J Chron Dis, Vol. 31, pp. 337-345 @ Pergamon Press Ltd. 1978. Printed in Great Britain
0021-6981/78/0501-0337 002.00/O
PLASMA LIPIDS AS COLLATERAL RISK FACTORS IN CORONARY ARTERY DISEASEA STUDY OF 371 MALES WITH CHEST PAIN DAVID W. SCOTT, ANTONIO M. GOTTO, JAMES S. COLE and G. ANTHONY GORRY Baylor College of Medicine, Houston, TX and The University of Kentucky, Lexington, KY U.S.A. (Received in revisedform 26 October 1977)
Abstract-A group of 371 males with chest pain was studied to ascertain the way in which the risk of coronary artery disease depends on the joint variation of plasma lipid concentrations. Patients were divided into two groups: one called diseased in which one or more major coronary vessels was shown on angiography to have at least a 25% stenosis; and the second called normal. For both groups, advanced techniques were used to estimate the joint probability density function which represents the way in which the two lipid concentrations vary jointly. With these density functions, we analyzed the risk of coronary artery disease as a function of plasma triglyceride concentration for fixed plasma cholesterol concentrations. We found that in general this risk increases markedly with increasing plasma triglyceride concentration, and this effect is more pronounced at higher cholesterol levels. These results suggest an association between elevated plasma triglyceride and the risk of coronary artery disease independent of that implied by the co-existing plasma cholesterol concentration. Our analytical approach can be used in other investigations of risk factors in coronary artery disease.
Investigations ,of the relat;lonship between plasma cholesterol and plasma triglyceride levels and coronary artery disease have suggested that elevated concentrations of plasma lipids contribute to the pathogenesis of the disease [l-7]. Epidemiological studies leave little doubt that hypercholesterolemia is a major risk factor for coronary atherosclerosis, but evidence concerning the risk resulting from hypertriglyceridemia is conflicting [8-141. The population studies of Keys et al. [15] indicate that the risk of coronary artery disease increases continuously with increasing concentration of plasma cholesterol. In a study in which coronary arteriography was used to assess coronary artery disease, a similar, but weaker relationship was found between the risk of the disease and serum triglyceride concentration [16]. These findings recently were supported by Gotto et al. [17] in a study of 496 patients with chest pain in which small, but statistically significant age-corrected correlations were found between plasma cholesterol and plasma triglyceride concentrations and the extent of coronary artery didase as measured by the number of coronary vessels with angiographically demonstrated occlusions. In the latter study, it was also found that the ranges of plasma lipid concentrations in the normal and diseased patient groups overlapped to a great extent, and there were 337
338
DAVID W. SCOTT,ANTONIO id.GOTTO, JAMESS. COLEand G. ANTHONY GORRY
only small (though statistically significant) differences between the mean plasma lipid concentrations of the normal group and of the diseased group. For the patients in this study, the correlation between plasma cholesterol and plasma triglyceride concentrations was relatively low, and this suggests that, insofar as identifying patients with coronary artery disease is concerned, there may be information in the plasma cholesterol concentration that is not in the plasma triglyceride concentration and vice versa. We have estimated joint probability density functions for plasma cholesterol and plasma triglyceride concentrations in normal and diseased males with chest pain. Here we shall use these distributions to show how the risk of coronary artery disease varies with the simultaneous variation of plasma cholesterol and plasma triglyceride levels. We shall demonstrate that elevated plasma triglyceride concentrations are associated with a risk of coronary artery disease over and above that implied by the co-existing levels of plasma cholesterol alone. METHODS
Data collection
The patient population studied has been described in detail previously [ 171 as have the methods used to obtain lipid and angiographic data. Here we briefly review the methods of data collection for the study. Patient selection. The patients selected for the study were chosen from those referred to the Cardiology Unit of the Methodist Hospital between January 1972 and March 1976 for evaluation of chest pain. Subjects were not referred for evaluation specifically because of hyperlipidemia, diabetes, obesity, hypertension, or other known risk factors. Cardiac catheterization was performed when indicated by one of the three examining cardiologists. Those patients with technically unsatisfactory coronary arteriograms (fewer than 5% of the patients studied) were excluded from our sample as were patients with valvular disease, cardiomyopaqhy, or recent myocardial infaraction. For the analysis reported here, we also have chosen to exclude women. After these exclusions, 371 male patients were