pre-requisite for entry into them [6]. Thus, patients who exhibit evidence of heart failure, unstable cardiac rhythms or angina during the days preceding discharge from hospital tend to be actively excluded from such programs. However the complex statistical models which form the conventional prognostic indices [2, 31are derived from populations which include such high risk patients. The second reason relates to the nature of the outcome predicted by the index. When entry to a rehabilitation program is based upon a low level exercise test before discharge from hospital, patients with an enhanced risk of death get eliminated. In such groups the *Author for correspondence 543
LIANGHsu et al.
544
mortality is low although the morbidity remains relatively high [7, 81. Thus in terms of the objectives of rehabilitation programs [I] there is an additional need to identify those likely to experience morbidity after discharge from hospital. In the investigation reported in this paper, an attempt was made to devise a statistical model for identifying individuals likely to develop significant cardiac events during the first 12 months following an acute myocardial infarction in such a selected group of survivors. This study was undertaken prospectively and confined to those who would be eligible to enter cardiac rehabilitation program on the basis of an ability to undertake a low level exercise test prior to discharge from hospital. By using such an approach, it was felt that a model which had specific relevance to conventional cardiac rehabilitation program [5,6] could be developed. METHODS
The study was conducted on patients discharged from the University of Alberta Hospital, after recovering from an episode of myocardial infarction. The diagnosis of acute myocardial infarction was based on the presence of any two of the following criteria: (1) typical history of chest pain, (2) diagnostic electrocardiographic changes with evolution, (3) diagnostic serum enzyme changes. All patients meeting the following criteria underwent a “low level” stress test on a bicycle ergometer prior to discharge from hospital and were subsequently enrolled in the cardiac rehabilitation program. The criteria were: (1) absence of pain in the chest for 2 days, preceding the test (2) a stable cardiac rhythm in the stepdown unit, (3) a systolic blood pressure in excess of 90 mmHg, (4) ability to ambulate in the ward, (5) absence of cardiac failure (i.e. absence of S,, bibasilar rales or lung congestion on chest X-ray film), and (6) absence of any orthopaedic problems which precluded exercise. Thus, acceptance into the Rehabilitation Program was dependent upon completion of the exercise test. Exercise
testing before discharge from hospital
All patients were tested on an electrically braked bicycle ergometer (Model No. E022 E1852, Siemans Elema). The electrocardiogram (12 leads) was recorded using the lead system described by Mason and Likar [9]. A 12 lead electrocardiogram was recorded before exercise, at the end of each stage of exercise, at the end of the exercise and again 5 min after completion of the exercise. The ST depression and ST slope in three electrocardiographic leads (V, , V, & AVF) and the heart rate were monitored continuously using a computerised system (Model MEI, Case Marquette). The load was set initially at 300 W and increased in 20 W stages every 3 min until one of the following end-points was (2) angina pectoris, (3) a attained: (1) a heart rate of 130 beats/min, horizontal/downsloping ST depression in excess of 2.0 mm at a point 80 msec after the J point, (4) severe dyspnoea or fatigue, (5) a fall in systolic blood pressure, (6) a systolic blood pressure > 220 mmHg, (7) ventricular tachycardia or premature ventricular contractions >25% of the beats. In patients taking a P-blocker, the exercise test was terminated at 110 W. A fall >5 mmHg in systolic blood pressure or an increase < 10 mmHg per stage of exercise were considered abnormal blood pressure responses. (The latter value was 5 mm for those taking a /J blocker). However, ability to generate a systolic blood pressure of > 150 mmHg was considered a normal response even if the mean rise in blood pressure per exercise stage was < 10 mmHg. Details of the Rehabilitation Program
The Rehabilitation Program has been described in detail previously [lo, 1I]. All patients, once admitted, were reviewed formally 10 weeks and 1 year after discharge. At these times, they underwent a conventional exercise test on a bicycle ergometer and were evaluated by their cardiologist and the cardiac rehabilitation team. During the first month following discharge from the hospital, the patients were contacted by telephone by the Rehabilitation Nurses in order to reinforce clinical
Coronary
Events
After
Infarction
545
instructions and to provide information regarding graded activity. After the patient attended for their 10 week review, they were offered a formal supervised exercise training program [12, 131. Only 25530% of the patients accepted this offer, mainly because of commitments at their place of employment or because their homes were outside the metropolitan areas. [It is emphasised that even those who did not attend the exercise program were retained on the Rehabilitation Program for purposes of clinical, psychological and dietary counselling---and were included in the present study]. At the end of 12 months, each patient was reviewed to establish specifically whether any of the following clinically significant coronary events had occurred: (1) death, (2) myocardial infarction, (3) development of unstable angina pectoris or heart failure necessitating admission to hospital for further investigation and therapy (e.g. significant adjustment to medication, coronary angioplasty or by-pass surgery). “Unstable angina” was defined as a changing situation presenting as angina pectoris of recent onset or of changing patterns, in either circumstance occurring on minimal effort or at rest [14]. For the purpose of the present analysis, all of the above were classified as “cardiac events”. In the case of those who had died, the case records were examined and the next of kin were interviewed. All the other patients were interviewed and none were lost to follow-up. One patient was contacted by telephone only. Statistical
analysis
Based upon previously published prognostic indices [6, 71 a series of 26 variables were considered likely to have a bearing upon the outcomes in these patients. These variables (Table 1) belonged to three categories: (1) patient characteristics such as age and sex (2) data from the coronary care unit (CCU) relating to the myocardial infarction and (3) data obtained from the low-level predischarge exercise test. Except for the age, the highest blood urea nitrogen and creatinekinase concentrations observed in the CCU, all the variables were discrete ones. The three continuous variables mentioned above were sub-divided into discrete categories as shown in Table 1.
Patient I.
characteristics Age:
by decade
2. Sex Data
from
I.
the coronary
Location
2. Type
of infarction:
3. History
of
fibrillation. 4.
care
umt
of myocardial
infarction:
non
ventricular
Q wave
:mtcro-septal. vs Q wave
arrhythmia:
no significant
complex
Presence
or absence
of atrial
arrhythmia
or absence
of heart
failure
or absence
of cardiomegaly
7. Highest 8.
level
Highes
of creatinekinase
blood
9. Presence
urea
mtrogen
or absence
lateral.
infero-lateral,
extensive
anterior.
premature
ventricular
contractions,
ventricular
tachycardia,
ventricular
arrhythmias.
5. Presence 6. Presence
mferior:posterlor,
infarction.
(alrial
nndior and,or
in CCU: in CCU:
of (a) previous
tibrillatmn.
shock lung
<2000
normal
atrial
durmg
congestion vs >2000
supraventricuiar
tachycardia).
in CCU.
in the chest
films
done
m CCU.
I.U.
vs elevated
myocardial
flutter.
the stay
(zS.Ommol/l).
Infarction,
(b) angina
> 3 months
myocardlal
infarction:
immediately
prior
to present
infract
(c) both. IO. Data
Reciprocal from
I.
ST-T
chaws
pre-discharge
Drugs
at time
2. Pre-exercise 3. Pre-exercise condition
in pre-cordial
exercise
of exercise
resting
test: /j-blockers.
12 lead
resting defect,
or absence
6. Presence
or absence of significant
up to 80msec
completed
of angina
after
during
of sign&cant
(I.0
of abnormal
systolic
9. Presence
or absence
of atrlal
Presence
or absence
of
ventricular
or absence in R-wave
or more during
exercise
mm)
arrhythmia
ventncular
ST-elevation blood
diuretics,
nil.
right bundle
branch
block,
other intra-ventricular
considered
horizontal
as a complete
ST-depression
stage).
persisting
during
arrhythmia
test (supra during
test.
response
during
ventricular
test (premature
the exercise
tachycardia, ventricular
test.
atrial
flutter
contractions
fibrillation).
of rate
dependent
amplitude
during
bundle
branch
block
excrc~
m Lead
V,
Change
in R-wave
amphtudc
during
exercise
in Lead
V,.
in R-wave
amplitude
during
exerwe
in Lead
AVF.
the change
stage of exercise
test (I .O mm or more
during
pressure
Change lead,
block,
of a 3-min
*l3.
each
digoxin,
vs rest.
branch
*l4. *For
or absence.
test.
