Decision
0. PAHLM,*
Rules for the ECG Diagnosis Myocardial infarction
D. CASE,? G. HOWARD,?
J. POPEA
of Inferior
AND W. K. HAISI.Y+
Received August Il. 1989
ECG measurements from 341 patients with inferior myocardial infarction (IMU and 327 normal subjects were used to develop and test decision rules for the ECG diagnosis of IMI. Recursive partitioning provided a simple decision rule with 75% sensitivity and 97% specificity, using Q amplitude and Q duration in aVF, Q duration in III, and T-wave axis in the frontal plane as decision variables. Dropping T-wave axis from the decision rule led to a 10% decrease in sensitivity. Multiple logistic regression provided sensitivities and specilicities which were similar to those for recursive partitioning. Both methods outperformed traditional noncontour criteria for IMI. ar 1990 Academic Press. hc.
The 12-lead electrocardiogram (ECG) is the most readily available method for diagnosing healed myocardial infarction (MI). ECG criteria for inferior MI reported in the literature usually have high specificity. Reported sensitivities range from 4% (1, 2) to 94% (3). These widely varying values may be due to inherent differences between the ECG criteria, but also to differences between the studied populations. In the development of criteria for ECG diagnosis, multiple linear discriminant techniques (4) as well as heuristic approaches have been used. In recent years recursive partitioning, a nonparametric classification method, has been tried for medical diagnosis and prognostication (5, 6). The purpose of the present study is to compare the utility of recursive partitioning and that of logistic regression for developing decision rules for the ECG diagnosis of inferior MI. A secondary purpose is to compare the performance of these decision rules to the performance of some published heuristic decision rules. MATERIALS
AND METHODS
Study Subjects Between November 2, 1981, and July 1, 1984,4822 subjects with a history of chest pain underwent coronary angiography and left ventriculography at North 332 OOlO-4809/90 $3.00 Copyright All rights
0 1994 by Academic Press. Inc. of reproduction in any form reserved.
ECG DIAGNOSIS
OF INFERIOR
333
INFARCTION
Carolina Baptist Hospital (Bowman Gray School of Medicine), Winston-Salem, North Carolina. After excluding subjects with ventricular preexcitation, valvular heart disease, or prior cardiac surgery, two study groups were selected. The ZMZ group (n = 341) included subjects with akinesia or dyskinesia of the basal inferior or basal inferior plus middle inferior wall segments (7) in the right anterior oblique (RAO) ventriculogram and >75% luminal narrowing of the corresponding coronary artery. Subjects with akinesia or dyskinesia also in other regions of the heart were not included in the group. Ages ranged from 25 to 79 years with a median of 56; 48 (14%) of the subjects were female. The normal group (n = 327) included subjects with no wall motion abnormalities in the RAO ventriculogram and a normal coronary angiogram. Ages ranged from 18 to 73 years with a median of 49; 185 (57%) of the subjects were female. Electrocardiographic
Measurements
A 12-lead ECG was recorded on each subject, less than 1 week prior to the angiographic investigation, using a computerized electrocardiograph (Marquette Electronics, Inc., Milwaukee, WI). Measurements of ECG waveforms were made with the Marquette 12-SL program on an IBM-AT-compatible microcomputer, and the measurements were transferred to a MicroVAX II for statistical evaluation. Twenty-nine different ECG measurements were considered in this study (Table 1). In addition to amplitudes and durations of Q waves and R waves in the limb leads, measurements were included from Vl, V5, and V6; these leads may be influenced if posterior or lateral extension of the infarct is present. In addition T wave axis and QRS axis in the frontal plane and QRS duration were considered. Learning-Test
Set Allocation
For the development and testing of decision rules, the subjects were randomized into a learning set of approximately two-thirds of the subjects (210 normals, 222 IMI patients) and a test set of approximately one-third of the subjects (117 normals, 119 patients). TABLE ECG
VARIABLES
1
CONSIDERED IN THE INFE~OR INFARCTION
PREDICTION
QRS axis in frontal plane T-wave axis in frontal plane QRS duration Q duration in leads I, II, III, aVL, aVF, VS, V6 Q amplitude in leads I, II, III, aVL, aVF, V5, V6 R duration in leads I, II, III, aVL, aVF, Vl R amplitude in leads I, II, III, aVL, aVF, Vl
OF
uil Recursive
PAHLM
tl
\i
Partitioning
