Vol. 52, No. 3
Printed in U.S.A.
T H E AMERICAN JOURNAL OF CLINICAL PATHOLOGY
Copyright © 1969 by Tho Williams & Wilkins Co.
SERUM LACTATE DEHYDROGENASE ISOENZYME AND TOTAL
LACTATE DEHYDROGENASE VALUES IN HEALTH AND DISEASE,
AND CLINICAL EVALUATION OF THESE TESTS BY MEANS OF
DISCRIMINANT ANALYSIS
JOHN H. CLICK, J R . , P H . D .
Department of Pathology and Oncology, Division of Clinical Laboratories,
University of Kansas Medical Center, Kansas City, Kansas 66108
ABSTRACT
Click, John H., Jr.: Serum lactate dehydrogenase isoenzyme and total lactate dehydrogenase values in health and disease, and clinical evaluation of these
tests by means of discriminant analysis. Am. J. Clin. Path., 52: 320-32S,
1969. Data concerning the lactate dehydrogenase isoenzyme and total lactate
dehydrogenase values for normals and various disease states are presented.
Analysis of some of these data by means of a computerized discriminant function program indicated that the above enzyme assays are useful in the differential diagnosis of infectious hepatitis, infectious mononucleosis, myocardial
infarction, and lung cancer. The usefulness of these assays for other diagnostic
situations was not investigated by this method. The use of discriminant analysis
as an aid to laboratory medicine is discussed and illustrated with respect to
the enzyme values in the following ways: (1) the reasons and the method for
using discriminant analysis; (2) its application for evaluating the diagnostic
usefulness of a test or group of tests; (3) its application for the differential diagnosis of a particular clinical state; and (4) the limitations of discriminant analysis
for these applications.
The use of lactic dehydrogenase (LDH)
isoenzyme patterns in clinical medicine is
well established, and a number of papers
have listed the patterns found in normals and
in various disease states. 1 " 3 ' 7 " 9 The present
study, which utilizes LDH isoenzyme and
total LDH values determined on sera from
patients at our medical center, was undertaken with two objectives in mind: first, to
establish statistical limits for the LDH isoenzyme and total LDH values in normals
and in different disease states; and, second,
to investigate the usefulness of these enzyme
assays in confirming some common diagnoses. This latter objective was studied by
means of discriminant analysis.6
MATERIALS AND METHODS
Enzyme assays. Serum LDH isoenzymes
were measured according to the method of
Received December 23, 1968.
This study was supported in part by National
Institutes of Health General Research Support
Grant No. 5-SO1-FR-05373-07.
Wright and associates.9 Serum total LDH
was determined by the procedure of Henry. 4
The usual specimen was serum obtained
after an overnight fast.
Data. A total of 650 LDH isoenzyme patterns was available, consisting of all results
obtained during a period of IS months on
hospitalized patients and outpatients. In
most of these cases, a total LDH measurement was also made on the same specimen
(or a second specimen which had been drawn
at the same time). The 650 isoenzyme patterns included some within-run duplicate
analyses of the same specimen, and some
series obtained on different days from the
same patients.
Dismissal diagnoses, coded according to
the Standard Nomenclature of Diseases and
Operations, were available for 510 of the
patients. These diagnoses were made by staff
physicians who were in charge of the cases.
Processing of data. The five LDH isoenzyme percentages, total LDH value, and
specimen identification information for each
320
Sept.
1969
EVALUATION OF LDH ISOENZYME AND TOTAL LDH TESTS
case were transferred to a separate punched
card. The series of cards obtained in this way
for all cases is referred to as the enzyme data
deck. Dismissal diagnoses and hospital number for each hospitalized patient included in
the study were obtained from the medical
records department on a second punched
card. The resulting series of cards constitutes
the diagnosis deck. The two decks of punched
cards thus obtained were used to produce the
following lists: tests results, by patient;
diagnoses, by patient; and the number and
type of each diagnosis encountered in the
study. These lists were generated on the
University Computing System with the aid
of Fortran IV programs written for this purpose. The lists were used to select cases for
the various calculations involved in the investigation.
