 Original investigation
 Open Access
 Published:
Novel unbiased equations to calculate triglyceriderich lipoprotein cholesterol from routine nonfasting lipids
Cardiovascular Diabetology volume 13, Article number: 56 (2014)
Abstract
Background
Nonfasting triglyceriderich lipoproteins cholesterol (TRLC) contributes to cardiovascular risk, in that it includes remnant cholesterol (RC). TRLC is computed as total C  [LDLC + HDLC]. Such calculation applies only if LDLC is directly measured, or obtained from a nonFriedewald’s formula, a method as yet never benchmarked against independent markers of TRL burden.
Methods
The Discriminant Ratio (DR) methodology was used in 120 type 2 diabetic patients in order: (i) to compute TRLC from nonfasting lipids; (ii) to establish the performance of TRLC and TRLC/apoAI (vs. TGbased markers) to grade TRLs and atherogenic dyslipidemia (AD); and (iii) to relate TRLC with nonfasting TG.
Results
Depending on apoB_{100} availability, TRLC (mg/dL) can be derived from nonfasting lipids in two ways: (a) total cholesterol (TC)  [(0.0106 * TC  0.0036 * TG + 0.017 * apoB_{100}  0.27) * 38.6]  HDLC; and (b) TC  [(0.0106 * TC  0.0036 * TG + 0.017 * [0.65 * (TC  HDLC) + 6.3]  0.27) * 38.6]  HDLC. Discrimination between log[TG] and TRLC was similar (DR 0.94 and 0.84, respectively), whereas that of log[TG]/HDLC was better than TRLC/apoAI (DR 1.01 vs. 0.65; p 0.0482). All Pearson’s correlations between pairs reached unity, allowing formulation of two unbiased equivalence equations: (a) TRLC = 97.8 * log[TG]  181.9; and (b) TRLC/apoAI = 8.15 * (log[TG]/HDLC)  0.18.
Conclusions
TRLC and log[TG] are as effective and interchangeable for assessing remnant atherogenic particles. For grading TRLAD, it is best to use log[TG]/HDLC, inherently superior to TRLC/apoAI, while measuring the same underlying variable.
Introduction
Cholesterol (C) in atherogenic particles other than lowdensity lipoproteins (LDL) is an emerging risk factor (RF) for ischemic heart disease, and is mostly found in fasting and nonfasting triglyceriderich lipoproteins (TRLs). TRLs comprise two clusters: (i) chylomicrons (CM; triglycerides (TG)rich lipoproteins (TRLs) of intestinal origin) and their remnants (CMR), each carrying one apolipoprotein (apo) B_{48}); and (ii) verylow density lipoproteins (VLDL; endogenous TRLs which originate in the liver, and their relatively TGdepleted remnants (VLDLR), each carrying one apoB_{100}) [1–13].
Table 1 describes the distribution of fasting and nonfasting lipid particles, TRLs, and TRL remnants distribution, with respective contribution to total cholesterol, TRLcholesterol (TRLC), and TRLremnant cholesterol (TRLRC), alongside their major corresponding apolipoprotein(s). Among TRLs, nonfasting residual TGrich particles are considered as a major contributor to residual vascular risk (RVR), even in patients on statins whose LDLC reaches target. These residual lipoproteins are a blend of chylomicrons remnants (CMR) and verylowdensity lipoprotein remnants (VLDLR). Their atherogenicity is related to their ability to deliver cholesterol in vessels walls.
Quantification of the cholesterol content of TGrich particles would be informative to better characterize their nonfasting atherogenic load. However this would require direct specific lipoproteins measurement beyond routine clinical practice. For this reason, several authors recently proposed to use a simple formula to measure “remnant cholesterol” (RC) from standard nonfasting lipids, “RC” being calculated as total C  (highdensitylipoprotein (HDL)C + LDLC) [10, 11]. Such equation however measures TRLC (the sum of CMC, CMRC, VLDLC and VLDLRC), and not RC. The latter is the sum of CMRC and VLDLRC, and accounts for only two out of four components of TRLC (Table 1).