Recursive partitioning (5) is a classification procedure in which a training set is repeatedly divided into smaller subgroups based on binary splits of selected decision variables (e.g.. Q-wave duration in lead aVF). Initially. the binary split of each variable under study that maximizes the “purity” (defined by the socalled Gini criterion) of the resulting classification is selected. The variable that gives the purest split of all variables studied is then used to divide the yet into two subgroups. This process is repeated recursively for each subsequent subgroup until each terminal node contains no more than five subjects, or until all subjects are classified correctly. The decision tree is then simplified on the basis of misclassification cost (i.e., cost of classifying normal as infarct or infarct as normal) and complexity (i.e., the number of terminal nodes). resulting in several subtrees. The “best” of these trees is chosen on the basis of misclassification costs determined using lo-fold cross-validation. Sensitivity and specificity are calculated in both the learning and the test sets. Misclassitication costs are adjusted to give high specificity. The “relative importance” of each variable is determined on the basis of the amount of impurity reduction attributed to that variable for the entire tree. The analysis was done using the interactive computer program CART (Classification and Regression Trees), distributed by California Statistical Software. Inc. (Lafayette, CA). Logistic
Regression
Multiple logistic regression was employed to establish the parametric relationship between the ECG measurements and the presence or absence of infarction. This technique fits a linear function to the log-odds of an infarction, LN(pI(l
- p)) = B, + B,X,
+ B2X2 + . . . + B,X, ,
where p is the probability of infarction, Bj is the ith unknown parameter (estimated by the procedure), and Xi is the ith ECG measurement. The selection of the subset of variables considered as optimal predictors was performed in two stages. In the first stage, standard forward and/or backward stepwise procedures were used. The forward stepwise procedure begins with no variables in the model. evaluates the significance of each, and selects the most significant one to be added to the model. The significance of each variable not in the model is evaluated after “controlling” for the variable in the model and the most significant one is added to the model. This procedure is continued until all significant variables are included in the model. The backward stepwise procedure begins with all variables in the model, and sequentially removes nonsignificant variables until only significant ones remain. During the second stage of the analysis the significance of interaction terms between those variables selected was evaluated. Once significant interactions were included. the forward and/or reverse stepwise procedure was again applied to ensure that no signifi-
ECG DIAGNOSIS
OF INFERIOR
335
INFARCTION
cant variables were omitted from the model and that all nonsignificant variables were removed. All testing was performed at an a! of 0.05. Given the logistic function relating the log-odds of an infarction to ECG measurements, the predicted probability that a particular patient had an infarction may be determined. Arbitrary “cutpoints” for the probability were used to classify individual subjects as infarcted or normal. The sensitivity and specificity were determined for each cutpoint and a Receiver Operating Characteristic (ROC) curve was generated to illustrate the performance of the logistic model. The T-axis variable was coded over the range -90” to 270”, as data in the region of the breakpoint (- 90/270) were quite sparse. Polynomial forms of T axis were also considered in the logistic model. The analysis was performed using the LOGIST procedure of the SAS (Statistical Analysis System, Cary, NC) package. RESULTS
Recursive Partitioning The CART program was first run using all ECG variables listed in Table 1 as input. Misclassification cost ratios (normal as infarct vs infarct as normal) of 3/l, 5/I, and 10/l were used in tree construction. Table 2A presents the variables selected and the resulting performance on the learning and test sets. For all
TABLE DATA
cost No.
ratio
Selected variables
2
ON DECISION
TREES
No. of nodes
Learning set (sens./spec.)
Test set (sens.ispec.)
A. Tree grown using all ECG variables 311 qdF, tax, qdL, qd2, ra2 6 0.8710.94 0.8210.91 S/l qdF, tax, qd3 4 0.75/0.97 0.7610.93 10/l qdF, tax, qa2 4 0.65/0.99 0.6310.97 B. Tree grown using the following five variables: Q duration in aVF and III, Q amplitude in aVF and III, and T-wave axis in the frontal plane 4 311 qdF, tax, qaF, qd3 6 0.79/0.96 0.8010.93 5 qdF, tax, qaF, qd3 5 0.71/0.98 0.7510.97 S/l 6 10/l qdF, tax, qaF 5 0.68/0.99 0.7010.96 C. Tree grown using the following four variables: Q duration in aVF and III and Q amplitude in aVF and III 7 3/l 4 0.7310.95 0.71/0.95 qdF, qd3, qaF 8 511 qdF, qd3, qaF 6 0.6510.99 0.65lO.97 9 10/l 3 0.55/1.00 0.5510.97 qdF, qaF 1 2 3
Note. qdF = Q duration in aVF; tax = T-wave axis in the frontal plane; qdL = Q duration in aVL; qd2 = Q duration in II; qd3 = Q duration in III; qa2 = Q amplitude in II.
