Estimation of VLDL, IDL, LDL, HDL₂, apoA-I, and apoB from the Friedewald inputs—apoB and IDL, but not LDL, are associated with mortality in type 1 diabetes

Figures & data

Table

ANN	artificial neural network
ApoA-I	Apolipoprotein A-I
ApoA-II	Apolipoprotein A-II
ApoB	Apolipoprotein B
ApoE	Apolipoprotein E
C	Cholesterol
EDTA	Ethylenediamine tetra-acetic acid
F-LDL-C	low-density lipoprotein cholesterol as calculated from the Friedewald formula (including the intermediate-density lipoprotein cholesterol)
HDL	high-density lipoprotein
IDL	intermediate-density lipoprotein
LDL	low-density lipoprotein
MLP	multilayer perceptron
TC	total serum cholesterol
TG	total serum triglycerides
UCF	Ultracentrifugation
VLDL	very-low-density lipoprotein

Figure 1.  Overview of the lipoprotein isolation and measurement procedures for Data set I. Plasma C and plasma TG are measured, and identical samples are also handled through two different procedures. In procedure A the HDL-C is measured after VLDL ultracentrifugation and precipitation of the apoB-containing lipoprotein particles. In procedure B, sequential ultracentrifugation is applied to physically isolate the individual VLDL, IDL, LDL, and HDL fractions. ▵HDL-C(AB) denotes the difference of the measured HDL-C in procedures A and B. (Key for the abbreviations: C = cholesterol; TG = triglycerides; VLDL = very-low-density lipoprotein; IDL = intermediate-density lipoprotein; LDL = low-density lipoprotein; HDL = high-density lipoprotein; UCF = ultracentrifugation.) See also Supplementary Figure 1.

Table I.  Characteristics of the lipid and apolipoprotein measures in Data set I.

Friedewald inputs ^a (mmol/L)					Friedewald inputs ^b (mmol/L)					Friedewald inputs ^c (mmol/L)
n=1,775	Mean	SD	Min	Max	n=343	Mean	SD	Min	Max	n=247	Mean	SD	Min	Max
Plasma TG	1.65	1.01	0.12	8.73	Plasma TG	1.59	1.11	0.12	8.73	Plasma TG	1.43	0.82	0.50	6.00
Plasma C	5.83	1.38	2.14	11.37	Plasma C	5.58	1.21	2.76	9.67	Plasma C	5.63	1.01	1.90	8.30
HDL-C	1.58	0.53	0.34	4.50	HDL-C	1.78	0.59	0.74	4.50	HDL-C	1.37	0.38	0.54	2.40
ANN regression estimates (mmol/L)					ANN regression estimate (mmol/L)					ANN regression estimates (g/L)
n=1,775	Mean	SD	Min	Max	n=343	Mean	SD	Min	Max	n=247	Mean	SD	Min	Max
VLDL-TG ^a	0.97	0.83	0.10	7.16	HDL2-C ^b	1.22	0.59	0.25	3.32	apoA-I ^c	1.57	0.28	0.95	2.32
IDL-C ^a	0.31	0.22	0.03	1.59						apoB ^c	1.15	0.25	0.59	1.86
LDL-C ^a	3.61	1.16	0.81	8.51

^a The limits for the Friedewald inputs to use the ANN regression approach are between 0.9×Min and 1.1×Max (see Results): 0.11 mmol/L = plasma TG = 9.60 mmol/L; 1.93 mmol/L = plasma C = 12.51 mmol/L; and 0.31 mmol/L = HDL-C = 4.95 mmol/L.

^b 0.11 mmol/L = plasma TG = 9.60 mmol/L; 2.49 mmol/L = plasma C = 10.64 mmol/L; and 0.67 mmol/L = HDL-C = 4.95 mmol/L.

^c 0.45 mmol/L = plasma TG = 6.60 mmol/L; 1.71 mmol/L = plasma C = 9.13 mmol/L; and 0.34 mmol/L = HDL-C = 2.64 mmol/L.

The software (freely available at http://www.computationalmedicine.fi/software/Lipido) takes the above Friedewald input limits automatically into account and does not provide estimates outside the specific input limits.

Figure 2.  Correlation plots for the cross-validation results for the ANN-estimated variables (Data set I; Table I). The dashed lines represent the actual regression lines, and the solid lines identify the 1:1 line. An r stands for the Pearson correlation coefficient between the measured and estimated variables. The equations for the regression lines are: A) y = 0.93x + 0.05; B) y = 0.61x + 0.11; C) y = 0.89x + 0.36; D) y = 0.88x + 0.14; E) y = 0.90x + 0.17; and F) y = 0.92x + 0.10.