available for our analysis. With the exceptions noted, these patients constitute a sequential sample of males evaluated for chest pain at the Methodist Hospital. Lipid and lipoprotein measurements. For each patient, plasma lipids were measured using a blood sample obtained after the patient had fasted for 12 hr and before the patient underwent angiography. Plasma cholesterol and triglyceride concentrations were determined according to the procedures of the Lipid Research Clinics Program [ 181. A further breakdown of these lipids by density was performed for the 118 patients who were classified as hyperlipidemic in accordance with the criteria set forth in [17]. The quantifying and phenotyping of plasma lipoproteins were performed following protocols of the Lipid Research Clinics Program [ 181. Coronary arteriography. For each patient, all the right and left heart pressures were measured, a Fick cardiac output was obtained, and a left ventricular cineangiogram was recorded. Then selective coronary arteriograms were obtained in accordance with the Sones procedure [ 191. Using the films, two cardiologists independently assessed the location and percentage stenosis of individual coronary lesions. In cases of disagreement, the films were reviewed by a third observer and a consensus was reached. The
Plasma
‘severity’ percentage coronary contained coronary ‘normal’ occlusion
Lipids as Collateral
Risk Factors
in Coronary
Artery
339
Disease
of coronary artery disease in a given patient was defined as the maximum stenosis found in any of the four major coronary arteries, and the ‘extent’ of artery disease was defined as the number of major coronary vessels which a stenosis of 25% or greater. Fifty-one patients had none of their major vessels occluded according to these criteria. Here, these patierits are called or ‘non-diseased’. The remaining 320, here called ‘diseased’, showed an of 25”:, or more in at least one of the major cor’onary vessels. MATHEMATICAL
ANALYSIS
Estimating probability density functions .for plasma lipid concentrations. A joint probability density function of plasma cholesterol and plasma triglyceride concentrations represents the way in which the two concentrations vary conjointly in a patient group. By comparing this density function for normal patients with chest pain with that for diseased patients with chest pain, we can identify ranges of the two concentrations in which the risk of coronary artery disease is relatively great. We also can assess the extent to which each plasma lipid level contributes to this risk in these regions. One approach to estimating a probability density function from sample data is to fit a functional form to the data by estimating the parameter(s) of the function used. The function used most commonly is the Gaussian or Normal distribution. If the Gaussian distribution fits the data poorly, a nonparametric technique, called kernel density estimation [20], can be used to estimate the density in question. Consider a patient group (say the diseased group) for which N, pairs of plasma lipid concentrations have been obtained, each from a different patient. Let these pairs be denoted (CHL,, TRG,), (CHL,, TRG,), . . , (CHL,,, TRG,,). The kernel estimate of the joint probability density function of (CHL, TRG) given the data (CHL,, TRG,) and two scaling constants h, and h, is: ,f,(CHL,
TRG)
= -&z
K[CHLh,CHLi
j.KiTRGqTRGj
)
(1)
wheref,(CHL, TRG) is the estimated joint density for plasma cholesterol (CHL) and plasma triglyceride (TRG) in the diseased population, and the kernel K(z) is defined by: K(z) =
15/16(~‘-1)~ o
for
-1
.29 216 P-c 10 _ 177
43 93
P>.95 P>.38
36 56
195 133
*One outlier (under the Gaussian assumption) was excluded from each of these samples.
we used the nonparametric kernel density estimation procedure to fit the data. The probability density function for the non-diseased population is unimodal with a mode at (CHL, TRG) = (195,122). On the other hand, the probability density function which best fits the data for the diseased population is distinctly bimodal with modes at (18.5, 122) and (233, 145). It is interesting that the univariate kernel probability density estimates of CHL and TRG separately for the diseased population are both unimodal and not bimodal. The probability density function given by equation (1) is a surface in three dimensions. Although there are several methods of depicting such surfaces, we chose to plot contours as seen when looking down on the surface from above. To compare the
Plasma
Lipids
as Collateral
o ZOO----Dseased
P
papulatlan
-Non-diseased
Risk Factors
(modes
population
in Coronary
Plasma
cholesterol
Disease
331
MI and M31 Mz)
( mode
220 a
Artery
concentration,
230
240
250
mg/lOOml
Fig. I. For the two patient groups, diseased and non-diseased males with chest pain, the estimated joint probability density functions for plasma lipid concentrations are shown as viewed from above. Each density function is represented by four contours of equal probability as discussed in the text. Patients were classified as diseased if they showed a stenosis of at least 25”:, in any of the four coronary arteries.
