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Discriminant ratio and biometrical equivalence of measured vs. calculated apolipoprotein B_{100} in patients with T2DM
Cardiovascular Diabetology volume 12, Article number: 39 (2013)
Abstract
Background
Apolipoprotein B_{100} (ApoB_{100}) determination is superior to lowdensity lipoprotein cholesterol (LDLC) to establish cardiovascular (CV) risk, and does not require prior fasting. ApoB_{100} is rarely measured alongside standard lipids, which precludes comprehensive assessment of dyslipidemia.
Objectives
To evaluate two simple algorithms for apoB_{100} as regards their performance, equivalence and discrimination with reference apoB_{100} laboratory measurement.
Methods
Two apoB_{100}predicting equations were compared in 87 type 2 diabetes mellitus (T2DM) patients using the Discriminant ratio (DR). Equation 1: apoB_{100} = 0.65*nonhighdensity lipoprotein cholesterol + 6.3; and Equation 2: apoB_{100} = −33.12 + 0.675*LDLC + 11.95*ln[triglycerides]. The underlying betweensubject standard deviation (SD_{U}) was defined as SD_{U} = √ (SD^{2}_{B}  SD^{2}_{W}/2); the withinsubject variance (V_{w}) was calculated for m (2) repeat tests as (V_{w}) = Σ(x_{j} x_{i})^{2}/(m1)), the withinsubject SD (SD_{w}) being its square root; the DR being the ratio SD_{U}/SD_{W}.
Results
All SD_{u}, SD_{w} and DR’s values were nearly similar, and the observed differences in discriminatory power between all three determinations, i.e. measured and calculated apoB_{100} levels, did not reach statistical significance. Measured Pearson’s productmoment correlation coefficients between all apoB_{100} determinations were very high, respectively at 0.94 (measured vs. equation 1); 0.92 (measured vs. equation 2); and 0.97 (equation 1 vs. equation 2), each measurement reaching unity after adjustment for attenuation.
Conclusion
Both apoB_{100} algorithms showed biometrical equivalence, and were as effective in estimating apoB_{100} from routine lipids. Their use should contribute to better characterize residual cardiometabolic risk linked to the number of atherogenic particles, when direct apoB_{100} determination is not available.
Introduction
Lowdensity lipoproteins (LDL) and their verylow density lipoprotein (VLDL) precursors represent the major atherogenic particles. Each contains a single apolipoprotein B_{100} (apoB_{100}) molecule, which ensures the structural integrity of the lipoprotein, and binds to the hepatic receptor for catabolic removal of LDL. The “smalldense” LDL phenotype confers a higher cardiovascular (CV) risk than that resulting from their cholesterol load. Therefore circulating apoB_{100} level more accurately reflects the number of atherogenic particles, 90% of apoB_{100} belonging to LDL irrespective of their size. The determination of apoB_{100} does not require prior fasting, unlike estimation of LDLcholesterol (LDLC) by Friedewald’s formula [1–8].
Numerous studies have demonstrated the superiority of apoB_{100} relative to LDLC to establish CV risk, and improvement of outcomes after lipidlowering drug (LLD) therapy [2–6, 9]. The Adult Treatment Panel III proposed that in individuals with elevated triglycerides (TG), nonhighdensity lipoprotein cholesterol (nonHDLC) should be treated as secondary therapy goal, after targeting LDLC; moreover nonHDLC appears a better predictor of CV risk than LDLC, especially in statintreated patients [2, 6]. However, the relationships between LDLC, nonHDLC and apoB_{100} are often less convergent than expected, and therefore less predictable in patients at high cardiometabolic risk, including those with high TG and/or the metabolic syndrome. In these patients, including those with type 2 diabetes mellitus (T2DM), nonHDLC and apoB100 are therefore less interchangeable than the reading of the general recommendations for the treatment of hypercholesterolemia would suggest.
In the absence of consensual guidelines, the current recommendation for hypercholesterolemic patients at high cardiometabolic risk is to bring at target three key modifiable variables: (i) LDLC; (ii) nonHDLC; and (iii) apoB_{100}[6, 10]. In real life however, apoB_{100} determination is rarely performed alongside routine lipids, which precludes such comprehensive assessment of residual dyslipidemia. Consequently, simple algorithms were proposed to estimate apoB_{100} level from routine lipids, based on LDLC and nonHDLC as freelyavailable biometrical equivalent to apoB_{100}[7, 8].
The aim of this study was to compare the performance and true equivalence of two apoB_{100}predicting algorithms in T2DM patients considered at high cardiometabolic risk, with reference to laboratory determination of apoB_{100} and against each other. We used the Discriminant Ratio (DR) methodology, which standardises comparisons between measurements by taking into account fundamental properties for assessing imprecision and practical performance of tests designed to quantify similar variables [7, 11–14]. Crossvalidation of these algorithms should prompt potential users to increasingly rely on them, to derive unbiased apoB_{100} values from landmark epidemiological or interventional databases, or from current standard lipids in specific situations where it is desirable to know the levels of nonHDLC and that of apoB_{100}.
