Validation of Estimated Small Dense Low-Density Lipoprotein Cholesterol Concentration in a Japanese General Population

Abstract

Aim: A high level of directly measured small dense low-density lipoprotein cholesterol (sdLDL-C) is a strong risk factor for atherosclerotic cardiovascular disease. A method for estimating sdLDL-C by using Sampson’s equation that includes levels of total cholesterol, high-density lipoprotein cholesterol (HDL-C), non-HDL-C and triglycerides (TG) has recently been proposed. We investigated the validation and exploration of estimated sdLDL-C level.

Methods: The associations between measured and estimated sdLDL-C levels were investigated in 605 Japanese subjects (men/women: 280/325; mean age: 65±15 years) who received annual health check-ups in the Tanno-Sobetsu Study, a population-based cohort.

Results: Estimated sdLDL-C level was highly correlated with measured sdLDL-C level in all subjects (R²=0.701), nondiabetic subjects without any medication (n=254, R²=0.686) and subjects with diabetes mellitus (n=128, R²=0.721). Multivariable regression analysis showed that levels of non-HDL-C, TG and γ-glutamyl transpeptidase (γGTP) were independent predictors of measured sdLDL-C level. In a stratification of the LDL window, all of the subjects with a combination of high non-HDL-C (≥ 170 mg/dL) and high TG (≥ 150 mg/dL) had high levels of measured and estimated sdLDL-C (≥ 35 mg/dL). Furthermore, machine learning-based estimation of sdLDL-C level by artificial intelligence software, Prediction One, was substantially improved by using components of Sampson’s equation (R²=0.803) and by using those components with the addition of γGTP and deletion of TC (R²=0.929).

Conclusions: sdLDL-C level estimated by Sampson’s equation can be used instead of measured sdLDL-C level in general practice. By building multiple machine learning models of artificial intelligence, a more accurate and practical estimation of sdLDL-C level might be possible.

Introduction

Low-density lipoprotein (LDL) is an atherogenic lipoprotein and a high level of LDL is a strong risk factor for coronary artery disease (CAD)¹⁾. LDL consists of small dense LDL (sdLDL) and large buoyant LDL (lbLDL) particles. LDL particles with a small size (≤ 25.5 nm) and a heavy gravity (1.044-1.063 g/mL) are defined as sdLDL particles, and sdLDL particles has been reported to be a more potent risk factor than lbLDL particles for CAD^2-4). Hence, accurate estimation of the amount of sdLDL particles is very important for prediction and prevention of CAD. A fully automated assay that directly measures sdLDL cholesterol (sdLDL-C) has recently been developed^{5, 6)}. That direct measurement system has been used in various cohort studies, all of which have consistently shown that sdLDL-C level is superior to LDL-C level for prediction of CAD^7-9). However, measurement of sdLDL-C level has not been widely adopted in general practice.

It has recently been proposed that the “LDL window” can be used to identify individuals with a high level of sdLDL-C by a stratification according to levels of non-HDL-C (or apolipoprotein B [ApoB]) and TG¹⁰⁾. Furthermore, Sampson et al. recently developed an equation for estimating sdLDL-C using levels of total cholesterol (TC), high-density lipoprotein cholesterol (HDL-C), non-HDL-C, triglycerides (TG) and calculated LDL-C by another Sampson’s equation^{11, 12)}. In the Multi-Ethnic Study of Atherosclerosis (MESA), subjects with more than the 80^th percentile of the estimated sdLDL-C level had a higher rate of all-cause atherosclerotic cardiovascular disease mortality than did those with less than the 80^th percentile of estimated sdLDL-C level¹²⁾. We recently showed that a high level of sdLDL-C calculated by Sampson’s equation was a more predominant predictor than indices of conventional lipid fractions for the development of ischemic heart disease during a 10-year period in a Japanese general population¹³⁾. We also showed that a high level of sdLDL-C calculated by Sampson’s equation can predict the development of hypertension during a 10-year period¹⁴⁾.

To the best of our knowledge, there has been only one report regarding the validation of estimated sdLDL-C calculated by Sampson’s equation, and it was shown that there was a weaker correlation between measured and estimated sdLDL-C levels in elderly patients with diabetes mellitus (n=1,542, mean age: 65 years) (R²=0.614) than in relatively young healthy subjects (n=673, mean age: 39 years) (R²=0.736)¹⁵⁾. Therefore, the validation and exploration of estimated sdLDL-C level have not been fully investigated, and a more accurate estimation of sdLDL-C is necessary.

In the present study, we investigated the validity of Sampson’s equation for estimating sdLDL-C in comparison with using levels of directly measured sdLDL-C, non-HDL-C, TG and ApoB as well as using the LDL window in a Japanese population who underwent health check-up examinations. Social implementation of artificial intelligence has recently become widespread¹⁶⁾, and machine learning models have been widely applied in medical fields. Hence, we also explored the estimation of sdLDL-C level using artificial intelligence software for deep machine learning programs, Prediction One (Sony Network Communications, Tokyo, Japan).

Methods

Study Subjects

In a population-based cohort, the Tanno-Sobetsu Study, a total of 605 Japanese subjects (men/women: 280/325) who were residents of Sobetsu Town, Hokkaido, Japan and received annual health examinations in 2017 were recruited. This study was approved by the Ethical Committee of Sapporo Medical University (number: 24-7-30) and was conducted in accordance with the Declaration of Helsinki. Written informed consent was obtained from all of the study subjects.

Measurements

Subjects were instructed to receive their physical examinations including blood pressure measurements, medical examinations, and blood and urine samplings after overnight fasting. Body mass index (BMI) was calculated as body weight in kilograms divided by height in meters squared. Estimated glomerular filtration rate (eGFR) was calculated by an equation for Japanese: eGFR (mL/min/1.73 m²)=194×serum creatinine−1.094×age−0.287×0.739 (if female)¹⁷⁾.

A self-administered questionnaire survey was performed to obtain information on smoking habit, alcohol drinking habit (≥ 3 times/ week) and use of drugs for diabetes mellitus, hypertension and dyslipidemia. Diabetes mellitus was diagnosed in accordance with the guidelines of the American Diabetes Association¹⁸⁾: fasting plasma glucose ≥ 126 mg/dL, hemoglobin A1c ≥ 6.5% or self-reported use of anti-diabetic drugs. Hypertension was diagnosed in accordance with the guidelines of the Japanese Society of Hypertension¹⁹⁾: systolic blood pressure ≥ 140 mmHg, diastolic blood pressure ≥ 90 mmHg or self-reported use of anti-hypertensive drugs. Dyslipidemia was diagnosed as LDL-C (direct method) ≥ 140 mg/dL, TG ≥ 150 mg/dL, HDL-C＜40 mg/dL, non-HDL-C ≥ 170 mg/dL or self-reported use of anti-dyslipidemic drugs.

Measured and Estimated sdLDL-C

Levels of TC, HDL-C, LDL-C and TG were measured by using enzymatic assays. Non-HDL-C level was calculated by subtracting HDL-C level from TC level. Plasma sdLDL-C concentration was directly measured by using a homogenous assay (sdLDL-EX SEIKEN; Denka Co., Tokyo, Japan)^{5, 6)}. A high level of sdLDL-C has been defined as 35 mg/dL or higher⁹⁾. LDL-C, lbLDL-C and sdLDL-C were calculated by using Sampson’s equations^{11, 12)}: LDL-C¹¹⁾=TC/0.948−HDL-C/0.971−(TG/8.56＋[TG×non-HDL-C]/2140 −TG²/16100)−9.44; lbLDL-C¹²⁾=1.43×LDL-C−(0.14×(In [TG]×LDL-C) -8.99; sdLDL-C¹²⁾=LDL-C −lbLDL-C. The correlation coefficients of LDL-C (direct method) with LDL-C (Friedewald’s equation²⁰⁾) (Supplementary Fig.1A) and LDL-C (Sampson’s equation¹¹⁾) (Supplementary Fig.1B) were 0.972 and 0.981, respectively, in the present study.

Supplementary Fig.1. Correlations of levels of LDL-C

A, B. Levels of low-density lipoprotein cholesterol (LDL-C) measured by a direct assay method were plotted against levels of LDL-C calculated by Friedewald’s equation (A) or Sampson’s equation (B) in all subjects (n=605, men/women: 280/325). Open circles and broken regression line: men; closed circles and solid regression line: women.

LDL Window

The “LDL window” was stratified by high (H-) and low (L-) levels of non-HDL-C (or ApoB) and TG¹⁰⁾. The cutoff values for non-HDL-C, ApoB and TG were 170 mg/dL, 110 mg/dL and 150 mg/dL, respectively. It was previously reported that subjects with a high level of sdLDL-C (＞31 mg/dL, defined as the range of the 4^th quartile) can be mainly placed at a window of H-non-HDL-C (≥ 170 mg/dL)/H-TG (≥ 150 mg/dL) (or H-ApoB [≥ 110 mg/dL]/H-TG [≥ 150 mg/dL])¹⁰⁾.