.iM
PAHLM , / Is 0 duration
IMI
NORMAL
t.7 II
in aVF
> 28 msec?!
NORMAL
IMI
FIG. I. Decision tree determined when CART algorithm considered all ECG variables.
three misclassification cost ratios Q durations in aVF and III, Q amplitudes in aVF and III, and T-wave axis in the frontal plane were always among the six most important variables. Figure I shows the tree determined using a 3/l misclassification cost ratio. The first split is on Q duration in aVF. For subjects with a Q duration exceeding 28 msec the decision rule assesses Q duration in aVL and classifies subjects with a duration less than or equal to 18 msec as infarcts. The subjects with a longer Q duration in aVL are next split by looking at Q duration in Lead II. Subjects with Q duration less than or equal to 28 msec in aVF are split on the T-wave axis in the frontal plane; those with a positive T-wave axis are considered normal. Subjects with a negative T-wave axis are finally split on R-wave amplitude in lead II. Specificities were 94% in the learning set and 91% in the test set; sensitivities were 78 and 82%, respectively. Decision trees constructed using the five most important variables only are presented in Table 2B. Figure 2 shows the tree determined when the misclassification cost ratio is set at 5/l. The first split is again on Q duration in aVF. For subjects with a Q wave wider than 28 msec the decision rule looks at the Qwave amplitude in aVF. For subjects with a Q width less than or equal to 28 msec the decision rule assesses the T-wave axis in the frontal plane and classifies those subjects with a positive Taxis as normal. Subjects with a negative Taxis are finally checked for Q duration in III. Specificities were 98% in the learning set and 97% in the test set. Sensitivities were 71 and 75%, respectively. Table 2C presents the results obtained when Taxis is excluded from the tree construction. Figure 3 shows the resulting tree when the misclassification cost ratio is set at 5/I.
ECG DIAGNOSIS
OF INFERIOR
Is Q duration
Is T-axis
Is 0 duration
> 0’7
in Ill > 22 msec?
337
INFARCTION
in aVF > 28 msec?
Is Q amplitude in aVF > 119 N?
NORMAL
IMI
NO&AL FIG. 2. Decision tree determined when CART algorithm considered five variables: Q amplitude in aVF and III, Q duration in aVF and III, and T-wave axis in the frontal plane.
Figure 4 summarizes the performance of the nine different classification trees. The figure also presents the performance of the following criteria: Hl: Q duration 2 30 ms and Q/R ratio 2 0.25 in leads aVF and III (I) H2: Q duration 2 30 ms in leads aVF and III H3: Q duration 2 30 ms in lead aVF (8). It is noted that the decision trees determined by all ECG variables do not outperform the trees determined by fewer (five or four) ECG variables, at least not on the independent test set. The five-variable tree presented in Fig. 2 (tree No. 5) seems to have the best overall performance, yielding 75% sensitivity and 97% specificity in the test set. Logistic Regression
Three separate models were considered. The first model used the stepwise algorithms to build the “best” model from the 29 available ECG variables. The second model was restricted to those variables traditionally considered to be the best predictors (Q amplitudes and Q durations in aVF and III). In addition, these four variables were an attractive choice as they are among the most significant univariately by logistic regression. The final model considered these four factors in conjunction with T-axis, a variable traditionally not employed as a primary diagnostic indicator, but one which was among the top five univariate predictors in our learning set. In the unrestricted model (free to select variables from the entire set) Q
1’AHI.M t-l 1 Is Cl duration
in aVF ,”
No
,,,A
-I-’
\i > 32 tnsec? --._ ._
,
Yes ._
Is Q amplitude
NORMAL
MI
NORMAL
‘-b in aVF
> 146,uV?
;
IMI
FIG. 3. Decision tree determined when CART algorithm considered four variables: Q amplitude in aVF and III and Q duration in aVF and III.