probability density functions of the diseased and non-diseased groups, we constructed for each distribution ten contours of equal probability. The vertical distance between the planes determining two adjacent contours is one-ninth of the maximum height of the density. We have depicted in Fig. 1 the highest four contours for the two distributions. It is apparent that one mode of the density function for diseased patients is close to the mode of the density function for normal patients. The other mode of the density function for the abnormal group is clearly displaced from the mode of the density function for the normal patients. A simple clustering technique was used to assign 146 and 174 diseased males to the left and right modes M, and M,, respectively. The linear function 250 CHL + 26.61 TRG-56865.25 was chosen for this process, since it is perpendicular to the line connecting the two modes M, and M, and intersects this line at the minimum off, (CHL, TRG) between M, and M,. Neither the mean ages nor the mean blood pressures differed significantly between the two modal groups. Only in the left coronary artery were the incidences of coronary artery disease perhaps significantly different (Table 2). When the mean occlusion for each vessel was calculated, more severe disease, particularly in the left coronary artery, was observed in the right modal group, the group with the more elevated plasma lipid concentrations (Table 3). For various fixed levels of plasma cholesterol concentrations, we computed the value of the likelihood ratio as a function of increasing plasma triglyceride concentration. The results of these calculations are displayed in Fig. 2. The solid portions of the graphs depict points where both density estimates exceed 10% of their respective maximum modal values. The dotted portion represent points where one or both density values fall between the 5 and 100,; levels. We believe the dotted lines are generally reliable estimates of risk ; however they are not as reliable as those of the solid portions of these graphs. The slopes of these lines are robust to changes in the scaling constants h,. and h, For low values of plasma cholesterol (say than 150 mg/dl), the likelihood ratio increases only slightly with increasing values of plasma triglyceride. As plasma
iess
142
DAVIII
W. SCOTT, ANTONIO M. GOTTO, JAMESS. COLE and G. ANTHONY GORRY
TABLE 2. ANALYSIS OF 320 DISEASEDPATIENTSBY MODE OF PROBABILITYDENSITYFUNCTION (PDF) TO WHICH THEY WERE ASSIGNED: PERCENTAGE* HAVING AT LEASTA 25% OCCLUSION 1~ A GIVEN CORONARY VESSEL
Vessel
:
Mode of PDF.; (CHL,TRG) = (185,122) (CHL, TRG) = (233,145)
Right
Left main
Circumflex
84 88 NS
15 13 NS
86 91 NS
*Percentages do not add to lOOO;,due to the presence of multiple-vessel -FSee text and Fig. I.
NS-Not
Left anterior descending
73 (P :.\74, disease.
significant.
TABLE 3. ANALYSISOF 320 DISEASEDPATIENTSBY MODEOFPROBABUTY DENSITYFUNCTION (PDF)To WHICH THEY WERE ASSIGNED: AVERAGE PERCENTAGEOCCLUSION IN EACH CORONARY VESSELFOR THE 320 DISEASED MALES
Vessel: Mode of PDF (CHL, TRG) = (185,122) (CHL, TRG) = (233,145)
NS-Not
Right
Left main
70
8
&z90)
i&
Circumflex
72
Left anterior descending
53
(P:po57)
significant.
cholesterol increases, the role of elevated plasma triglyceride concentrations as a risk factor assumes increasin.g importance. Not only do the curves of the likelihood ratio for these higher values of plasma cholesterol rise with increasing plasma triglyceride, but the slopes of these curves increase dramatically as well. Furthermore, the value of plasma triglyceride af which the likelihood ratio begins to increase sharply generally decreases with increasing plasma cholesterol. For the patients we studied, the prior odds of disease were quite high, 0 (D) = 32051 = 6.3 :l. To illustrate the use of equation (3), we consider two hypothetical patients with (CHL, TRG) values of (200,50) and (200,250). Frbm Fig. 2 the likelihood ratios at these values are 0.36 and 2.52, respectively. The estimated posterior odds of disease are 2.3 :l and 15.8 :l, respectively ; thus an increase in plasma triglyceride from 50 to 250 mg/dl results in a 7-fold increase in risk of disease for this plasma cholesterol level. Wilson and Lees [23] showed a reciprocal relationship between the concentrations of very low and low density lipoproteins (LDL) in man. A variety of studies in the past few years have provided evidence that there may be an inverse relationship between the concentration of plasma high density lipoproteins (HDL), and the risk of CAD [24-271. Further, Miller et al. [28] have recently reported that concentrations of plasma HDL-cholesterol are independently and inversely related to the concentrations of plasma triglyceride and of LDL-cholesterol. The HDL-cholesterol concentrations appear to be highest in subjects who are at lowest risk for developing coronary artery disease. In our patient group, HDL-cholesterol was determined only for those men judged to be hyperlipidemic [17]. For the 118 patients in this group, plasma triglyceride concentration was negatively correlated with plasma HDL-cholesterol concentration (R = - 0.178, P < O.OS),but no statistically significant correlation was
Plasma
Lipids as Collateral a 7
F
Risk Factors
CHL = Plasma cholesterol concentration (mg/lOOml)
in Coronary
Artery
Disease
343
: I’
25 t
kHL=200 I’ ‘$I !,’ \
L
-04 P zz 23 i 2
-1
0
50 Plasma
100 I50 200 250 triglyceride concentration,
300 350 mg/lOOml
Fig. 2. Likelihood ratio as a function of plasma triglyceride concentration for several fixed concentrations of plasma cholesterol. The relationship of the likelihood ratio to the risk of coronary artery disease is discussed in the text.