Statistical Analysis

Numeric variables were expressed as means±standard deviation (SD) for normal distributions or medians (interquartile ranges) for skewed distributions. The distribution of each parameter was tested for its normality using the Shapiro-Wilk W test. Comparisons between two groups for parametric and nonparametric factors were performed by using Student’s t-test and the Mann-Whitney U test, respectively. The chi-square test was performed for intergroup differences in percentages of parameters. Pearson’s correlation analysis was performed to investigate correlations between two variables. Non-normally distributed variables were logarithmically transformed for regression analyses. Multivariable regression analysis was performed to identify independent determinants of measured and estimated sdLDL-C levels after consideration of multicollinearity using age, sex and variables with a significant correlation (r ≥ 0.25, P＜0.05) as independent predictors, showing standardized regression coefficient (β), percentage of variance for the selected independent predictors explained (R²), and Akaike’s information criterion (AIC). Parameters with a lower AIC score constitute a better-fit model. Machine learning analysis was performed by using artificial intelligence software, Prediction One (Sony Network Communications, Tokyo, Japan). A p value of less than 0.05 was considered statistically significant. All data other than data from machine learning analyses were analyzed by using EZR²¹⁾ and JMP Pro 17.1.0 (SAS Institute, Cary, NC).

Results

Characteristics of the Study Subjects

Basal characteristics of the enrolled subjects (n=605, men/women: 280/325) are shown in Table 1. Women had significantly higher levels of LDL-C (direct method) and HDL-C than did men. There were no significant sex differences in levels of measured and estimated sdLDL-C and percentages of subjects with comorbidities of hypertension, diabetes mellitus and dyslipidemia. Basal characteristics of nondiabetic subjects without any medication (n=254, men/women: 121/133) and subjects with diabetes mellitus (n=128, men/women: 63/65) are also shown in Supplementary Table 1 and Supplementary Table 2, respectively.

Table 1.Characteristics of the recruited subjects

	Total (n= 605)	Men (n= 280)	Women (n= 325)	P
Age (years)	65±15	65±15	65±15	0.766
Body mass index	23.4±3.9	24.1±3.7	23.0±4.1	0.005
Waist circumference (cm)	85±10.9	86.7±10.8	83.5±11.0	＜0.001
Systolic BP (mmHg)	137±21	138±19	137±23	0.755
Diastolic BP (mmHg)	77±11	78±11	76±11	0.011
Comorbidity
Hypertension	350 (57.9)	167 (59.6)	183 (56.3)	0.408
Diabetes mellitus	69 (11.4)	38 (13.6)	31 (9.54)	0.120
Dyslipidemia	336 (55.5)	146 (52.1)	190 (58.5)	0.119
Anti-dyslipidemic drugs	132 (21.8)	47 (16.8)	85 (26.2)	0.005
Biochemical data
AST (IU/L)	25 (21-28)	26 (21-30)	24 (20-26)	＜0.001
ALT (IU/L)	22 (15-25)	25 (17-30)	19 (14-22)	＜0.001
γGTP (IU/L)	33 (16-34)	43 (20-43)	25 (15-26)	＜0.001
Blood urea nitrogen (mg/dL)	16±5	17±5	15±4	＜0.001
Creatinine (mg/dL)	0.8 (0.7-0.9)	0.9 (0.8-1.0)	0.7 (0.6-0.8)	＜0.001
eGFR (mL/min/1.73m2)	67±14	68±15	66±13	0.028
Uric acid (mg/dL)	5.3±1.3	6.0±1.2	4.8±1.1	＜0.001
TC (mg/dL)	207±35	199±32	214±36	＜0.001
LDL-C (mg/dL)	120±29	115±28	124±30	＜0.001
HDL-C (mg/dL)	65±19	59±16	70±20	＜0.001
Non-HDL-C (mg/dL)	142±33	140±34	144±32	0.115
Measured sdLDL-C (mg/dL)	45.2±17.7	45.4±18.3	45.0±17.3	0.767
≥ 35 mg/dL	416 (68.8)	188 (67.1)	228 (70.2)	0.430
≥ 45 mg/dL	266 (44.0)	118 (42.1)	148 (45.5)	0.499
Estimated sdLDL-C (mg/dL)	34.3±11.0	34.7±11.7	34.1±10.4	0.496
≥ 35 mg/dL	261 (43.1)	120 (42.9)	141 (43.4)	0.934
≥ 45 mg/dL	98 (16.2)	48 (17.1)	50 (15.4)	0.402
ApoB (mg/dL)	75±20	75±19	77±21	0.162
TG (mg/dL)	109 (67-122)	123 (68-134)	96 (65-113)	0.011
Fasting glucose (mg/dL)	99 (89-104)	102(91-108)	97 (87-101)	＜0.001
Hemoglobin A1c (%)	5.7 (5.3-5.8)	5.7 (5.3-5.9)	5.6 (5.3-5.8)	0.189

Variables are expressed as number (%), means±SD or medians (interquartile ranges).

ALT, alanine transaminase; ApoB, apolipoprotein B; AST, aspartate transaminase; BP, blood pressure; eGFR, estimated glomerular filtration rate; γ GTP, γ-glutamyl transpeptidase; HDL-C, high-density lipoprotein cholesterol; LDL-C, low-density lipoprotein cholesterol; sdLDL-C, small dense low-density lipoprotein cholesterol; TC, total cholesterol; TG, triglycerides.

Supplementary Table 1.Characteristics of nondiabetic subjects without any medication

	Total (n = 254)	Men (n = 121)	Women (n = 133)	P
Age (years)	63±16	63±16	63±16	0.930
Body mass index	23.6±3.7	24.3±3.7	23.0±3.5	0.007
Waist circumference (cm)	85.4±11.0	87.3±11.2	83.6±10.5	0.007
Systolic BP (mmHg)	136±21	135±18	137±23	0.443
Diastolic BP (mmHg)	76±11	77±11	75±11	0.155
Comorbidity
Hypertension	135 (53.1)	63 (52.1)	72 (54.1)	0.743
Dyslipidemia	136 (53.5)	63 (52.1)	73 (54.9)	0.654
Biochemical data
AST (IU/L)	23 (20-28)	25 (21-29)	26 (22-31)	0.007
ALT (IU/L)	19 (14-27)	23 (17-32)	16 (14-21)	＜0.001
γGTP (IU/L)	22 (16-34)	28 (20-42)	18 (15-26)	＜0.001
Blood urea nitrogen (mg/dL)	15±4	16±5	14±4	0.009
Creatinine (mg/dL)	0.8 (0.7-0.9)	0.9 (0.8-1.0)	0.7 (0.6-0.8)	＜0.001
eGFR (mL/min/1.73m2)	69±14	70±15	67±14	0.205
Uric acid (mg/dL)	5.4±1.3	6.1±1.2	4.8±1.1	＜0.001
TC (mg/dL)	207±36	199±34	214±35	＜0.001
LDL-C (mg/dL)	121±30	117±30	125±29	0.026
HDL-C (mg/dL)	65±20	58±15	70±21	＜0.001
Non-HDL-C (mg/dL)	142±33	140±34	144±31	0.331
Measured sdLDL-C (mg/dL)	45.1±16.9	45.2±18.0	45.1±15.9	0.996
≥ 35 mg/dL	176 (69.3)	81 (66.9)	95 (71.4)	0.441
≥ 45 mg/dL	113 (44.5)	50 (41.3)	63 (47.4)	0.335
Estimated sdLDL-C (mg/dL)	34.0±11.4	34.7±12.3	33.4±10.5	0.355
≥ 35 mg/dL	105 (41.3)	53 (43.8)	52 (39.1)	0.449
≥ 45 mg/dL	43 (16.9)	22 (18.2)	21 (15.8)	0.613
ApoB (mg/dL)	79±18	79±18	75±21	0.567
TG (mg/dL)	88 (64-122)	94 (66-142)	92 (70-129)	＜0.001
Fasting glucose (mg/dL)	94 (89-101)	95 (90-104)	93 (88-100)	0.008
Hemoglobin A1c (%)	5.5 (5.3-5.7)	5.5 (5.2-5.7)	5.5 (5.3-5.7)	0.506

Variables are expressed as number (%), means±SD or medians (interquartile ranges).