The selection of cases from these lists was
based on the following criteria: (a) a given
patient was included only once in a calculation; (b) when a choice had to be made between duplicate results on the same specimen, or among several results from one
patient, it was done in a random manner;
(c) in selecting cases for inclusion in a specific
disease category, all cases which met one of
the following two criteria were included: (1)
those cases in which only the one specific
disease was listed in the dismissal diagnosis,
or (2) when other diseases were listed along
with the specific disease in question, the case
was included only if all of the other listed
diseases in the dismissal diagnosis gave mean
values for LDH isoenzymes and total LDH
within the normal range.
Punched cards corresponding to the cases
chosen in the above manner were then drawn
from the enzyme data deck for further processing. Most of the calculations were performed using the Biomedical Computer
Programs of the University of California
(BMD, version of September 1965), on the
University Computing System.
HESULTS
AND
DISCUSSION
Precision of Methods
Table 1 gives the precision in measuring
the LDH isoenzyme percentages and total
LDH units. Data are listed for both withinrun and day-to-day reproducibility. The
321
calculated standard deviations for the isoenzymes are based on the following data:
within-run—28 pairs of duplicate measurements on patient sera, each pair being obtained from a different run; between runs—
seven thawed aliquots of a frozen pooled
specimen measured during a period of 1
month, and 10 reconstituted aliquots of a
commercial lyophilized control serum analyzed during a 6-week period. The calculated standard deviations for the total LDH
measurements were derived from the followTABLE 1
CALCULATED STANDARD D E V I A T I O N S FOR S I N G L E
M E A S U R E M E N T S OF L D H ISOENZYME AND
TOTAL L D H VALUES*
Standard Deviationf
Between runs
LDH Isoenzyme
Within
run
1
2
3
4
5
Total L D H
1.75
1.09
1.72
1.12
0.73
35.5
Frozen
pool
Lyophilized
pool
4.20
2.12
2.65
1.81
1.11
60.4
3.76
2.97
1.01
0.S4
0.07
* The analyses upon which this table is based
are described in the text.
t Values for L D H isoenzymes are expressed as
percentage of total L D H , and values for total
L D H are given in units per ml.
TABLE 2
N O R M A L R A N G E FOR SERUM T O T A L L D H
L D H ISOENZYME V A L U E S *
As Percent
of Total
AND
As U./ml.
LDH Isoenzyme
1
2
3
4
5
Total L D H
Mean
S.D.
Mean
S.D.
32
36
24
5.5
3.5
3.0
1.5
1.5
120
155
112
21
12
431
29
30
33
10
6
90
4
3
* T h e analyses upon which this table is based
and the methods for calculations are described in
t h e text.
322
Vol. 52
GLICK
ing: within run— 9 9 pairs of duplicate
measurements on various specimens of reconstituted lyophilized control sera, measured during a period of 1 montli; between
runs—30 aliquots of a frozen serum pool,
measured during a 1-month interval.