amplitude and Q duration in II, R amplitude in lead II, Q duration in III and VS, QRS duration, and a cubic polynomial in T axis were selected (all P (r 0.0046). In addition, a significant interaction between QRS duration and Q duration in III was found (P = 0.0012). No other interaction terms or variables proved significant (P > 0.05). The ROC curve associated with this model is presented in Fig. 5 and the estimated parameters are provided in Table 3. The model that jointly employs Q amplitudes and durations in III and aVF (but no T-axis information) was reduced to contain only factors for Q amplitude in aVF and Q duration in III, with estimated parameters provided in Table 4. All variables were highly significant (P % 0.0001). The interaction between these factors, as well as their quadratic terms, were nonsignificant (P > 0.05). The ROC curve associated with this model is presented in Fig. 5. Similarly, the model that jointly employs Taxis and the variables mentioned above was reduced to contain factors for Q-wave amplitude in aVF and Q duration in III and a cubic polynomial for T axis. Unlike the previous model, an interaction term between Q amplitude in aVF and Q duration in III was statistically significant (P = 0.0095), and a quadratic form was required to model T axis (P I 0.0001). Parameter estimates and standard errors are provided in Table 5, and the ROC curve is provided in Fig. 5. T-wave axis in the frontal plane had an unexpectedly large impact on the prediction of infarction. With T axis values below -30” or above 150” the estimated probability of infarction is almost 100% regardless of the other factors in the model. Only between this range did the Q-wave amplitude in aVF or the
ECG DIAGNOSIS
OF INFERIOR
1NFARCTION
339
0.95.
0.90.
1
s 0.05. E N S 1 0.80.
/
T I ;
2
A
0.75.
T Y
‘b
P
0.70. A
I20 msec (m = 45) specificity was similar to that obtained for all subjects, but there was a IO-15% reduction in sensitivity. It should be noted, however, that the number of subjects with a wide QRS complex is rather small and that this finding may not persist in a larger study population. It should be pointed out that there may be systematic differences between different methods of calculating wavelet durations and amplitudes as well as Twave axis in the frontal plane. The measurements used in the present study were made by algorithms equivalent to those in commercially available, computer-based ECG recorders. Measurements made by algorithms implemented in other recorders, or made visually, may produce results that are different from the ones presented here and that may affect the performance of the decision rules. REFERENCES 1. HURD, H. P., II. STARLING, M. R., CRAWFORD. M. H., DLABAL, P. W.. AND O’ROUKKE. R. A. Comparative accuracy of electrocardiographic and vectorcardiographic criteria for inferior myocardial infarction. Circulation 63, 1025 (1981). 2. MYERS, G. B., KLEIN, H. A., AND HIRATZKAS, T. V. Correlation of electrocardiographic and pathologic findings in posterior infarction. Amer. Heart J. 38, 547 (1949). 3. WARNER, R., HILL, N. E., SHEEHE, P. R., MOOKHERIEE, S., FRUEHAN. T.. AND SMUI.YAN. H. Improved electrocardiographic criteria for the diagnosis of inferior myocardial infarction. Circulation
66, 422 (1982).
4. PIPBERGER, H. V. Methods of diagnostic ECG classification. 11, “Computer Applicalion in ECG and VCG Analysis” (C. Zywietz and B. Schneider, Eds.). pp. 296-306. North-Holland. Amsterdam, 1973. 5. BRIEMAN, L., FRIEDMAN, J. H., OLSHEN, R. A., AND STONE, C. J. “Classification and Regression Trees.” Wadsworth, Belmont. CA. 1984. 6. COOK, E. F., AND GOLDMAN, L. Empiric comparison of multivariate analytic techniques: Advantages and disadvantages of recursive partitioning analysis. J. Chronic Dis. 17,721 (1984). 7. WAGNER. G. S., COWAN. M. J., FLOWERS, N. C., GINZTON, L. E., LAKS, M. M.. SELVESTER R. H.. AND SWIRYN, S. R. Report of Committee on Nomenclature of Myocardial Wall Segments. “Proceedings, 1983 Engineering Foundation Conference on Computerized Interpretation of the ECG.” pp. 361-369. Engineering Foundation Press. New York. 1984.
ECG
DIAGNOSIS
OF
INFERIOR
INFARCTION
345
8. ANDERSON, W. D., WAGNER, N. B., LEE, K. L., WHITE, R. D., YUSCHAK, J., BEHAR, V. S., SELVESTER, R. H., IDEKER, R. E., AND WAGNER, G. S. Evaluation of a QRS system for estimating myocardial infarct size. VI. Identification of screening criteria for non-acute myocardial infarcts. Amer. J. Curdiol. 61, 729 (1988). 9. ABREU-LIMA, C., CORREIA, D. M., ALMEIDA, J., ANTUNES-LOPES, M., AND CERQUEIRAGOMES, M. A new ECG classification system for myocardial infarction based on receiveroperating characteristic curve analysis and information theory. Circulation 67, 1252 (1983). 10. WARNER, R. A., HILL, N. E., AND LYNCH, T. Usefulness of abnormalities of repolarization in the electrocardiographic diagnosis of healed myocardial infarction. J. Electrocardiol. 21, S93 (1988). 11. EISENSTEIN, I., SANMARCO, M. E., MADRID, W. L., AND SELVESTER, R. H. Electrocardiographic and vectorcardiographic diagnosis of posterior wall myocardial infarction. Significance of the T wave. Chest 88, 409 (1985).