found between HDL-cholesterol concentration and extent of coronary artery disease. No statistically significant relationship was found between the ratio of HDLcholesterol to total cholesterol and the extent of coronary artery disease. The failure to find a significant ‘protective effect’ may reflect the fact that all patients in this sample were hyperlipidemic. DISCUSSION
To investigate the joint roles of plasma cholesterol and plasma triglyceride concentrations in coronary artery disease, we estimated their joint probability density functions for diseased and non-diseased males presenting with chest pain. The estimated density for the diseased group had two modes, one virtually indistinguishable from the single mode of the density for the non-diseased population. Using lipid concentrations as a guide, we placed each diseased patient in one of two groups corresponding to the two modes of the density function for diseased patients. Comparison of these two groups of diseased males revealed no significant differences in age, blood pressure, or location of occlusion except in the left coronary arterty; however, the group with higher lipid concentrations had more severe occlusion on the average, particularly in the left coronary artery. Using the two density functions, we constructed curves of the likelihood ratio as a function of plasma triglyceride for various fixed levels of plasma cholesterol. By holding plasma cholesterol‘fixed, we eliminated any effect due solely to a correlation between the two lipids. The results indicated an association between increased plasma triglyceride concentration and increased risk of coronary artery disease in males with chest pain. For low values of plasma cholesterol, the likelihood ratio shows only a slight increase with increasing plasma triglyceride ; however, for large values of plasma cholesterol, the role of elevated plasma triglyceride as a risk factor is clear. Not only do
344
DAVID W. SCOTT,ANTONIOM. GOTTO,JAMES S. COLE and G. ANTHONYGORRY
the curves of the likelihood ratio rise with increasing plasma triglyceride, but the slopes of these curves increase dramatically with increasing plasma cholestrol. Because we had plasma HDL-cholesterol concentrations for only the patients classified as hyperlipidemic, it is not surprising that we were unable to find a ‘protective effect’ for HDL, but the negative correlation we found between plasma HDLcholesterol and plasma triglyceride concentrations is consistent with such an effect. Nonetheless, an association between increased plasma triglyceride concentration and increased risk of coronary artery disease in the males with chest pain we studied has been demonstrated clearly by our analysis. The same analysis can be applied to other investigations of the relationships between plasma lipids and the risk of coronary artery disease. Acknowledgements-This research was supported in part by the National Heart and Blood Vessel Research and Demonstration Center, Baylor College of Medicine, a grant-supported research project of the National Heart, Lung, and Blood Institute, National Institues of Health, Grant No. 17269.
REFERENCES 1. 2. 3 4: 5. 6. 7. 8. 9. 10.
11. 12. 13. 14. 15. 16. 17.
18. 19. 20. 21. 22.
Kannel WB, Castelli WP, Gordon T, McNamara PM: Serum cholesterol, lipoproteins and the risk of coronary heart disease. Ann Int Med 74:1-12, 1971. Stamler J: Epidemiology of coronary heart disease. Med Clin 57:5-46, 1973. Keys A: Coronary heart disease, the global picture. Atherosclerosis 22:149-192, 1975 Brown DF: Blood lipids and lipoproteins in atherogenesis. Am J Med 46:691-704, 1969 Albrink MJ, Man EB: Serum triglycerides in coronary artery disease. Arch Int Med 103:4-8, 1959 Brown DF, Doyle JT, Kinch SH: Serum triglycerides in health and in ischemic heart disease. New Engl J Med 273 1941-952, 1965 Sale1 AF, Riggs K, Mason DT, Amsterdam EA, Zelis R: The importance of type IV hyperlipoproteinemia as a predisposing factor in coronary artery disease. Am J Med 57:897-903, 1974 Carlson LA, Bottiger LE: Ischaemic heart disease in relation to fasting values of plasma triglycerides and cholesterol. Lancet 1:865-868, 1972 Rhoads GG, Gulbrandsen CL, Kagan A: Serum lipoproteins and coronary heart disease in a population study of Hawaii Japanese men. New Engl J Med 294:293-298,1976 Hazzard WR, Goldstein JL, Schrott HG, Motulsky AG, Bierman EL: Hyperlipidemia in coronary heart disease. III. Evaluation of lipoprotein phenotypes of 156 genetically defined survivors of myocardial infarction. J clin Invest 52:1569-1577, 1973 Goldstein JL, Hazzard WR, Schrott HG, Bierman EL, Motulsky AG: Hyperlipidemia in coronary heart disease. I. Lipid levels in 500 survivors of myocardial infarction. J clin Invest 52:1533-1542,1973 Ostrander LD, Neff BJ, Block WD, Francis T, Epstein FH: Hyperglycemia and hypertriglyceridemia among persons with coronary heart disease. Ann Int Med 67:34-41,1967 Albrink MJ, Meigs JW, Man EB: Serum lipids, hypertension and coronary artery disease. Am J Med 31:4-23,196l Blackburn H: Concepts and controversies about the prevention of coronary heart disease. In: Cardiovascular Problems Russek H. I. (Ed) University Park Press, Baltimore, 1975 Keys A, Taylor HL, Blackburn H, Brozek J, Anderson JT, Simonson E: Coronary heart disease among Minnesota business and professional men followed 15 years. Circulation 28 :38 l-395,1963 Cohn PF, Gabbay SI, Weglicki WB: Serum lipid levels in angiographically defined coronary artery disease. Ann Int Med 84:241-245, 1976 Gotto AM, Gorry GA, Thompson JR, Cole JS, Trost R, Yeshurun D, DeBakey ME: Relationship between plasma lipid concentration and coronary artery disease in 496 patients. Circulation 56:5, 875-883, 1977 Manual of Laboratory Operations. Lipid Research Clinics Program. Vol. I DHEW Publication No. NIH-75-628,1974 Sones FM, Shiney EK : Cine coronary arteriography. Mod Concepts Cardiovasc Dis 31:735-738,1962 Parzen E: On estimation of a probability density function and mode. Ann Math Statist 33:1065-1076, 1962 Scott DW, Tapia RA, Thompson JR: Kernel density estimation revisited. J Nonlinear Anal 1:339-372, 1977 Lusted LB: Introduction to Medical Decision Making. Charles C. Thomas, Publ, 1968
Plasma
23. 24. 25.