ALT, alanine transaminase; ApoB, apolipoprotein B; AST, aspartate transaminase; BP, blood pressure; eGFR, estimated glomerular filtration rate; γ GTP, γ-glutamyl transpeptidase; HDL-C, high-density lipoprotein cholesterol; LDL-C, low-density lipoprotein cholesterol; sdLDL-C, small dense low-density lipoprotein cholesterol; TC, total cholesterol; TG, triglycerides.

Supplementary Table 2.Characteristics of subjects with diabetes mellitus

	Total (n = 128)	Men (n = 63)	Women (n = 65)	P
Age (years)	68±14	68±13	68±15	0.771
Body mass index	24.1±4.7	24.6±4.0	23.7±5.3	0.238
Waist circumference (cm)	86.7±11.3	88.3±10.7	85.3±11.9	0.136
Systolic BP (mmHg)	140±21	142±20	138±22	0.224
Diastolic BP (mmHg)	76±11	78±12	74±10	0.023
Comorbidity
Hypertension	85 (66.4)	48 (76.1)	37 (56.9)	0.021
Diabetes mellitus
Medication (+)	69 (53.9)	31 (49.2)	38 (58.5)	0.297
Medication (-)	59 (46.1)	32 (50.8)	27 (41.5)	0.297
Dyslipidemia	79 (61.7)	35 (55.6)	44 (67.7)	0.160
Biochemical data
AST (IU/L)	25 (22-30)	26 (22-32)	24 (22-27)	＜0.001
ALT (IU/L)	19 (15-28)	24 (17-31)	18 (15-22)	＜0.001
γGTP (IU/L)	22 (16-36)	30 (20-44)	20 (15-26)	0.448
Blood urea nitrogen (mg/dL)	16±6	17±6	15±6	＜0.001
Creatinine (mg/dL)	0.8 (0.7-0.9)	0.9 (0.8-1.0)	0.7 (0.6-0.8)	＜0.001
eGFR (mL/min/1.73m2)	65±16	67±18	63±15	0.146
Uric acid (mg/dL)	5.3±1.2	5.8±1.1	4.8±1.1	＜0.001
TC (mg/dL)	203±33	200±29	205±36	0.453
LDL-C (mg/dL)	116±29	115±27	118±31	0.531
HDL-C (mg/dL)	62±17	59±16	66±18	0.038
Non-HDL-C (mg/dL)	140±32	141±31	139±33	0.737
Measured sdLDL-C (mg/dL)	45.1±16.4	47.1±17.5	43.2±15.2	0.188
≥ 35 mg/dL	90 (70.3)	47 (74.6)	43 (66.2)	0.299
≥ 45 mg/dL	59 (46.1)	32 (50.8)	27 (41.5)	0.297
Estimated sdLDL-C (mg/dL)	34.6±10.4	35.2±10.9	34.0±10.0	0.564
≥ 35 mg/dL	57 (44.5)	29 (46.0)	28 (43.1)	0.739
≥ 45 mg/dL	19 (14.8)	9 (14.3)	10 (15.4)	0.863
ApoB (mg/dL)	74±21	73±20	75±21	0.432
TG (mg/dL)	93 (71-133)	96 (71-135)	92 (70-129)	0.148
Fasting glucose (mg/dL)	104 (91-127)	107 (98-134)	100 (88-120)	0.100
Hemoglobin A1c (%)	6.0 (5.5-6.7)	6.2 (5.7-6.9)	5.8 (5.5-6.4)	0.350

Variables are expressed as number (%), means±SD or medians (interquartile ranges).

ALT, alanine transaminase; ApoB, apolipoprotein B; AST, aspartate transaminase; BP, blood pressure; eGFR, estimated glomerular filtration rate; γ GTP, γ-glutamyl transpeptidase; HDL-C, high-density lipoprotein cholesterol; LDL-C, low-density lipoprotein cholesterol; sdLDL-C, small dense low-density lipoprotein cholesterol; TC, total cholesterol; TG, triglycerides.

Correlations of Measured and Estimated sdLDL-C Levels with Lipid Parameters

There were significant correlations between directly measured and estimated levels of sdLDL-C in all subjects (Fig.1A; r=0.837, P＜0.001), in nondiabetic subjects without any medication (Fig.1B; r=0.828, P＜0.001) and in subjects with diabetes mellitus (Fig.1C; r=0.849, P＜0.001). The correlation equations between measured (Y) and estimated (X) levels of sdLDL-C were ‘Y=1.34×X– 0.97’ in all subjects (R²=0.701), ‘Y=1.23×X−3.41’ in nondiabetic subjects withoxref ref-type="bibr"ut any medication (R²=0.686), and ‘Y=1.34×X−1.16’ in subjects with diabetes mellitus (R²=0.721).

Fig.1. Correlations between measured and estimated sdLDL-C levels

A-C. Levels of directly measured small dense low-density lipoprotein cholesterol (sdLDL-C) were plotted against levels of estimated sdLDL-C calculated by Sampson’s equation in all subjects (n=605, men/women: 280/325) (A), in nondiabetic subjects without any medication (n=254, men/women: 121/133) (B) and in subjects with diabetes mellitus (DM) (n=128, men/women: 63/65) (C). Open circles and broken regression line: men; closed circles and solid regression line: women.

There were significant correlations between directly measured and estimated levels of sdLDL-C in subjects with dyslipidemia (Supplementary Fig.2A; r=0.814, P＜0.001), in subjects without dyslipidemia (Supplementary Fig.2B; r=0.783, P＜0.001), in dyslipidemic subjects treated with anti-dyslipidemic drugs (Supplementary Fig.2C; r=0.851, P＜0.001) and in dyslipidemic subjects treated without anti-dyslipidemic drugs (Supplementary Fig.2D; r=0.739, P＜0.001).

Supplementary Fig.2. Correlations of measured and estimated sdLDL-C levels in subjects with dyslipidemia A, B

Levels of measured small dense low-density lipoprotein cholesterol (sdLDL-C) were plotted against levels of estimated sdLDL-C in subjects with dyslipidemia (DL) (A) and non-DL (B). C, D. Levels of measured sdLDL-C were plotted against levels of estimated sdLDL-C in subjects with DL in the presence (C) and absence (D) of treatment with anti-DL drugs. Open circles and broken regression line: men; closed circles and solid regression line: women.

Measured (Supplementary Table 3) and estimated (Supplementary Table 4) levels of sdLDL-C were significantly correlated with BMI, waist circumference, systolic and diastolic blood pressures, and several markers of liver function, lipid profiles and glucose metabolism. Measured level of sdLDL-C was positively correlated with levels of non-HDL-C (Fig.2A; r=0.719, P＜0.001), logarithmically transformed (Log) TG (Fig.2B; r=0.686, P＜0.001) and ApoB (Fig.2C; r=0.530, P＜0.001). Estimated level of sdLDL-C was positively correlated with levels of non-HDL-C (Fig.2D; r=0.852, P＜0.001), Log TG (Fig.2E; r=0.788, P＜0.001) and ApoB (Fig.2F; r=0.605, P＜0.001). The coefficients of determination (R²) of non-HDL-C, TG and ApoB with estimated sdLDL-C were higher than those with measured sdLDL-C in all subjects (Fig.2). The results for correlations of measured and estimated sdLDL-C with non-HDL, TG and ApoB in nondiabetic subjects without any medication (Supplementary Fig.3) and subjects with diabetes mellitus (Supplementary Fig.4) were almost the same as those in all subjects (Fig.2).

Supplementary Table 3.Correlation analyses for measured sdLDL-C

	Total (n = 605)		Men (n = 280)		Women (n = 325)
	r	p	r	p	r	p
Age (years)	0.025	0.535	-0.078	0.192	0.119	0.031
Body mass index	0.114	0.005	0.052	0.384	0.165	0.003
Waist circumference (cm)	0.159	＜0.001	0.081	0.176	0.230	＜0.001
Systolic BP (mmHg)	0.175	＜0.001	0.185	0.002	0.170	0.002
Diastolic BP (mmHg)	0.247	＜0.001	0.311	＜0.001	0.189	＜0.001
Log AST	0.174	＜0.001	0.223	＜0.001	0.126	0.023
Log ALT	0.217	＜0.001	0.257	＜0.001	0.191	＜0.001
Log γGTP	0.265	＜0.001	0.318	＜0.001	0.233	＜0.001
Blood urea nitrogen (mg/dL)	0.054	0.186	0.049	0.412	0.056	0.313
Log Creatinine	0.050	0.224	0.048	0.423	0.056	0.317
eGFR (mL/min/1.73m2)	-0.556	0.172	0.001	0.992	-0.118	0.033
Uric acid (mg/dL)	0.192	＜0.001	0.227	＜0.001	0.198	＜0.001
TC (mg/dL)	0.535	＜0.001	0.606	＜0.001	0.507	＜0.001
LDL-C (mg/dL)	0.516	＜0.001	0.450	＜0.001	0.578	＜0.001
HDL-C (mg/dL)	-0.250	＜0.001	-0.326	＜0.001	-0.211	＜0.001
Non-HDL-C (mg/dL)	0.719	＜0.001	0.741	＜0.001	0.702	＜0.001
Estimated sdLDL-C (mg/dL)	0.837	＜0.001	0.852	＜0.001	0.823	＜0.001
ApoB (mg/dL)	0.530	＜0.001	0.479	＜0.001	0.577	＜0.001
Log TG	0.686	＜0.001	0.735	＜0.001	0.648	＜0.001
Log Fasting glucose	0.157	＜0.001	0.173	0.004	0.140	0.012
Log Hemoglobin A1c	0.124	0.002	0.164	0.006	0.076	0.172

ALT, alanine transaminase; ApoB, apolipoprotein B; AST, aspartate transaminase; BP, blood pressure; eGFR, estimated glomerular filtration rate; γ GTP, γ-glutamyl transpeptidase; HDL-C, high-density lipoprotein cholesterol; LDL-C, low-density lipoprotein cholesterol; sdLDL-C, small dense low-density lipoprotein cholesterol; TC, total cholesterol; TG, triglycerides.