Methods and statistical analysis
We studied 87 consecutive (84% white Caucasians; 6% NorthAfricans; 5% subSaharan Africans) patients with T2DM, treated or not with lipidlowering drug(s) (LLD). All lipid values were obtained in the fasting state, on two nonconsecutive days. The timespan between sampling, obtained during regular outpatients’ followup visits, was 2–6 months. The following biologic variables were recorded: glycated hemoglobin (HbA_{1c}), fasting lipids (total cholesterol [C], HDLC, and TG). Fasting duration was ≥10hours, with last intake of food allowed at dinner the day before sampling. No change in LLD(s) was allowed during the interval that separated the two days of sampling.
Total C and TG were determined using the SYNCHRON system (Beckman Coulter Inc., Brea, CA). HDLC was determined with the ULTRANgeneous reagent (Genzyme Corporation, Cambridge, MA). ApoB_{100} was measured with immunonephelometry on BNII Analyzer (Siemens Healthcare Products GmbH, Marburg, Germany) from the same blood samples destined for routine lipids determination. The withinsubject coefficients of variation were as follows: 5.4% [total C]; 7.1% [HDLC]; and 6.9% [apoB_{100}]. LDLC was computed with Friedewald’s formula [1]; nonHDLC by subtracting HDLC from total C.
Besides direct measurement, ApoB_{100} level was calculated from routine lipids using the two following equations:
based on fasting or nonfasting lipids [ref. 7]
based on fasting lipids only [ref. 8]
The presence of atherogenic dyslipidemia (AD) was defined as the combined occurrence of decreased HDLC (<40 [males] or <50 mg/dL [females]) plus elevated fasting TG (≥150 mg/dL) using baseline lipid values (ie, before any LLD(s) in treated patients) [15]. Glomerular filtration rate was estimated using the Modified Diet in Renal Disease formula [16].
The Discriminant Ratio (DR) methodology compares different tests measuring the same underlying physiological variable by determining the ability of a test to discriminate between different subjects, and the comparison of discrimination between different tests as well as the underlying correlation between pairs of tests adjusting for the attenuating effect of withinsubject variation [7, 11–14]. In a comparison study where duplicates measurements are performed in each subject, the measured betweensubject standard deviation (SD_{B}) is calculated as the SD of the subject mean values calculated from the 2 replicates.

The standard mathematical adjustment to yield the underlying betweensubject SD (SD_{U}) is: SD_{U} = √ (SD^{2}_{B}  SD^{2}_{W}/2);

The withinsubject variance (V_{w}) is calculated for m repeat tests as (V_{w}) = Σ(x_{j} x_{i})^{2}/(m1)), the withinsubject SD (SD_{w}) being its square root;

The DR represents the ratio SD_{U}/SD_{W}
Confidence limits for DR’s and the testing for equivalence of different DR’s were calculated and differences were considered significant for p < 0.05. Given sample size and number of replicates, the minimal detectable significant difference in DR for the present study was 0.42. Coefficients of correlation between pairs of tests used to estimate apoB_{100} (measured vs. estimated) were adjusted to include an estimate of the underlying correlation, as standard coefficients tend to underestimate the true correlation between tests, due to withinsubject variation [13].
The study was performed in accordance with the institutional review board of StLuc Academic Hospital.
Results
The patients’ characteristics are described in Table 1. Mean age (1 SD) was 65 (10) years, with a male gender predominance. Mean body mass index was in the overweight/obese range, and patients had longstanding diabetes (mean duration 15 (8) years), and high prevalence of metabolic syndrome or of its defining nonglycaemic features, as well as macroangiopathies (coronary [25%] and peripheral [11%] artery disease and/or cerebrovascular disease [5%]). LLDs were widely prescribed, mostly as statins (74%) and/or fibrates (43%). Mean glycaemic control, as reflected by HbA_{1c}, was suboptimal at 62 (11) mmol/mol. The current lipid profile was typical of that of patients with the usual form of T2DM, i.e. associated with features of the metabolic syndrome and insulin resistance: low HDLC, raised nonHDLC, apoB_{100}, TG, and high frequency (49%) of AD.
Figure 1 illustrates the plots of untransformed values of measured apoB_{100} vs. estimated apoB_{100} from equations 1 and 2, the values representing the means of the two estimates obtained on different days. The linear regression formula for equation 1 was: calculated apoB_{100} = 0.871 × measured apoB_{100} + 9.64 mg/dL (R^{2} = 0.8756); whereas that of equation 2 was: calculated apoB_{100} = 0.812 x measured apoB_{100} + 16.0 mg/dL (R^{2} = 0.8451). The figure also shows the homoscedastic behaviour on repeat testing of the data spread. The alignment of the regression lines was not affected by mean baseline TG levels obtained on day 1 and 2.
