Critical Evaluation of Indices Used to Assess β-Cell Function

Chao Cao; Han-Chow E Koh; Dominic N Reeds; Bruce W Patterson; Samuel Klein; Bettina Mittendorfer

doi:10.2337/db23-0613

. 2023 Nov 28;73(3):391–400. doi: 10.2337/db23-0613

Critical Evaluation of Indices Used to Assess β-Cell Function

Chao Cao ¹, Han-Chow E Koh ¹, Dominic N Reeds ¹, Bruce W Patterson ¹, Samuel Klein ^1,², Bettina Mittendorfer ^1,^3,^✉

PMCID: PMC10882145 PMID: 38015795

Abstract

The assessment of β-cell function, defined as the relationship between insulin secretion rate (ISR) and plasma glucose, is not standardized and often involves any of a number of β-cell function indices. We compared β-cell function by using popular indices obtained during basal conditions and after glucose ingestion, including the HOMA-B index, the basal ISR (or plasma insulin)-to-plasma glucose concentration ratio, the insulinogenic and ISRogenic indices, the ISR (or plasma insulin)-to-plasma glucose concentration areas (or incremental areas) under the curve ratio, and the disposition index, which integrates a specific β-cell function index value with an estimate of insulin sensitivity, between lean people with normal fasting glucose (NFG) and normal glucose tolerance (NGT) (n = 50) and four groups of people with obesity (n = 188) with 1) NFG-NGT, 2) NFG and impaired glucose tolerance (IGT), 3) impaired fasting glucose (IFG) and IGT, and 4) type 2 diabetes. We also plotted the ISR-plasma glucose relationship before and after glucose ingestion and used a statistical mixed-effects model to evaluate group differences in this relationship (i.e., β-cell function). Index-based group differences in β-cell function produced contradicting results and did not reflect the group differences of the actual observed ISR-glucose relationship or, in the case of the disposition index, group differences in glycemic status. The discrepancy in results is likely due to incorrect mathematical assumptions that are involved in computing indices, which can be overcome by evaluating the relationship between ISR and plasma glucose with an appropriate statistical model. Data obtained with common β-cell function indices should be interpreted cautiously.

Article Highlights

We evaluated differences in β-cell function, defined as the relationship between insulin secretion rate (ISR) and plasma glucose, among lean people with normoglycemia and people with obesity and different glycemic status (normoglycemia, prediabetes, type 2 diabetes) by using an oral glucose tolerance test in conjunction with popular β-cell function indices.
Additionally, we plotted the ISR-plasma glucose relationship and evaluated group differences in this relationship with a statistical mixed-effects model.
β-Cell function indices produced results that did not reflect the observed group differences in the ISR-glucose relationship presumably because of incorrect mathematical assumptions involved in computing indices.
β-Cell function indices should be used cautiously.

Graphical Abstract

Introduction

Insulin secretion from β-cells is a key regulator of plasma glucose concentration during basal and postprandial conditions (1,2). The assessment of β-cell function, defined as the relationship between insulin secretion rate (ISR) and plasma glucose, is not standardized and includes assessments made during basal conditions, after glucose or mixed meal ingestion, and during intravenous glucose infusion (3–5). Moreover, a variety of indices, including the HOMA of β-cell function (HOMA-B), the basal ISR-to-basal plasma glucose concentration ratio, the insulinogenic, C-peptideogenic, and ISRogenic indices, and the ISR (or insulin concentration)-to-plasma glucose concentration areas under the curve (AUC) (or incremental AUC [iAUC]) ratios during the first 30 min after glucose or meal ingestion or the entire postprandial period have been used to measure β-cell function (3,4). The specific index used might affect the results and conclusions of a study because of inherent limitations in the assumptions of different indices. First, the use of plasma insulin concentration as a surrogate for ISR (HOMA-B, insulinogenic index, insulin-glucose AUC ratio) can affect the assessment because plasma insulin concentration represents the balance between insulin secretion and plasma insulin clearance. Second, the use of ratios that relate ISR (or surrogates) to plasma glucose can be problematic because ratios can produce misleading results when the regression of the two variables has a nonzero intercept, the two variables in the ratio do not change in linear proportion, or ratios with different denominators are compared (6,7). Furthermore, the disposition index (DI) has been proposed as a robust measure of β-cell function because it integrates β-cell function with insulin sensitivity. The DI was originally developed as the product of the acute rise in plasma insulin concentration after an intravenous glucose injection and the insulin sensitivity index obtained from an intravenous glucose tolerance test (IVGTT) because it was noted that the relationship between these two variables can be described as a rectangular hyperbola (8,9). The DI is now also determined by other methods as a fasting/basal DI (i.e., the product of any measure of β-cell function and insulin sensitivity obtained during overnight fasting conditions, such as the product of HOMA-B and HOMA of insulin sensitivity [HOMA-IS]) and as an oral DI (i.e., product of any β-cell function index and any measure of insulin sensitivity assessed during a glucose or mixed meal ingestion test) (3,8,10–13). However, the assessment of the DI is not appropriate if the measure of β-cell function is not reliable or the relationship between the β-cell function and insulin sensitivity indices cannot be described by a rectangular hyperbola.

The purpose of the current study was to compare β-cell function assessed by using popular indices obtained during basal conditions and after glucose ingestion in lean people with normal fasting glucose (NFG) and normal glucose tolerance (NGT) and four groups of people with obesity with different glycemic status, including 1) NFG and NGT (OB-NFG-NGT group), 2) NFG and impaired glucose tolerance (IGT) (OB-NFG-IGT group), 3) impaired fasting glucose (IFG) and IGT (OB-IFG-IGT group), and 4) type 2 diabetes (T2D) (OB-T2D group). We hypothesized that β-cell function assessed by using different indices would produce conflicting results and that many indices would not reliably reflect the relationship between ISR and plasma glucose over a physiological range of glucose concentrations.