Supplementary Table 4.Correlation analyses for estimated sdLDL-C

	Total (n= 605)		Men (n= 280)		Women (n= 325)
	r	p	r	p	r	p
Age (years)	0.005	0.912	-0.168	0.005	0.172	0.002
Body mass index	0.193	＜0.001	0.123	0.040	0.252	＜0.001
Waist circumference (cm)	0.222	＜0.001	0.146	0.014	0.292	＜0.001
Systolic BP (mmHg)	0.159	＜0.001	0.093	0.119	0.215	＜0.001
Diastolic BP (mmHg)	0.224	＜0.001	0.246	＜0.001	0.200	＜0.001
Log AST	0.139	＜0.001	0.110	0.066	0.163	0.003
Log ALT	0.237	＜0.001	0.259	＜0.001	0.220	＜0.001
Log γGTP	0.241	＜0.001	0.264	＜0.001	0.225	＜0.001
Blood urea nitrogen (mg/dL)	0.004	0.945	-0.013	0.831	0.011	0.837
Log Creatinine	0.098	0.016	0.088	0.141	0.113	0.043
eGFR (mL/min/1.73m2)	-0.087	0.033	-0.001	0.992	-0.190	＜0.001
Uric acid (mg/dL)	0.208	＜0.001	0.191	0.001	0.253	＜0.001
TC (mg/dL)	0.604	＜0.001	0.707	＜0.001	0.560	＜0.001
LDL-C (mg/dL)	0.636	＜0.001	0.627	＜0.001	0.670	＜0.001
HDL-C (mg/dL)	-0.352	＜0.001	-0.425	＜0.001	-0.315	＜0.001
Non-HDL-C (mg/dL)	0.852	＜0.001	0.886	＜0.001	0.826	＜0.001
Measured sdLDL-C (mg/dL)	0.837	＜0.001	0.852	＜0.001	0.823	＜0.001
ApoB (mg/dL)	0.605	＜0.001	0.159	0.008	0.125	0.025
Log TG	0.788	＜0.001	0.785	＜0.001	0.806	＜0.001
Log Fasting glucose	0.151	＜0.001	0.151	0.011	0.145	0.009
Log Hemoglobin A1c	0.145	＜0.001	0.592	＜0.001	0.629	＜0.001

ALT, alanine transaminase; ApoB, apolipoprotein B; AST, aspartate transaminase; BP, blood pressure; eGFR, estimated glomerular filtration rate; γ GTP, γ-glutamyl transpeptidase; HDL-C, high-density lipoprotein cholesterol; LDL-C, low-density lipoprotein cholesterol; sdLDL-C, small dense low-density lipoprotein cholesterol; TC, total cholesterol; TG, triglycerides.

Fig.2. Correlations of measured and estimated sdLDL-C levels with lipid profiles

A-C. Levels of measured small dense low-density lipoprotein cholesterol (sdLDL-C) were plotted against levels of non-high-density lipoprotein cholesterol (non-HDL-C) (A), logarithmically transformed (Log) triglycerides (TG) (B) and apolipoprotein B (ApoB) (C) in all subjects (n=605, men/women: 280/325). D-F. Levels of estimated sdLDL-C were plotted against levels of non-HDL-C (D), Log TG (E) and ApoB (F) in all subjects. Open circles and broken regression line: men; closed circles and solid regression line: women.

Supplementary Fig.3. Correlations of measured and estimated sdLDL-C levels with lipid profiles in nondiabetic subjects without any medication

A-C. Levels of measured small dense low-density lipoprotein cholesterol (sdLDL-C) were plotted against levels of non-high-density lipoprotein cholesterol (non-HDL-C) (A), logarithmically transformed (Log) triglycerides (TG)(B) and apolipoprotein B (ApoB) (C) in nondiabetic subjects without any medication (n=254, men/women: 121/133). D-F. Levels of estimated sdLDL-C were plotted against levels of non-HDL-C (D), TG (E) and ApoB (F) in nondiabetic subjects without any medication. Open circles and broken regression line: men; closed circles and solid regression line: women.

Supplementary Fig.4. Correlations of measured and estimated sdLDL-C levels with lipid profiles in subjects with diabetes mellitus

A-C. Levels of measured small dense low-density lipoprotein cholesterol (sdLDL-C) were plotted against levels of non-high-density lipoprotein cholesterol (non-HDL-C) (A), logarithmically transformed (Log) triglycerides (TG) (B) and apolipoprotein B (ApoB) (C) in subjects with diabetes mellitus (n=128, men/women: 63/65). D-F. Levels of estimated sdLDL-C were plotted against levels of non-HDL-C (D), TG (E) and ApoB (F) in subjects with diabetes mellitus. Open circles and broken regression line: men; closed circles and solid regression line: women.

Multivariable Regression Analyses for Measured and Estimated sdLDL-C Levels

Using age, sex and variables with a significant correlation (r ≥ 0.25, P＜0.05) as independent predictors after consideration of multicollinearity, stepwise and subsequent multivariable regression analyses showed that measured sdLDL-C concentration was independently associated with γ-glutamyl transpeptidase (γGTP) (β=0.075, P=0.004), non-HDL-C (β=0.447, P＜0.001), Log TG (β=0.447, P＜0.001) and ApoB (β=0.084, P=0.015) after adjustment of age, sex, BMI and systolic blood pressure (Model 1: R²=0.695, AIC: 4,493) (Table 2). However, measured sdLDL-C level was not significantly associated with LDL-C (direct method) level (β=0.106, P=0.162) (Model 2: R²=0.693, AIC: 4,497).

Table 2.Multivariable regression analyses for measured and estimated sdLDL-C

	Measured sdLDL-C				Estimated sdLDL-C
	Model 1		Model 2		Model 1		Model 2
	β	P	β	P	β	P	β	P
Age	-0.003	0.919	0.004	0.876	0.001	0.965	-0.007	0.541
Sex (Men)	-0.038	0.118	-0.036	0.142	-0.007	0.541	0.002	0.857
Body mass index	-0.055	0.021	-0.054	0.024	0.015	0.195	0.012	0.234
Systolic BP	0.074	0.006	0.071	0.009	0.029	0.019	0.024	0.032
Log γGTP	0.075	0.004	0.077	0.003	-0.003	0.827	-0.005	0.676
Non-HDL-C	0.444	＜0.001	0.398	＜0.001	0.584	＜0.001	0.213	＜0.001
Log TG	0.447	＜0.001	0.477	＜0.001	0.507	＜0.001	0.651	＜0.001
ApoB	0.084	0.015	-	-	0.048	0.003	-	-
LDL-C	-	-	0.106	0.162	-	-	0.386	＜0.001
R2	0.695		0.693		0.933		0.945
AIC	4,493		4,497		3,003		2,886

AIC, Akaike’s information criterion; ApoB, apolipoprotein B; β, standardized regression coefficient; BP, blood pressure; γGTP, γ-glutamyl transpeptidase; HDL-C, high-density lipoprotein cholesterol; LDL-C, low-density lipoprotein cholesterol; sdLDL-C, small dense low-density lipoprotein cholesterol; TG, triglycerides.

On the other hand, estimated sdLDL-C concentration was independently associated with non-HDL-C (β=0.584, P＜0.001), Log TG (β=0.507, P＜0.001) and ApoB (β=0.048, P=0.003) after adjustment of age, sex, BMI, systolic blood pressure and γGTP (Model 1: R²=0.933, AIC: 3,003) (Table 2). Unlike measured sdLDL-C level, estimated sdLDL-C level was significantly associated with LDL-C (direct method) level (β=0.386, P＜0.001) (Model 2: R²=0.945, AIC: 2,886).