As for RC, nonfasting TRLC is usually not measured, but derived according to the formula set out above: TRLC = total C minus [LDLC + HDLC] [8–11]. Whereas LDLC can be inferred from Friedewald’s equation in fasting conditions, this calculation underestimates LDLC in moderate to severe hypertriglyceridemia (200400 mg/dL), and is inapplicable for fasting TG >400 mg/dL [14]. To overcome this inaccuracy, a novel method for estimating LDLC from standard lipid profile using an adjustable factor for the TG:VLDLC ratio was recently proposed by Martin et al. [15, 16].
By its very nature, Friedewald’s equation is unusable in the nonfasting state. This is because in the presence of elevated fasting TG or in nonfasting conditions, the CtoTG content of remnant lipoproteins (RLPs) infringes the steady 1/5 ratio (20% C and 80% TG) at the core of Friedewald’s method [14–20]. Determining nonfasting TRLC using a Friedewaldderived LDLC level is methodologically inadequate, as it merely equates TRLC with onefifth of nonfasting TG, thus failing to provide additional information beyond TG levels [8, 10, 11].
The lack of a simple and suitable method to determine TRLC currently limits its clinical use for evaluating RVR, unless adequate alternatives to determine nonfasting LDLC are used. To circumvent this difficulty, an alternative approach is to derive LDLC from apoB_{100}, waiving the bias generated by applying a fixed CtoTG ratio that assumes constant and identical composition for all RLPs. A disadvantage of this method is the requirement for direct apoB_{100} measurement, limiting its use unless apoB_{100} is inferred from routine lipids, as previously described [17–21].
The aims of this study were: (i) to provide relevant equations to estimate TRLC from nonfasting lipids, regardless apoB_{100} availability; (ii) to establish the performance and equivalence of TGbased markers vs. TRLC and TRLC/apoAI, a continuous estimator of atherogenic dyslipidemia (AD); and (iii) to derive an unbiased equation predicting TRLC from nonfasting TG. We used the Discriminant Ratio (DR) methodology which standardizes comparisons between measurements by taking into account fundamental properties for assessing imprecision and practical performance of tests designed to quantify similar variables [19, 22, 23].
Methods
We studied 120 consecutive (86% white Caucasians) patients with T2DM, treated or not with lipidlowering drug(s) (LLD). Age; gender; diabetes duration; smoking history; anthropometric indices; hypertension and metabolic syndrome (MetS) prevalence, the latter defined according to the harmonized criteria of Alberti et al.[24]; habitual ethanol intake; current glucoselowering drugs, and LLDs were analysed. Hypertension was defined as systolic ≥140 and/or diastolic blood pressure ≥90 mmHg, and/or treatment with antihypertensive drugs. Glomerular filtration rate was estimated (eGFR) using the Modification of Diet in Renal Disease formula [25]. Albuminuria was defined as an albumin excretion ≥30 μg.mg creatinine^{1}.1.73 m^{2} from firstmorning sample. Coronary and peripheral artery disease (CAD and PAD) were diagnosed as in [26], while stroke was defined according to UK Prospective Diabetes Study (UKPDS) criteria [27]. Atherogenic dyslipidemia (AD) was defined according to [28–30].
The following variables were measured in the nonfasting state: glycated haemoglobin (HbA_{1c}), total C; HDLC; TG; apoAI and apoB_{100}, with total C and TG determined with SYNCHRON system (Beckman Coulter Inc., Brea, CA); HDLC with ULTRANgeneous reagent (Genzyme Corporation, Cambridge, MA); apoAI and apoB_{100} by immunonephelometry (BNII Analyzer, Siemens Healthcare Products GmbH, Marburg, Germany). Nonfasting routine lipids, apoAI and apoB_{100} were measured on two nonconsecutive days for DR calculation, with a 46 months’ interval between samples. A nonHDLC/apoB_{100} ratio >2.6 was an exclusion criterion because highly suggestive for Type III hyperlipoproteinemia [31]. The withinsubjects coefficients of variation were: 5.4% [total C]; 7.1% [HDLC]; 4.9% (apoAI) and 6.9% [apoB_{100}].