Range of Values for Normals and Various
Diseases
Table 2 lists the normal limits for single
determinations of the LDH isoenzyme percentages, total LDH units, and LDH isoenzyme units. These values were calculated
TABLE 3
M E A N AND STANOAUD E R R O R O F S E R U M T O T A L L D H
AND L D H
ISOENZYMES IN
VAUIOUS D I S E A S E S *
LDH Isoenzyme!- X
Diagnosis
No. of
Cases
Total LDHf
l
2
3
4
5
U./ml
Anemia, hypochromic,
microcytic
Anemia, pernicious
3
Arteriosclerotic h e a r t
disease
Bronchitis, chronic
11
Cancer, colon
2
9
4
Cancer—liver, gallbladder, pancreas
Cancer, lung
10
Cirrhosis, liver
10
Common bile duct obstruction
Diabetes mellitus
Emphysema, obstructive
Glomerulonephritis,
chronic
H e a r t congestion, p a s sive
H e p a t i t i s , chronic
6
3
5
10
3
12
2
H e p a t i t i s , infectious
7
Hodgkin's disease
6
Leukemia, granulocytic
Leukemia, lymphocytic
4
Lupus erythematosus
5
Mononucleosis, infec-
5
3
tious
Muscular dystrophy,
progressive
4
412(37)
28.0(1.7)
-0.1(0.6)
3212(2232) 42.0(2.0)
40.9(30.1)
30.9(1.7)
471(58)
1.0(0.8)
370(20)
29.0(1.6)
-0.5(0.2)
015(221)
23.2(2.4)
0.3(1.0)
647(85)
22.8(1.7)
1.1(1.0)
2097(1076) 28.2(3.0)
11.5(5.2)
567(70)
27.3(2.0)
1.2(0.8)
488(52)
21.7(4.4)
-0.4(1.1)
30.2(1.5)
494(36)
1.0(0.3)
468(57)
27.7(2.3)
0.1(0.5)
564(70)
33.3(5.3)
2.6(2.0)
30.6(2.9)
801(164)
4.8(2.9)
659(91)
24.0(0.0)
1.3(0.7)
13.0(2.5)
2057(901)
2.4(1.3)
25.3(3.7)
715(203)
1.3(0.9)
750(202)
34.0(5.3)
3.8(1.2)
645(114)
26.3(3.2)
1.6(0.9)
26.2(3.1)
486(58)
0.3(0.8)
22.6(3.0)
1452(258)
6.8(1.9)
960(132)
34.2(5.3)
6.5(0.6)
31.0(3.5)
-0.7(0.6)
33.0(0.0)
28.9(25.8)
35.3(1.5)
0.3(0.6)
37.3(1.4)
-0.5(0.2)
39.5(3.6)
2.3(2.2)
31.8(1.4)
1.3(0.7)
36.8(2.1)
17.8(12.1)
34.6(1.3)
1.2(0.8)
30.7(3.5)
-0.1(0.8)
33.8(1.0)
0.3(0.4)
34.5(1.6)
0.1(0.4)
33.7(1.8)
0.9(0.4)
28.8(2.4)
1.5(1.2)
30.5(0.5)
1.3(0.9)
19.3(2.6)
3.6(1.5)
39.0(2.5)
3.9(2.9)
36.0(3.7)
3.3(2.2)
38.3(3.9)
2.3(0.6)
34.6(1.4)
0.3(0.5)
29.6(1.1)
7.6(2.0)
36.2(1.3)
5.5(1.7)
31.0(3.2)
5.3(0.3) 4.7(1.2)
0.4(0.2)
0.1(0.1) 1.0(0.5)
19.5(3.5)
3.5(0.5) 2.0(0.0)
13.2(9.8)
8.0(6.2) 8.7(7.4)
20.2(1.3)
4.2(0.7) 4 . 2 ( 0 . 6 )
0.2(0.4) - 0 . 2 ( 0 . 3 )
1.3(0.7)
26.0(1.3)
4.7(0.6) 3.0(0.5)
-0.5(0.2) -0.3(0.3) -0.1(0.3)
26.0(2.5)
6.0(1-7) 5.0(1.1)
1.4(1.9)
2.0(3.1) 4.3(3.6)
25.7(1.7)
0.1(1.0) 13.6(3.1)
1.4(0.5)
1.0(0.0) 14.6(5.6)
25.5(2.2)
4.3(1.1) 4.7(2.7)
15.7(11.9) 9.1(0.9) 14.4(9.1)
26.1(1.3)
5.4(0.7) 6.0(2.4)
0.9(0.4)
0.9(0.4) 4.9(2.9)