26. 27. 28.
Lipids as Collateral
Risk Factors
in Coronary
Artery Disease
345
Wilson DE, Lees RS: Metabolic relationships among the plasma lipoproteins. Reciprocal changes in the concentrations of very low and low density lipoproteins in man. J din Invest 51:1051-1057, 1972 Miller GJ, Miller NE: Plasma-high-density-lipoprotein concentration and development of ischaemic heart disease. Lancet 1:16-19, 1975 Castelli WP, Doyle JT, Gordon T, Hames C, Hulley SB, Kagan A, McGee D, Vicic WJ, Zukel WJ: Ischaemic heart-disease in relation to fasting values of plasma triglycerides and cholesterol. Stockholm Prospective Study. Lancet 1:865-868,1972 Glueck CJ, Fallat RW, Millett F, Gartside P, Elston RC, Go RCP: Familial hyper-r*-lipoproteinaemia: studies in 18 kindreds. Metabolism 24:1234-1265, 1975 Berg K, Borresen A, Dahlen G: Serum high-density-lipoprotein and atherosclerotic heart-disease. Lancet I :499-501,1976 Miller GJ, Miller NE, Ashcroft MT: Inverse relationship in Jamaica between plasma high-density lipoprotein cholesterol concentration and coronary-disease risk as predicted by multiple risk-factor status. Clin Sci Mol Med 5 I :4755482, 1976
0021-6981/78/0501-0337 002.00/O
PLASMA LIPIDS AS COLLATERAL RISK FACTORS IN CORONARY ARTERY DISEASEA STUDY OF 371 MALES WITH CHEST PAIN DAVID W. SCOTT, ANTONIO M. GOTTO, JAMES S. COLE and G. ANTHONY GORRY Baylor College of Medicine, Houston, TX and The University of Kentucky, Lexington, KY U.S.A. (Received in revisedform 26 October 1977)
Abstract-A group of 371 males with chest pain was studied to ascertain the way in which the risk of coronary artery disease depends on the joint variation of plasma lipid concentrations. Patients were divided into two groups: one called diseased in which one or more major coronary vessels was shown on angiography to have at least a 25% stenosis; and the second called normal. For both groups, advanced techniques were used to estimate the joint probability density function which represents the way in which the two lipid concentrations vary jointly. With these density functions, we analyzed the risk of coronary artery disease as a function of plasma triglyceride concentration for fixed plasma cholesterol concentrations. We found that in general this risk increases markedly with increasing plasma triglyceride concentration, and this effect is more pronounced at higher cholesterol levels. These results suggest an association between elevated plasma triglyceride and the risk of coronary artery disease independent of that implied by the co-existing plasma cholesterol concentration. Our analytical approach can be used in other investigations of risk factors in coronary artery disease.
Investigations ,of the relat;lonship between plasma cholesterol and plasma triglyceride levels and coronary artery disease have suggested that elevated concentrations of plasma lipids contribute to the pathogenesis of the disease [l-7]. Epidemiological studies leave little doubt that hypercholesterolemia is a major risk factor for coronary atherosclerosis, but evidence concerning the risk resulting from hypertriglyceridemia is conflicting [8-141. The population studies of Keys et al. [15] indicate that the risk of coronary artery disease increases continuously with increasing concentration of plasma cholesterol. In a study in which coronary arteriography was used to assess coronary artery disease, a similar, but weaker relationship was found between the risk of the disease and serum triglyceride concentration [16]. These findings recently were supported by Gotto et al. [17] in a study of 496 patients with chest pain in which small, but statistically significant age-corrected correlations were found between plasma cholesterol and plasma triglyceride concentrations and the extent of coronary artery didase as measured by the number of coronary vessels with angiographically demonstrated occlusions. In the latter study, it was also found that the ranges of plasma lipid concentrations in the normal and diseased patient groups overlapped to a great extent, and there were 337
338
DAVID W. SCOTT,ANTONIO id.GOTTO, JAMESS. COLEand G. ANTHONY GORRY
only small (though statistically significant) differences between the mean plasma lipid concentrations of the normal group and of the diseased group. For the patients in this study, the correlation between plasma cholesterol and plasma triglyceride concentrations was relatively low, and this suggests that, insofar as identifying patients with coronary artery disease is concerned, there may be information in the plasma cholesterol concentration that is not in the plasma triglyceride concentration and vice versa. We have estimated joint probability density functions for plasma cholesterol and plasma triglyceride concentrations in normal and diseased males with chest pain. Here we shall use these distributions to show how the risk of coronary artery disease varies with the simultaneous variation of plasma cholesterol and plasma triglyceride levels. We shall demonstrate that elevated plasma triglyceride concentrations are associated with a risk of coronary artery disease over and above that implied by the co-existing levels of plasma cholesterol alone. METHODS
