Correlations between measurements of different factors

Correlations between measurements some time apart (Table 3, right), which avoid artefactual same-sample effects, showed that apoB and LDL-C were not just two equivalent ways of assaying LDL particles, nor were apoA₁ and HDL-C two equivalent ways of assaying HDL particles. For, there was a highly significantly negative correlation between apoB and HDL-C (c = −0.20, SE 0.02), but not between LDL-C and apoA₁ (c = 0.00, SE 0.02). Moreover, the ratios LDL-C/apoB and HDL-C/apoA₁ were positively correlated with each other (c = 0.17, SE 0.02), showing that both were informative. These correlations have been independently replicated²⁴ (Supplementary material online, Table A6).

Table 3

Correlation coefficients (c) between measurements of different lipid-related factors

	Same sample (9805)	Different sample (2 × 1042)
Within LDL particles
ApoB vs. LDL-C	0.85	0.68
Within HDL particles
ApoA1 vs. HDL-C	0.70	0.64
Between LDL and HDL particles
ApoB vs. apoA1	0.09	−0.06
ApoB vs. HDL-C	−0.22	−0.20
ApoB vs. HDL-C/apoA1	−0.39	−0.25
LDL-C vs. apoA1	0.06	0.00
LDL-C vs. HDL-C	−0.06	−0.08
LDL-C vs. HDL-C/apoA1	−0.13	−0.13
LDL-C/apoB vs. apoA1	−0.04	0.11
LDL-C/apoB vs. HDL-C	0.24	0.18
LDL-C/apoB vs. HDL-C/apoA1	0.39	0.17

Open in a separate window

The standard error of each c, estimated as (1 − c²)/√N, is <0.022. Same sample: all 9805 controls in the present study. Different sample: 1042 controls with re-measurement 2–3 years later (yielding two independent estimates of each correlation coefficient; their average is tabulated).

The negative correlation between apoB and HDL-C corresponds to the correlations of triglycerides with high apoB and low HDL-C (and, particularly, with a low ratio of HDL-C to apoA₁; Supplementary material online, Table A7).

Joint relationship of risk to measured values of more than one factor

Table 4 (and Supplementary material online, Table A8) gives the improvements in fit when one or several extra terms were added into the logistic regression. The χ² for adding apoB alone (279.7) was virtually as great as that for adding both LDL-related factors, apoB and LDL-C (281.3: Table 4). Indeed, given the measured value of apoB, that of LDL-C was slightly negatively related to risk. The χ² for adding LDL-C alone was, in contrast, only 175.2, giving a χ² of 106.1 (281.3–175.2; P < 0.00001) for the addition of apoB given LDL-C.

Table 4

Comparison of predictive strengths for myocardial infarction relative risk of adding different combinations of lipid-related terms

Added lipid-related terms	Degrees of freedom (df)	Improvement in fit (χ2)a	Direction of association of respective terms
LDL related
LDL-C	1	175.2	+
ApoB	1	279.7	+
ApoB, LDL-C	2	281.3	+, −
HDL related
HDL-C	1	290.6	−
ApoA1	1	212.9	−
ApoA1, HDL-C	2	312.6	−, −
HDL related, with apoB already in the model
HDL-C	1	187.7	−
ApoA1	1	278.5	−
ApoA1, HDL-C	2	287.2	−, −

Open in a separate window

^aImprovement in the prediction of relative risk by the addition of the measured values of various lipid-related terms to the basic model in which relative risk depends only on age, sex, smoking, and BMI (and, where indicated, the measured value of apoB). The χ² value is twice the improvement in the log-likelihood on addition of extra terms (with df = no. of extra terms).

Taken singly, without any information about LDL particles, HDL-C was somewhat more informative than the other HDL-related factor, apoA₁ (χ² = 290.6 and 212.9, respectively: Table 4). However, part of the negative predictive power of HDL-C came from its negative association with apoB (Table 3). Given apoB, the gain from adding HDL-C was reduced and that from adding apoA₁ was increased, so apoA₁ became more informative than HDL-C (χ² = 278.5 and 187.7, respectively, Table 4). In the joint relationship of risk to the measurements of apoB, apoA₁, and HDL-C the regression coefficient for HDL-C remained slightly negative.