ST depressjon
or absence
Change
presence
the J-point).
or absence
II.
left bundle
(2 min
8. Presence
$12.
antagonists.
smus rhythm
exercise
7. Presence
tachycardia.
calcium
I2 lead electrocardiogram:
of stages of exercise
Presence
inferwr
ml
5. Presence
IO.
with
electrocardiogram:
4. Number
for
lead\
test
was categorized
BS follo\r\:
increase.
during
decrease,
the test.
unchanged,
absent
R waves.
or atrial > IO/min,
fibrillation). ventricular
546
LIANGHsu et al
The subsequent statistical analysis was carried out in two stages. In the first stage, the association between the categories of each variable and the presence or absence of coronary events during the first 12 months were analysed with a cross-tabulation analysis. A chi-square test of independence was used for the statistical analysis. In instances where a single category of a multi-category (three or more) variable was significantly associated with subsequent cardiac events, the other categories were pooled together to form a dichotomous variable (e.g. decrease in R wave amplitude in V,) for better prediction in stage two of the analysis. In the second stage, all the 26 variables utilized in stage one were entered into a step-wise discriminant function analysis program (Statistical Package for Social Sciences) to obtain the best possible discrimination between the two groups. An Amdahl computer was used for high speed analysis. The different categories of each variable were assigned numerical values (O/l) prior to entry into the program since only numerical values were accepted for analysis by the program. During the analysis a single additional variable was entered in turn into the set of discriminating variables. The variables entered were selected on the basis of “maximizing” Rao’s V. [ 151.The program calculated the canonical correlation for the discriminant function and the canonical discriminant function coefficients for each of the discriminating variables. (Refer Appendix I for details). The program also classified each patient into one of the two groups (coronary event vs no events) using the “Jack-knife” method of Lachenbruch [16]. In this method, a single patient is removed and the discriminant function analysis carried out on the remaining (n - 1) patients. The resulting discriminant function equation was then applied to the data from the removed patient to predict the group (coronary event or no events) the patient belonged to. This analysis was performed sequentially on each patient and the predicted group compared with the actual group in each case. This method provides a relatively unbiased estimation of the error rate of the discriminant function analysis [16]. RESULTS
During the period of enrolment for the study 205 patients with acute myocardial infarctions were admitted to the coronary care unit of the hospital. Of these 205 patients 41 died in hospital. Thus, the overall in-hospital mortality was 20%. (The in-hospital mortality for those under 70 years of age was 9.3%). Of the remaining 164, 19 patients were not accepted for a pre-discharge exercise test on the basis of clinical criteria given above. This study was conducted on 145 patients who were diagnosed as having had an acute myocardial infarction and subsequently underwent a low level pre-discharge exercise test between 1st February 1981 and 3 1st July 1982. The clinical data from these patients are summarised in Table 2. Exercise test
One hundred and forty-four patients were in sinus rhythm at the time of the pre-discharge exercise test. One patient was in atria1 fibrillation. The resting electrocardiogram demonstrated right bundle branch block, in six patients, and an intraventricular conduction defect of indeterminate type in five. In the remaining patients the resting electrocardiogram showed a normal pattern of conduction. At the time of the exercise test, 55 patients (37.9%) were taking B adrenergic blocking drugs, 24 patients (16.5%) digoxin and 14 patients (9.7%) a calcium antagonist. Ten patients were taking more than one drug. Sixty-three patients were not taking any medications. The average load completed by the group was 73.1 W (_+2.2 W). Eighteen patients (12.4%) were unable to perform more than one stage of exercise. Twenty-three patients (15.9%) performed four or more stages of exercise. Twenty patients (13.8%) developed angina and 49 patients (33.8%) developed significant ST-segment depression during the exercise test. Significant ST-segment elevation during the exercise test was found in 32 patients (22.1%). Thirty-seven patients (25.5%) demonstrated an abnormal systolic blood
Coronary
Events After Infarction
547
TABLE 2. CLINICAL. CHARACTERISTICSOF THE 145 PATIENTS
125 20 5 14 29 62 31 4
86.2 13.8 3.4 97 20.1 42.8 21.4 2.8
MI angina >3 months both
I7 27 17
II.7 18.6 11.7
an&o-septal lateral extensive anterior inferior/posterior infero-lateral
33 9 IO 81 I2
22.8 6.2 6.9 55.9 8.3
112 33
77.2 22.8
History of heart failure or shock in CCU
28
19.4
History of cardiomegaly or lung congestion on X-ray in CCU
47
32.4
Peak creatinekinase I.U./l < 2000 > 2000
106 39
73. I 26.9
Blood urea nitrogen normal elevated
II4 31
78.6 21.4
Reciprocal ST changes absent present
104 41
71.7 28.3
I5 35 8 87
10.4 24.1 5.5 60.0
20 I25
13.8 86.2
males
Sex
Age (yr)
females 20-30 >3&40 > 40-50 > 5&60 > 6G-70 >70
History of
Location of MI
Type of MI Q wave non-Q wave
Ventricular arrhythmias in CCU complicated PVC’s ventricular tachycardia ventricular fibrillation nil Atrial tachyarrhythmia in CCU present absent
pressure response during the test. Only seven patients ventricular arrhythmias during exercise.
(4.8%) developed
significant
Follow up
During the 12 months following discharge from hospital, 10 patients died, 8 had a second episode of infarction and 52 had exacerbations of symptoms which necessitated major adjustments in management. The details of these latter 52 patients are as follows: 13 patients proceeded to by-pass surgery for symptoms; 3 had angioplasty, 3 developed heart failure and 33 patients developed unstable angina [14]. Thus a total of 48.2% of these patients developed clinically significant “cardiac events” during the period under review. Of these events, 56.9% occurred within 2 months of the myocardial infarction and 80.4% within 5 months of the infarction. Discriminant
function
analysis
The data obtained from the review were then analysed in two stages as defined in the Methods. In the first stage, the following variables were found to be associated significantly with the occurrence of new cardiac events: (1) history of myocardial infarction or angina prior to present myocardial infarction; (2) cardiomegaly or lung congestion in chest X-rays taken in CCU; (3) angina during the exercise test; (4) decrease in R-wave amplitude in V, during the exercise test (Table 3).
LIANG Hsu et al
548
TABLE 3. THE SIGNWLANT VARIABLESON UNIVARIAE ANALYSES.CHI-SQUARE TEST (WITH YATES CORRECTION) WAS DONE FOR STATTSTKAL ANALYslS
No event
Coronary event
absent present
51 24
33 37
2. Cardiomegaly and/or lung congestion in chest X-ray at CCU
absent present
58
31
3. Angina
during
absent present
70 5
54 15
4. Change in V.
in R-wave amplitude
decrease
2
9
<0.05
Variable 1.
History of myocardial or angina
infarction
exercise test
P
In stage two (of the analysis) all 26 variables were entered into a stepwise discriminant function analysis. This analysis defined the following variables as providing the best separation between those with a coronary event from the individuals with no coronary events during the first year after the myocardial infarction: (1) type of myocardial infarction: non-Q wave vs Q wave infarction (MITY); (2) history of myocardial infarction or angina (HOMI); (3) cardiomegaly or lung congestion in the chest X-ray films done in the CCU (CXR); (4) angina during the exercise test (ANG); (5) change in R-wave amplitude in V, during exercise test: decrease in amplitude vs rest (RLA); (6) atria1 arrhythmias during the exercise test (AT). The canonical correlation coefficient for the discriminant function was 0.468. The standardised canonical discriminant function coefficients for the discriminating variables are given in Table 4. These coefficients (sign ignored) represent the relative contribution of each variable to the discriminant function. The sign (in this case all positive) merely denotes whether the variable is making a positive or negative contribution to the risk. Presence of cardiomegaly or lung congestion in the chest X-rays taken in the CCU was the most important variable in the discrimination with a standardised discriminant function coefficient of 0.6756. The discriminant function equation was as follows: discriminant score (DS) = 1.487021 (RLA) + 0.8515889 (HOMI) + 1.178666 (CXR) + 1.014507 (MITY) + 1.665806 (ANG) + 2.987021 (AT) - 1.394238 (refer Appendix for details of the calculation). The group centroids (the mean of the discriminant scores) for discriminant scores were: No event group = -0.49944, coronary event group = 0.55242. The discriminant scores for the patient population are graphically displayed in Fig. 1. The “jack-knife” procedure applied to the discriminant analysis described above predicted correctly 72.6% of those without events and 7 1.2% of those who developed events. Thus the overall predictive accuracy was 71.9%. A closer evaluation of the data in Fig. 1 indicated that, among patients having discriminant scores greater than + 0.20, 82.0% developed cardiac events. Among patients with scores less than -0.70, 79.4% did not develop cardiac events. Between -0.70 and +0.20, the two groups were mixed in a manner which made separation difficult. Of the original 145 patients reviewed 36.0% had scores greater than +0.20 and 24.5% had scores less than -0.70.