Percentage of Subjects with a High Level of sdLDL-C in the “LDL Window”

Basal characteristics of all subjects in the LDL window using levels of non-HDL-C and TG are shown in Supplementary Table 5. The mean values of measured sdLDL-C in the H-non-HDL-C/H-TG group and L-non-HDL-C/L-TG group were 74.1 mg/dL and 38.3 mg/dL, respectively. The proportions of subjects with high levels of measured/estimated sdLDL-C (≥ 35 mg/dL) were higher in the H-non-HDL-C/H-TG group (100%/100%) than in the L-non-HDL-C/L-TG group (42.5%/69.5%) (Fig.3A).

Supplementary Table 5.Characteristics of subjects with low and high levels of non-HDL-C and TG

	L-non-HDL-C/L-TG (n= 426)	L-non-HDL-C/H-TG (n= 54)	H-non-HDL-C/L-TG (n= 85)	H-non-HDL-C/H-TG (n= 40)
Age (years)	66±15	64±13	66±13	58±15
Men/Women	196/230	33/21	24/61	27/13
Body mass index	23.2±3.9	24.6±3.9	23.5±4.1	24.7±3.5
Waist circumference (cm)	84.2±11.4	87.9±9.3	85.6±9.5	88.7±9.2
Systolic BP (mmHg)	136±21	141±21	140±21	136±19
Diastolic BP (mmHg)	76±11	79±11	78±11	82±11
Comorbidity
Hypertension	241 (53.1)	35 (64.8)	53 (62.4)	21 (52.5)
Diabetes mellitus	43 (10.1)	11 (20.4)	8 (9.4)	7 (17.5)
Dyslipidemia	157 (36.9)	54 (100)	85 (100)	40 (100)
Biochemical data
AST (IU/L)	23 (20-27)	28 (22-32)	23 (20-28)	26 (22-33)
ALT (IU/L)	19 (14-24)	26 (20-34)	18 (15-24)	26 (20-34)
γGTP (IU/L)	21 (15-32)	36 (20-54)	21 (16-32)	32 (23-68)
Blood urea nitrogen (mg/dL)	16±5	15±5	16±5	14±4
Creatinine (mg/dL)	0.8 (0.7-0.9)	0.8 (0.7-0.9)	0.8 (0.7-0.9)	0.8 (0.7-0.9)
eGFR (mL/min/1.73m2)	67±13	65±15	63±14	72±20
Uric acid (mg/dL)	5.2±1.2	6.0±1.3	5.5±1.3	6.0±1.3
TC (mg/dL)	197±29	194±24	253±25	243±27
LDL-C (mg/dL)	112±22	105±22	164±14	142±33
HDL-C (mg/dL)	68±18	54±17	67±19	46±11
Non-HDL-C (mg/dL)	129±23	141±19	186±14	197±25
Measured sdLDL-C (mg/dL)	38.3±13.1	55.4±12.2	59.5±16.4	74.1±16.2
≥ 35 mg/dL	181 (42.5)	52 (96.3)	79 (92.9)	40 (100)
≥ 45 mg/dL	113 (26.5)	43 (79.6)	70 (82.3)	40 (100)
Estimatedsd LDL-C (mg/dL)	29.2±7.1	41.6±5.8	44.7±6.7	57.3±8.5
≥ 35 mg/dL	96 (22.5)	45 (83.3)	80 (94.1)	40 (100)
≥ 45 mg/dL	3 (0.7)	16 (29.6)	41 (48.2)	38 (95.0)
ApoB (mg/dL)	70±17	76±16	97±15	95±22
TG (mg/dL)	77 (61-100)	189 (167-212)	92 (70-129)	217 (178-369)
Fasting glucose (mg/dL)	94 (89-103)	98 (90-111)	98 (85-122)	98 (91-113)
Hemoglobin A1c (%)	5.5 (5.3-5.8)	5.6 (5.3-6.0)	5.5 (5.4-5.8)	5.6 (5.3-6.1)

Variables are expressed as number (%), means±SD or medians (interquartile ranges).

ALT, alanine transaminase; ApoB, apolipoprotein B; AST, aspartate transaminase; BP, blood pressure; eGFR, estimated glomerular filtration rate; γ GTP, γ-glutamyl transpeptidase; H-, high; HDL-C, high-density lipoprotein cholesterol; L-, low; LDL-C, low-density lipoprotein cholesterol; sdLDL-C, small dense low-density lipoprotein cholesterol; TC, total cholesterol; TG, triglycerides.

Fig.3. Stratification of high levels of measured and estimated sdLDL-C in the LDL window

A. Percentages of subjects with high levels of measured and estimated small dense low-density lipoprotein cholesterol (sdLDL-C) (≥ 35 mg/dL) in the low-density lipoprotein (LDL) window stratified by low (L-) and high (H-) levels of non-high-density lipoprotein cholesterol (non-HDL-C) (＜170 mg/dL and ≥ 170 mg/dL) and triglycerides (TG) (＜150 mg/dL and ≥ 150 mg/dL) in all subjects. The LDL window comprised four groups: L-non-HDL-C/L-TG (n=426), L-non-HDL-C/H-TG (n=54), H-non-HDL-C/L-TG (n=85) and H-non-HDL-C/H-TG (n=40). B. Percentages of subjects with high levels of measured and estimated sdLDL-C (≥ 35 mg/dL) in the LDL window stratified by apoprotein B (ApoB) (＜110 mg/dL and ≥ 110 mg/dL) and L- and H-TG in all subjects. The LDL window comprised four groups: L-ApoB/L-TG (n=492), L- ApoB/H-TG (n=88), H-ApoB/L-TG (n=19) and H- ApoB/H-TG (n=6).

Basal characteristics of all subjects in the LDL window using levels of ApoB and TG are shown in Supplementary Table 6. The mean values of measured sdLDL-C in the H-non-HDL-C/H-TG group and L-non-HDL-C/L-TG group were 76.4 mg/dL and 41.0 mg/dL, respectively. The proportions of subjects with high levels of measured/estimated sdLDL-C (≥ 35 mg/dL) were higher in the H-ApoB/H-TG group (100%/100%) than in the L-ApoB/L-TG group (62.0%/32.5%) (Fig.3B).

Supplementary Table 6.Characteristics of subjects with low and high levels of ApoB and TG

	L-ApoB/L-TG (n= 492)	L-ApoB/H-TG (n= 88)	H-ApoB/L-TG (n= 19)	H-ApoB/H-TG (n= 6)
Age (years)	66±15	62±14	69±10	64±13
Men/Women	214/278	57/31	6/13	3/3
Body mass index	23.2±3.9	24.7±3.8	23.7±4.2	24.5±3.0
Waist circumference (cm)	84.3±11.2	88.1±9.2	87.3±10.6	89.8±10.4
Systolic BP (mmHg)	137±21	139±20	142±20	139±22
Diastolic BP (mmHg)	76±11	80±11	77±8	87±8
Comorbidity
Hypertension	281 (57.1)	51 (58.0)	13 (68.4)	4 (66.7)
Diabetes mellitus	47 (9.6)	17 (19.3)	4 (21.1)	1 (16.7)
Dyslipidemia	223 (45.3)	88 (100)	19 (100)	6 (100)
Biochemical data
AST (IU/L)	23 (20-27)	27 (22-32)	23 (21-25)	26 (22-34)
ALT (IU/L)	19 (14-24)	26 (20-34)	20 (17-24)	18 (9-43)
γGTP (IU/L)	21 (15-32)	33 (22-56)	20 (17-27)	35 (19-63)
Blood urea nitrogen (mg/dL)	16±5	15±5	17±5	14±3
Creatinine (mg/dL)	0.8 (0.7-0.9)	0.8 (0.7-0.9)	0.7 (0.6-0.9)	0.9 (0.7-1.1)
eGFR (mL/min/1.73m2)	67±14	69±18	63±12	59±6
Uric acid (mg/dL)	5.2±1.2	6.0±1.3	5.5±1.2	5.7±1.8
TC (mg/dL)	204±34	212±33	257±31	258±30
LDL-C (mg/dL)	118±27	117±29	172±19	178±28
HDL-C (mg/dL)	68±18	51±16	65±19	47±10
Non-HDL-C (mg/dL)	136±29	161±34	192±21	211±23
Measured sdLDL-C (mg/dL)	41.0±15.2	62.5±16.6	63.3±16.0	76.4±14.8
≥ 35 mg/dL	305 (62.0)	86 (97.7)	19 (100)	6 (100)
≥ 45 mg/dL	167 (33.9)	77 (87.5)	16 (84.2)	6 (100)
Estimated sdLDL-C (mg/dL)	31.3±8.6	47.3±10.2	45.5±9.6	61.8±4.8
≥ 35 mg/dL	160 (32.5)	79 (89.8)	16 (84.2)	6 (100)
≥ 45 mg/dL	32 (6.5)	48 (54.5)	12 (63.2)	6 (100)
ApoB (mg/dL)	73±18	82±18	117±5	126±18
Triglycerides (mg/dL)	81 (63-102)	196 (171-249)	94 (82-128)	179 (166-232)
Fasting glucose (mg/dL)	94 (88-103)	98 (91-112)	98 (9-105)	98 (89-124)
Hemoglobin A1c (%)	5.5 (5.3-5.8)	5.6 (5.3-6.0)	5.7 (5.5-6.1)	5.8 (5.2-6.5)

Variables are expressed as number (%), means±SD or medians (interquartile ranges).