Research Design and Methods

Study Participants

The current study is a secondary analysis of data obtained from 238 participants (50 lean [BMI ≥18.5 and <25.0 kg/m²] and 188 with obesity [BMI ≥30.0 and <50.0 kg/m²]) who participated in five ongoing studies (clinical trial reg. nos. NCT02994459, NCT03408613, NCT02706262, NCT04131166, and NCT01977560, clinicaltrials.gov) that included a frequently sampled 2-h oral glucose tolerance test (OGTT). Participants provided written informed consent before initiation of the study protocols, which were approved by the institutional review board of Washington University, and completed a screening evaluation after a 12-h overnight fast that included a medical history and physical examination and standard blood tests. Potential participants were excluded if they 1) had a medical condition or received treatment that could affect the study outcome measures, 2) consumed excessive amounts of alcohol (men >21 drinks/week, women >14 drinks/week), 3) had ≥3% body weight changes within the past 6 months, or 4) participated in structured exercise for >90 min/week. All participants who were lean had NFG (<100 mg/dL) and NGT (2-h OGTT plasma glucose <140 mg/dL). Among the 188 participants with obesity, 83 had NFG-NGT, 52 had NFG-IGT, 30 had IFG-IGT, and 23 had T2D. Participants with isolated IFG (IFG-NGT) were not included in this study because only four participants in our studies met this condition. Participants with T2D were instructed to stop taking glucagon-like peptide 1 receptor agonists for 2 weeks, oral diabetes medications for 3 days, and insulin for 1 day before the metabolic studies were conducted.

Metabolic Testing, Sample Processing, and Calculations

Body composition was assessed by using DEXA (iDXA; GE Healthcare). Plasma glucose, insulin, and C-peptide concentrations were measured before and at 10, 20, 30, 60, 90, and 120 min after ingesting 75 g of glucose. ISR was determined by fitting the plasma C-peptide concentration time course to a two-compartment model (14). The following indices commonly used to evaluate β-cell function were calculated: 1) HOMA-B, which is calculated as 20 times fasting plasma insulin in mU/L divided by fasting plasma glucose in mmol/L minus 3.5, and HOMA2-B, which is derived from fasting plasma glucose and insulin concentrations by using publicly available modeling software (https://www.dtu.ox.ac.uk/homacalculator) (15,16); 2) the insulinogenic index, which is calculated as the difference in plasma insulin concentration between time 0 (before glucose ingestion) and 30 min after glucose ingestion (ΔI_0–30) divided by the difference in plasma glucose concentration between 0 and 30 min (ΔG_0–30) (4); 3) the C-peptideogenic index, which is calculated as plasma ΔC-peptide_0–30 divided by ΔG_0–30 (17,18); 4) the ISRogenic index, which is calculated as ΔISR_0–30 divided by ΔG_0–30 (19); 5) the insulin concentration or ISR AUC during the first 30 min or the entire OGTT divided by the plasma glucose concentration AUC_0–30 or AUC_0–120, respectively (20); and 6) the insulin concentration or ISR iAUC during the entire OGTT divided by the plasma glucose concentration iAUC during the entire OGTT (21,22). The basal DI was calculated as the product of various measures of basal β-cell function (e.g., HOMA-B) and the HOMA-IS (3,4). The HOMA-IS represents the inverse of the HOMA of insulin resistance, which is calculated as the product of fasting plasma insulin concentration in mU/L and fasting plasma glucose concentration in mmol/L divided by 22.5 (15,16). The oral DI was calculated as the product of various dynamic β-cell function indices obtained during the OGTT and the oral glucose insulin sensitivity (OGIS) index, which represents a model-based dynamic measure of whole-body insulin sensitivity that includes plasma glucose and insulin concentrations before and at 90 min and 120 min after ingestion of 75 g of glucose and correlates with the metabolic clearance rate of glucose during a hyperinsulinemic clamp procedure (23). In addition, we calculated the oral DI with the Matsuda insulin sensitivity index, another OGTT-based measure of whole-body insulin sensitivity (24). A subset of 156 (of a total of 238) study participants completed a hyperinsulinemic-euglycemic clamp procedure (insulin infusion rate 50 mU/m² body surface area/min) to determine whole-body insulin sensitivity (22,25,26). For these participants, DI values were also calculated as the product of various dynamic β-cell function indices obtained during the OGTT and the glucose infusion rate during the clamp procedure adjusted for both fat-free mass and the plasma insulin concentration during the clamp procedure (i.e., whole-body insulin sensitivity).

Statistical Analysis

One-way ANOVA was used to evaluate differences in participant characteristics, β-cell function index values, and other metabolic outcome variables among the groups. Group differences in β-cell function, as defined as the relationship between ISR and plasma glucose during the OGTT, were evaluated by using a mixed-effects model with ISR as the dependent variable, group and time during the OGTT as fixed factors, and plasma glucose concentration as a covariate. P ≤ 0.05 was considered statistically significant. To evaluate whether a rectangular hyperbolic relationship existed between a specific measure of insulin sensitivity and β-cell function, we determined the regression coefficient of the log-transformed values for insulin sensitivity and β-cell function (27,28). Data are presented as mean ± SEM for normally distributed data sets and as median (interquartile range) for skewed data sets. Statistical analyses were performed by using Stata 16.0 (StataCorp LLC) software. Our study included both men and women, but we did not include sex as a factor in the statistical analysis because the purpose of our study was to evaluate whether different metrics of β-cell function applied to the same study participants results in the same conclusion. A person’s sex affects the different measurements equally and is therefore not a determinant of the conclusion.

Data and Resource Availability

Data generated from this study are available from the corresponding author upon reasonable request. No resources were generated.

Results

Characteristics of Study Participants

Participants with obesity were slightly older than lean participants, and among the participants with obesity, those in the OB-IFG-IGT and OB-T2D groups were ∼10 years older than those in the OB-NFG-NGT group (Table 1). The contribution of body fat to total body mass was not different among the groups with obesity. Insulin sensitivity, as assessed using either HOMA-IS, the OGIS index, or the Matsuda-IS index, was lower in all groups with obesity compared with the lean group and decreased progressively from the OB-NFG-NGT to the OB-NGT-IGT to the OB-IFG-IGT group, but was higher in the OB-T2D group compared with the OB-IFG-IGT group.

Table 1.