TABLE 4. STANDARDISED CANON,CAL DIsCRlMINANT FUNCTlON COEFIWXENTS FOR THE “ARlABLES SELECTED FOR THE DlSCRlMlNANT FUNCTION EQUATION
Coefficient
Variable CXR in CCU (cardiomegaly or congestion) Type of MI (non Q wave vs Q wave) Change in R-wave amplitude in V, (decrease vs rest) History of MI or angina Angina during exercise test Atrial arrhvthmia durine exercise test Note: the magnitude variable.
of the coefficients
denotes
the relative
+0.6756 + 0.4282 + 0.4264 +0.4128 f0.3988 +0.3554 importance
of each
Coronary Events After Infarction SYMBOL --____
GROUP LABEL __-___________ NO EVENTS CORONARY EVENT
0 1
ALL
F R E Q u E N C V
10
GROUPS
STACKED
HISTOGRAM
00 00
5
n ”
549
0111 1111 !rfix,
E
I
-2.0
I
-1.0
cm
a
z
111111 111111
111 1111
0 0111 11111
I
I
0.0 OISCRIMINANT
00 111 111 111
SCORE
+1.0
0 111 111 111 111
0 01 11
01 1 11
I
+2.0
GO 1 11
I
+3.0
FIG. 1. The discriminant function scores of the patients are shown.
DISCUSSION
In this study, an attempt has been made to predict the clinical outcome in patients who enrolled in a Cardiac Rehabilitation Program where the ability to undertake a low-level pre-discharge exercise test was a criterion for acceptance. Such patients are conventionally considered to be low risk individuals who have a relatively good prognosis in terms of mortality [e.g. 17,3]. The findings of the present study, while confirming the low mortality over a 12 month period, also emphasised the high morbidity in these patients. Approximately 50% of these patients developed significant cardiovascular events which required major modifications to management [see also 31. In addition, the majority of these events occurred within the first few months after the initial infarction (56.9% of the events within 2 months; 80.4% within 5 months). The statistical model defined by the discriminant function analysis presented here suggests that it is possible to identify a subset of individuals who are likely to develop clinically significant events. The individual factors which were defined in the present study as having a bearing upon prognosis have been identified also in several other prognostic indices reported previously [6,7]. The new feature of the present study is its application to individuals within a group which excludes individuals at an enhanced risk. Such patients not only enroll in Cardiac Rehabilitation Programs but also feature in the majority of early and late entry secondary prevention trials [18-201. Further, as the discriminant score can be calculated for each patient, the predicted one year outcome can be ascertained for any one individual within the group. It is suggested that analyses of this nature could be used in the planning of secondary prevention programs in patients. In general, the therapeutic measures which have been advocated for the purposes of secondary prevention in patients who recover from myocardial infarction are (1) b-blocker therapy (2) antiarrhythmic therapy (3) treatment with platelet stabilizing agents (4) anticoagulant therapy and (5) revascularization procedures (See [21] for review). The conventional clinical trials undertaken with these various therapeutic measures have yielded little evidence in support of a claim for an overwhelming therapeutic benefit, particularly when this benefit is measured in terms of mortality [21]. For instance, in the BHAT Study [20] a reduction in mortality of approximately 30% (over 24 months) was claimed for those given propranolol. In reality, this improvement represented a reduction in mortality from 9.5 to 7%. There are two important factors which have to be considered when evaluating these trials. The first is that, because of the low “event rate” (i.e. mortality in the case of most secondary prevention trials), many individuals would be treated “unnecessarily”. The second is that the information derived from such trials is applicable only to those patients
550
LIANG Hsu et al.
who meet the entry criteria. The former factor implies that large numbers of patients would be required to complete trials. Ignorance of the latter results in the application of regimes of treatments to many patients who are unlikely to benefit from them-for instance the treatment of all patients who recover from a myocardial infarction with /I blockers. Analysis of morbidity statistics as outlined in this study indicate that an alternative strategy is feasible in planning clinical trials and regimes of management. If it is possible to identify individuals at risk who have an enhanced likelihood of developing cardiovascular morbidity, it should be possible also to target the therapy to these patients and to assess its effect in terms of morbidity. Further, since the occurrence of events is greater in these subjects when compared with the general population of post infarction patients, the numbers of recruits necessary to complete such trials would be relatively small. Another related issue is the relevance of these findings to other Institutions. It is recognised that many of the prognostic indices developed in the past [6,7] could not be used to predict the outcome of patients treated in institutions other than that in which the initial study was completed [8]. It is unlikely that the statistical model developed in the present study would fare any better in this regard. One explanation for this apparent anomaly lies in the essential nature of the medical care given to patients in hospital. The management of patients cannot be equated simply with the various drug regimes administered. The latter could clearly be standardised, but the overall care of the patient is essentially a reflection of the “Institutional Identity”. It is suggested that this factor is one of the major unknowns which is reflected in morbidity and mortality statistics, and which makes it difficult to extrapolate statistical models from one institution to another. In terms of Cardiac Rehabilitation Programs, it is emphasised that the process of rehabilitation cannot be equated with regimes of exercise training alone. Thus, the ability to undertake exercise should not be the sole prerequisite for enrolling in such programs. However, even for patients who make a relatively good recovery from an infarction, a statistical model of the outcome would provide useful information for targetting clinical surveillance. As the majority of the coronary events tend to occur within the first few months after discharge from hospital a pre-discharge evaluation of each patient with a view to identifying those likely to develop events should be mandatory. For instance, it could be argued that those who are identified as very likely to develop morbid events should be aggressively evaluated and managed without awaiting developments. Conversely, those in whom it is difficult to make predictions should be subjected to a more vigorous form of clinical surveillance and follow up. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
9. 10. 11.
Wenger NK: Research related to rehabilitation. Circulation 60: 1636-1639, 1979 Luria MH, Knoke JD, Margolis RM, Hendricks FH, Kuplic JB: Acute myocardial infarction: prognosis after recovery. AM Intern Med 85: 561-565, 1976 Norris RM, Caughey DE, Deeming LW, Mercer CJ, Scott PJ: Coronary prognostic index for predicting survival after recovery from acute myocardial infarction. Lancet 2: 485487, 1970 Moss AJ: Factors influencing prognosis after myocardial infarction, Curr Prob Cardiol 4: 6-53, 1979 Special Issue: J Cardiac Rehabil 2: 429-512, 1982 Shaw LW: Effects of a prescribed supervised exercise program on mortality and cardiovascular morbidity in patients after a myocardial infarction. Am J Cardiol 48: 39-46, 1981 Theroux P, Waters DD, Halphen C, Debaisieux JC, Mizgala HF: Prognostic value of exercise testing soon after myocardial infarction. N Engl J Med 301: 341--345, 1979 Dwyer EM Jr, McMaster P, Greenberg H, and the Multicentre Post-infarction Research Group: Non-fatal cardiac events and recurrent infarction in the year after acute myocardial infarction. J Am Coil Cardiol 4: 695-702, 1984 Mason RE, Likar I: A new system of multiple-lead exercise electrocardiography. Am Heart J 71: 196-205, 1966 Kappagoda CT: Rehabilitation after Myocardial Infarction. New York: Medical Examination Publishing Co. Inc., 1984. pp. 93-129 Teo KK, Kappagoda CT: An approach to the rehabilitation of patients after myocardial infarction. Mod Med Can 39 (suppl. 8): 11-26, 1984
12. Kappagoda CT, Greenwood PV: Physical training with minimal hospital supervision of patients after coronary artery bypass surgery. Arch Phys Med Rehabil 65: 57-60, 1984 13.