0. PAHLM,*
Rules for the ECG Diagnosis Myocardial infarction
D. CASE,? G. HOWARD,?
J. POPEA
of Inferior
AND W. K. HAISI.Y+
Received August Il. 1989
ECG measurements from 341 patients with inferior myocardial infarction (IMU and 327 normal subjects were used to develop and test decision rules for the ECG diagnosis of IMI. Recursive partitioning provided a simple decision rule with 75% sensitivity and 97% specificity, using Q amplitude and Q duration in aVF, Q duration in III, and T-wave axis in the frontal plane as decision variables. Dropping T-wave axis from the decision rule led to a 10% decrease in sensitivity. Multiple logistic regression provided sensitivities and specilicities which were similar to those for recursive partitioning. Both methods outperformed traditional noncontour criteria for IMI. ar 1990 Academic Press. hc.
The 12-lead electrocardiogram (ECG) is the most readily available method for diagnosing healed myocardial infarction (MI). ECG criteria for inferior MI reported in the literature usually have high specificity. Reported sensitivities range from 4% (1, 2) to 94% (3). These widely varying values may be due to inherent differences between the ECG criteria, but also to differences between the studied populations. In the development of criteria for ECG diagnosis, multiple linear discriminant techniques (4) as well as heuristic approaches have been used. In recent years recursive partitioning, a nonparametric classification method, has been tried for medical diagnosis and prognostication (5, 6). The purpose of the present study is to compare the utility of recursive partitioning and that of logistic regression for developing decision rules for the ECG diagnosis of inferior MI. A secondary purpose is to compare the performance of these decision rules to the performance of some published heuristic decision rules. MATERIALS
AND METHODS
Study Subjects Between November 2, 1981, and July 1, 1984,4822 subjects with a history of chest pain underwent coronary angiography and left ventriculography at North 332 OOlO-4809/90 $3.00 Copyright All rights
0 1994 by Academic Press. Inc. of reproduction in any form reserved.
ECG DIAGNOSIS
OF INFERIOR
333
INFARCTION
Carolina Baptist Hospital (Bowman Gray School of Medicine), Winston-Salem, North Carolina. After excluding subjects with ventricular preexcitation, valvular heart disease, or prior cardiac surgery, two study groups were selected. The ZMZ group (n = 341) included subjects with akinesia or dyskinesia of the basal inferior or basal inferior plus middle inferior wall segments (7) in the right anterior oblique (RAO) ventriculogram and >75% luminal narrowing of the corresponding coronary artery. Subjects with akinesia or dyskinesia also in other regions of the heart were not included in the group. Ages ranged from 25 to 79 years with a median of 56; 48 (14%) of the subjects were female. The normal group (n = 327) included subjects with no wall motion abnormalities in the RAO ventriculogram and a normal coronary angiogram. Ages ranged from 18 to 73 years with a median of 49; 185 (57%) of the subjects were female. Electrocardiographic
Measurements
A 12-lead ECG was recorded on each subject, less than 1 week prior to the angiographic investigation, using a computerized electrocardiograph (Marquette Electronics, Inc., Milwaukee, WI). Measurements of ECG waveforms were made with the Marquette 12-SL program on an IBM-AT-compatible microcomputer, and the measurements were transferred to a MicroVAX II for statistical evaluation. Twenty-nine different ECG measurements were considered in this study (Table 1). In addition to amplitudes and durations of Q waves and R waves in the limb leads, measurements were included from Vl, V5, and V6; these leads may be influenced if posterior or lateral extension of the infarct is present. In addition T wave axis and QRS axis in the frontal plane and QRS duration were considered. Learning-Test
Set Allocation
For the development and testing of decision rules, the subjects were randomized into a learning set of approximately two-thirds of the subjects (210 normals, 222 IMI patients) and a test set of approximately one-third of the subjects (117 normals, 119 patients). TABLE ECG
VARIABLES
1
CONSIDERED IN THE INFE~OR INFARCTION
PREDICTION
QRS axis in frontal plane T-wave axis in frontal plane QRS duration Q duration in leads I, II, III, aVL, aVF, VS, V6 Q amplitude in leads I, II, III, aVL, aVF, V5, V6 R duration in leads I, II, III, aVL, aVF, Vl R amplitude in leads I, II, III, aVL, aVF, Vl
OF
uil Recursive
PAHLM
tl
\i
Partitioning