27.3(1.4)
9.3(4.3) 11.0(0.0)
0.6(0.2)
2.0(1.4) 0.8(0.0)
28.0(1.3)
4.4(0.0) 3.0(0.7)
0.8(0.4)
0.1(0.4) 0.9(0.6)
25.9(1.2)
7.0(1.0) 5.0(1.4)
0.4(0.5)
1.3(0.0) 2.8(1.9)
24.0(2.1)
5.0(1.1) 4.0(1.5)
0.7(0.4)
0.6(0.4) 1.4(1.2)
22.1(2.1)
5.3(0.8) 14.8(5.8)
1.0(0.5)
1.4(0.7) 23.0(12.2)
25.0(5.0)
4.5(1.5) 16.0(6.0)
1.4(0.3)
0.7(0.6) 16.5(9.0)
21.1(3.1) 11.0(2.4) 35.4(7.2)
6.3(2.1) 17.3(7.1) 176.1(114.S)
4.8(0.7) 4.0(0.8)
27.5(2.8)
3.0(2.3)
1.0(0.7) 1.2(1.2)
20.5(2.6)
4.7(0.5) 4.7(1.0)
1.7(2.1)
1.7(1.4) 4.8(3.0)
29.0(5.5)
5.0(1.5) 1.5(0.5)
1.2(1.1) - 0 . 8 ( 0 . 8 )
2.6(1.9)
26.8(2.7)
5.6(0.5) 5.8(2.4)
0.5(0.5)
0.6(0.4) 2.3(1.5)
29.8(1.6)
9.8(1.0) 8.2(1.8)
9.8(2.5) 12.0(2.4) 19.8(6.9)
22.2(3.8)
4.5(0.3) 2.7(1.4)
3.5(2.0)
2.1(0.5) 2.6(2.5)
Sept. 1969
323
EVALUATION OF LDH ISOENZYME AND TOTAL LDH TESTS
TABLE 3—Continued
LDH Isoenzymef't
No. of
Cases
Total LDHf
Myocardial infarction
1-3 clays before test
Myocardial infarction
4.-8 days before test
Myocardial infarction
9-17 clays before test
P a n c r e a t i t i s , acute
10
1577(248)
7
1174(207)
4
400(38)
3
861 (358)
Pneumonia, bronchial
9
656(70)
Pneumonia, lobar
0
774(253)
P r o s t a t e hypertrophy,
benign
Pulmonary embolism
4
541(87)
5
736(152)
Sclerosis, amyotrophic
lateral
Ulcer, duodenal
0
459(49)
0
366 (45)
Diagnosis
l
2
3
4
5
42.2(3.6)
20.0(4.9)
37.3(2.9)
11.6(4.0)
28.5(1.7)
0.4(0.4)
25.3(4.7)
4.0(4.2)
27.5(2.4)
2.3(1.2)
32.0(3.6)
4.7(3.1)
33.2(4.6)
2.4(1.7)
25.2(3.3)
1.7(0.6)
31.2(2.0)
0.7(0.4)
31.7(2.2)
-0.3(0.4)
32.8(1.2)
10.2(2.4)
33.4(2.2)
7.2(3.2)
36.5(1.9)
0.3(0.4)
33.7(2.3)
4.2(4.1)
37.3(1.1)
2.5(0.8)
32.8(1.2)
2.4(1.9)
32.5(1.7)
0.5(0.6)
34.8(1.7)
2.6(1.0)
34.3(1.5)
0.1(0.5)
30.7(2.6)
-0.6(0.5)
17.2(2.3)
4.1(1.2)
18.3(2.2)
2.8(1.0)
25.0(2.0)
0.1(0.4)
24.3(1.8)
2.6(2.0)
24.1(1.7)
1.4(0.5)
22.2(2.5)
1.3(1.4)
23.2(2.6)
0.3(0.7)
25.0(2.5)
2.0(2.0)
20.3(1.8)
0.3(0.0)
24.2(2.0)
-0.6(0.6)
4.7(1.1)
2.S(1.4)
4.4(0.9)
2.2(1.0)
6.0(0.4)
0.7(0.4)
8.3(3.3)
3.7(1.0)
0.1(1.1)
1.6(0.6)
5.8(1.4)
3.4(3.3)
5.0(0.7)
0.5(0.3)
6.6(2.4)
3.6(2.0)
5.0(0.9)
0.2(0.0)
4.7(0.8)
-0.3(0.4)
4.1(1.2)
O.S(3.0)
0.4(2.1)
7.0(1.2)
5.0(1.1)
1.0(1.2)
8.3(1.2)
8.0(2.7)
4.9(1.5)
3.1(1.0)
0.3(1.0)
S.3(5.5)
0.0(2.3)
3.2(1.7)
S.4(1.7)
8.5(2.0)
3.2(1.0)
0.6(0.9)
3.2(1.0)
0.0(0.7)
U./ml
* Calculations were made on the University Computing System, utilizing the BMDOID data description program. Cases were selected as described in "Materials and Methods."