Raffo JA, Luksic IY, Kappagoda CT, Mary DASG, on myocardial ischaemia in patients with coronary
Whitaker W, Linden RJ: Effects of physical training artery disease. Br Heart J 43: 262-269, 1980
Coronary
14. 15. 16. 17. 18. 19.
20. 21. 22.
Events
551
After Infarction
Russell RO, Rackley CE, Kouchoukos NT: Unstable angina pectoris: do we know the best management? Am J Cardiol 48: 59&591, 1981 K.lecka WR: Discriminant analysis. In: Statistical Package for tke !%&I Sciences. Nie NH, Hull CH, Jenkins JG, Steinbrenner K, Bent DH (Eds). 2nd edn. New York: McGraw-Hill, 1975. pp. 434467 Lachenbruch PA: An almost unbiased method of obtaining confidence intervals for the probability of misclassification in discriminant analysis. Biometrics 23: 639645, 1967 Mulcahy R, Hickey N, Graham I, McKenzie G: Factors influencing long-term prognosis in male patients surviving a first coronary attack. Br Heart J 37: 158-165, 1975 The Norwegian Multicentre Study Group: Timolol-induced reduction in mortality and reinfarction in patients surviving acute myocardial infarction. N Engl J Med 304: 801-807, 1981 Yusuf S, Rossi P, Ramsdale D, Peto R, Furse L, Motwani R, Parish S, Gray R, Bennett D, Bray C, chest pain and morbidity by early intravenous Sleight P: Reduction in infarct size, arrhythmias, /I-blockade in suspected acute myocardial infarction, Drugs 25 (Suppl. 2): 303-307, 1983 Beta-blocker Heart Attack Trial Research Group: A randomized trial of propranolol in patients with acute myocardial infarction I: Mortality results. JAMA 247: 170771714, 1982 May G’S, Furberg CD, Eberlein KA, Geraci BJ: Secondary prevention after myocardial infarction: A review of short-term acute phase trials. Prog Cardiovasc Dis 25: 335-359, 1982 Tatsuoka MM: In Selected topics in advanced statistics; an elementary approach. No. 6: Discriminant Analysis: the Study of Group Differences. Illinois: Insitute for Personality and Ability Testing, 1970. pp. l-57
APPENDIX Details of the calculation of the discriminant scores (DS) are given below. The numerical to analyses) for the different categories of the discriminating variables were as follows:
values assigned
(prior
(I) Chest X-ray in CCU (CXR): Presence of cardiomegaly and/or lung congestion = I; absence of either = 0. (2) Type of myocardial infarction (MITY): non Q wave = 1; Q wave = 0. (3) Change in R-wave amplitude in V, during exercise test (RLA): decrease = I, increase, no change or no R-wave in V, = 0. (4) History of myocardial infarction and/or angina 3 > months duration (HOMI): absent = 0; present = 1. (5) Angina during exercise test (ANG): absent = 0, present = 1. (6) Atria1 arrhythmia during exercise test (AT): absent = 0, present = I. The discriminant DS = 1.487021
function
equation
(CXR) + 1.014507
was as follows: (MITY)
+ 1.665806
(RLA) + 0.8515889 + 1.178666
(ANG)
(HOMI) + 2.987021
(AT) - 1.394238.
The last value (- 1.394238) is a constant in the equation. The DS for any individual can be calculated by substituting the appropriate value for CXR, MITY, RLA, etc. The coefficients for each variable in the equation are referred to as unstandardised discriminant function coefficients. These coefficients are used for computation of the discriminant scores and do not denote the relative importance of the variables since they have been adjusted for the measurement scales and variability in the original variables (cf. with standard discriminant function coefficients). The mathematical objective of discriminant analyses is to weight and form one or more linear combinations of the discriminating variables so as to define groups which are statistically distinct as possible [15]. The resultant discriminant equations are of the form D, = d,,Z, + d,*Z, + + di,,Z,, where Di is the discriminant score on the discriminant function i, the d’s are the weighting (discriminant function) coefficients and the Z, are the values of the p discriminating variables used in the analyses. The maximum number of discriminant functions which can be derived is one less than the number of groups or equal to the number of discriminating variables, if there are more groups than variables (present study: 2 groups; thus 1 discriminant function). The discriminant function coefficients are derived by solving the general eigenvector problem WA = Ba, where B and W are, respectively, the between-group and within-group sums of squares and cross-products matrices (refer [15, 221 for further details). A stepwise selection method was used in the present study. The process begins by choosing the single variable which has the highest discriminating power between the two groups. This initial variable is then paired with each of the other available variables, one at a time, and the discriminant function analysis computed. The new variable which in conjunction with the initial variable produces the best discrimination is selected as the second variable to “enter the equation”. These two are then combined with each of the remaining variables, one at a time, to form triplets which are evaluated in a similar manner. The triplet with the best discriminating power determines the third variabIe to be selected. This procedure of locating the next variable that would yield the best discrimination given the variables already selected, continues until all variables are selected or no additional variables provide a minimum level of improvement. As variables are selected for inclusion, some variables previously selected may lose their discriminating power. This occurs because the information that they contain about group differences is now available in some combination of the other included variables. Such variables are redundant and are eliminated. Thus, at the beginning of each step, each of the previously selected variables is tested to determine if it still makes a significant contribution to discrimination. If any are eligible for removal, the least useful is eliminated. A variable which has been removed at one step may re-enter at a later step if it satisfies the selection criterion at that time. The stepwise selection criterion used in the present study was RaO’s V, a generalised distance measure. The variable selected was the one which contributes to the largest increase in RaO’s V when added to the previous variables. (This amounts to the greatest overall separation of the groups.) However, a variable was included in
552
LIANG Hsu et al.
to the discriminant function equation only if its partial multivariate F ratio (a measure of the discrimination introduced by the new variable after taking into account the discrimination already achieved by the other already selected variables) was greater than 1.0. At each step a similar test was made of all variables already selected. Here, the test was whether the particular variable still added a significant amount to the separation, given the other variables now in the equation. As more variables are selected, it is possible that some of those entered earlier may no longer be contributing to the separation. Again a multivariate partial F-test of the discriminating power added by the variable in question at that stage was performed and the variable removed if the F ratio was less than 1.0. The program also calculated the canonical correlation coefficient for the discriminant function. This is a measure of the ability of the discriminant function to discriminate between the groups. The square of the canonical correlation coefficient is the proportion of the variance in the discriminant function explained by the groups [12].
0021-9681/86 $3.00+0.00 Pergamon JournalsLtd
PREDICTION OF CORONARY EVENTS FOLLOWING MYOCARDIAL INFARCTION USING A DISCRIMINANT FUNCTION ANALYSIS LIANG Hsu,
MANOHARA
P. J. SENARATNE, SANGADASA DE-SILVA,
RICHARD E. ROSSALL
and
TISSA KAPPAGODA*
Division of Cardiology, Department of Medicine, 8-104 Clinical Sciences Building, University of
Alberta, Edmonton, Alberta, Canada T6G 2E3 (Received in revised form 6 November 1985)
Abstract-This study was undertaken to derive an index for predicting coronary events in the first year after a myocardial infarction in “low-risk” patients enrolling in a Cardiac Rehabilitation Program. Data from 145 consecutive patients were analysed. The events were classified as follows: angina requiring further therapy, re-infarction and coronary death. Seventy patients had events: Angina-52, Re-infarction-S, Coronary Death-IO. A discriminant function analysis was performed to predict such events using data available at the time of discharge from hospital. The following were significant predictors: (1) previous infarction/angina, (2) radiological evidence of cardiomegaly or lung congestion in the Coronary Care Unit, (3) Non-Q wave infarction and (4, 5 and 6) angina, atria1 arrhythmias and a decrease in R wave amplitude in V, during a pre-discharge exercise test. The jack-knife method classified correctly 71.2% of those with events and 72.6% of those without events. In patients with discriminant scores > +0.2, 82% developed events.