Data collection
The patient population studied has been described in detail previously [ 171 as have the methods used to obtain lipid and angiographic data. Here we briefly review the methods of data collection for the study. Patient selection. The patients selected for the study were chosen from those referred to the Cardiology Unit of the Methodist Hospital between January 1972 and March 1976 for evaluation of chest pain. Subjects were not referred for evaluation specifically because of hyperlipidemia, diabetes, obesity, hypertension, or other known risk factors. Cardiac catheterization was performed when indicated by one of the three examining cardiologists. Those patients with technically unsatisfactory coronary arteriograms (fewer than 5% of the patients studied) were excluded from our sample as were patients with valvular disease, cardiomyopaqhy, or recent myocardial infaraction. For the analysis reported here, we also have chosen to exclude women. After these exclusions, 371 male patients were available for our analysis. With the exceptions noted, these patients constitute a sequential sample of males evaluated for chest pain at the Methodist Hospital. Lipid and lipoprotein measurements. For each patient, plasma lipids were measured using a blood sample obtained after the patient had fasted for 12 hr and before the patient underwent angiography. Plasma cholesterol and triglyceride concentrations were determined according to the procedures of the Lipid Research Clinics Program [ 181. A further breakdown of these lipids by density was performed for the 118 patients who were classified as hyperlipidemic in accordance with the criteria set forth in [17]. The quantifying and phenotyping of plasma lipoproteins were performed following protocols of the Lipid Research Clinics Program [ 181. Coronary arteriography. For each patient, all the right and left heart pressures were measured, a Fick cardiac output was obtained, and a left ventricular cineangiogram was recorded. Then selective coronary arteriograms were obtained in accordance with the Sones procedure [ 191. Using the films, two cardiologists independently assessed the location and percentage stenosis of individual coronary lesions. In cases of disagreement, the films were reviewed by a third observer and a consensus was reached. The
Plasma
‘severity’ percentage coronary contained coronary ‘normal’ occlusion
Lipids as Collateral
Risk Factors
in Coronary
Artery
339
Disease
of coronary artery disease in a given patient was defined as the maximum stenosis found in any of the four major coronary arteries, and the ‘extent’ of artery disease was defined as the number of major coronary vessels which a stenosis of 25% or greater. Fifty-one patients had none of their major vessels occluded according to these criteria. Here, these patierits are called or ‘non-diseased’. The remaining 320, here called ‘diseased’, showed an of 25”:, or more in at least one of the major cor’onary vessels. MATHEMATICAL
ANALYSIS
Estimating probability density functions .for plasma lipid concentrations. A joint probability density function of plasma cholesterol and plasma triglyceride concentrations represents the way in which the two concentrations vary conjointly in a patient group. By comparing this density function for normal patients with chest pain with that for diseased patients with chest pain, we can identify ranges of the two concentrations in which the risk of coronary artery disease is relatively great. We also can assess the extent to which each plasma lipid level contributes to this risk in these regions. One approach to estimating a probability density function from sample data is to fit a functional form to the data by estimating the parameter(s) of the function used. The function used most commonly is the Gaussian or Normal distribution. If the Gaussian distribution fits the data poorly, a nonparametric technique, called kernel density estimation [20], can be used to estimate the density in question. Consider a patient group (say the diseased group) for which N, pairs of plasma lipid concentrations have been obtained, each from a different patient. Let these pairs be denoted (CHL,, TRG,), (CHL,, TRG,), . . , (CHL,,, TRG,,). The kernel estimate of the joint probability density function of (CHL, TRG) given the data (CHL,, TRG,) and two scaling constants h, and h, is: ,f,(CHL,
TRG)
= -&z
K[CHLh,CHLi
j.KiTRGqTRGj
)
(1)
wheref,(CHL, TRG) is the estimated joint density for plasma cholesterol (CHL) and plasma triglyceride (TRG) in the diseased population, and the kernel K(z) is defined by: K(z) =
15/16(~‘-1)~ o
for
-1
.29 216 P-c 10 _ 177
43 93
P>.95 P>.38
36 56
195 133
*One outlier (under the Gaussian assumption) was excluded from each of these samples.