TRLC was calculated from nonfasting lipids by subtracting [LDLC + HDLC] from total C, with LDLC computed using Planella’s formula [17, 19]:
Normal TRLC values from 50 apparentlyhealthy lean Caucasians, untreated with LLD and without familial hypercholesterolemia or earlyonset parental CV disease, were (mg/dL): 24 (mean); 21 (median); 17 (SD); 2 (minimum); 71 (maximum); 13 (percentile 25) and 29 (percentile 75).
Each patient gave written informed consent; the study was performed in agreement with Helsinki’s Declaration; Good Clinical Practice principles; and the local Institutional Review Board.
Statistics
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 attenuation due to withinsubject variation [22]. 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}) 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 (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 [22].
Results are presented as means (±1 standard deviation [SD]), or as proportions (%). The significance of differences between means was assessed by Student’s t test, or by Welch’s test for data sets with significant differences in SDs, and by Chi^{2} test for differences in proportions. Results were considered statistically significant or nonsignificant (NS) for p <0.05 or p ≥0.05, respectively.
Results
Patients’ characteristics are described in Table 2. Mean age (1 SD) was 67 (11) years, with a male gender predominance. Mean body mass index was in the overweight range. Patients had longstanding diabetes (mean duration 16 (9) years), with a majority also having hypertension (89%), and a MetS phenotype (92%). Current smokers amounted to 13%; habitual ethanol intake was 10 (18) U/week. Mean glycaemic control, as reflected by HbA_{1c}, was suboptimal at 7.79 (1.32)% (62 (10) mmol/mol). Overall microangiopathy prevalence was 58%: retinopathy 37%; polyneuropathy 28% and/or (micro) albuminuria 29%.
Most patients were on LLDs: statins (81%) and/or fibrates (38%). Current mean lipids and lipoproteins values were illustrative of patients with the usual form of T2DM, i.e. associated with central adiposity, insulin resistance (IR) and MetS: low HDLC with raised nonHDLC, apoB_{100}, TG and TRLC, together with a high prevalence of AD (58%). Overall macroangiopathy prevalence was 33%: CAD [23%]; PAD [11%] and/or cerebrovascular disease [7%].
Figure 1 shows the plots of untransformed values on two different days for TG; TRLC; log[TG]/HDLC; and TRLC/apoAI, respectively. Relative median daytoday variations were: 36% (TG); 39% (TRLC); 16% (log[TG]/HDLC); and 46% (TRLC/apoAI), respectively. Figure 1 also shows the heteroscedastic arrangement of the data spread on repeat measurements.
The precision, discrimination and interrelation of each nonfasting estimate, expressed as underlying betweensubject standard deviation (SD_{u}), global withinsubject standard deviation (SD_{w}), discriminant ratio (DR); and measured Pearson’s productmoment correlation coefficients are shown in Table 3. For the log[TG] vs. TRLC comparison, the respective SD_{u}/SD_{w} (DRs) were 0.94 and 0.84, and the difference in discriminatory power between the two determinations did not reach statistical significance. As regards the log[TG]/HDLC vs. TRLC/apoAI comparison, the respective DRs were 1.01 and 0.65, the discriminatory power of log[TG]/HDLC being significantly better than of TRLC/apoAI (p 0.0482).
The Pearson’s correlations between each pair of tests were high, respectively 0.92 (log[TG] vs. TRLC) and 0.89 (log[TG]/HDLC vs. TRLC/apoAI), each correlation reaching unity, once values were adjusted for attenuation prior to correlation (Table 3).
Figure 2 shows the plots of untransformed values (means of Day 1 and Day 2) for log[TG] vs. TRLC, and log[TG]/HDLC vs. TRLC/apoAI. The equations of the unbiased lines of equivalence relating each pair of tests were:
Practically, these equations allow for calculating TRLC without bias from standard nonfasting lipids, depending on apoB_{100} availability (units mg/dL):

1.