INTRODUCTION
THE MAJORITY of patients who recover from an episode of myocardial infarction embark upon a life of chronic ill health. It is evident that Cardiac Rehabilitation Programs should not be viewed as exercise training programs per se. They have the added responsibility of providing long term clinical surveillance for such patients [l]. Since the provision of such “after care” is a relatively expensive process, in terms of both personnel and equipment, it would be useful to identify individuals who are likely to encounter clinically significant events amongst those enrolling in such programs. Although there are many reports of prognostic indices developed for post-infarction patients [e.g. 2-4 (review)] they cannot be adapted readily for the needs of clients who traditionally enroll in Cardiac Rehabilitation Programs, for two main reasons. The first relates to the population under scrutiny. The majority of such programs emphasise the value of exercise training as a therapeutic modality [5] and the ability to undertake exercise is often a pre-requisite for entry into them [6]. Thus, patients who exhibit evidence of heart failure, unstable cardiac rhythms or angina during the days preceding discharge from hospital tend to be actively excluded from such programs. However the complex statistical models which form the conventional prognostic indices [2, 31are derived from populations which include such high risk patients. The second reason relates to the nature of the outcome predicted by the index. When entry to a rehabilitation program is based upon a low level exercise test before discharge from hospital, patients with an enhanced risk of death get eliminated. In such groups the *Author for correspondence 543
LIANGHsu et al.
544
mortality is low although the morbidity remains relatively high [7, 81. Thus in terms of the objectives of rehabilitation programs [I] there is an additional need to identify those likely to experience morbidity after discharge from hospital. In the investigation reported in this paper, an attempt was made to devise a statistical model for identifying individuals likely to develop significant cardiac events during the first 12 months following an acute myocardial infarction in such a selected group of survivors. This study was undertaken prospectively and confined to those who would be eligible to enter cardiac rehabilitation program on the basis of an ability to undertake a low level exercise test prior to discharge from hospital. By using such an approach, it was felt that a model which had specific relevance to conventional cardiac rehabilitation program [5,6] could be developed. METHODS
The study was conducted on patients discharged from the University of Alberta Hospital, after recovering from an episode of myocardial infarction. The diagnosis of acute myocardial infarction was based on the presence of any two of the following criteria: (1) typical history of chest pain, (2) diagnostic electrocardiographic changes with evolution, (3) diagnostic serum enzyme changes. All patients meeting the following criteria underwent a “low level” stress test on a bicycle ergometer prior to discharge from hospital and were subsequently enrolled in the cardiac rehabilitation program. The criteria were: (1) absence of pain in the chest for 2 days, preceding the test (2) a stable cardiac rhythm in the stepdown unit, (3) a systolic blood pressure in excess of 90 mmHg, (4) ability to ambulate in the ward, (5) absence of cardiac failure (i.e. absence of S,, bibasilar rales or lung congestion on chest X-ray film), and (6) absence of any orthopaedic problems which precluded exercise. Thus, acceptance into the Rehabilitation Program was dependent upon completion of the exercise test. Exercise
testing before discharge from hospital
All patients were tested on an electrically braked bicycle ergometer (Model No. E022 E1852, Siemans Elema). The electrocardiogram (12 leads) was recorded using the lead system described by Mason and Likar [9]. A 12 lead electrocardiogram was recorded before exercise, at the end of each stage of exercise, at the end of the exercise and again 5 min after completion of the exercise. The ST depression and ST slope in three electrocardiographic leads (V, , V, & AVF) and the heart rate were monitored continuously using a computerised system (Model MEI, Case Marquette). The load was set initially at 300 W and increased in 20 W stages every 3 min until one of the following end-points was (2) angina pectoris, (3) a attained: (1) a heart rate of 130 beats/min, horizontal/downsloping ST depression in excess of 2.0 mm at a point 80 msec after the J point, (4) severe dyspnoea or fatigue, (5) a fall in systolic blood pressure, (6) a systolic blood pressure > 220 mmHg, (7) ventricular tachycardia or premature ventricular contractions >25% of the beats. In patients taking a P-blocker, the exercise test was terminated at 110 W. A fall >5 mmHg in systolic blood pressure or an increase < 10 mmHg per stage of exercise were considered abnormal blood pressure responses. (The latter value was 5 mm for those taking a /J blocker). However, ability to generate a systolic blood pressure of > 150 mmHg was considered a normal response even if the mean rise in blood pressure per exercise stage was < 10 mmHg. Details of the Rehabilitation Program
The Rehabilitation Program has been described in detail previously [lo, 1I]. All patients, once admitted, were reviewed formally 10 weeks and 1 year after discharge. At these times, they underwent a conventional exercise test on a bicycle ergometer and were evaluated by their cardiologist and the cardiac rehabilitation team. During the first month following discharge from the hospital, the patients were contacted by telephone by the Rehabilitation Nurses in order to reinforce clinical
Coronary
Events
After
Infarction
545
instructions and to provide information regarding graded activity. After the patient attended for their 10 week review, they were offered a formal supervised exercise training program [12, 131. Only 25530% of the patients accepted this offer, mainly because of commitments at their place of employment or because their homes were outside the metropolitan areas. [It is emphasised that even those who did not attend the exercise program were retained on the Rehabilitation Program for purposes of clinical, psychological and dietary counselling---and were included in the present study]. At the end of 12 months, each patient was reviewed to establish specifically whether any of the following clinically significant coronary events had occurred: (1) death, (2) myocardial infarction, (3) development of unstable angina pectoris or heart failure necessitating admission to hospital for further investigation and therapy (e.g. significant adjustment to medication, coronary angioplasty or by-pass surgery). “Unstable angina” was defined as a changing situation presenting as angina pectoris of recent onset or of changing patterns, in either circumstance occurring on minimal effort or at rest [14]. For the purpose of the present analysis, all of the above were classified as “cardiac events”. In the case of those who had died, the case records were examined and the next of kin were interviewed. All the other patients were interviewed and none were lost to follow-up. One patient was contacted by telephone only. Statistical
analysis
Based upon previously published prognostic indices [6, 71 a series of 26 variables were considered likely to have a bearing upon the outcomes in these patients. These variables (Table 1) belonged to three categories: (1) patient characteristics such as age and sex (2) data from the coronary care unit (CCU) relating to the myocardial infarction and (3) data obtained from the low-level predischarge exercise test. Except for the age, the highest blood urea nitrogen and creatinekinase concentrations observed in the CCU, all the variables were discrete ones. The three continuous variables mentioned above were sub-divided into discrete categories as shown in Table 1.
Patient I.
characteristics Age:
by decade
2. Sex Data
from
I.
the coronary
Location
2. Type
of infarction:
3. History
of
fibrillation. 4.
care
umt
of myocardial
infarction:
non
ventricular
Q wave
:mtcro-septal. vs Q wave
arrhythmia:
no significant
complex
Presence
or absence
of atrial
arrhythmia
or absence
of heart
failure
or absence
of cardiomegaly
7. Highest 8.
level
Highes
of creatinekinase
blood
9. Presence
urea
mtrogen
or absence
lateral.
infero-lateral,
extensive
anterior.
premature
ventricular
contractions,
ventricular
tachycardia,
ventricular
arrhythmias.
5. Presence 6. Presence
mferior:posterlor,
infarction.
(alrial
nndior and,or
in CCU: in CCU:
of (a) previous
tibrillatmn.
shock lung
<2000
normal
atrial
durmg
congestion vs >2000
supraventricuiar
tachycardia).
in CCU.
in the chest
films
done
m CCU.
I.U.
vs elevated
myocardial
flutter.
the stay
(zS.Ommol/l).