Participant demographic characteristics, glycemic status, and insulin sensitivity

Characteristic	Lean	OB-NFG-NGT	OB-NFG-IGT	OB-IFG-IGT	OB-T2D
Participants, n	50	83	52	30	23
Sex, n
Male	19	15	10	10	4
Female	31	68	42	20	19
Race, %
White	80	45	65	63	65
Black	6	55	31	33	26
Asian	14	0	2	0	0
Other	0	0	2	4	9
Age (years)	33 ± 1	40 ± 1 ^a	41 ± 1 ^a	48 ± 2 ^a ^, ^b ^, ^c	53 ± 2 ^a ^, ^b ^, ^c ^, ^d
Body surface area (m²)	1.76 ± 0.02	2.12 ± 0.02 ^a	2.17 ± 0.03 ^a	2.24 ± 0.04 ^a	2.01 ± 0.04 ^a ^, ^b ^, ^c ^, ^d
BMI (kg/m²)	22.6 ± 0.2	37.6 ± 0.5 ^a	39.3 ± 0.6 ^a ^, ^b	39.7 ± 1.0 ^a ^, ^b	36.7 ± 1.3 ^a ^, ^c ^, ^d
Body fat (%)	28.2 ± 1.1	46.3 ± 0.8 ^a	48.0 ± 0.8 ^a	46.8 ± 1.4 ^a	47.6 ± 0.6 ^a
Glucose
Basal plasma glucose (mg/dL)	85 ± 1	87 ± 1	92 ± 1 ^a ^, ^b	107 ± 1 ^a ^, ^b ^, ^c	132 ± 5 ^a ^, ^b ^, ^c ^, ^d
2-h OGTT glucose (mg/dL)	102 ± 3	110 ± 2 ^a	162 ± 2 ^a ^, ^b	183 ± 6 ^a ^, ^b ^, ^c	291 ± 12 ^a ^, ^b ^, ^c ^, ^d
AUC_0–30 (mg/dL × 30 min)	3,250 ± 54	3,168 ± 41	3,498 ± 48 ^a ^, ^b	3,941 ± 89 ^a ^, ^b ^, ^c	5,385 ± 223 ^a ^, ^b ^, ^c ^, ^d
iAUC_0–30 (mg/dL × 30 min)	690 ± 46	566 ± 30	751 ± 43 ^b	727 ± 50 ^b	1,440 ± 146 ^a ^, ^b ^, ^c ^, ^d
AUC_0–120 (mg/dL × 120 min)	13,982 ± 322	14,200 ± 234	18,366 ± 217 ^a ^, ^b	21,050 ± 385 ^a ^, ^b ^, ^c	31,486 ± 1,220 ^a ^, ^b ^, ^c ^, ^d
iAUC_0–120 (mg/dL × 120 min)	3,739 ± 289	3,792 ± 224	7,377 ± 224 ^a ^, ^b	8,195 ± 311 ^a ^, ^b ^, ^c	15,706 ± 821 ^a ^, ^b ^, ^c ^, ^d
Insulin
Basal plasma insulin (pmol/L)	33.8 ± 2.0	74.6 ± 4.7 ^a	113.3 ± 9.2 ^a ^, ^b	184.4 ± 19.7 ^a ^, ^b ^, ^c	90.9 ± 6.8 ^a ^, ^d
AUC_0–30 (nmol/L × 30 min)	6.4 ± 0.5	11.1 ± 0.7 ^a	11.9 ± 0.8 ^a	12.3 ± 1.1 ^a	5.8 ± 0.4 ^b ^, ^c ^, ^d
iAUC_0–30 (nmol/L × 30 min)	5.4 ± 0.5	8.9 ± 0.7 ^a	8.5 ± 0.6 ^a	6.8 ± 0.8	3.2 ± 0.3 ^a ^, ^b ^, ^c ^, ^d
AUC_0–120 (nmol/L × 120 min)	39.5 ± 2.8	70.0 ± 4.0 ^a	94.8 ± 6.2 ^a ^, ^b	110.8 ± 8.7 ^a ^, ^b ^, ^c	45.4 ± 4.3 ^b ^, ^c ^, ^d
AUC_0–120 (nmol/L × 120 min)	35.4 ± 2.6	61.1 ± 3.7 ^a	81.2 ± 5.3 ^a ^, ^b	88.7 ± 7.6 ^a ^, ^b	34.5 ± 3.9 ^b ^, ^c ^, ^d
C-peptide
Basal plasma C-peptide (ng/mL)	1.6 ± 0.1	2.5 ± 0.1 ^a	3.5 ± 0.1 ^a ^, ^b	4.5 ± 0.2 ^a ^, ^b ^, ^c	2.7 ± 0.2 ^a ^, ^c ^, ^d
AUC_0–30 (ng/mL × 30 min)	114 ± 6	154 ± 6 ^a	179 ± 6 ^a ^, ^b	191 ± 10 ^a ^, ^b	116 ± 8 ^b ^, ^c ^, ^d
iAUC_0–30 (ng/mL × 30 min)	67 ± 5	78 ± 5	74 ± 4	57 ± 6 ^b ^, ^c	34 ± 3 ^a ^, ^b ^, ^c ^, ^d
AUC_0–120 (ng/mL × 120 min)	811 ± 32	1,051 ± 37 ^a	1,295 ± 44 ^a ^, ^b	1,354 ± 63 ^a ^, ^b	830 ± 65 ^b ^, ^c ^, ^d
iAUC_0–120 (ng/mL × 120 min)	622 ± 28	748 ± 30 ^a	876 ± 35 ^a ^, ^b	811 ± 52 ^a	503 ± 46 ^a ^, ^b ^, ^c ^, ^d
ISR
Basal ISR (pmol/min)	123 ± 5	229 ± 9 ^a	329 ± 16 ^a ^, ^b	428 ± 26 ^a ^, ^b ^, ^c	235 ± 20 ^a ^, ^c ^, ^d
AUC_0–30 (nmol)	14.7 ± 0.9	21.9 ± 1.0 ^a	24.3 ± 1.1 ^a	23.9 ± 1.5 ^a	13.4 ± 0.9 ^b ^, ^c ^, ^d
iAUC_0–30 (nmol)	11.0 ± 0.8	15.1 ± 0.8 ^a	14.4 ± 0.8 ^a	11.1 ± 1.2 ^b ^, ^c	6.4 ± 0.5 ^a ^, ^b ^, ^c ^, ^d
AUC_0–120 (nmol)	78 ± 38	117 ± 4 ^a	153 ± 6 ^a ^, ^b	158 ± 7 ^a ^, ^b	90 ± 7 ^b ^, ^c ^, ^d
iAUC_0–120 (nmol)	63 ± 3	90 ± 4 ^a	113 ± 5 ^a ^, ^b	107 ± 6 ^a ^, ^b	62 ± 56 ^b ^, ^c ^, ^d
HOMA-IR	1.10 (0.92–1.49)	2.54 (1.65–3.19) ^a	3.56 (2.65–5.56) ^a ^, ^b	6.48 (4.98–10.08) ^a ^, ^b ^, ^c	4.91 (3.59–6.02) ^a ^, ^b ^, ^d
HOMA-IS	0.92 (0.67–1.09)	0.39 (0.31–0.61) ^a	0.28 (0.18–0.38) ^a ^, ^b	0.15 (0.10–0.20) ^a ^, ^b ^, ^c	0.20 (0.17–0.28) ^a ^, ^b ^, ^d
OGIS index	441 (417–467)	388 (350–421) ^a	328 (291–358) ^a ^, ^b	268 (237–297) ^a ^, ^b ^, ^c	293 (278–323) ^a ^, ^b ^, ^d
Matsuda-IS index	5.6 (4.5–8.0)	3.2 (2.5–4.2) ^a	2.1 (1.3–2.6) ^a ^, ^b	1.1 (0.9–1.7) ^a ^, ^b ^, ^c	1.8 (1.5–2.1) ^a ^, ^b ^, ^d