ALT, alanine transaminase; ApoB, apolipoprotein B; AST, aspartate transaminase; BP, blood pressure; eGFR, estimated glomerular filtration rate; γ GTP, γ-glutamyl transpeptidase; H-, high; HDL-C, high-density lipoprotein cholesterol; L-, low; LDL-C, low-density lipoprotein cholesterol; sdLDL-C, small dense low-density lipoprotein cholesterol; TC, total cholesterol; TG, triglycerides.

Machine Learning-Based Estimation of sdLDL-C Level by Prediction One

In a simple regression analysis, there was a significant correlation between levels of measured sdLDL-C and estimated sdLDL-C calculated by using Sampson’s equation (Model 0, R²=0.701, P＜0.001) (Table 3). Multivariable regression analysis for measured sdLDL-C showed that the coefficient of determination (R²) in Model 1 using components of Sampson’s equation including levels of TC, HDL-C, non-HDL-C and TG was 0.596, which was lower than that in Model 0. When artificial intelligence software, Prediction One, was used for estimation of sdLDL-C level, the coefficient of determination in Model 1 was 0.803 (Fig.4A), which was higher than that in Model 1 by multiple regression analysis using components of Sampson’s equation (R²=0.596) as well as that in Model 0 by simple regression analysis using Sampson’s equation (R²=0.701). After the addition of γGTP level to Model 1, the coefficient of determination in Prediction One was not improved (Model 2, R²=0.805) (Fig.4B). However, when TC level was deleted in Model 2, the coefficient of determination in Prediction One was improved at maximum (Model 3, R²=0.929) (Fig.4C), and it was higher than that in multivariable regression analysis (R²=0.598) (Table 3).

Table 3.Estimation of measured sdLDL-C by Sampson’s equation and Prediction One (n = 605)

	Simple regression		Multivariable regression		Prediction One
	R2	P	R2	P	R2	P
Model 0	0.701	＜0.001	-	-	-	-
Model 1	-	-	0.596	＜0.001	0.803	＜0.001
Model 2	-	-	0.596	＜0.001	0.805	＜0.001
Model 3	-	-	0.598	＜0.001	0.929	＜0.001

Model 0: Estimated sdLDL-C calculated by using Sampson’s equation.

Model 1: Components of Sampson’s equation including TC, HDL-C, non-HDL-C and TG.

Model 2: Model 1＋γGTP.

Model 3: Model 2－TC.

γGTP, γ-glutamyl transpeptidase; HDL-C, high-density lipoprotein cholesterol; sdLDL-C, small dense low-density lipoprotein cholesterol; TC, total cholesterol; TG, triglycerides.

Fig.4. Correlations between measured and Prediction One-estimated sdLDL-C levels

A-C. Levels of directly measured small dense low-density lipoprotein cholesterol (sdLDL-C) were plotted against levels of Prediction One-estimated sdLDL-C using Model 1 (A), Mode 2 (B) and Model 3 (C) in all subjects (n=605, men/women: 280/325).

Model 1: Components of Sampson’s equation including TC, HDL-C, non-HDL-C and TG.

Model 2: Model 1 + γGTP=TC, HDL-C, non-HDL-C, TG and γGTP.

Model 3: Model 2 – TC=HDL-C, non-HDL-C, TG and γGTP.　

Open circles and broken regression line: men; closed circles and solid regression line: women.

Difference of Estimated and Measured Levels of sdLDL-C

The difference between levels of directly measured sdLDL-C and estimated sdLDL-C by Sampson’s equation (ΔsdLDL-C [Sampson]: ‘measured’ - ‘estimated’ sdLDL-C) was 10.8±10.4 mg/dL in all subjects (Table 4), suggesting that estimated sdLDL-C generally tended to be lower than measured sdLDL-C. There was no significant difference in ΔsdLDL-C [Sampson] between subgroups of sex, diabetes mellitus or anti-dyslipidemic drugs. In subjects with dyslipidemia or those with higher levels of measured sdLDL-C, ΔsdLDL-C [Sampson] was significantly augmented.

Table 4.Comparisons of the difference between estimated and measured sdLDL-C

Category	ΔsdLDL-C [Sampson]		ΔsdLDL-C [Prediction One]		P＊
	mg/dL	p	mg/dL	p
All subjects	10.8±10.4	-	0.2±4.9		＜0.001
Sex	10.7±10.3		0.1±5.0		＜0.001
Men	10.9±10.5	0.827	0.4±4.8	0.500	＜0.001
Women
Diabetes mellitus	10.0±9.4		-0.1±5.6		＜0.001
+	11.0±10.6	0.469	0.3±4.8	0.579	＜0.001
−
Dyslipidemia	12.2±10.9		0.3±5.0		＜0.001
+	9.1±9.5	＜0.001	0.1±4.8	0.655	＜0.001
−
Anti-dyslipidemic drugs	10.1±9.1		0.1±5.3		＜0.001
+	11.4±10.8	0.380	0.3±4.8	0.664	＜0.001
−
Measured sdLDL-C	14.7±9.7		1.2±5.1		＜0.001
≥ 35 mg/dL	2.4±6.0	＜0.001	-1.9±5.1	＜0.001	＜0.001
＜35 mg/dL
Measured sdLDL-C
Q1 (6.0-32.3)	1.6±6.1		-2.0±3.5		＜0.001
Q2 (32.5-42.5)	7.1±5.2	＜0.001	-1.2±3.8	0.041	＜0.001
Q3 (42.6-55.9)	12.1±6.5	＜0.001	0.3±3.5	＜0.001	＜0.001
Q4 (56.0-122.5)	22.5±9.6	＜0.001	3.9±6.1	＜0.001	＜0.001

ΔsdLDL-C [Sampson]=measured sdLDL-C − estimated sdLDL-C by Sampson’s equation

ΔsdLDL-C [Prediction One]=measured sdLDL-C − Prediction One-estimated sdLDL-C (using Model 3 in Table 3 and Fig. 4C)

Model 3: HDL-C, non-HDL-C, TG and γGTP.

γGTP, γ-glutamyl transpeptidase; HDL-C, high-density lipoprotein cholesterol; sdLDL-C, small dense low-density lipoprotein cholesterol; TG, triglycerides.

^＊Comparison of [Sampson] vs. [Prediction One].

The difference between levels of directly measured sdLDL-C and estimated sdLDL-C by Prediction One (ΔsdLDL-C [Prediction One]: ‘measured’ - ‘estimated’ sdLDL-C) was 0.2±4.9 mg/dL in all subjects, which was significantly smaller than ΔsdLDL-C [Sampson] (Table 4). There was no significant difference in ΔsdLDL-C [Prediction One] between subgroups of sex, diabetes mellitus, dyslipidemia or anti-dyslipidemic drugs. In subjects with higher levels of measured sdLDL-C, ΔsdLDL-C [Prediction One] was significantly augmented. Values of ΔsdLDL-C [Prediction One] were significantly smaller than those of ΔsdLDL-C [Sampson] in subgroup analyses including sex, diabetes mellitus, dyslipidemia, anti-dyslipidemic drugs and measured sdLDL-C levels (Table 4).

Discussion

The present study showed that sdLDL-C level calculated by Sampson’s equation was highly correlated with directly measured sdLDL-C level in a Japanese general population (R²=0.701) including subgroups of nondiabetic subjects without any medication (R²=0.686) and subjects with diabetes mellitus (R²=0.721). Multivariable regression analyses showed that components of the LDL window, including non-HDL-C, TG and ApoB, as well as γGTP were significantly independent predictors of measured sdLDL-C level. Furthermore, the estimation of sdLDL-C level was improved by using machine learning models including components of Sampson’s equation and those with the addition of γGTP and deletion of TC, although exact formula could not be provided by Prediction One, a machine learning software produced by a company. Taken together, calculation of sdLDL-C level by Sampson’s equation is well validated and would be useful for prediction of CAD in a general practice.