Infarction,
(b) angina
> 3 months
myocardlal
infarction:
immediately
prior
to present
infract
(c) both. IO. Data
Reciprocal from
I.
ST-T
chaws
pre-discharge
Drugs
at time
2. Pre-exercise 3. Pre-exercise condition
in pre-cordial
exercise
of exercise
resting
test: /j-blockers.
12 lead
resting defect,
or absence
6. Presence
or absence of significant
up to 80msec
completed
of angina
after
during
of sign&cant
(I.0
of abnormal
systolic
9. Presence
or absence
of atrlal
Presence
or absence
of
ventricular
or absence in R-wave
or more during
exercise
mm)
arrhythmia
ventncular
ST-elevation blood
diuretics,
nil.
right bundle
branch
block,
other intra-ventricular
considered
horizontal
as a complete
ST-depression
stage).
persisting
during
arrhythmia
test (supra during
test.
response
during
ventricular
test (premature
the exercise
tachycardia, ventricular
test.
atrial
flutter
contractions
fibrillation).
of rate
dependent
amplitude
during
bundle
branch
block
excrc~
m Lead
V,
Change
in R-wave
amphtudc
during
exercise
in Lead
V,.
in R-wave
amplitude
during
exerwe
in Lead
AVF.
the change
stage of exercise
test (I .O mm or more
during
pressure
Change lead,
block,
of a 3-min
*l3.
each
digoxin,
vs rest.
branch
*l4. *For
or absence.
test.
ST depressjon
or absence
Change
presence
the J-point).
or absence
II.
left bundle
(2 min
8. Presence
$12.
antagonists.
smus rhythm
exercise
7. Presence
tachycardia.
calcium
I2 lead electrocardiogram:
of stages of exercise
Presence
inferwr
ml
5. Presence
IO.
with
electrocardiogram:
4. Number
for
lead\
test
was categorized
BS follo\r\:
increase.
during
decrease,
the test.
unchanged,
absent
R waves.
or atrial > IO/min,
fibrillation). ventricular
546
LIANGHsu et al
The subsequent statistical analysis was carried out in two stages. In the first stage, the association between the categories of each variable and the presence or absence of coronary events during the first 12 months were analysed with a cross-tabulation analysis. A chi-square test of independence was used for the statistical analysis. In instances where a single category of a multi-category (three or more) variable was significantly associated with subsequent cardiac events, the other categories were pooled together to form a dichotomous variable (e.g. decrease in R wave amplitude in V,) for better prediction in stage two of the analysis. In the second stage, all the 26 variables utilized in stage one were entered into a step-wise discriminant function analysis program (Statistical Package for Social Sciences) to obtain the best possible discrimination between the two groups. An Amdahl computer was used for high speed analysis. The different categories of each variable were assigned numerical values (O/l) prior to entry into the program since only numerical values were accepted for analysis by the program. During the analysis a single additional variable was entered in turn into the set of discriminating variables. The variables entered were selected on the basis of “maximizing” Rao’s V. [ 151.The program calculated the canonical correlation for the discriminant function and the canonical discriminant function coefficients for each of the discriminating variables. (Refer Appendix I for details). The program also classified each patient into one of the two groups (coronary event vs no events) using the “Jack-knife” method of Lachenbruch [16]. In this method, a single patient is removed and the discriminant function analysis carried out on the remaining (n - 1) patients. The resulting discriminant function equation was then applied to the data from the removed patient to predict the group (coronary event or no events) the patient belonged to. This analysis was performed sequentially on each patient and the predicted group compared with the actual group in each case. This method provides a relatively unbiased estimation of the error rate of the discriminant function analysis [16]. RESULTS
During the period of enrolment for the study 205 patients with acute myocardial infarctions were admitted to the coronary care unit of the hospital. Of these 205 patients 41 died in hospital. Thus, the overall in-hospital mortality was 20%. (The in-hospital mortality for those under 70 years of age was 9.3%). Of the remaining 164, 19 patients were not accepted for a pre-discharge exercise test on the basis of clinical criteria given above. This study was conducted on 145 patients who were diagnosed as having had an acute myocardial infarction and subsequently underwent a low level pre-discharge exercise test between 1st February 1981 and 3 1st July 1982. The clinical data from these patients are summarised in Table 2. Exercise test
One hundred and forty-four patients were in sinus rhythm at the time of the pre-discharge exercise test. One patient was in atria1 fibrillation. The resting electrocardiogram demonstrated right bundle branch block, in six patients, and an intraventricular conduction defect of indeterminate type in five. In the remaining patients the resting electrocardiogram showed a normal pattern of conduction. At the time of the exercise test, 55 patients (37.9%) were taking B adrenergic blocking drugs, 24 patients (16.5%) digoxin and 14 patients (9.7%) a calcium antagonist. Ten patients were taking more than one drug. Sixty-three patients were not taking any medications. The average load completed by the group was 73.1 W (_+2.2 W). Eighteen patients (12.4%) were unable to perform more than one stage of exercise. Twenty-three patients (15.9%) performed four or more stages of exercise. Twenty patients (13.8%) developed angina and 49 patients (33.8%) developed significant ST-segment depression during the exercise test. Significant ST-segment elevation during the exercise test was found in 32 patients (22.1%). Thirty-seven patients (25.5%) demonstrated an abnormal systolic blood
Coronary
Events After Infarction
547
TABLE 2. CLINICAL. CHARACTERISTICSOF THE 145 PATIENTS
125 20 5 14 29 62 31 4
86.2 13.8 3.4 97 20.1 42.8 21.4 2.8
MI angina >3 months both
I7 27 17
II.7 18.6 11.7
an&o-septal lateral extensive anterior inferior/posterior infero-lateral
33 9 IO 81 I2
22.8 6.2 6.9 55.9 8.3
112 33
77.2 22.8
History of heart failure or shock in CCU
28
19.4
History of cardiomegaly or lung congestion on X-ray in CCU
47
32.4
Peak creatinekinase I.U./l < 2000 > 2000
106 39
73. I 26.9
Blood urea nitrogen normal elevated
II4 31
78.6 21.4
Reciprocal ST changes absent present
104 41
71.7 28.3
I5 35 8 87
10.4 24.1 5.5 60.0
20 I25
13.8 86.2
males
Sex
Age (yr)
females 20-30 >3&40 > 40-50 > 5&60 > 6G-70 >70
History of
Location of MI
Type of MI Q wave non-Q wave
Ventricular arrhythmias in CCU complicated PVC’s ventricular tachycardia ventricular fibrillation nil Atrial tachyarrhythmia in CCU present absent
pressure response during the test. Only seven patients ventricular arrhythmias during exercise.
(4.8%) developed
significant
Follow up
During the 12 months following discharge from hospital, 10 patients died, 8 had a second episode of infarction and 52 had exacerbations of symptoms which necessitated major adjustments in management. The details of these latter 52 patients are as follows: 13 patients proceeded to by-pass surgery for symptoms; 3 had angioplasty, 3 developed heart failure and 33 patients developed unstable angina [14]. Thus a total of 48.2% of these patients developed clinically significant “cardiac events” during the period under review. Of these events, 56.9% occurred within 2 months of the myocardial infarction and 80.4% within 5 months of the infarction. Discriminant
function
analysis
The data obtained from the review were then analysed in two stages as defined in the Methods. In the first stage, the following variables were found to be associated significantly with the occurrence of new cardiac events: (1) history of myocardial infarction or angina prior to present myocardial infarction; (2) cardiomegaly or lung congestion in chest X-rays taken in CCU; (3) angina during the exercise test; (4) decrease in R-wave amplitude in V, during the exercise test (Table 3).
LIANG Hsu et al
548
TABLE 3. THE SIGNWLANT VARIABLESON UNIVARIAE ANALYSES.CHI-SQUARE TEST (WITH YATES CORRECTION) WAS DONE FOR STATTSTKAL ANALYslS
No event
Coronary event
absent present
51 24
33 37
2. Cardiomegaly and/or lung congestion in chest X-ray at CCU
absent present
58
31
3. Angina
during
absent present
70 5
54 15
4. Change in V.
in R-wave amplitude
decrease
2
9
<0.05
Variable 1.