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Data are mean ± SEM or median (interquartile range) unless otherwise indicated. One-way ANOVA with post hoc testing was used to compare participant outcomes among groups.

Value significantly different from the corresponding value in the lean group, P < 0.05.

Value significantly different from the corresponding value in the OB-NFG-NGT group, P < 0.05.

Value significantly different from the corresponding value in the OB-NFG-IGT group, P < 0.05.

Value significantly different from the corresponding value in the OB-IFG-IGT group, P < 0.05.

Basal (fasted condition) plasma glucose concentration and the plasma glucose concentration AUC_0–120 and iAUC_0–120 were not different between the OB-NFG-NGT and lean groups and progressively increased from the OB-NGT-IGT to the OB-IFG-IGT to the OB-T2D group (Table 1 and Fig. 1A). Basal plasma insulin and C-peptide concentrations and basal ISRs were nearly double in the OB-NFG-NGT group compared with the lean group and increased progressively from the OB-NFG-NGT to the OB-NFG-IGT to the OB-IFG-IGT group (Table 1). Basal plasma insulin and C-peptide concentrations and basal ISR in the OB-T2D group were not different from the corresponding values in the OB-NFG-NGT group (Table 1). The insulin and C-peptide concentration AUC_0–120 and iAUC_0–120 and ISR AUC_0–120 and iAUC_0–120 values increased progressively from the lean to the OB-NFG-NGT to the OB-NFG-IGT group, with only a small or no further increase in the OB-IFG-IGT compared with the OB-NFG-IGT group (Table 1 and Fig. 1B–D), and both the insulin and C-peptide concentration and ISR AUC_0–120 and iAUC_0–120 were lower in the OB-T2D group than the OB-IFG-IGT group (Table 1 and Fig. 1C and D).

Metabolic response to glucose ingestion. Plasma glucose (A), insulin (B), and C-peptide (C) concentrations and ISR (D) before and every 30 min for 2 h after ingesting 75 g of glucose in the lean, OB-NFG-NGT, OB-NFG-IGT, OB-IFG-IGT, and OB-T2D groups.

β-Cell Function Assessed as the Relationship Between ISR and Plasma Glucose During the OGTT

By visually evaluating the ISR-plasma glucose concentration relationship during the first 30 min of the OGTT when plasma glucose concentration is increasing, in conjunction with a statistical mixed-effects model analysis, we found that the relationship between ISR and glucose was 1) not different between the OB-NFG-NGT and OB-NFG-IGT groups and greater in these two groups compared with the lean group (P < 0.05), 2) lower in the OB-IFG-IGT group than in both the OB-NFG-NGT and OB-NFG-IGT groups (P < 0.05) and not different in the OB-IFG-IGT and lean groups, and 3) much lower in the OB-T2D group than in all other groups (P < 0.05) (Fig. 2). Expressing ISR relative to body surface area (in m²), evaluating the ISR-plasma glucose relationship during the entire 2-h OGTT, or using plasma insulin instead of ISR did not affect the relative differences or similarities among groups (data not shown).

The relationship between ISR and plasma glucose before and every 10 min for 30 min after glucose ingestion. Data are mean ± SEM.

β-Cell Function Assessed by Using β-Cell Function Indices

Indices Based on Basal Data

Indices that involve only basal metabolic values showed no difference in β-cell function between the OB-T2D and lean group (HOMA-B and HOMA2-B) or were even higher in the OB-T2D group than the lean group (basal ISR-to-glucose ratio) (Table 2). Furthermore, they showed higher values in the groups with obesity but without diabetes compared with both the lean group and the OB-T2D group and higher values in the OB-NFG-IGT and OB-IFG-IGT groups compared with the OB-NFG-NGT group, without a difference between the OB-NFG-IGT and the OB-IFG-IGT groups.

Table 2.