apoB _{ 100 } is available alongside standard nonfasting lipids:
\begin{array}{ll}\mathbf{TRL}\mathbf{\u2012}\mathbf{C}=\mathbf{TC}& \left[\left(0.0106\phantom{\rule{0.5em}{0ex}}*\phantom{\rule{0.5em}{0ex}}\mathbf{TC}0.0036\phantom{\rule{0.5em}{0ex}}*\phantom{\rule{0.5em}{0ex}}\mathbf{TG}+0.017\right.\right.\\ \left.\left.*\phantom{\rule{0.5em}{0ex}}\mathbf{apo}{\mathbf{B}}_{\mathbf{100}}0.27\right)\phantom{\rule{0.5em}{0ex}}*\phantom{\rule{0.5em}{0ex}}38.6\right]\mathbf{HDL}\mathbf{\u2012}\mathbf{C}\end{array} 
2.
apoB _{ 100 } level is not available, and is computed according to [19]:
\begin{array}{ll}\mathbf{TRL}\mathbf{\u2012}\mathbf{C}=\mathbf{TC}& \left[\left(0.0106\phantom{\rule{0.5em}{0ex}}*\phantom{\rule{0.5em}{0ex}}\mathbf{TC}0.0036\phantom{\rule{0.5em}{0ex}}*\phantom{\rule{0.5em}{0ex}}\mathbf{TG}+0.017\right.\right.\\ \left.*\phantom{\rule{0.5em}{0ex}}\left[0.65\phantom{\rule{0.5em}{0ex}}*\phantom{\rule{0.5em}{0ex}}\left(\mathbf{TC}\mathbf{\u2012}\mathbf{HDL}\mathbf{\u2012}\mathbf{C}\right)+6.3\right]0.27\right)\\ \left.*\phantom{\rule{0.5em}{0ex}}38.6\right]\mathbf{HDL}\mathbf{\u2012}\mathbf{C}\end{array}
Discussion
Measuring TG represents an easy means to estimate the combined mass of fasting or nonfasting TRLs, as surrogate for their cholesterol load. An excess of TRLs, including RLPs, throughout the nycthemeron epitomizes CMR conditions such the MetS, IR and the common form of T2DM. Elevated levels of TRLC contribute, alongside LDLC, to plaque formation and progression. TRLC is a modifiable driver of RVR. Whereas TG as such are not atherogenic, the welldemonstrated association between fasting or nonfasting TG and CVD is underlied by the atherogenicity of TRLs, especially that of RLPs [2–6, 8–11, 32, 33].
In fasting conditions, hypertriglyceridemia >150 mg/dL is categorized as “elevated” VLDL, corresponding to TRLC levels >30 mg/dL. Such assumption of equivalence is valid only if the composition of VLDL, in terms of C and TG, is in a ratio of 1/5. This is not necessarily the case in CMR states where nonVLDL TRLs (among which numerous RLPs) coexist alongside VLDL. Likewise, in nonfasting conditions, TRLs are further heterogeneous, in size and composition, being populated by various TGenriched and relatively TGdepleted lipoproteins (including remnants from the endogenous and exogenous pathways). The C/TG ratio of nonfasting TRLs substantially differs from that of fasting TRLs, the latter essentially consisting of standard VLDL with 20% cholesterol [1, 3, 13–17, 20, 21].
For this reason, recent articles on the usefulness of “RC” as residual risk marker relied by default on Friedewald’s formula to estimate the LDLC component of the equation. Doing so, their authors did not distinguish TRLC from RC. Such an oversimplification ascribes to RC all the observed risk of nonfasting TRLC. Besides, their rationale for extending the use of Friedewald’s equation to determine LDLC in nonfasting samples, in place of a direct assay, relied upon a linear relationship between calculated and measured LDLC in a reference subgroup, such a relationship being a selffulfilling prophecy [8, 10, 11, 14].
The present results provide unbiased and physiologicallyconsistent equations to determine TRLC from nonfasting lipids, regardless apoB_{100} availability. As expected, nonfasting TRLC and log[TG] were highly correlated, with adjusted Pearson’s coefficient reaching unity. Since both measures have uniform precision and discrimination, they provide similar information for ranking patients according to nonfasting TRLs, and are interchangeable. Yet, conceptually and educationally, determining TRLC as surrogate for TRLs is more attractive, since it quantifies the atherogenic component directly involved in driving CV risk, including all the cholesterol load from RLPs. In this context, the DR method provides an unbiased equivalence equation allowing to predict TRLC from log[TG], or viceversa.