The precision and discrimination of the three apoB_{100} estimates, expressed as underlying betweensubject Standard Deviation (SD_{u}), global withinsubject Standard Deviation (SD_{w}), and Discriminant Ratio (DR) are shown in Table 2. All SD_{u}, SD_{w} and DR’s values were almost similar, and the observed differences in discriminatory power between all three determinations did not reach statistical significance.
The measured Pearson’s product–moment correlation coefficients between the three apoB_{100} determinations methods were very high, respectively 0.94 (measured vs. equation 1 apoB_{100}); 0.92 (measured vs. equation 2 apoB_{100}); and 0.97 (equation 1 vs. equation 2 apoB_{100}), each reaching unity (1.00) once values were correlated after adjustment for attenuation (Table 3).
Discussion
This study demonstrates that in patients with T2DM, two simple equations published to date were as effective to calculate apoB_{100} concentration from routine lipids [7, 8]. In addition, as the underlying correlation between apoB_{100} levels estimated by the two formulas reached unity, once preanalytical and analytical attenuation was taken into account, these two algorithms may be used interchangeably to assess an equivalent underlying biological variable. Even though the two algorithms were developed from lipid values obtained in different populations and conditions, each formula can substitute for each other, being as precise and interchangeable.
Although equation 1 was computed using lipid values from a small cohort (n = 45) of Caucasian T2DM patients, and equation 2 used fasting lipids from an extensive cohort (n = 73047) of healthy Koreans representative of a general Asian population, the two means of estimating apoB_{100} were perfectly correlated, and as effective and precise. This illustrates the performance of the comparison of measurements methods based on the DR methodology, which requires only limited samples (n ≥20 for 2 replicates), as long as the sample represents a meaningful clinical range for the variable under study [see appendix of [13] for a detailed discussion on sample size requirements for estimating DRs].
ApoB_{100} metabolism and physiology are comparable in diabetic and nondiabetic subjects, as well as in different ethnic groups. The equations appear applicable across the two major ethnic groups that provided the source data, and uninfluenced by baseline TG values. An inherent advantage of equation 1 is the inclusion of lipid values that do not require sampling in the fasting state, whereas equation 2 requires a fasting lipid panel [7, 8]. Another limitation of equation 2, in terms of routine clinical practice, is that LDLC is usually calculated from Friedewald’s formula, which induces systematic and linear underestimation once fasting TG rise above 200 mg/dl, confining the applicability of equation 2 to patients with fasting TG <400 mg/dL, unless direct LDLC measurement is available [2].
For use in equation 1, nonHDLC offers the added advantage of being derived from the compute of two robust, wellestablished measurements methods, namely total cholesterol and HDLC [7]. Although Cho et al. used direct, and hence more expensive measurements of LDLC, contributing to enhance accuracy of their algorithm [8], there is an intrinsic rationale to opt for equation 1 in populations with high prevalence of hypertriglyceridemia, such as patients with AD [6, 10, 15, 17–19]. They belong to the highest cardiometabolic risk category, for which it is recommended to assess (and bring to target), both nonHDLC and apoB_{100}, on top of LDLC [6, 10, 20].
There is still no consensus among the various players on the ultimate relevance to measure apoB_{100}, nonHDLC, or both, for baseline or residual CV risk classification, One might wonder what is the advantage of being able to dispose of apoB_{100} from an equation that incorporates nonHDLC, since the latter is considered by ATPIII as adequate and sufficient. Notwithstanding the ongoing debate, the apoB_{100} concept is intrinsically easier to apprehend than nonHDLC, which contains in itself a ferment of educational failure because it represents a state of otherness defined by a nonnumber, instead of a single atherogenic lipid variable [21].
In conclusion, this study demonstrates the biometrical equivalence of two original apoB_{100} algorithms, which are as effective in estimating the concentration of apoB_{100} from routine lipids, and may be used interchangeably. One approach requires fasting blood lipids, while the other is not influenced by fasting status, and therefore independent of food intake prior to sampling. These algorithms should contribute to better characterize residual cardiometabolic risk linked to the number of atherogenic particles in patients with available standard lipids, but in whom apoB_{100} assay was not performed for various reasons. The practical implications of these findings are directly relevant to routine clinical practice.
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Hermans, M.P., Ahn, S.A. & Rousseau, M.F. Discriminant ratio and biometrical equivalence of measured vs. calculated apolipoprotein B_{100} in patients with T2DM. Cardiovasc Diabetol 12, 39 (2013). https://doi.org/10.1186/147528401239
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DOI: https://doi.org/10.1186/147528401239
Keywords
 ApoB_{100}
 LDLC
 NonHDLC
 Discriminant ratio
 Type 2 diabetes
 Cardiovascular risk