The two strongest risk factors were apoB and, given apoB, apoA₁. Moreover, their joint effect was much stronger than that of either alone [χ² = 558.2 for their joint fit: Supplementary material online, Table A8 (279.7+278.5 in Table 4)]. Measurements of LDL-C and HDL-C were weaker predictors (χ² = 462.9 for their joint fit: Supplementary material online, Table A8). ApoB was positively and apoA₁ negatively associated with risk, and the ratio apoB/apoA₁ encapsulated almost all the risk prediction from these two measurements, or from all four measurements (Supplementary material online, Table A8). When all four measurements were fitted, the improvement in predictive power over just apoB and apoA₁ was conventionally significant, but slight (χ² = 567.0–558.2=8.8 on 2 df; P = 0.02: Supplementary material online, Table A8).

Joint relationship of risk to usual values

The joint relationship of risk with two strongly correlated factors, such as apoB and LDL-C, cannot be as easily corrected for measurement error²⁵ as single-factor relationships can be. If, however, both analytes are expressed comparably, in units of 2SD, then their sum is approximately uncorrelated with the difference between them. When risk is related jointly to this sum and difference, the appropriate correction factors for the two terms should therefore be approximately independent of each other. As the sum (apoB +LDL-C) is more reproducible in measurements taken a few years apart than is the difference (apoB−LDL-C), correction for the effects of measurement error has less effect on the regression coefficient for the sum than on that for the difference.

Numerical detail of joint relationship (Supplementary material online, Panel A1):

The log relative risk (with both analytes in units of 2SD) was:

which depends strongly on measured apoB but not on measured LDL-C. After correction for measurement error, however, this formula became:

which rearranges to:

This indicates that, given the usual value of apoB, the usual value of LDL-C was strongly negatively correlated with risk (regression coefficient –1.05, SE 0.26, P < 0.0001).

Causal relevance of low-density lipoprotein particles

Plasma apoB reflects precisely the total number of LDL-related particles (LDL particles or their triglyceride-rich precursors). As LDL particles greatly outnumber their precursors, plasma apoB is closely correlated with the number of LDL particles per unit volume. Genetic defects that decrease clearance of LDL particles cause familial hypercholesterolaemia and very high risk, showing that LDL particles can actually cause coronary artery disease. Likewise, statin treatment increases clearance of LDL particles and, in randomized trials, causes a substantial reduction in apoB, in LDL-C, and in risk.²⁶ Hence, the strong association of apoB with MI risk must to some considerable extent reflect the causal relationship between LDL particles and disease. Our finding that, for a given usual apoB, lower LDL-C was associated with a higher risk of MI supports previous suggestions²⁷ that, on average, LDL particles with low cholesterol content per particle (small, dense LDL particles) are particularly hazardous. Reliable assessment of the risks caused by particular types of LDL particle requires, however, more direct measurement of the numbers of particles of different types and subtypes, allowing their inter-relationships to be explored.

Causal relevance of high-density lipoprotein particles

Plasma apoB is not strongly related to apoA₁, but it is strongly inversely related to HDL-C. (This is partly because triglyceride-rich LDL precursors can remove cholesterol from the larger HDL particles, reducing HDL-C levels but not HDL particle numbers.) To the extent that adjustment for apoB can allow for the effects of the LDL-related particles on risk and on the HDL system, the independent relevance of the HDL system is best assessed by its relationship with risk given apoB. This was stronger for low apoA₁ than for low HDL-C. These associations of risk with low levels of HDL-related factors presumably reflect a real protective effect of some type(s) of HDL particle, since the HDL system is, among other things, responsible for reverse cholesterol transport. The difference between apoA₁ and HDL-C in the strengths of their independent associations with risk (given apoB) suggests that some types of HDL particle may be more protective than others. Unfortunately, however, uncertainty in the extrapolation of post-infarction HDL-C (and triglyceride) values in cases back to their pre-infarction values precluded further pursuit of this. Nonetheless, the strong correlation of apoA₁ with low risk provides evidence of a real protective effect of at least some type(s) of small HDL particle.

