We assessed whether the relationship between insulin secretion and sensitivity predicted development of type 2 diabetes in American Indians participating in a longitudinal epidemiologic study. At baseline, when all participants did not have diabetes, 1,566 underwent oral tests and 420 had intravenous measures of glucose regulation, with estimates of insulin secretion and sensitivity. Standardized major axis regression was used to study the relationship between secretion and sensitivity. Distances away from and along the regression line estimated compensatory insulin secretion and secretory demand, respectively. This relationship differed according to glucose tolerance and BMI category. The distance away from the line is similar to the disposition index (DI), defined as the product of estimated secretion and sensitivity, but the regression line may differ from a line with constant DI (i.e., it is not necessarily hyperbolic). Participants with the same DI but different levels of insulin secretion and sensitivity had different incidence rates of diabetes; lower sensitivity with higher secretory demand was associated with greater diabetes risk. Insulin secretion and insulin sensitivity, analyzed together, predict diabetes better than DI alone. Physiologically, this may reflect long-term risk associated with increased allostatic load resulting from the stimulation of insulin hypersecretion by increased glycemia.

## Introduction

Defects in tissue sensitivity to insulin and insulin secretion are two physiologic abnormalities associated with type 2 diabetes (1). As type 2 diabetes develops, insulin sensitivity typically declines and insulin secretion becomes deficient (2). In general, to maintain normal glucose levels, a decrease in insulin sensitivity is accompanied by compensatory upregulation of insulin secretion and vice versa. Studies of the relationship between insulin sensitivity and insulin secretion have led to improved understanding of the development of type 2 diabetes (3).

This relationship is thought to be reciprocal and to be approximated by a hyperbola (4). Several studies have provided evidence to support this hypothesis for measures of insulin secretion and sensitivity obtained through intravenous glucose tolerance tests and oral glucose tolerance tests (OGTT) (5–7). The hyperbolic relationship implies a constant association between these two metabolic variables, which is captured in the disposition index (DI). The DI is a measure of the ability of β-cells to compensate for insulin resistance and is defined as the product of insulin secretion and insulin sensitivity (8). Glycemia is often thought to be a function of the DI (9) (which may be taken to imply that all individuals who have the same DI have the same risk of developing type 2 diabetes).

The DI is a strong predictor of diabetes (7,10,11). Utzschneider et al. (7) found that the DI was a better predictor of diabetes than either insulin secretion or insulin sensitivity alone. Lorenzo et al. (11) found that a model including DI alone was similar in predicting diabetes to a model with measures of insulin secretion and sensitivity together. However, these studies relied on the assumption of a hyperbolic relationship between insulin secretion and sensitivity. While the glucose homeostatic response, reflected in the DI, is a major determinant of glucose tolerance, mild increases in glycemia may provide part of the signal required to maintain normal homeostasis in the presence of decreased insulin sensitivity, and the corresponding physiologic stress (termed allostatic load) may increase the long-term risk of developing diabetes (10).

In the current study, we first estimated the relationship between insulin secretion and insulin sensitivity, measured through intravenous measures and OGTT-based surrogate indices using standardized major axis (SMA) regression to account for the variability (biologic variability and measurement error) in both variables. We then tested whether this relationship differed according to glucose tolerance or BMI categories. We studied how homeostatic response and allostatic load predicted type 2 diabetes when the relationship between insulin secretion and sensitivity was not necessarily hyperbolic. We investigated whether participants with the same DI, but different insulin sensitivity and secretion values, had the same incidence of diabetes. Finally, we compared different variables related to insulin secretion and sensitivity in their ability to predict development of diabetes.