β-Cell function indices

	Lean	OB-NFG-NGT	OB-NFG-IGT	OB-IFG-IGT	OB-T2D
Basal
HOMA-B	96 ± 6	199 ± 14 ^a	257 ± 27 ^a ^, ^b	252 ± 27 ^a ^, ^b	90 ± 9 ^b ^, ^c ^, ^d
HOMA2-B	83 ± 3	132 ± 6 ^a	158 ± 9 ^a ^, ^b	167 ± 13 ^a ^, ^b	77 ± 6 ^b ^, ^c ^, ^d
Basal ISR-to-basal glucose	1.4 ± 0.1	2.6 ± 0.1 ^a	3.6 ± 0.2 ^a ^, ^b	4.0 ± 0.2 ^a ^, ^b	1.9 ± 0.2 ^a ^, ^b ^, ^c ^, ^d
Early (0–30 min) OGTT
Insulinogenic index	8.4 ± 0.8	17.8 ± 1.4 ^a	12.4 ± 1.0 ^a ^, ^b	9.7 ± 1.0 ^b	2.4 ± 0.3 ^a ^, ^b ^, ^c ^, ^d
C-peptideogenic index × 10⁻²	109 ± 9	163 ± 10 ^a	104 ± 6 ^b	75 ± 7 ^a ^, ^b ^, ^c	26 ± 3 ^a ^, ^b ^, ^c ^, ^d
ISRogenic index	17 ± 1	28 ± 2 ^a	19 ± 1 ^b	14 ± 1 ^b ^, ^c	5 ± 1 ^a ^, ^b ^, ^c ^, ^d
Insulin AUC_0–30-to-glucose AUC_0–30	1.9 ± 0.2	3.5 ± 0.2 ^a	3.4 ± 0.2 ^a	3.1 ± 0.3 ^a	1.1 ± 0.1 ^a ^, ^b ^, ^c ^, ^d
Insulin iAUC_0–30-to-glucose iAUC_0–30	8.5 ± 0.8	19.1 ± 1.9 ^a	13 ± 1.2 ^a ^, ^b	9.4 ± 1 ^b ^, ^c	2.7 ± 0.4 ^a ^, ^b ^, ^c ^, ^d
ISR AUC_0–30-to-glucose AUC_0–30	4.5 ± 0.3	6.9 ± 0.3 ^a	7.0 ± 0.3 ^a	6.1 ± 0.4^a^*	2.6 ± 0.2 ^a ^, ^b ^, ^c ^, ^d
ISR iAUC_0–30-to-glucose iAUC_0–30	17 ± 1	33 ± 3 ^a	21 ± 1 ^b	15 ± 1 ^b ^, ^c	5 ± 1 ^a ^, ^b ^, ^c ^, ^d
Total (0–120 min) OGTT
Insulin AUC_0–120-to-glucose AUC_0–120	2.9 ± 0.2	4.9 ± 0.3 ^a	5.2 ± 0.3 ^a	5.3 ± 0.4 ^a	1.6 ± 0.2 ^a ^, ^b ^, ^c ^, ^d
Insulin iAUC_0–120-to-glucose iAUC_0–120	12.7 ± 1.5	22.5 ± 2.7 ^a	11.5 ± 0.8 ^b	11.4 ± 1.1 ^b	2.5 ± 0.3 ^a ^, ^b ^, ^c ^, ^d
ISR AUC_0–120-to-glucose AUC_0–120	5.6 ± 0.2	8.3 ± 0.3 ^a	8.3 ± 0.3 ^a	7.6 ± 0.4 ^a	3.1 ± 0.3 ^a ^, ^b ^, ^c ^, ^d
ISR iAUC_0–120-to-glucose iAUC_0–120	16 (12–26)	23 (18–36)	15 (13–19) ^b	14 (10–18) ^b	4 (3–6) ^a ^, ^b ^, ^c ^, ^d

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Data are mean ± SEM or median (interquartile range). One-way ANOVA with post hoc testing was used to compare outcomes among groups.

Value significantly different from the corresponding value in the lean group, P < 0.05.

Value significantly different from the corresponding value in the OB-NFG-NGT group, P < 0.05.

Value significantly different from the corresponding value in the OB-NFG-IGT group, P < 0.05.

Value significantly different from the corresponding value in the OB-IFG-IGT group, P < 0.05.

Value tended to be different from the value in the OB-NFG-IGT group, P = 0.07.

Indices Based on the First 30 min of the OGTT

β-Cell function indices assessed during the first 30 min of the OGTT (insulinogenic index, C-peptideogenic index, ISRogenic index, and insulin concentration-to glucose or ISR-to-glucose AUC_0–30 and iAUC_0–30 ratios) showed much lower (twofold or more) values in the OB-T2D than all other groups and much higher values (50% to more than twofold higher) in the OB-NFG-NGT than the lean group (Table 2). However, the differences in β-cell function indices in the OB-NFG-IGT and OB-IFG-IGT groups compared with the lean and OB-NFG-NGT groups and between the OB-NFG-IGT and the OB-IFG-IGT groups varied among the different indices. Values were 1) not different among the three groups with obesity but without diabetes (insulin AUC_0–30-to-glucose AUC_0–30 and ISR AUC_0–30-to-glucose AUC_0–30 ratios); 2) lower in both the OB-NFG-IGT and OB-IFG-IGT groups than the OB-NFG-NGT group (all except the insulin and ISR AUC_0–30-to-glucose AUC_0–30 ratios) with either no difference between the OB-NFG-IGT and OB-IFG-IGT groups or lower values in the OB-IFG-IGT than the OB-NFG-NGT group; and 3) values in OB-NFG-IGT and the OB-IFG-IGT groups that were either higher than, or not different from, the values in the lean group.

Indices Based on the Entire (0–120 min) OGTT

β-Cell function indices generated from data obtained during the entire 120 min of the OGTT (insulin concentration-to-glucose or ISR-to-glucose AUC_0–120 and iAUC_0–120 ratios) showed lower values in the OB-T2D group compared with all other groups. In addition, the values were higher in the groups with obesity but without diabetes compared with the lean group and not different among the three groups with obesity when total insulin concentration-to-glucose or total ISR-to-glucose ratios were used (Table 2). However, values were ∼50% lower in the OB-NFG-IGT and the OB-IFG-IGT groups compared with the OB-NFG-NGT group, without a difference among the OB-NFG-IGT, the OB-IFG-IGT, and the lean groups, when incremental insulin concentration-to-glucose or incremental ISR-to-glucose ratios were used.