we used the nonparametric kernel density estimation procedure to fit the data. The probability density function for the non-diseased population is unimodal with a mode at (CHL, TRG) = (195,122). On the other hand, the probability density function which best fits the data for the diseased population is distinctly bimodal with modes at (18.5, 122) and (233, 145). It is interesting that the univariate kernel probability density estimates of CHL and TRG separately for the diseased population are both unimodal and not bimodal. The probability density function given by equation (1) is a surface in three dimensions. Although there are several methods of depicting such surfaces, we chose to plot contours as seen when looking down on the surface from above. To compare the
Plasma
Lipids
as Collateral
o ZOO----Dseased
P
papulatlan
-Non-diseased
Risk Factors
(modes
population
in Coronary
Plasma
cholesterol
Disease
331
MI and M31 Mz)
( mode
220 a
Artery
concentration,
230
240
250
mg/lOOml
Fig. I. For the two patient groups, diseased and non-diseased males with chest pain, the estimated joint probability density functions for plasma lipid concentrations are shown as viewed from above. Each density function is represented by four contours of equal probability as discussed in the text. Patients were classified as diseased if they showed a stenosis of at least 25”:, in any of the four coronary arteries.
probability density functions of the diseased and non-diseased groups, we constructed for each distribution ten contours of equal probability. The vertical distance between the planes determining two adjacent contours is one-ninth of the maximum height of the density. We have depicted in Fig. 1 the highest four contours for the two distributions. It is apparent that one mode of the density function for diseased patients is close to the mode of the density function for normal patients. The other mode of the density function for the abnormal group is clearly displaced from the mode of the density function for the normal patients. A simple clustering technique was used to assign 146 and 174 diseased males to the left and right modes M, and M,, respectively. The linear function 250 CHL + 26.61 TRG-56865.25 was chosen for this process, since it is perpendicular to the line connecting the two modes M, and M, and intersects this line at the minimum off, (CHL, TRG) between M, and M,. Neither the mean ages nor the mean blood pressures differed significantly between the two modal groups. Only in the left coronary artery were the incidences of coronary artery disease perhaps significantly different (Table 2). When the mean occlusion for each vessel was calculated, more severe disease, particularly in the left coronary artery, was observed in the right modal group, the group with the more elevated plasma lipid concentrations (Table 3). For various fixed levels of plasma cholesterol concentrations, we computed the value of the likelihood ratio as a function of increasing plasma triglyceride concentration. The results of these calculations are displayed in Fig. 2. The solid portions of the graphs depict points where both density estimates exceed 10% of their respective maximum modal values. The dotted portion represent points where one or both density values fall between the 5 and 100,; levels. We believe the dotted lines are generally reliable estimates of risk ; however they are not as reliable as those of the solid portions of these graphs. The slopes of these lines are robust to changes in the scaling constants h,. and h, For low values of plasma cholesterol (say than 150 mg/dl), the likelihood ratio increases only slightly with increasing values of plasma triglyceride. As plasma
iess
142
DAVIII
W. SCOTT, ANTONIO M. GOTTO, JAMESS. COLE and G. ANTHONY GORRY
TABLE 2. ANALYSIS OF 320 DISEASEDPATIENTSBY MODE OF PROBABILITYDENSITYFUNCTION (PDF) TO WHICH THEY WERE ASSIGNED: PERCENTAGE* HAVING AT LEASTA 25% OCCLUSION 1~ A GIVEN CORONARY VESSEL
Vessel
:
Mode of PDF.; (CHL,TRG) = (185,122) (CHL, TRG) = (233,145)
Right
Left main
Circumflex
84 88 NS
15 13 NS
86 91 NS
*Percentages do not add to lOOO;,due to the presence of multiple-vessel -FSee text and Fig. I.
NS-Not
Left anterior descending
73 (P :.\74, disease.
significant.
TABLE 3. ANALYSISOF 320 DISEASEDPATIENTSBY MODEOFPROBABUTY DENSITYFUNCTION (PDF)To WHICH THEY WERE ASSIGNED: AVERAGE PERCENTAGEOCCLUSION IN EACH CORONARY VESSELFOR THE 320 DISEASED MALES
Vessel: Mode of PDF (CHL, TRG) = (185,122) (CHL, TRG) = (233,145)
NS-Not
Right
Left main
70
8
&z90)
i&
Circumflex
72
Left anterior descending
53
(P:po57)
significant.