Recursive partitioning (5) is a classification procedure in which a training set is repeatedly divided into smaller subgroups based on binary splits of selected decision variables (e.g.. Q-wave duration in lead aVF). Initially. the binary split of each variable under study that maximizes the “purity” (defined by the socalled Gini criterion) of the resulting classification is selected. The variable that gives the purest split of all variables studied is then used to divide the yet into two subgroups. This process is repeated recursively for each subsequent subgroup until each terminal node contains no more than five subjects, or until all subjects are classified correctly. The decision tree is then simplified on the basis of misclassification cost (i.e., cost of classifying normal as infarct or infarct as normal) and complexity (i.e., the number of terminal nodes). resulting in several subtrees. The “best” of these trees is chosen on the basis of misclassification costs determined using lo-fold cross-validation. Sensitivity and specificity are calculated in both the learning and the test sets. Misclassitication costs are adjusted to give high specificity. The “relative importance” of each variable is determined on the basis of the amount of impurity reduction attributed to that variable for the entire tree. The analysis was done using the interactive computer program CART (Classification and Regression Trees), distributed by California Statistical Software. Inc. (Lafayette, CA). Logistic
Regression
Multiple logistic regression was employed to establish the parametric relationship between the ECG measurements and the presence or absence of infarction. This technique fits a linear function to the log-odds of an infarction, LN(pI(l
- p)) = B, + B,X,
+ B2X2 + . . . + B,X, ,
where p is the probability of infarction, Bj is the ith unknown parameter (estimated by the procedure), and Xi is the ith ECG measurement. The selection of the subset of variables considered as optimal predictors was performed in two stages. In the first stage, standard forward and/or backward stepwise procedures were used. The forward stepwise procedure begins with no variables in the model. evaluates the significance of each, and selects the most significant one to be added to the model. The significance of each variable not in the model is evaluated after “controlling” for the variable in the model and the most significant one is added to the model. This procedure is continued until all significant variables are included in the model. The backward stepwise procedure begins with all variables in the model, and sequentially removes nonsignificant variables until only significant ones remain. During the second stage of the analysis the significance of interaction terms between those variables selected was evaluated. Once significant interactions were included. the forward and/or reverse stepwise procedure was again applied to ensure that no signifi-
ECG DIAGNOSIS
OF INFERIOR
335
INFARCTION
cant variables were omitted from the model and that all nonsignificant variables were removed. All testing was performed at an a! of 0.05. Given the logistic function relating the log-odds of an infarction to ECG measurements, the predicted probability that a particular patient had an infarction may be determined. Arbitrary “cutpoints” for the probability were used to classify individual subjects as infarcted or normal. The sensitivity and specificity were determined for each cutpoint and a Receiver Operating Characteristic (ROC) curve was generated to illustrate the performance of the logistic model. The T-axis variable was coded over the range -90” to 270”, as data in the region of the breakpoint (- 90/270) were quite sparse. Polynomial forms of T axis were also considered in the logistic model. The analysis was performed using the LOGIST procedure of the SAS (Statistical Analysis System, Cary, NC) package. RESULTS
Recursive Partitioning The CART program was first run using all ECG variables listed in Table 1 as input. Misclassification cost ratios (normal as infarct vs infarct as normal) of 3/l, 5/I, and 10/l were used in tree construction. Table 2A presents the variables selected and the resulting performance on the learning and test sets. For all
TABLE DATA
cost No.
ratio
Selected variables
2
ON DECISION
TREES
No. of nodes
Learning set (sens./spec.)
Test set (sens.ispec.)
A. Tree grown using all ECG variables 311 qdF, tax, qdL, qd2, ra2 6 0.8710.94 0.8210.91 S/l qdF, tax, qd3 4 0.75/0.97 0.7610.93 10/l qdF, tax, qa2 4 0.65/0.99 0.6310.97 B. Tree grown using the following five variables: Q duration in aVF and III, Q amplitude in aVF and III, and T-wave axis in the frontal plane 4 311 qdF, tax, qaF, qd3 6 0.79/0.96 0.8010.93 5 qdF, tax, qaF, qd3 5 0.71/0.98 0.7510.97 S/l 6 10/l qdF, tax, qaF 5 0.68/0.99 0.7010.96 C. Tree grown using the following four variables: Q duration in aVF and III and Q amplitude in aVF and III 7 3/l 4 0.7310.95 0.71/0.95 qdF, qd3, qaF 8 511 qdF, qd3, qaF 6 0.6510.99 0.65lO.97 9 10/l 3 0.55/1.00 0.5510.97 qdF, qaF 1 2 3
Note. qdF = Q duration in aVF; tax = T-wave axis in the frontal plane; qdL = Q duration in aVL; qd2 = Q duration in II; qd3 = Q duration in III; qa2 = Q amplitude in II.