History of myocardial or angina
infarction
exercise test
P
In stage two (of the analysis) all 26 variables were entered into a stepwise discriminant function analysis. This analysis defined the following variables as providing the best separation between those with a coronary event from the individuals with no coronary events during the first year after the myocardial infarction: (1) type of myocardial infarction: non-Q wave vs Q wave infarction (MITY); (2) history of myocardial infarction or angina (HOMI); (3) cardiomegaly or lung congestion in the chest X-ray films done in the CCU (CXR); (4) angina during the exercise test (ANG); (5) change in R-wave amplitude in V, during exercise test: decrease in amplitude vs rest (RLA); (6) atria1 arrhythmias during the exercise test (AT). The canonical correlation coefficient for the discriminant function was 0.468. The standardised canonical discriminant function coefficients for the discriminating variables are given in Table 4. These coefficients (sign ignored) represent the relative contribution of each variable to the discriminant function. The sign (in this case all positive) merely denotes whether the variable is making a positive or negative contribution to the risk. Presence of cardiomegaly or lung congestion in the chest X-rays taken in the CCU was the most important variable in the discrimination with a standardised discriminant function coefficient of 0.6756. The discriminant function equation was as follows: discriminant score (DS) = 1.487021 (RLA) + 0.8515889 (HOMI) + 1.178666 (CXR) + 1.014507 (MITY) + 1.665806 (ANG) + 2.987021 (AT) - 1.394238 (refer Appendix for details of the calculation). The group centroids (the mean of the discriminant scores) for discriminant scores were: No event group = -0.49944, coronary event group = 0.55242. The discriminant scores for the patient population are graphically displayed in Fig. 1. The “jack-knife” procedure applied to the discriminant analysis described above predicted correctly 72.6% of those without events and 7 1.2% of those who developed events. Thus the overall predictive accuracy was 71.9%. A closer evaluation of the data in Fig. 1 indicated that, among patients having discriminant scores greater than + 0.20, 82.0% developed cardiac events. Among patients with scores less than -0.70, 79.4% did not develop cardiac events. Between -0.70 and +0.20, the two groups were mixed in a manner which made separation difficult. Of the original 145 patients reviewed 36.0% had scores greater than +0.20 and 24.5% had scores less than -0.70.
TABLE 4. STANDARDISED CANON,CAL DIsCRlMINANT FUNCTlON COEFIWXENTS FOR THE “ARlABLES SELECTED FOR THE DlSCRlMlNANT FUNCTION EQUATION
Coefficient
Variable CXR in CCU (cardiomegaly or congestion) Type of MI (non Q wave vs Q wave) Change in R-wave amplitude in V, (decrease vs rest) History of MI or angina Angina during exercise test Atrial arrhvthmia durine exercise test Note: the magnitude variable.
of the coefficients
denotes
the relative
+0.6756 + 0.4282 + 0.4264 +0.4128 f0.3988 +0.3554 importance
of each
Coronary Events After Infarction SYMBOL --____
GROUP LABEL __-___________ NO EVENTS CORONARY EVENT
0 1
ALL
F R E Q u E N C V
10
GROUPS
STACKED
HISTOGRAM
00 00
5
n ”
549
0111 1111 !rfix,
E
I
-2.0
I
-1.0
cm
a
z
111111 111111
111 1111
0 0111 11111
I
I
0.0 OISCRIMINANT
00 111 111 111
SCORE
+1.0
0 111 111 111 111
0 01 11
01 1 11
I
+2.0
GO 1 11
I
+3.0
FIG. 1. The discriminant function scores of the patients are shown.
DISCUSSION
In this study, an attempt has been made to predict the clinical outcome in patients who enrolled in a Cardiac Rehabilitation Program where the ability to undertake a low-level pre-discharge exercise test was a criterion for acceptance. Such patients are conventionally considered to be low risk individuals who have a relatively good prognosis in terms of mortality [e.g. 17,3]. The findings of the present study, while confirming the low mortality over a 12 month period, also emphasised the high morbidity in these patients. Approximately 50% of these patients developed significant cardiovascular events which required major modifications to management [see also 31. In addition, the majority of these events occurred within the first few months after the initial infarction (56.9% of the events within 2 months; 80.4% within 5 months). The statistical model defined by the discriminant function analysis presented here suggests that it is possible to identify a subset of individuals who are likely to develop clinically significant events. The individual factors which were defined in the present study as having a bearing upon prognosis have been identified also in several other prognostic indices reported previously [6,7]. The new feature of the present study is its application to individuals within a group which excludes individuals at an enhanced risk. Such patients not only enroll in Cardiac Rehabilitation Programs but also feature in the majority of early and late entry secondary prevention trials [18-201. Further, as the discriminant score can be calculated for each patient, the predicted one year outcome can be ascertained for any one individual within the group. It is suggested that analyses of this nature could be used in the planning of secondary prevention programs in patients. In general, the therapeutic measures which have been advocated for the purposes of secondary prevention in patients who recover from myocardial infarction are (1) b-blocker therapy (2) antiarrhythmic therapy (3) treatment with platelet stabilizing agents (4) anticoagulant therapy and (5) revascularization procedures (See [21] for review). The conventional clinical trials undertaken with these various therapeutic measures have yielded little evidence in support of a claim for an overwhelming therapeutic benefit, particularly when this benefit is measured in terms of mortality [21]. For instance, in the BHAT Study [20] a reduction in mortality of approximately 30% (over 24 months) was claimed for those given propranolol. In reality, this improvement represented a reduction in mortality from 9.5 to 7%. There are two important factors which have to be considered when evaluating these trials. The first is that, because of the low “event rate” (i.e. mortality in the case of most secondary prevention trials), many individuals would be treated “unnecessarily”. The second is that the information derived from such trials is applicable only to those patients
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who meet the entry criteria. The former factor implies that large numbers of patients would be required to complete trials. Ignorance of the latter results in the application of regimes of treatments to many patients who are unlikely to benefit from them-for instance the treatment of all patients who recover from a myocardial infarction with /I blockers. Analysis of morbidity statistics as outlined in this study indicate that an alternative strategy is feasible in planning clinical trials and regimes of management. If it is possible to identify individuals at risk who have an enhanced likelihood of developing cardiovascular morbidity, it should be possible also to target the therapy to these patients and to assess its effect in terms of morbidity. Further, since the occurrence of events is greater in these subjects when compared with the general population of post infarction patients, the numbers of recruits necessary to complete such trials would be relatively small. Another related issue is the relevance of these findings to other Institutions. It is recognised that many of the prognostic indices developed in the past [6,7] could not be used to predict the outcome of patients treated in institutions other than that in which the initial study was completed [8]. It is unlikely that the statistical model developed in the present study would fare any better in this regard. One explanation for this apparent anomaly lies in the essential nature of the medical care given to patients in hospital. The management of patients cannot be equated simply with the various drug regimes administered. The latter could clearly be standardised, but the overall care of the patient is essentially a reflection of the “Institutional Identity”. It is suggested that this factor is one of the major unknowns which is reflected in morbidity and mortality statistics, and which makes it difficult to extrapolate statistical models from one institution to another. In terms of Cardiac Rehabilitation Programs, it is emphasised that the process of rehabilitation cannot be equated with regimes of exercise training alone. Thus, the ability to undertake exercise should not be the sole prerequisite for enrolling in such programs. However, even for patients who make a relatively good recovery from an infarction, a statistical model of the outcome would provide useful information for targetting clinical surveillance. As the majority of the coronary events tend to occur within the first few months after discharge from hospital a pre-discharge evaluation of each patient with a view to identifying those likely to develop events should be mandatory. For instance, it could be argued that those who are identified as very likely to develop morbid events should be aggressively evaluated and managed without awaiting developments. Conversely, those in whom it is difficult to make predictions should be subjected to a more vigorous form of clinical surveillance and follow up. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
9. 10. 11.