t The first figure in any row and column is the mean for all cases in the disease group. The second
figure (in parentheses) is the calculated standard ei-ror of the mean.
| Figures in the top row for each diagnosis are LDH isoenzymes expressed as percentages of the total
LDH. Figures in the bottom row for each diagnosis are LDH isoenzyme units expressed in standardized
form. The latter were calculated by means of the following formula: (calculated isoenzyme units minus
normal mean units for this isoenzyme (from Table 2) divided by standard deviation (in units) for this
isoenzyme, from Table 2).
from patient data according to the procedure
described by Hoffmann.5 Estimation of the
normal limits for LDH isoenzyme percentages was based on single determinations
from 240 patients. These were the first patients available for the study, excluding
those with total LDH values greater than
1000 units per ml. For each of the five isoenzymes, a frequency distribution of 20 class
intervals was plotted on normal probability
paper and a line for "normals" was drawn.
The mean was read opposite 50% on this
line, and the standard deviation was estimated from the following formula: (difference between the values opposite 97.5% and
2.5 % on normal line) divided by 4. Normal
limits expressed as units were calculated from
single determinations on 545 different patients, including those in the first group. For
each patient, LDH isoenzyme units were
obtained as the product of the appropriate
percentage and the total LDH units. The
mean and standard deviation for the isoenzyme and total units were then obtained in
the above manner. Patients with a total
LDH greater than 1000 units per ml. were
excluded.
Table 3 shows the values obtained for the
enzyme assays in various disease states. The
figures given here include the mean and
standard error for LDH isoenzyme percentages, total LDH units, and LDH isoenzyme units. The latter are given in
standardized form, i.e., in standard deviations from the normal means. Expressed in
this way, a single result within the range
— 2 to + 2 would be considered normal.
Hoffmann has formulated a similar but ex-
324
GLICK
paneled scale which has for normal limits the
range 90 to HO.5 A number of the diseases
listed in Table 3 are associated with one or
more abnormal LDH isoenzyme values. This
can be most readily seen by examining the
standardized form of the isoenzyme units.
Usefulness of LDH Isoenzyme and Total
LDH Values in Clinical Diagnosis
Entry of the enzyme data into a computerized discriminant analysis program. It seemed
worthwhile to evaluate in some objective
way the diagnostic usefulness of LDH isoenzyme and total LDH values. A partial
solution is simply to note the statistical limits
of the test results for various diseases (Table
3). The assays are best suited to the detection of diseases which cause abnormal values.
However, a test result is usually used in a
differential diagnostic setting, where the
problem is to distinguish among several
possible clinical states. This can be dealt
with by discriminant analysis, which separates preselected groups in a mathematically
optimal manner. Accordingly, it was decided
to evaluate the assays in this fashion.
As applied here, discriminant analysis
begins with two or more groups of individuals
with different diseases (the differential
diagnosis set). One or more test values are
associated with each individual in each disease group. From these data, equations are
derived (one for each group in the set) which
are linear functions of the test values and
which separate the groups in an optimal
manner. For example, if it is desired to discriminate among three diseases on the basis
of five different tests, the test data from three
different groups of individuals who were
preassigned to the three disease categories
would be required. Three linear equations,
corresponding to the three diseases, would
be computed from these data. Each equation
would contain six terms. Five of the terms
would be coefficients for the five test values,
and the sixth term a constant. Subsequent
to these calculations, a given individual,
suspected of having one of the three diseases,
could be assigned to one of the disease groups
in the following manner; the five test results
for this "unknown." individual would be
substituted in each of t h e three equations
Vol. 52
and the resulting three values compared.