While the concept of low HDLC as unconditional RF is strongly debated, the coexistence of elevated fasting TG together with low fasting HDLC allows identifying patients with AD, in whom residual risk is particularly high, even when onstatin LDLC is controlled [28–30, 33, 34]. An explanation for the accrued RVR from AD in the fasting state is that it could be a marker for high numbers of postprandial TRLs and elevated nonfasting TRLC. This is supported by results from an ACCORDLipid substudy, in which fenofibrate similarly lowered nonfasting TG in all T2DM participants, while reducing postprandial apoB_{48} excursions only in individuals with elevated fasting TG at baseline, a subgroup in which fenofibrate reduced CV outcomes [35].
In the presence of fasting hypertriglyceridemia (>150 mg/dL), the HDLC cutoffs defining AD (≤40 mg/dL [men] and ≤50 mg/dL [women]) are transposable to nonfasting conditions, because remnant TRLs have little influence on HDLC. Contrariwise, there are currently no standards or agreement defining (i) the upper physiological value for nonfasting TG; (ii) the sampling time after meal; and (iii) the lipid content and composition of the previous meal. For all these reasons we suggest to use either [TRLC/apoAI] or [log[TG]/HDLC] to assess postprandial AD as a continuous variable.
As the underlying correlation between TRLC and log[TG] on one hand, and between TRLC/apoAI and log[TG]/HDLC on the other hand, reached unity once preanalytical and analytical attenuation were taken into account, these two approaches may be used interchangeably to assess equivalent biological measures. While there was no significant difference between the discriminating performance of log[TG] compared to TRLC, the discrimination of the ratio log[(TG]/HDLC was clearly and significantly higher than the TRLC/apoAI ratio to quantify the severity of nonfasting AD in patients at high CMR. Given the perfect concordance between pairs of measurements, the clinician may prefer to expressing CV risk linked to TRLC (intuitively more educational than log[TG]), and to determine CV risk related to AD by calculating log[TG]/HDLC, which is superior to TRLC/apoAI. The latter has the inconvenience to require apoAI determination on top of routine lipids. Regarding biometric equivalence between atherogenicantiatherogenic ratios, we previously reported that nonHDLC/HDLC provides CV risk stratification similar to the apoB_{100}/apoAI ratio [36].
In this study, the performance of the above measures to that of a direct measurement of RC was not assessed, since the latter is not part of routine risk assessment. As regards cohort’s size, we compared the performance of two means to assess the burden of atherogenic TRL in 120 patients, an ample number given the DR methodology, which only requires ≥20 samples with 2 replicates as long as they represent a clinicallymeaningful range for the variable under study [see Appendix of[22]for a detailed discussion on sample size requirements for estimating DRs]. The fact that patients had T2DM in this study does not limit the applicability of the findings, since the metabolic and pathophysiological fundamentals of TRL, CMR and RC are similar in diabetic and nondiabetic subjects, at increasing levels along a continuum, from normal to impaired fasting glucose, and from prediabetes to T2DM [37, 38].
In conclusion, estimating TRLC requires formulas which reflect the complex compositional changes in nonfasting TRLs, the latter consisting of particles not exclusively generated along the VLDL pathway, in which TGcontent is heterogeneous and changes dynamically. We provide two unbiased equations to estimate the burden of TRLC based on routine nonfasting lipids, depending on apoB_{100} measurement availability. Our results show that TRLC and log[TG] are as effective and interchangeable to assess the atherogenic load of nonfasting TRLs. However, to grade TRLrelated AD, it is better to use log[TG]/HDLC, which is inherently superior to TRLC/apoAI, while measuring the same underlying variable.
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Hermans, M.P., Ahn, S.A. & Rousseau, M.F. Novel unbiased equations to calculate triglyceriderich lipoprotein cholesterol from routine nonfasting lipids. Cardiovasc Diabetol 13, 56 (2014). https://doi.org/10.1186/147528401356
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DOI: https://doi.org/10.1186/147528401356
Keywords
 Remnant cholesterol
 Triglycerides
 Nonfasting
 Chylomicrons
 Lipoprotein
 Diabetes
 Atherogenic dyslipidemia