Wenger NK: Research related to rehabilitation. Circulation 60: 1636-1639, 1979 Luria MH, Knoke JD, Margolis RM, Hendricks FH, Kuplic JB: Acute myocardial infarction: prognosis after recovery. AM Intern Med 85: 561-565, 1976 Norris RM, Caughey DE, Deeming LW, Mercer CJ, Scott PJ: Coronary prognostic index for predicting survival after recovery from acute myocardial infarction. Lancet 2: 485487, 1970 Moss AJ: Factors influencing prognosis after myocardial infarction, Curr Prob Cardiol 4: 6-53, 1979 Special Issue: J Cardiac Rehabil 2: 429-512, 1982 Shaw LW: Effects of a prescribed supervised exercise program on mortality and cardiovascular morbidity in patients after a myocardial infarction. Am J Cardiol 48: 39-46, 1981 Theroux P, Waters DD, Halphen C, Debaisieux JC, Mizgala HF: Prognostic value of exercise testing soon after myocardial infarction. N Engl J Med 301: 341--345, 1979 Dwyer EM Jr, McMaster P, Greenberg H, and the Multicentre Post-infarction Research Group: Non-fatal cardiac events and recurrent infarction in the year after acute myocardial infarction. J Am Coil Cardiol 4: 695-702, 1984 Mason RE, Likar I: A new system of multiple-lead exercise electrocardiography. Am Heart J 71: 196-205, 1966 Kappagoda CT: Rehabilitation after Myocardial Infarction. New York: Medical Examination Publishing Co. Inc., 1984. pp. 93-129 Teo KK, Kappagoda CT: An approach to the rehabilitation of patients after myocardial infarction. Mod Med Can 39 (suppl. 8): 11-26, 1984
12. Kappagoda CT, Greenwood PV: Physical training with minimal hospital supervision of patients after coronary artery bypass surgery. Arch Phys Med Rehabil 65: 57-60, 1984 13.
Raffo JA, Luksic IY, Kappagoda CT, Mary DASG, on myocardial ischaemia in patients with coronary
Whitaker W, Linden RJ: Effects of physical training artery disease. Br Heart J 43: 262-269, 1980
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Russell RO, Rackley CE, Kouchoukos NT: Unstable angina pectoris: do we know the best management? Am J Cardiol 48: 59&591, 1981 K.lecka WR: Discriminant analysis. In: Statistical Package for tke !%&I Sciences. Nie NH, Hull CH, Jenkins JG, Steinbrenner K, Bent DH (Eds). 2nd edn. New York: McGraw-Hill, 1975. pp. 434467 Lachenbruch PA: An almost unbiased method of obtaining confidence intervals for the probability of misclassification in discriminant analysis. Biometrics 23: 639645, 1967 Mulcahy R, Hickey N, Graham I, McKenzie G: Factors influencing long-term prognosis in male patients surviving a first coronary attack. Br Heart J 37: 158-165, 1975 The Norwegian Multicentre Study Group: Timolol-induced reduction in mortality and reinfarction in patients surviving acute myocardial infarction. N Engl J Med 304: 801-807, 1981 Yusuf S, Rossi P, Ramsdale D, Peto R, Furse L, Motwani R, Parish S, Gray R, Bennett D, Bray C, chest pain and morbidity by early intravenous Sleight P: Reduction in infarct size, arrhythmias, /I-blockade in suspected acute myocardial infarction, Drugs 25 (Suppl. 2): 303-307, 1983 Beta-blocker Heart Attack Trial Research Group: A randomized trial of propranolol in patients with acute myocardial infarction I: Mortality results. JAMA 247: 170771714, 1982 May G’S, Furberg CD, Eberlein KA, Geraci BJ: Secondary prevention after myocardial infarction: A review of short-term acute phase trials. Prog Cardiovasc Dis 25: 335-359, 1982 Tatsuoka MM: In Selected topics in advanced statistics; an elementary approach. No. 6: Discriminant Analysis: the Study of Group Differences. Illinois: Insitute for Personality and Ability Testing, 1970. pp. l-57
APPENDIX Details of the calculation of the discriminant scores (DS) are given below. The numerical to analyses) for the different categories of the discriminating variables were as follows:
values assigned
(prior
(I) Chest X-ray in CCU (CXR): Presence of cardiomegaly and/or lung congestion = I; absence of either = 0. (2) Type of myocardial infarction (MITY): non Q wave = 1; Q wave = 0. (3) Change in R-wave amplitude in V, during exercise test (RLA): decrease = I, increase, no change or no R-wave in V, = 0. (4) History of myocardial infarction and/or angina 3 > months duration (HOMI): absent = 0; present = 1. (5) Angina during exercise test (ANG): absent = 0, present = 1. (6) Atria1 arrhythmia during exercise test (AT): absent = 0, present = I. The discriminant DS = 1.487021
function
equation
(CXR) + 1.014507
was as follows: (MITY)
+ 1.665806
(RLA) + 0.8515889 + 1.178666
(ANG)
(HOMI) + 2.987021
(AT) - 1.394238.
The last value (- 1.394238) is a constant in the equation. The DS for any individual can be calculated by substituting the appropriate value for CXR, MITY, RLA, etc. The coefficients for each variable in the equation are referred to as unstandardised discriminant function coefficients. These coefficients are used for computation of the discriminant scores and do not denote the relative importance of the variables since they have been adjusted for the measurement scales and variability in the original variables (cf. with standard discriminant function coefficients). The mathematical objective of discriminant analyses is to weight and form one or more linear combinations of the discriminating variables so as to define groups which are statistically distinct as possible [15]. The resultant discriminant equations are of the form D, = d,,Z, + d,*Z, + + di,,Z,, where Di is the discriminant score on the discriminant function i, the d’s are the weighting (discriminant function) coefficients and the Z, are the values of the p discriminating variables used in the analyses. The maximum number of discriminant functions which can be derived is one less than the number of groups or equal to the number of discriminating variables, if there are more groups than variables (present study: 2 groups; thus 1 discriminant function). The discriminant function coefficients are derived by solving the general eigenvector problem WA = Ba, where B and W are, respectively, the between-group and within-group sums of squares and cross-products matrices (refer [15, 221 for further details). A stepwise selection method was used in the present study. The process begins by choosing the single variable which has the highest discriminating power between the two groups. This initial variable is then paired with each of the other available variables, one at a time, and the discriminant function analysis computed. The new variable which in conjunction with the initial variable produces the best discrimination is selected as the second variable to “enter the equation”. These two are then combined with each of the remaining variables, one at a time, to form triplets which are evaluated in a similar manner. The triplet with the best discriminating power determines the third variabIe to be selected. This procedure of locating the next variable that would yield the best discrimination given the variables already selected, continues until all variables are selected or no additional variables provide a minimum level of improvement. As variables are selected for inclusion, some variables previously selected may lose their discriminating power. This occurs because the information that they contain about group differences is now available in some combination of the other included variables. Such variables are redundant and are eliminated. Thus, at the beginning of each step, each of the previously selected variables is tested to determine if it still makes a significant contribution to discrimination. If any are eligible for removal, the least useful is eliminated. A variable which has been removed at one step may re-enter at a later step if it satisfies the selection criterion at that time. The stepwise selection criterion used in the present study was RaO’s V, a generalised distance measure. The variable selected was the one which contributes to the largest increase in RaO’s V when added to the previous variables. (This amounts to the greatest overall separation of the groups.) However, a variable was included in
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to the discriminant function equation only if its partial multivariate F ratio (a measure of the discrimination introduced by the new variable after taking into account the discrimination already achieved by the other already selected variables) was greater than 1.0. At each step a similar test was made of all variables already selected. Here, the test was whether the particular variable still added a significant amount to the separation, given the other variables now in the equation. As more variables are selected, it is possible that some of those entered earlier may no longer be contributing to the separation. Again a multivariate partial F-test of the discriminating power added by the variable in question at that stage was performed and the variable removed if the F ratio was less than 1.0. The program also calculated the canonical correlation coefficient for the discriminant function. This is a measure of the ability of the discriminant function to discriminate between the groups. The square of the canonical correlation coefficient is the proportion of the variance in the discriminant function explained by the groups [12].