To the best of our knowledge, there were two previous studies that focused on the association between levels of measured and estimated sdLDL-C^{12, 15)}. Using a large number of US subjects (n=20,171), Sampson et al. proposed a formula for calculating sdLDL-C and showed that the estimated sdLDL-C level was highly correlated with measured sdLDL-C level (R²=0.745)¹²⁾. However, correlations of estimated sdLDL-C with other lipid parameters including TG, non-HDL-C and ApoB were not investigated. Another study using 2,215 Japanese subjects showed that there was a stronger correlation between estimated and measured levels of sdLDL-C in 673 healthy subjects (R²=0.736) than in 1,542 patients with diabetes mellitus (R²=0.614)¹⁵⁾. The correlations of measured sdLDL-C or estimated sdLDL-C with non-HDL-C and TG were weaker in patients with diabetes mellitus than in healthy subjects in that study¹⁵⁾. Furthermore, calculated levels of sdLDL-C by Sampson’s equation were underestimated by anti-dyslipidemic drugs including statins and pemafibrate in the previous study¹⁵⁾. On the other hand, in the present study, the correlation between estimated and measured levels of sdLDL-C was weaker in nondiabetic subjects without any medication (R²=0.686) (Fig.1B) than in subjects with diabetes mellitus (R²=0.721) (Fig.1C). Furthermore, there was no significant difference in ΔsdLDL-C [Sampson] between subjects with and without anti-dyslipidemic drugs (Table 4). One of the possible reasons for the discrepancy of results might be different backgrounds. In the previous study, the mean ages of healthy control subjects and patients with diabetes mellitus were 39 years and 65 years, respectively¹⁵⁾. On the other hand, in the present study, the mean ages of nondiabetic subjects without any medication and subjects with diabetes mellitus were 63 years and 68 years, respectively. In addition, nonfasting plasma samples collected 1-4 hours after breakfast were used in some patients with diabetes mellitus in the previous study¹⁵⁾, whereas fasting plasma was used for lipid variables in all subjects in the present study. This variation in blood sampling timing may contribute to the observed discrepancy. Another possible reason is a relatively small number of participants in the present study (n=605). The above-mentioned reasons including age, blood sampling and the number of recruited subjects may have affected the discrepancy of results.

Since estimated sdLDL-C was calculated by levels of various lipids including non-HDL-C, HDL-C, TG and TC, it is reasonable that correlations of estimated sdLDL-C with non-HDL, TG and ApoB were higher than those of measured sdLDL-C (Fig.2). Correlation between measured and estimated sdLDL-C (R²=0.701) (Fig.1A) was higher than correlations of measured sdLDL-C with non-HDL-C (R²=0.517), TG (R²=0.417) and ApoB (R²=0.281) (Fig.2A-C). Therefore, estimated sdLDL-C would be superior to non-HDL-C, TG and ApoB for identifying measured sdLDL-C.

Multivariable regression analyses showed that measured sdLDL-C level was independently associated with levels of non-HDL-C, TG and ApoB but not with LDL-C (direct method) level. On the other hand, estimated sdLDL-C level was independently associated with levels of non-HDL-C, TG, ApoB and LDL-C (direct method). Since estimated sdLDL-C level was calculated by using levels of TC, HDL-C, non-HDL-C and TG, it makes sense that LDL-C (direct method) was independently associated with estimated sdLDL-C. In addition to the lipid profiles, γGTP level was independently associated with measured sdLDL-C but not with estimated sdLDL-C. γGTP is a sensitive but nonspecific biomarker for liver injury and excessive alcohol intake²²⁾. Elevated γGTP is widely recognized as a risk factor for hypertension^{23, 24)}, diabetes mellitus^{25, 26)}, chronic kidney disease^{27, 28)}, CAD^{29, 30)} and metabolic syndrome³¹⁾. Furthermore, it has been reported that increased insulin resistance is associated with an increase in sdLDL-C level³²⁾. Elevated γGTP in association with metabolic syndrome may contribute to increased sdLDL-C level. Although the reason why γGTP level was associated with measured sdLDL-C but not estimated sdLDL-C in the present study remains unclear, it should be noted that individuals with elevated γGTP level are at high risk for CAD even if estimated sdLDL-C is not elevated.

The present study showed for the first time the percentages of subjects with a high level of estimated sdLDL-C (≥ 35 mg/dL) in the LDL window in comparison with directly measured sdLDL-C. Hayashi et al. showed that the mean values of measured sdLDL-C in the H-non-HDL-C/H-TG group and L-non-HDL-C/L-TG group were 51.0 mg/dL and 20.9 mg/dL, respectively, in healthy control subjects and 71.7 mg/dL and 27.8 mg/dL, respectively, in subjects with diabetes mellitus¹⁰⁾. In the present study, mean values of measured sdLDL-C in the H-non-HDL-C/H-TG group and L-non-HDL-C/L-TG group were 74.1 mg/dL and 38.3 mg/dL, respectively. In both studies, the percentages of subjects in the H-non-HDL-C/H-TG group with high levels of sdLDL-C (≥ 35 mg/dL) were higher than the percentages of subjects in the L-non-HDL-C/L-TG group with high levels of sdLDL-C. In a stratification by the LDL window, all of the subjects in the H-non-HDL-C/H-TG group had high levels of measured and estimated sdLDL-C (≥ 35 mg/dL) in the present study, suggesting that subjects with a high risk for CAD can be easily inferred from the LDL window.

In the present study, we additionally explored estimation of sdLDL-C level using Prediction One, artificial intelligence software. When sdLDL-C level was estimated by using the same factors in Sampson’s equation including TC, HDL-C, non-HDL-C and TG, the coefficient of determination was higher in estimated sdLDL-C level by using Prediction One (R²=0.803) (Fig.4A) than that by using Sampson’s equation (R²=0.701) (Table 3). After the addition of γGTP and deletion of TC in Prediction One according to results of multiple regression analyses, the coefficient of determination was improved at maximum (R²=0.929) (Fig.4C), suggesting that estimation of sdLDL-C level using artificial intelligence can have higher accuracy and that more precise estimation would be possible using several machine learning models. Furthermore, values of ΔsdLDL-C [Prediction One] were significantly smaller than those of ΔsdLDL-C [Sampson] in all subjects as well as subgroup analyses including sex, diabetes mellitus, dyslipidemia, anti-dyslipidemic drugs and measured sdLDL-C levels. However, unfortunately, specific details of Prediction One are confidential and cannot be disclosed. Therefore, we could not provide formula or exact results for the improvement of the Sampson’s formula.

The present study has some limitations. First, since the study subjects were residents who received annual health examinations in a rural town, the possibility of selection bias cannot be excluded. Second, since only Japanese people were enrolled, the results obtained in the present study might not be applicable to other races. Lastly, sdLDL-C level was measured by using frozen plasma samples that were collected in 2017 and had been stored at −80℃ for 6 years, though it has been reported that there was no major difference between sdLDL-C levels in fresh plasma samples and stored plasma samples¹⁵⁾.

In conclusion, sdLDL-C level estimated by Sampson’s equation can be used instead of directly measured sdLDL-C level in general practice. Machine learning of artificial intelligence may offer more accurate estimation of sdLDL-C level. By building multiple machine learning models, more appropriate and practical prediction might be possible.

Conflicts of Interest

The authors declare that they have no competing interests.

Financial Support

M.T. and M.F. were supported by grants from Japan Society for the Promotion of Science (22K08313, 23K07993).

Authors’ Contributions

K.E., Mare.T and M.F. designed the study, performed data collection and statistical analyses, and wrote the paper. R.K. and Maki.T. measured sdLDL-C levels. T.S., I.H., K.N. and M.K. performed data collection and discussed the data. N.H. performed data collection. Y.A. and H.O. performed statistical analyses. S.T. supervised the analyses. All authors approved the final version of manuscript.

Acknowledgements

The authors are grateful to Keita Numata and Takashi Hisasue for data management.