.iM
PAHLM , / Is 0 duration
IMI
NORMAL
t.7 II
in aVF
> 28 msec?!
NORMAL
IMI
FIG. I. Decision tree determined when CART algorithm considered all ECG variables.
three misclassification cost ratios Q durations in aVF and III, Q amplitudes in aVF and III, and T-wave axis in the frontal plane were always among the six most important variables. Figure I shows the tree determined using a 3/l misclassification cost ratio. The first split is on Q duration in aVF. For subjects with a Q duration exceeding 28 msec the decision rule assesses Q duration in aVL and classifies subjects with a duration less than or equal to 18 msec as infarcts. The subjects with a longer Q duration in aVL are next split by looking at Q duration in Lead II. Subjects with Q duration less than or equal to 28 msec in aVF are split on the T-wave axis in the frontal plane; those with a positive T-wave axis are considered normal. Subjects with a negative T-wave axis are finally split on R-wave amplitude in lead II. Specificities were 94% in the learning set and 91% in the test set; sensitivities were 78 and 82%, respectively. Decision trees constructed using the five most important variables only are presented in Table 2B. Figure 2 shows the tree determined when the misclassification cost ratio is set at 5/l. The first split is again on Q duration in aVF. For subjects with a Q wave wider than 28 msec the decision rule looks at the Qwave amplitude in aVF. For subjects with a Q width less than or equal to 28 msec the decision rule assesses the T-wave axis in the frontal plane and classifies those subjects with a positive Taxis as normal. Subjects with a negative Taxis are finally checked for Q duration in III. Specificities were 98% in the learning set and 97% in the test set. Sensitivities were 71 and 75%, respectively. Table 2C presents the results obtained when Taxis is excluded from the tree construction. Figure 3 shows the resulting tree when the misclassification cost ratio is set at 5/I.
ECG DIAGNOSIS
OF INFERIOR
Is Q duration
Is T-axis
Is 0 duration
> 0’7
in Ill > 22 msec?
337
INFARCTION
in aVF > 28 msec?
Is Q amplitude in aVF > 119 N?
NORMAL
IMI
NO&AL FIG. 2. Decision tree determined when CART algorithm considered five variables: Q amplitude in aVF and III, Q duration in aVF and III, and T-wave axis in the frontal plane.
Figure 4 summarizes the performance of the nine different classification trees. The figure also presents the performance of the following criteria: Hl: Q duration 2 30 ms and Q/R ratio 2 0.25 in leads aVF and III (I) H2: Q duration 2 30 ms in leads aVF and III H3: Q duration 2 30 ms in lead aVF (8). It is noted that the decision trees determined by all ECG variables do not outperform the trees determined by fewer (five or four) ECG variables, at least not on the independent test set. The five-variable tree presented in Fig. 2 (tree No. 5) seems to have the best overall performance, yielding 75% sensitivity and 97% specificity in the test set. Logistic Regression
Three separate models were considered. The first model used the stepwise algorithms to build the “best” model from the 29 available ECG variables. The second model was restricted to those variables traditionally considered to be the best predictors (Q amplitudes and Q durations in aVF and III). In addition, these four variables were an attractive choice as they are among the most significant univariately by logistic regression. The final model considered these four factors in conjunction with T-axis, a variable traditionally not employed as a primary diagnostic indicator, but one which was among the top five univariate predictors in our learning set. In the unrestricted model (free to select variables from the entire set) Q
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FIG. 3. Decision tree determined when CART algorithm considered four variables: Q amplitude in aVF and III and Q duration in aVF and III.