The unknown individual would be assigned
to the disease group corresponding to the
equation which yielded the numerical ly
greatest result. The reliability of this assignment can be calculated as a probability between 0 and 1. Zieve and Hill10, l l and Zieve
and associates12 have applied this form of
analysis to the separation of two groups (normal persons and those with one of several
liver disorders), based on the results of nine
different tests of liver function. These authors, in an elegant series of papers, also discuss the theory and limitations of discriminant analysis as applied to medical diagnosis.
Four diseases were selected from Table 3
for this evaluation (infectious hepatitis,
infectious mononucleosis, myocardial infarction, and lung cancer).* For each of these
disorders, a differential diagnosis set was
assembled in the following manner: each set
consisted of a group of patients with the
disease in question, four other groups of
patients with diseases which might logically
enter into the differential diagnosis of the
disease in question, and a sixth unknown
group consisting of patients who had one of
the five diseases in the set. For example, the
differential diagnosis set for infectious mononucleosis consisted of groups of individuals
with infectious mononucleosis, infectious
hepatitis, granulocytic leukemia, lymphocytic leukemia, Hodgkin's disease, and an
unknown group of individuals, each of whom
had one of these five disorders. The first five
groups in each set were used by the
BMD07M stepwise discriminant program to
calculate five discriminant equations. The
unknown group did not enter into these
calculations, but its members were subsequently assigned by the program to one of
the five disease categories. For a given set,
the input to the BMD07M program consisted in the entry of individual test results
* The four diseases were chosen for the following
reasons: (a) they were common diseases which
had one or more abnormal enzyme values; (b)
data for other diseases which might enter into
their differential diagnosis were also present in
Table 3. Of course, other diseases might have
been selected, and this report does not imply that
the I/DH assays have no diagnostic value in other
situations.
Sept. 1969
EVALUATION OF LDH ISOENZYME AND TOTAL LDH TESTS
by disease group. The output included a listing of the discriminant equations, statistical
parameters for evaluating the separation of
the disease groups, and the assignment of
each individual case in both known and unknown categories to the disease for which
the probability (computed from the disease
discriminating equations and the individual
case data) was greatest. The BMD07M program was carried out four times on each of
the four differential diagnosis sets. Each
time the enzyme data were entered into the
computations in a different form, as follows:
(a) LDH isoenzymes, as percentages; (b)
LDH isoenzymes, as units, i.e., percent
multiplied by total LDH units; (c) LDH isoenzymes, as standardized units (see Table 3
for calculation); and (d) LDH isoenzymes,
as percentages, plus total LDH units.
The results of this type of analysis can be
used in two ways: first, they are useful in
evaluating the diagnostic capability of a
test or group of tests; second, they can aid
the physician in arriving at the differential
diagnosis of a particular patient. These two
applications are illustrated with respect to
the LDH isoenzyme and total LDH data in
the next two sections. Following these is a
brief discussion of the limitations of discriminant analysis.
Use of discriminant analysis results to
evaluate the usefulness of LDH isoenzyme and
total LDH tests for the differential diagnosis of
infectious hepatitis, infectious mononucleosis,
myocardial infarction, and lung cancer. As
noted above, the discriminant analysis of
each differential diagnosis set included the
assignment of each individual case in both
known and unknown categories to one of the
diseases in the set. From this assignment
matrix, the following "reliability ratio" was
manually calculated for each disease group
in the set:
a
d + FNi + FPt
where d is the number of cases of disease-^
in the set which were correctly assigned to
the diseasc-i category by the program;
FNi (false-negative) is the number of cases
of disease-i which were assigned to other
than the disease-i category; and FP, (false-
325
positive) is the number of cases other than
disease-t which were assigned to the disease-t
category. This ratio was used to judge the
usefulness of the enzyme data in the differential diagnosis of disease-z in the set presented.
Obviously, a ratio less than 0.5, in which the
sum of false-negatives and false-positives
exceeds the correct assignments, indicates
that the disease in question cannot be
reliably distinguished from the other diseases
in the set by means of the enzyme data.