Disposition Index

The DI is based on the premise of a rectangular hyperbolic relationship between the paired measures of insulin sensitivity and β-cell function, whereby the product of insulin sensitivity and β-cell function is a constant (3,8,9). Accordingly, a decrease in insulin sensitivity is offset by a proportional increase in β-cell function, and an increase in insulin sensitivity is offset by a proportional decrease in β-cell function to maintain normoglycemia. In DI assessments made during basal conditions, the relationship between HOMA-IS as the measure of insulin sensitivity and either fasting plasma insulin concentration or HOMA-B as the measure of β-cell function represented a rectangular hyperbola (regression coefficient of the log-transformed data >0.95 and <1.05); however, there were no, or minimal, differences in the relationship between insulin sensitivity and β-cell function among groups with different glycemic status (Supplementary Fig. 1). The relationship between insulin sensitivity and β-cell function did not meet criteria for a rectangular hyperbola (regression coefficient of the log-transformed data <0.8 or >1.2) in assessments made during basal conditions that used HOMA-IS as the measure of insulin sensitivity and the basal ISR or the basal ISR-to-basal glucose concentration ratio as the measure of β-cell function (Supplementary Fig. 1) and in dynamic DI assessments made during the OGTT (Supplementary Figs. 2 and 3). In fact, many of the dynamic assessments made after an oral glucose load did not show a statistically significant relationship between insulin sensitivity and β-cell function. Only the OGIS paired with insulin concentration AUC_0–120, and the OGIS paired with the insulin concentration AUC_0–120-to-glucose concentration AUC_0–120 ratio resembled a curvilinear (but not quite a rectangular hyperbolic) relationship. In addition, differences or similarities in DI values among various groups were not consistent with differences or similarities in glycemic control assessed during the OGTT (Table 3 and Supplementary Table 1). For example, the DI was generally much greater (up to double) in the OB-NFG-NGT group compared with the lean group (Table 3), even though glycemic control (basal plasma glucose concentration and plasma glucose concentration AUC during the OGTT) were not different between the two groups (Fig. 1A). In contrast, the DI value was often not different or greater in the dysglycemic groups with obesity but without diabetes compared with the OB-NFG-NGT group or the lean group (Table 3 and Supplementary Table 1). Replacing the OGIS index with the Matsuda-IS index in the DI calculations did not change any of the conclusions made (data not shown). Moreover, in the subset of participants who completed a hyperinsulinemic-euglycemic clamp procedure the relationship between whole-body insulin sensitivity (assessed as the glucose infusion rate adjusted for fat-free mass and plasma insulin) and various β-cell function indices did not resemble a rectangular hyperbola (Supplementary Fig. 4), and the corresponding DI values produced inconsistent group differences in β-cell function and results that were not always congruent with the differences in glycemic status among groups (i.e., in some cases, the DI values were lower in the OB-NFG-NGT compared with the lean group, despite no difference in plasma glucose concentration during the OGTT between the two groups) (Supplementary Table 2).

Table 3.

DI calculated as the product of a measure of insulin sensitivity and a measure of β-cell function

	Lean	OB-NFG-NGT	OB-NFG-IGT	OB-IFG-IGT	OB-T2D
Basal DI, defined as product of HOMA-IS index and
Fasting plasma insulin	28.5 ± 0.3	28.2 ± 0.2	26.7 ± 0.3 ^a ^, ^b	22.8 ± 0.2 ^a ^, ^b ^, ^c	19.0 ± 0.6 ^a ^, ^b ^, ^c ^, ^d
HOMA-B	84 ± 5	84 ± 7	65 ± 8 ^a ^, ^b	32 ± 1 ^a ^, ^b ^, ^c	19 ± 2 ^a ^, ^b ^, ^c ^, ^d
Basal ISR	110 ± 5	99 ± 6 ^a	92 ± 5 ^a	62 ± 4 ^a ^, ^b ^, ^c	51 ± 4 ^a ^, ^b ^, ^c ^, ^d
Basal ISR-to-basal glucose	1.31 ± 0.06	1.49 ± 0.28	1.02 ± 0.06 ^a	0.58 ± 0.04 ^a ^, ^b ^, ^c	0.41 ± 0.04 ^a ^, ^b ^, ^c ^, ^d
Early (0–30 min of OGTT) oral DI, defined as product of OGIS index and
Insulinogenic index × 10⁻²	38 ± 4	66 ± 5 ^a	38 ± 3 ^b	25 ± 2 ^a ^, ^b ^, ^c	7 ± 1 ^a ^, ^b ^, ^c ^, ^d
C-peptideogenic index	48 ± 4	62 ± 4 ^a	33 ± 2 ^a ^, ^b	20 ± 2 ^a ^, ^b ^, ^c	8 ± 1 ^a ^, ^b ^, ^c ^, ^d
ISRogenic index × 10⁻²	74 ± 6	105 ± 6 ^a	61 ± 4 ^b	38 ± 3 ^a ^, ^b ^, ^c	14 ± 2 ^a ^, ^b ^, ^c ^, ^d
Insulin AUC_0–30 × 10⁻⁵	28 ± 2	41 ± 2 ^a	37 ± 2 ^a	32 ± 3 ^b	18 ± 1 ^a ^, ^b ^, ^c ^, ^d
ISR AUC_0–30 × 10⁻⁵	64 ± 4	82 ± 3 ^a	77 ± 3 ^a	63 ± 4 ^b ^, ^c	41 ± 3 ^a ^, ^b ^, ^c ^, ^d
Insulin AUC_0–30-to-glucose AUC_0–30	863 ± 69	1,277 ± 67 ^a	1,045 ± 59 ^a ^, ^b	806 ± 59 ^b ^, ^c	345 ± 32 ^a ^, ^b ^, ^c ^, ^d
Insulin iAUC_0–30-to-glucose iAUC_0–30	3,774 ± 337	7,177 ± 688 ^a	4,001 ± 359 ^b	2,457 ± 248 ^a ^, ^b ^, ^c	797 ± 105 ^a ^, ^b ^, ^c ^, ^d
ISR AUC_0–30-to-glucose AUC_0–30	1,967 ± 116	2,577 ± 95 ^a	2,215 ± 92 ^b	1,602 ± 89 ^a ^, ^b ^, ^c	792 ± 69 ^a ^, ^b ^, ^c ^, ^d
ISR iAUC_0–30-to-glucose iAUC_0–30	7,749 ± 541	12,505 ± 1,124 ^a	6,555 ± 429 ^a ^, ^b	4,237 ± 385 ^a ^, ^b ^, ^c	1,561 ± 202 ^a ^, ^b ^, ^c ^, ^d
Total (0–120 min of OGTT) oral DI, defined as product of OGIS index and
Insulin AUC_0–120 × 10⁻⁵	173 ± 1	255 ± 11 ^a	288 ± 14 ^a	283 ± 17 ^a	136 ± 13 ^a ^, ^b ^, ^c ^, ^d
Insulin AUC_0–120-to-glucose AUC_0–120	1,265 ± 87	1,801 ± 73 ^a	1,575 ± 77 ^a ^, ^b	1,366 ± 87 ^b	464 ± 52 ^a ^, ^b ^, ^c ^, ^d
Insulin iAUC_0–120-to-glucose iAUC_0–120	5,774 ± 731	8,456 ± 1,031 ^a	3,475 ± 191 ^a ^, ^b	2,914 ± 234 ^a ^, ^b ^, ^c	728 ± 100 ^a ^, ^b ^, ^c ^, ^d
ISR AUC_0–120 × 10⁻⁶	34 ± 1	44 ± 1 ^a	49 ± 2 ^a ^, ^b	42 ± 1 ^a ^, ^c	27 ± 2 ^a ^, ^b ^, ^c ^, ^d
ISR AUC_0–120-to-glucose AUC_0–120	2,485 ± 101	3,083 ± 90 ^a	2,659 ± 91 ^b	2,016 ± 89 ^a ^, ^b ^, ^c	916 ± 91 ^a ^, ^b ^, ^c ^, ^d
ISR iAUC_0–120-to-glucose iAUC_0–120	10,776 ± 1,714	12,747 ± 1,616	5,026 ± 204 ^a ^, ^b	3,645 ± 252 ^a ^, ^b ^, ^c	1,305 ± 158 ^a ^, ^b ^, ^c ^, ^d