References

• 1)  Siri-Tarino PW, Krauss RM: The early years of lipoprotein research: from discovery to clinical application. J Lipid Res, 2016; 57: 1771-1777
• 2)  Hirano T: Pathophysiology of Diabetic Dyslipidemia. J Atheroscler Thromb, 2018; 25: 771-782
• 3)  Krauss RM: Small dense low-density lipoprotein particles: clinically relevant? Curr Opin Lipidol, 2022; 33: 160-166
• 4)  Austin MA, Breslow JL, Hennekens CH, Buring JE, Willett WC, Krauss RM: Low-density lipoprotein subclass patterns and risk of myocardial infarction. Jama, 1988; 260: 1917-1921
• 5)  Hirano T, Ito Y, Saegusa H, Yoshino G: A novel and simple method for quantification of small, dense LDL. J Lipid Res, 2003; 44: 2193-2201
• 6)  Ito Y, Fujimura M, Ohta M, Hirano T: Development of a homogeneous assay for measurement of small dense LDL cholesterol. Clin Chem, 2011; 57: 57-65
• 7)  Hoogeveen RC, Gaubatz JW, Sun W, Dodge RC, Crosby JR, Jiang J, Couper D, Virani SS, Kathiresan S, Boerwinkle E, Ballantyne CM: Small dense low-density lipoprotein-cholesterol concentrations predict risk for coronary heart disease: the Atherosclerosis Risk In Communities (ARIC) study. Arterioscler Thromb Vasc Biol, 2014; 34: 1069-1077
• 8)  Tsai MY, Steffen BT, Guan W, McClelland RL, Warnick R, McConnell J, Hoefner DM, Remaley AT: New automated assay of small dense low-density lipoprotein cholesterol identifies risk of coronary heart disease: the Multi-ethnic Study of Atherosclerosis. Arterioscler Thromb Vasc Biol, 2014; 34: 196-201
• 9)  Higashioka M, Sakata S, Honda T, Hata J, Yoshida D, Hirakawa Y, Shibata M, Goto K, Kitazono T, Osawa H, Ninomiya T: Small Dense Low-Density Lipoprotein Cholesterol and the Risk of Coronary Heart Disease in a Japanese Community. J Atheroscler Thromb, 2020; 27: 669-682
• 10)  Hayashi T, Koba S, Ito Y, Hirano T: Method for estimating high sdLDL-C by measuring triglyceride and apolipoprotein B levels. Lipids Health Dis, 2017; 16: 21
• 11)  Sampson M, Ling C, Sun Q, Harb R, Ashmaig M, Warnick R, Sethi A, Fleming JK, Otvos JD, Meeusen JW, Delaney SR, Jaffe AS, Shamburek R, Amar M, Remaley AT: A New Equation for Calculation of Low-Density Lipoprotein Cholesterol in Patients With Normolipidemia and/or Hypertriglyceridemia. JAMA Cardiol, 2020; 5: 540-548
• 12)  Sampson M, Wolska A, Warnick R, Lucero D, Remaley AT: A New Equation Based on the Standard Lipid Panel for Calculating Small Dense Low-Density Lipoprotein-Cholesterol and Its Use as a Risk-Enhancer Test. Clin Chem, 2021; 67: 987-997
• 13)  Inyaku M, Tanaka M, Sato T, Endo K, Mori K, Hosaka I, Mikami T, Umetsu A, Ohnishi H, Akiyama Y, Hanawa N, Furuhashi M: Calculated small dense low-density lipoprotein cholesterol level is a predominant predictor for new onset of ischemic heart disease. J Atheroscler Thromb, 2024; 31: 232-248
• 14)  Tanaka M, Sato T, Endo K, Inyaku M, Mori K, Hosaka I, Mikami T, Akiyama Y, Ohnishi H, Hanawa N, Furuhashi M: An increase in calculated small dense low-density lipoprotein cholesterol predicts new onset of hypertension in a Japanese cohort. Hypertens Res, 2023;
• 15)  Hirano T, Ito Y: Accuracy of Small Dense Low-density Lipoprotein-cholesterol Concentration Estimated via Sampson’s Equation in Healthy Subjects and Patients with Diabetes. J Atheroscler Thromb, 2023; 30: 979-989
• 16)  Sundstrom J, Schon TB: Machine Learning in Risk Prediction. Hypertension, 2020; 75: 1165-1166
• 17)  Matsuo S, Imai E, Horio M, Yasuda Y, Tomita K, Nitta K, Yamagata K, Tomino Y, Yokoyama H, Hishida A, Collaborators developing the Japanese equation for estimated GFR: Revised equations for estimated GFR from serum creatinine in Japan. Am J Kidney Dis, 2009; 53: 982-992
• 18)  American Diabetes Association: 2. Classification and Diagnosis of Diabetes. Diabetes Care, 2017; 40: S11-S24
• 19)  Umemura S, Arima H, Arima S, Asayama K, Dohi Y, Hirooka Y, Horio T, Hoshide S, Ikeda S, Ishimitsu T, Ito M, Ito S, Iwashima Y, Kai H, Kamide K, Kanno Y, Kashihara N, Kawano Y, Kikuchi T, Kitamura K, Kitazono T, Kohara K, Kudo M, Kumagai H, Matsumura K, Matsuura H, Miura K, Mukoyama M, Nakamura S, Ohkubo T, Ohya Y, Okura T, Rakugi H, Saitoh S, Shibata H, Shimosawa T, Suzuki H, Takahashi S, Tamura K, Tomiyama H, Tsuchihashi T, Ueda S, Uehara Y, Urata H, Hirawa N: The Japanese Society of Hypertension Guidelines for the Management of Hypertension (JSH 2019). Hypertens Res, 2019; 42: 1235-1481
• 20)  Friedewald WT, Levy RI, Fredrickson DS: Estimation of the concentration of low-density lipoprotein cholesterol in plasma, without use of the preparative ultracentrifuge. Clin Chem, 1972; 18: 499-502
• 21)  Kanda Y: Investigation of the freely available easy-to-use software ‘EZR’ for medical statistics. Bone Marrow Transplant, 2013; 48: 452-458
• 22)  Whitfield JB: Gamma glutamyl transferase. Crit Rev Clin Lab Sci, 2001; 38: 263-355
• 23)  Liu CF, Gu YT, Wang HY, Fang NY: Gamma-glutamyltransferase level and risk of hypertension: a systematic review and meta-analysis. PLoS One, 2012; 7: e48878
• 24)  Kunutsor SK, Apekey TA, Cheung BM: Gamma-glutamyltransferase and risk of hypertension: a systematic review and dose-response meta-analysis of prospective evidence. J Hypertens, 2015; 33: 2373-2381
• 25)  Miyamori D, Tanaka M, Furuhashi M, Ohnishi H, Koyama M, Osanami A, Higashiura Y, Numata K, Hisasue T, Hanawa N, Moniwa N, Miura T: Prediction of new onset of diabetes mellitus during a 10-year period by using a combination of levels of alanine aminotransferase and gamma-glutamyl transferase. Endocr J, 2021; 68: 1391-1402
• 26)  Park JY, Han K, Kim HS, Cho JH, Yoon KH, Kim MK, Lee SH: Cumulative Exposure to High gamma-Glutamyl Transferase Level and Risk of Diabetes: A Nationwide Population-Based Study. Endocrinol Metab (Seoul), 2022; 37: 272-280
• 27)  Shen ZW, Xing J, Wang QL, Faheem A, Ji X, Li J, Bian WW, Jiang Z, Li XJ, Xue FZ, Liu J: Association between serum gamma-glutamyltransferase and chronic kidney disease in urban Han Chinese: a prospective cohort study. Int Urol Nephrol, 2017; 49: 303-312
• 28)  Shibata M, Sato KK, Uehara S, Koh H, Oue K, Kambe H, Morimoto M, Hayashi T: Serum Gamma-Glutamyltransferase, Daily Alcohol Consumption, and the Risk of Chronic Kidney Disease: The Kansai Healthcare Study. J Epidemiol, 2020; 30: 163-169
• 29)  Fraser A, Harris R, Sattar N, Ebrahim S, Smith GD, Lawlor DA: Gamma-glutamyltransferase is associated with incident vascular events independently of alcohol intake: analysis of the British Women’s Heart and Health Study and Meta-Analysis. Arterioscler Thromb Vasc Biol, 2007; 27: 2729-2735
• 30)  Rahmani J, Miri A, Namjoo I, Zamaninour N, Maljaei MB, Zhou K, Cerneviciute R, Mousavi SM, Varkaneh HK, Salehisahlabadi A, Zhang Y: Elevated liver enzymes and cardiovascular mortality: a systematic review and dose-response meta-analysis of more than one million participants. Eur J Gastroenterol Hepatol, 2019; 31: 555-562
• 31)  Lee DS, Evans JC, Robins SJ, Wilson PW, Albano I, Fox CS, Wang TJ, Benjamin EJ, D’Agostino RB, Vasan RS: Gamma glutamyl transferase and metabolic syndrome, cardiovascular disease, and mortality risk: the Framingham Heart Study. Arterioscler Thromb Vasc Biol, 2007; 27: 127-133
• 32)  Haffner SM, Mykkanen L, Robbins D, Valdez R, Miettinen H, Howard BV, Stern MP, Bowsher R: A preponderance of small dense LDL is associated with specific insulin, proinsulin and the components of the insulin resistance syndrome in non-diabetic subjects. Diabetologia, 1995; 38: 1328-1336