amplitude and Q duration in II, R amplitude in lead II, Q duration in III and VS, QRS duration, and a cubic polynomial in T axis were selected (all P (r 0.0046). In addition, a significant interaction between QRS duration and Q duration in III was found (P = 0.0012). No other interaction terms or variables proved significant (P > 0.05). The ROC curve associated with this model is presented in Fig. 5 and the estimated parameters are provided in Table 3. The model that jointly employs Q amplitudes and durations in III and aVF (but no T-axis information) was reduced to contain only factors for Q amplitude in aVF and Q duration in III, with estimated parameters provided in Table 4. All variables were highly significant (P % 0.0001). The interaction between these factors, as well as their quadratic terms, were nonsignificant (P > 0.05). The ROC curve associated with this model is presented in Fig. 5. Similarly, the model that jointly employs Taxis and the variables mentioned above was reduced to contain factors for Q-wave amplitude in aVF and Q duration in III and a cubic polynomial for T axis. Unlike the previous model, an interaction term between Q amplitude in aVF and Q duration in III was statistically significant (P = 0.0095), and a quadratic form was required to model T axis (P I 0.0001). Parameter estimates and standard errors are provided in Table 5, and the ROC curve is provided in Fig. 5. T-wave axis in the frontal plane had an unexpectedly large impact on the prediction of infarction. With T axis values below -30” or above 150” the estimated probability of infarction is almost 100% regardless of the other factors in the model. Only between this range did the Q-wave amplitude in aVF or the
ECG DIAGNOSIS
OF INFERIOR
1NFARCTION
339
0.95.
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/
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2
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I20 msec (m = 45) specificity was similar to that obtained for all subjects, but there was a IO-15% reduction in sensitivity. It should be noted, however, that the number of subjects with a wide QRS complex is rather small and that this finding may not persist in a larger study population. It should be pointed out that there may be systematic differences between different methods of calculating wavelet durations and amplitudes as well as Twave axis in the frontal plane. The measurements used in the present study were made by algorithms equivalent to those in commercially available, computer-based ECG recorders. Measurements made by algorithms implemented in other recorders, or made visually, may produce results that are different from the ones presented here and that may affect the performance of the decision rules. REFERENCES 1. HURD, H. P., II. STARLING, M. R., CRAWFORD. M. H., DLABAL, P. W.. AND O’ROUKKE. R. A. Comparative accuracy of electrocardiographic and vectorcardiographic criteria for inferior myocardial infarction. Circulation 63, 1025 (1981). 2. MYERS, G. B., KLEIN, H. A., AND HIRATZKAS, T. V. Correlation of electrocardiographic and pathologic findings in posterior infarction. Amer. Heart J. 38, 547 (1949). 3. WARNER, R., HILL, N. E., SHEEHE, P. R., MOOKHERIEE, S., FRUEHAN. T.. AND SMUI.YAN. H. Improved electrocardiographic criteria for the diagnosis of inferior myocardial infarction. Circulation
66, 422 (1982).
4. PIPBERGER, H. V. Methods of diagnostic ECG classification. 11, “Computer Applicalion in ECG and VCG Analysis” (C. Zywietz and B. Schneider, Eds.). pp. 296-306. North-Holland. Amsterdam, 1973. 5. BRIEMAN, L., FRIEDMAN, J. H., OLSHEN, R. A., AND STONE, C. J. “Classification and Regression Trees.” Wadsworth, Belmont. CA. 1984. 6. COOK, E. F., AND GOLDMAN, L. Empiric comparison of multivariate analytic techniques: Advantages and disadvantages of recursive partitioning analysis. J. Chronic Dis. 17,721 (1984). 7. WAGNER. G. S., COWAN. M. J., FLOWERS, N. C., GINZTON, L. E., LAKS, M. M.. SELVESTER R. H.. AND SWIRYN, S. R. Report of Committee on Nomenclature of Myocardial Wall Segments. “Proceedings, 1983 Engineering Foundation Conference on Computerized Interpretation of the ECG.” pp. 361-369. Engineering Foundation Press. New York. 1984.
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DIAGNOSIS
OF
INFERIOR
INFARCTION
345
8. ANDERSON, W. D., WAGNER, N. B., LEE, K. L., WHITE, R. D., YUSCHAK, J., BEHAR, V. S., SELVESTER, R. H., IDEKER, R. E., AND WAGNER, G. S. Evaluation of a QRS system for estimating myocardial infarct size. VI. Identification of screening criteria for non-acute myocardial infarcts. Amer. J. Curdiol. 61, 729 (1988). 9. ABREU-LIMA, C., CORREIA, D. M., ALMEIDA, J., ANTUNES-LOPES, M., AND CERQUEIRAGOMES, M. A new ECG classification system for myocardial infarction based on receiveroperating characteristic curve analysis and information theory. Circulation 67, 1252 (1983). 10. WARNER, R. A., HILL, N. E., AND LYNCH, T. Usefulness of abnormalities of repolarization in the electrocardiographic diagnosis of healed myocardial infarction. J. Electrocardiol. 21, S93 (1988). 11. EISENSTEIN, I., SANMARCO, M. E., MADRID, W. L., AND SELVESTER, R. H. Electrocardiographic and vectorcardiographic diagnosis of posterior wall myocardial infarction. Significance of the T wave. Chest 88, 409 (1985).