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Data are mean ± SEM. One-way ANOVA with post hoc testing was used to compare outcomes among groups.

Value significantly different from the corresponding value in the lean group, P < 0.05.

Value significantly different from the corresponding value in the OB-NFG-NGT group, P < 0.05.

Value significantly different from the corresponding value in the OB-NFG-IGT group, P < 0.05.

Value significantly different from the corresponding value in the OB-IFG-IGT group, P < 0.05.

Discussion

We evaluated the ability of commonly used indices of β-cell function to identify differences in the relationship between ISR and plasma glucose or, in the case of the DI, the relationship between β-cell function and insulin sensitivity, among lean people with normoglycemia or people with obesity with different glycemic status. Our data demonstrate that 1) values of all indices of β-cell function were higher in the OB-NFG-NGT group than in the lean group; 2) basal β-cell function indices failed to detect β-cell dysfunction in the OB-T2D group compared with the lean group; 3) dynamic indices of β-cell function identified marked β-cell dysfunction in the OB-T2D group, but differences in dynamic indices of β-cell function among the groups with obesity but without diabetes and in the OB-NFG-IGT and OB-IFG-IGT groups compared with the lean group were inconsistent, and values for β-cell function were higher, lower, or not different between specific groups depending on the β-cell function index used; and 4) the basal and dynamic DI values often produced results that were inconsistent with the differences in glycemic status among the study groups. These findings demonstrate that β-cell function indices are not interchangeable and that many indices provide an inaccurate assessment of β-cell function depending on the groups being compared.

The discrepancy in results obtained with different β-cell function indices is likely due to several erroneous assumptions and mathematical relationships that underlie the β-cell function index values. First, the ISR during an OGTT is determined by the ability of β-cells to respond to the amount of glucose in the circulation, which is a function of both basal β-cell glucose sensitivity and the response of β-cells to a change in plasma glucose after glucose ingestion. However, the insulinogenic, C-peptideogenic, and ISRogenic indices and the insulin, C-peptide or ISR iAUC-to-glucose iAUC ratios evaluate the change in insulin, C-peptide, and ISR relative to the change in plasma glucose after glucose ingestion but do not evaluate the total ISR (or the total amount of insulin as a surrogate for ISR) that is available relative to plasma glucose. The HOMA-B, HOMA2-B, and the basal ISR-to-basal glucose ratio, on the other hand, focus entirely on basal conditions. Second, the insulinogenic, C-peptideogenic, and ISRogenic indices assume a linear relationship between plasma glucose and either plasma insulin, C-peptide, or ISR during the first 30 min after glucose ingestion, which we found was not always correct. The nonlinear relationship can only be appreciated with more frequent (e.g., every 10 min) blood sampling as in our study (Fig. 2). Third, all β-cell function indices in our study involve a ratio of ISR (or surrogate measure, e.g., plasma insulin or C-peptide concentration) and plasma glucose concentration or a ratio of the change in ISR (or surrogates) and the change in glucose or a ratio of the ISR (or surrogate) AUC and glucose AUC or respective iAUCs. Using ratios to describe physiological processes can produce spurious results when there is not a fixed or standardized denominator or the relationship between the two variables in the ratio is not linear or does not have a zero intercept (6,7). These conditions were not always met in the ISR-glucose relationship in the different groups we studied. Accordingly, using ratios to describe the relationship between ISR (or surrogates) and plasma glucose concentration to compare β-cell function among groups that have different plasma glucose concentrations during an OGTT is not valid. In contrast, we found that using ratios to compare the OB-NFG-NGT group with the lean group was reliable because plasma glucose concentrations were the same in both groups. Fourth, many indices use plasma insulin concentration as a surrogate for ISR. However, plasma insulin concentration represents the balance between insulin secretion and insulin clearance and is therefore not a direct measure of β-cell activity.