Causal relevance of triglyceride-rich precursors

Triglyceride-rich precursors of LDL particles are important determinants of the plasma levels of particular types of LDL particle and (as they can remove cholesterol from some HDL particles) of particular types of HDL particle. Our statistical analyses sought to elucidate the effects of LDL and HDL particles on disease, so it was not appropriate to adjust for triglyceride levels, even if these do correlate with some aspects of the HDL and LDL system of particles. (Moreover, triglyceride levels change after the onset of MI, distorting case–control comparisons of them.)

Risk prediction from a single blood sample

Given the usual values of apoB and apoA₁, the usual values of LDL-C and HDL-C appeared to be informatively related to risk. Given the measured values of apoB and apoA₁, however, the measured values of LDL-C and HDL-C were only weakly related to risk, and for risk prediction from a single set of measurements on a single blood sample what matters is the relevance of the measured values.

In this study, the ratio apoB/apoA₁ encapsulated almost all the information from measurements of these two lipoproteins and of both cholesterol fractions (Table 2, Supplementary material online, Table A8). It was substantially more informative than the ratio LDL-C/HDL-C, more than twice as informative as either LDL-C or non-HDL cholesterol (the main biochemical treatment criteria in various current guidelines^28,29) and about five times as informative as total cholesterol.

Routine measurement of apoB, apoA₁, and their ratio apoB/apoA₁ is widely practicable, and the present results indicate that there is about seven-fold variation in the relative risk of MI between the top and bottom deciles of the measured values of this ratio in UK heart disease patients (Figure 1). Moreover, the apoB/apoA₁ ratio is informative even in old age (70–79) and is highly reproducible, with a self-correlation coefficient of 0.81 in the present study between measurements on samples taken a few years apart (Table 2). Although the present study was restricted to the UK, the large INTERHEART case–control study³⁰ demonstrated the global importance of a single measurement of this ratio, and reported it to be better than any cholesterol-based ratios. (We note, however, that time from onset of symptoms in cases was not corrected for in their HDL-C analyses.)

If total and HDL cholesterol are the only measurements available, then our study suggests that risk prediction would be better based on their ratio than on their difference, non-HDL cholesterol, which was substantially less predictive of risk. This was also found in a meta-analysis of prospective studies.²¹ In those studies (none with posted blood samples), a 1.33 lower usual value of total/HDL cholesterol was associated with relative risks of 0.56 and 0.60, respectively, for ischaemic heart disease mortality at ages 40–59 and 60–69 years. In the present study of non-fatal MI (at a median age of 60 years), the corresponding relative risk was 0.58, in close agreement.

Case–control designs have inherent limitations, but our analyses are unaffected by any uncertainties of calibration and have incorporated appropriate adjustments for the main potential biases, and for the regression dilution bias. In addition, a range of sensitivity analyses (Supplementary material online, Table A9) have confirmed that alternative adjustments make little difference. Furthermore, the ratio apoB/apoA₁ should be little affected by methodological problems. The conclusion that single measurements of apoB and apoA₁ are more predictive than single measurements of LDL-C and HDL-C is consistent with a recent review,⁷ and is what would be expected if, given the usual apoB and apoA₁, the usual LDL-C is negatively related to risk.

The chief acknowledgement is to patients and relatives, and medical and nursing staff from the UK hospitals in the ISIS-3 study.⁹ Jill Barton and Kathy Jayne co-ordinated the case–control study. Sample storage, retrieval, and assay was co-ordinated by S.C., Karen Kourellias, Martin Radley, and L.Y. (and involved help from many people).