The value of the ratio assigned to each
disease is subject to several types of variation. For a given disease, the reliability ratio
depends on the other diseases in the differential diagnosis set. Also, the ratio, which
varies with the number of cases in each disease group in the set, will be more reliable as
the number of cases in each group increases.
Although this reliability ratio does not
directly utilize many of the statistical
parameters available as output from the
discriminant function program, it does give
some indication about the usefulness of the
tests in question for the differential diagnosis of a given disease by either statistical
or nonstatistical means. The ratio is thus a
useful screen for evaluating the diagnostic
capability of tests. It is not intended to replace the parameters furnished as output
when the discriminant function program is
used to classify a particular unknown case.
The results of this study are summarized
in Table 4. The reliability ratios indicate that
infectious hepatitis, infectious mononucleosis, myocardial infarction, and lung cancer
can be fairly well distinguished from the
other diseases in their respective sets by
means of these enzyme assays. On the other
hand, diseases with low ratios, such as common duct obstruction or pulmonary embolism, cannot be distinguished from other low
ratio diseases in the same set.
Another feature which is apparent in Table
4 is the dependence of the reliability ratio for
a given disease upon the form in which the
data are entered into the program. The first
column of ratios was derived from the LDH
isoenzyme percentages only, whereas the
ratios in the remaining two columns were
based on the isoenzyme and total LDH
values. It is logical to anticipate differences
326
Vol. 52
GLTCK
TABLE 4
EVALUATION OF T H E U S E F U L N E S S OF SERUM L D H
FOR THE D I A G N O S I S OF C E R T A I N
Cases
1
Disease
H e p a t i t i s , infectious
Hepatitis, chronic
Cirrhosis, liver
Common bile duct obstruction
Cancer—liver, gallbladder,
or pancreas (mixed group)
VALUES
Ratio, CI (C + FN + FP), When Different
forms of the Variables are Entered into
the Discriminant Analysis Program
Diseases in Each Differential Diagnosis Set
Set
ISOENZYME AND T O T A L L D H
D I S E A S E S BY M E A N S OF DISCRIMINANT F U N C T I O N S *
Five isoenzymes
as percentages
Five isoenzymes Five isoenzymes
as either units
as percentages,
or standardized
plus total
units
LDH units
Knowns
Unknowns
5
2
7
2
2
0
3
1
0.07
0.40
0.38
0.00
0.71
0.50
0.23
0.09
0.67
0.33
0.61
0.00
8
2
0.31
0.12
0.2S
2
Mononucleosis, infectious
Hepatitis, infectious
Leukemia, granulocytic
Leukemia, lymphocytic
Hodgkin's disease
3
5
3
3
4
2
2
1
0
2
0.71
0.86
0.4.0
0.28
0.12
0.G7
0.50
0.40
0.22
0.11
0.83
0.8G
0.40
0.33
0.50
3
Myocardial infarction 1-3
days before test
Pulmonary embolism
Pancreatitis, acute
Pneumonia, bronchial
Pneumonia, lobar
0
4
0.73
0.30
0.73
4
3
8
4
1
0
1
2
0.14
0.15
0.50
0.17
0.2S
0.20
O.GO
0.27
0.25
0.12
0.4G
0.28
Cancer, lung
Pneumonia, bronchial
Pneumonia, lobar
Bronchitis, chronic
Emphysema, obstructive
5
8
4
6
6
1
1
2
3
4
0.14
0.30
0.28
0.21
0.33
0.71
0.43
0.17
0.40
0.27
0.55
0.31
0.33
0.27
0.38
4
* T h e cases were selected from those listed in Table 3 as described in the text. I n three instances,
the same disease group was used in two different differential diagnosis sets. F o r these three, identical
known and unknown cases were used in both sets. Calculations, including the " r e l i a b i l i t y " ratio, are
described in the text. T h e ratios are based on the classification by the discriminant analysis program
of all cases, both known and unknown. For each disease, the same known and unknown cases were
used for all 4 forms of d a t a entry into the BMD07M program. 59% of the known cases and 39% of the
unknown cases in the table were classified correctly by the program.
in the ratios of column 1 vs. those of Columns
2 and 3 since the latter two are derived from
data which include an additional test. Lung
cancer, for example, is much more readily
recognized if the total LDH value is taken
into account. However, differences in reliability ratios between Columns 2 and 3 are
not as easy to anticipate (myocardial infarction), and this suggests that some trial and
error entry of different forms of the data
might be necessary in order to obtain the
best discrimination of a particular disease.