Figure 3.  Bland-Altman plots for the cross-validation results for the ANN-estimated variables (Data set I; Table I). The solid line in the middle represents the mean bias and the two others the mean±2 SD. The dashed lines represent the regression lines for the biases. A) Bias as a function of VLDL-TG: y = − 0.012x + 0.015 with r=0.054; B) bias as a function of IDL-C: y = − 0.17x + 0.055 with r=0.23; C) bias as a function of LDL-C: y = − 0.019x + 0.063 with r=0.042; D) bias as a function of HDL₂-C: y = − 0.031x + 0.036 with r=0.079; E) bias as a function of apoA-I: y = − 0.027x + 0.050 with r=0.068; and F) bias as a function of apoB: y = − 0.022x + 0.034 with r=0.069.

Figure 4.  Correlation and Bland-Altman plots for the (IDL + LDL)-C estimates calculated via the Friedewald formula (F-LDL-C) and via the (cross-validated) ANN regression models. The dashed lines in the correlation figures (A and B) represent the regression lines, and the solid lines denote the 1:1 lines. An r stands for the Pearson correlation coefficient between the measured and estimated variables. In the Bland-Altman plots (C and D) the solid line in the middle represents the mean bias and the two others the mean±2 SD. The dashed lines represent the regression lines for the biases. The equations for the regression lines are: A) y = 0.90x + 0.40; and B) y = 0.94x − 0.22. C) Bias as a function of (IDL + LDL)-C: y = − 0.04x + 0.18 with r=0.11; and D) bias as a function of F-LDL-C: y = 0.03x − 0.53 with r=0.070.

Table II.  The distributions of 14 plasma lipid and lipoprotein measures in Data set II consisting of 4,084 patients with type 1 diabetes [20], [25]. The presented Cox hazard regression coefficients and hazard ratios for all-cause mortality are adjusted for age and sex.

Variable ^a	Mean ^b	SD ^b	b^c	P	HR ^d	95% CI
ApoB	1.00	0.26	0.45	<0.0001	1.57	1.40	1.76
ApoB:apoA-I	0.69	0.22	0.45	<0.0001	1.56	1.40	1.75
IDL-C	0.24	0.12	0.37	<0.0001	1.45	1.35	1.55
VLDL-TG	0.72	0.70	0.30	<0.0001	1.35	1.27	1.44
Plasma TG	1.28	0.88	0.28	<0.0001	1.33	1.25	1.41
Non-HDL-C	3.62	1.10	0.26	<0.0001	1.29	1.21	1.39
TC:HDL-C	4.08	1.76	0.24	<0.0001	1.27	1.19	1.35
Plasma C	4.96	1.05	0.21	<0.0001	1.23	1.14	1.34
F-LDL-C	3.04	0.96	0.14	0.0066	1.15	1.04	1.28
LDL-C	3.17	0.76	0.08	0.1806	1.08	0.96	1.22
HDL3-C	0.49	0.06	−0.02	0.7674	0.98	0.86	1.12
ApoA-I	1.49	0.26	−0.14	0.0347	0.87	0.76	0.99
HDL-C	1.33	0.39	−0.38	<0.0001	0.69	0.60	0.79
HDL2-C	0.85	0.36	−0.39	<0.0001	0.68	0.58	0.79

^a The limits for the Friedewald inputs in the ANN-based regression modeling slightly reduced the number of patients available for the analyses (see Table I): 4,078 patients were available for VLDL-TG, IDL-C, and LDL-C estimations (all 279 deaths included); 3,970 for HDL₂-C and HDL₃-C (22 deaths in patients out of limits); 3,955 for apoA-I, apoB, and apoB to apoA-I ratio (9 deaths in patients out of limits). Use of the Friedewald formula to calculate F-LDL-C was possible for 4,032 patients (9 deaths in patients out of limits). Plasma TG, plasma C, HDL-C, non-HDL-C, and plasma C to HDL-C ratio were available for all 4,084 patients.

^b In mmol/L for the TG and C values and in g/L for the apolipoprotein measures.

^c Estimated regression coefficient.

^d Each hazard ratio refers to the relative risk for an increase of one SD in the value of the variable.

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