Many of the computational issues involved in β-cell function indices can be overcome by using a statistical mixed regression model to evaluate the relationship between ISR and plasma glucose. A regression model can take differences in plasma glucose concentration at different times during a metabolic study into account and allows the comparison of the relationship between ISR and plasma glucose over a dynamic range of glucose concentrations among groups. By using this approach, we obtained results that are consistent with visual inspection of the data (Fig. 2), namely that the relationship between ISR and plasma glucose (i.e., β-cell function) was higher in the OB-NFG-NGT and the OB-NFG-IGT groups compared with the lean group, without a difference between the OB-NFG-NGT and the OB-NFG-IGT groups; lower in the OB-IFG-IGT than the OB-NFG-NGT and OB-NFG-IGT groups; and much lower in the OB-T2D group than all other groups. This observation is also consistent with the maintenance of normoglycemia despite insulin resistance in the OB-NFG-NGT group and the progressively worsening glycemic status with worsening insulin sensitivity in the dysglycemic groups with obesity as well as the severe hyperglycemia in the OB-T2D group despite insulin sensitivity values that are not different from the other groups with obesity. There are additional ways to evaluate β-cell function during an OGTT that involve sophisticated mathematical modeling, i.e., the oral minimal model method (5). The oral minimal model method has previously been used to evaluate β-cell function among groups of participants with different glycemic status (29) and generated results that are consistent with the results we obtained by statistically analyzing group differences in the ISR-glucose relationship and interpreting the results in the context of insulin sensitivity. In addition, there are methods to evaluate β-cell function that include intravenous glucose challenges (IVGTT, hyperglycemic clamp, or graded glucose infusion [9,30–33]). Some of them (hyperglycemic clamp, graded glucose infusion [30–32]) were specifically designed to overcome the issues related to the ratios we highlight in this study. However, intravenous glucose challenges do not stimulate intestinal factors (the incretin system) involved in insulin secretion that are important during normal physiological conditions and a critical component of β-cell dysfunction in people with T2D (34,35).

The DI was developed to assess the balance between insulin sensitivity and the ability of β-cells to produce an adequate amount of insulin to maintain normoglycemia because it was noted that the product of the acute insulin response after an intravenous glucose injection and the insulin sensitivity index obtained from an IVGTT was constant, and therefore, the relationship between the acute insulin response and the insulin sensitivity index was represented by a rectangular hyperbola (9). The DI obtained from an IVGTT has demonstrated clinical relevance because it is a strong predictor of diabetes risk (36,37). In the current study, we evaluated the DI as the product of insulin sensitivity (measured during static or dynamic glucose challenge conditions) and β-cell function (measured by using various indices of β-cell function), which has been done in many previous studies (3,10,12,38–45). Our data demonstrate that an assessment of a basal DI that involved insulin concentration–based β-cell function values (fasting plasma insulin or HOMA-B) and insulin sensitivity (HOMA-IS) fulfills the criteria of a rectangular hyperbola, but an assessment of the basal DI that used ISR-based measures of β-cell function or a dynamic DI obtained during an oral glucose challenge did not provide a rectangular hyperbolic relationship between the indices of β-cell function and insulin sensitivity, which has been shown in previous studies (18,28,46). There are several explanations for the discrepancy in DI outcomes when assessed by using an IVGTT or OGTT. First, the stimulation of insulin secretion after a large intravenous glucose bolus and the resulting increase in plasma insulin represents a very different physiological condition from the stimulation of insulin secretion and the resulting increase in plasma insulin after glucose ingestion (25,35). In fact, the oral DI correlates poorly with the original DI when assessed in the same participants (47). Second, combinations of measures of β-cell action and insulin sensitivity (13,28) that demonstrated (or approximated) a rectangular hyperbolic relationship in our study and others (13,28) involved the HOMA-IS paired with the HOMA-B, the HOMA-IS paired with fasting plasma insulin concentration, and the OGIS (or Matsuda-IS) index paired with the insulin concentration AUC_0–120 or the insulin concentration AUC_0–120-to-glucose concentration AUC_0–120 but not the ISR-based β-cell function measures as shown in the present study and DeFronzo et al. (18). It is likely that the differences between DI measures that use insulin rather than ISR as a measure of β-cell function are because 1) plasma insulin concentration is not the same as ISR and insulin resistance is associated with a decrease in plasma insulin clearance (26,48), which alters plasma insulin concentration independent of β-cell function, and 2) the use of plasma insulin concentration in both the measure of β-cell function and insulin sensitivity produces a codependence bias (27). Together, these findings suggest that 1) the original DI has validity in identifying an imbalance in circulating insulin and glucose but is not a measure of β-cell function and 2) the basal DI and oral DI do not reliably assess the appropriateness of insulin secretion for a given insulin sensitivity.

In summary, the assessment of group differences in β-cell function by using popular indices produces contradicting results, even when applied to the same participants under the same study conditions. The discrepancy in results is likely due to incorrect mathematical assumptions involved in indices. We propose the assessment of group differences (or treatment effects) in β-cell function by evaluating the relationship between ISR and plasma glucose before and after glucose ingestion by visual inspection in conjunction with an appropriate statistical model because it provides an unbiased assessment during clinically and physiologically meaningful conditions.

This article contains supplementary material online at https://doi.org/10.2337/figshare.24596388.

Article Information

Acknowledgments. The authors thank the staff of the Center for Human Nutrition at Washington University School of Medicine and the Clinical and Translational Research Unit for assistance in conducting the metabolic studies and technical assistance in processing the study samples. The authors also thank the study participants.

Funding. This study was supported by National Institutes of Health grant R01 DK115400, Washington University School of Medicine Nutrition Obesity Research Center grant P30 DK056341, Washington University School of Medicine Diabetes Research Center grant P30 DK020579, Washington University School of Medicine Institute of Clinical and Translational Sciences grant UL1 TR002345, American Diabetes Association grant 1-18-ICTS-119, and Longer Life Foundation grant 2019-011.

The funders had no role in the study design, data collection, analysis, and interpretation of the results.

Duality of Interest. No potential conflicts of interest relevant to this article were reported.

Author Contributions. C.C., H.-C.E.K., D.N.R., B.W.P., S.K., and B.M. contributed to the data acquisition, data analysis, data interpretation, and revision of the manuscript. C.C. and B.M. wrote the first draft of the manuscript. B.M. designed the study. B.M. is the guarantor of this work and, as such, had full access to all the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis.

Funding Statement

This study was supported by National Institutes of Health grant R01 DK115400, Washington University School of Medicine Nutrition Obesity Research Center grant P30 DK056341, Washington University School of Medicine Diabetes Research Center grant P30 DK020579, Washington University School of Medicine Institute of Clinical and Translational Sciences grant UL1 TR002345, American Diabetes Association grant 1-18-ICTS-119, and Longer Life Foundation grant 2019-011.

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PERMALINK

Critical Evaluation of Indices Used to Assess β-Cell Function

Chao Cao

Han-Chow E Koh

Dominic N Reeds

Bruce W Patterson

Samuel Klein

Bettina Mittendorfer