It is noteworthy that the conversion of a
given set of data into standardized form
(Column 2) does not change the results of
such an analysis.
Use of discriminant analysis in conjunction
with the differential diagnosis of an individual
case. The use of computers as a diagnostic
aid is becoming more common, and, regardless of the particular approach, most technics
ultimately rely on some sort of comparison
Sept. 1969
EVALUATION OF LDH ISOENZYME AND TOTAL LDH TESTS
between the patient's test data and test data
for known types of disease. It would be
desirable if the latter known data base could
be generated in the hospital in which it is to
be used, and could be continually updated.
This accumulation of a disease-test result
data base would not be too difficult in a
hospital which has computerized its laboratory facilities and medical records, and the
effort would certainly extend the usefulness
of most laboratory tests.
As envisioned in this report, computerized
discriminant analysis could aid the physician
in arriving at a differential diagnosis in the
following way: the patient's test data and
known data for all of the diseases selected by
the physician would be entered into a discriminant program. The output would assign
the patient to the disease category for which
the probability was greatest. Such a procedure would not involve much computer time,
and it might yield a more reliable diagnosis,
particularly when many different test
results were being considered, as in multichannel screening. Of course, one does not
expect that unknown cases will be classified
correctly as often as known cases, since the
latter are used to compute the discriminating
equations. This is illustrated in the legend of
Table 4, in which the known and unknown
cases were assigned to the correct disease
group 59% and 39% of the time, respectively. These values increase to 75% and
70%, respectively, when the comparison is
limited to those diseases in Table 4 for which
the enzyme tests are discriminator}' and for
which the associated probabilities are
greatest, i.e., infectious hepatitis, infectious
mononucleosis, myocardial infarction, and
lung cancer. Thus, the assignment of an
unknown case to a particular disease category by the program, together with an
associated high probability for this selection,
would give the physician some assurance
that the assignment was valid.
Limitations of discriminant analysis for
clinical diagnosis. Zieve and Hill 1 1 have
discussed the limitations of discriminant
analysis as applied to clinical diagnosis, and
the reader is referred to their paper for a
more complete presentation of the subject.
The limitations can be divided into two cate-
327
gories for the purpose of discussing their
significance on the applications presented
here. The first type of restriction pertains to
the assumptions involved in the development of discriminant analysis; i.e., the tests
are lineai-ly related, all groups in the set have
a common dispersion matrix, and the test
values are metric. The second type of limitation is due to extraneous factors which might
be present in one or more members of the
set; e.g., an individual might have several
disorders which do not have additive effects
on the test values.
In regard to the use of discriminant analysis for evaluating the diagnostic capability
of a group of tests, the first type of limitation
is the principal one involved, since the individuals who make up the different groups
can be selected on the basis of single clinical
states.
When the purpose of a discriminant analysis is the classification of an unknown case,
the second type of limitation might be the
dominant one and lead to a false assignment.
There is no simple solution to the problem of
classifying an individual who has several
disorders which affect the test values in a
nonadditive fashion. If a false assignment is
suspected because of other clinical features,
a second discriminant analysis, utilizing the
same groups but different tests, might enforce or nullify the original classification.
Acknowledgments. Mrs. Suzzanc Knowles, Miss
Carolyn Crocker, Mrs. Cleojeanne Robertson,
and Mr. Joseph Timberlake performed most of
the analyses upon which this report is based.
T h e author also benefited from discussions with
Drs. K h a t a b Hassanein and Malcolm E . Turner,
J r . , of the D e p a r t m e n t of Biometry. Many useful suggestions were supplied by D r s . Russell J .
Eilers, Harold J. Grady, and R o b e r t T. Manning,
who have kindly reviewed the manuscript.
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