cholesterol increases, the role of elevated plasma triglyceride concentrations as a risk factor assumes increasin.g importance. Not only do the curves of the likelihood ratio for these higher values of plasma cholesterol rise with increasing plasma triglyceride, but the slopes of these curves increase dramatically as well. Furthermore, the value of plasma triglyceride af which the likelihood ratio begins to increase sharply generally decreases with increasing plasma cholesterol. For the patients we studied, the prior odds of disease were quite high, 0 (D) = 32051 = 6.3 :l. To illustrate the use of equation (3), we consider two hypothetical patients with (CHL, TRG) values of (200,50) and (200,250). Frbm Fig. 2 the likelihood ratios at these values are 0.36 and 2.52, respectively. The estimated posterior odds of disease are 2.3 :l and 15.8 :l, respectively ; thus an increase in plasma triglyceride from 50 to 250 mg/dl results in a 7-fold increase in risk of disease for this plasma cholesterol level. Wilson and Lees [23] showed a reciprocal relationship between the concentrations of very low and low density lipoproteins (LDL) in man. A variety of studies in the past few years have provided evidence that there may be an inverse relationship between the concentration of plasma high density lipoproteins (HDL), and the risk of CAD [24-271. Further, Miller et al. [28] have recently reported that concentrations of plasma HDL-cholesterol are independently and inversely related to the concentrations of plasma triglyceride and of LDL-cholesterol. The HDL-cholesterol concentrations appear to be highest in subjects who are at lowest risk for developing coronary artery disease. In our patient group, HDL-cholesterol was determined only for those men judged to be hyperlipidemic [17]. For the 118 patients in this group, plasma triglyceride concentration was negatively correlated with plasma HDL-cholesterol concentration (R = - 0.178, P < O.OS),but no statistically significant correlation was
Plasma
Lipids as Collateral a 7
F
Risk Factors
CHL = Plasma cholesterol concentration (mg/lOOml)
in Coronary
Artery
Disease
343
: I’
25 t
kHL=200 I’ ‘$I !,’ \
L
-04 P zz 23 i 2
-1
0
50 Plasma
100 I50 200 250 triglyceride concentration,
300 350 mg/lOOml
Fig. 2. Likelihood ratio as a function of plasma triglyceride concentration for several fixed concentrations of plasma cholesterol. The relationship of the likelihood ratio to the risk of coronary artery disease is discussed in the text.
found between HDL-cholesterol concentration and extent of coronary artery disease. No statistically significant relationship was found between the ratio of HDLcholesterol to total cholesterol and the extent of coronary artery disease. The failure to find a significant ‘protective effect’ may reflect the fact that all patients in this sample were hyperlipidemic. DISCUSSION
To investigate the joint roles of plasma cholesterol and plasma triglyceride concentrations in coronary artery disease, we estimated their joint probability density functions for diseased and non-diseased males presenting with chest pain. The estimated density for the diseased group had two modes, one virtually indistinguishable from the single mode of the density for the non-diseased population. Using lipid concentrations as a guide, we placed each diseased patient in one of two groups corresponding to the two modes of the density function for diseased patients. Comparison of these two groups of diseased males revealed no significant differences in age, blood pressure, or location of occlusion except in the left coronary arterty; however, the group with higher lipid concentrations had more severe occlusion on the average, particularly in the left coronary artery. Using the two density functions, we constructed curves of the likelihood ratio as a function of plasma triglyceride for various fixed levels of plasma cholesterol. By holding plasma cholesterol‘fixed, we eliminated any effect due solely to a correlation between the two lipids. The results indicated an association between increased plasma triglyceride concentration and increased risk of coronary artery disease in males with chest pain. For low values of plasma cholesterol, the likelihood ratio shows only a slight increase with increasing plasma triglyceride ; however, for large values of plasma cholesterol, the role of elevated plasma triglyceride as a risk factor is clear. Not only do
344
DAVID W. SCOTT,ANTONIOM. GOTTO,JAMES S. COLE and G. ANTHONYGORRY
the curves of the likelihood ratio rise with increasing plasma triglyceride, but the slopes of these curves increase dramatically with increasing plasma cholestrol. Because we had plasma HDL-cholesterol concentrations for only the patients classified as hyperlipidemic, it is not surprising that we were unable to find a ‘protective effect’ for HDL, but the negative correlation we found between plasma HDLcholesterol and plasma triglyceride concentrations is consistent with such an effect. Nonetheless, an association between increased plasma triglyceride concentration and increased risk of coronary artery disease in the males with chest pain we studied has been demonstrated clearly by our analysis. The same analysis can be applied to other investigations of the relationships between plasma lipids and the risk of coronary artery disease. Acknowledgements-This research was supported in part by the National Heart and Blood Vessel Research and Demonstration Center, Baylor College of Medicine, a grant-supported research project of the National Heart, Lung, and Blood Institute, National Institues of Health, Grant No. 17269.
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in Coronary
Artery Disease
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Wilson DE, Lees RS: Metabolic relationships among the plasma lipoproteins. Reciprocal changes in the concentrations of very low and low density lipoproteins in man. J din Invest 51:1051-1057, 1972 Miller GJ, Miller NE: Plasma-high-density-lipoprotein concentration and development of ischaemic heart disease. Lancet 1:16-19, 1975 Castelli WP, Doyle JT, Gordon T, Hames C, Hulley SB, Kagan A, McGee D, Vicic WJ, Zukel WJ: Ischaemic heart-disease in relation to fasting values of plasma triglycerides and cholesterol. Stockholm Prospective Study. Lancet 1:865-868,1972 Glueck CJ, Fallat RW, Millett F, Gartside P, Elston RC, Go RCP: Familial hyper-r*-lipoproteinaemia: studies in 18 kindreds. Metabolism 24:1234-1265, 1975 Berg K, Borresen A, Dahlen G: Serum high-density-lipoprotein and atherosclerotic heart-disease. Lancet I :499-501,1976 Miller GJ, Miller NE, Ashcroft MT: Inverse relationship in Jamaica between plasma high-density lipoprotein cholesterol concentration and coronary-disease risk as predicted by multiple risk-factor status. Clin Sci Mol Med 5 I :4755482, 1976