## Research Design and Methods

### Participants

A longitudinal epidemiologic study of type 2 diabetes was conducted from 1965 to 2007 in an American Indian community in Arizona, a high-risk population for this condition (12). We considered two data sets from this study, the OGTT data set and the IV/CLAMP data set. In both data sets, participants’ baseline examination was the first examination performed after they turned 18 years old. Participants were followed up until they developed diabetes or until their last follow-up examination, whichever came first. The OGTT data set contains observations from 1,566 participants without diabetes who had baseline OGTTs taken from 1973 to 1986. The IV/CLAMP data set includes data from 420 participants without diabetes for whom baseline intravenous measures were collected from 1983 to 2003. The current study classified participants using the 2006 guidelines from the World Health Organization (13) as having normal glucose regulation (NGR) (fasting plasma glucose [FPG] <110 mg/dL and 2-h plasma glucose (2-h PG) <140 mg/dL), impaired fasting glucose (110 ≤ FPG < 126 mg/dL and 2-h PG <140 mg/dL), impaired glucose tolerance (FPG <126 mg/dL and 140 ≤ 2-h PG < 200 mg/dL) or diabetes (FPG ≥126 mg/dL or 2-h PG ≥200 mg/dL). We combined participants with impaired fasting glucose and impaired glucose tolerance and designated them as having impaired glucose regulation (IGR). Based on BMI, participants were also classified as normal weight (BMI <25 kg/m^{2}), overweight (25 ≤ BMI < 30 kg/m^{2}), and obese (BMI ≥30 kg/m^{2}).

### Measures of Insulin Secretion and Sensitivity

The gold-standard measures for insulin secretion and sensitivity, acute insulin response (AIR) and *M* value, are derived from the first-phase insulin response to intravenous glucose infusion and a hyperinsulinemic-euglycemic clamp, respectively. In large epidemiologic studies, measures of insulin secretion and sensitivity obtained from OGTTs that are comparable to the gold standards can be used (14). Participants in the OGTT data set had plasma glucose and serum insulin concentrations measured at fasting (G_{0} and I_{0}, respectively) and 120 min after undergoing a 75-g OGTT (G_{120} and I_{120}, respectively); the measures of insulin secretion and sensitivity used were 120-min corrected insulin response (CIR_{120} = [I_{120}/(G_{120} ∗ [G_{120} − 70 mg/dL])]) and insulin sensitivity index (ISI_{0} = [10^{4}/(I_{0} ∗ G_{0})]), respectively, and their DI was calculated as DI_{O} = ISI_{0} ∗ CIR_{120}. Several surrogate indices of insulin secretion and sensitivity can be calculated from OGTTs. However, we used CIR_{120} for secretion, because we did not have 30-min measurements of plasma glucose and serum insulin in the OGTT data set, and it correlated better with AIR than other indices that could have been calculated with the available data. We used ISI_{0} for sensitivity, because its correlation with *M* value is slightly higher than that of other indices (14), and its calculation does not involve measures at 120 min after the OGTT, decreasing interdependence of secretion and sensitivity indices calculated from the same OGTT test. In the IV/CLAMP data set, insulin secretion was calculated as the average incremental plasma insulin concentration 3–5 min after a 25-g glucose bolus (AIR) and sensitivity (*M*) by the rate of glucose disposal from a hyperinsulinemic-euglycemic glucose clamp, which has been previously described (15,16); the DI was calculated as DI_{IV} = *M* ∗ AIR.

### Statistical Analysis

The relationship between baseline insulin secretion and sensitivity was studied by estimating ln (CIR_{120} or AIR) as a function of ln (ISI_{0} or *M* value) using SMA regression (17). SMA regression is used if estimating the relationship between *x* and *y* when both are subject to variability and the relationship between them is thought to be symmetric (it seems arbitrary which variable is on the *x*-axis and which variable is on the *y*-axis; we obtain the same line if we model *y* as a function of *x* or *x* as a function of *y*, and the biologic interpretation of the results is identical regardless of which variable is on each axis) (18,19). While ordinary least squares (linear) regression minimizes the vertical distance (in *y*) between each point and the line, SMA regression minimizes the distance in both directions (*x* and *y*) (i.e., it minimizes the area of the right triangle defined by vertical and horizontal lines from each point to the line) (18,19). In contrast to orthogonal regression, which minimizes the perpendicular distance of each point from the line, the line fit by SMA regression provides more precise CIs for the slope (17). The models fit by the SMA regression were chosen after comparing their fit with models from linear and orthogonal regression using SE of the residuals and CIs for intercepts and slopes (Supplementary Material). If the slopes of the regressions were not significantly different from −1 (i.e., the 95% CI for the slope included −1), a hyperbolic relationship was assumed (Supplementary Material). Participants were divided for analysis by glucose tolerance category (NGR and IGR) and by BMI category (normal weight, overweight, and obese). To investigate whether this relationship differed by glucose tolerance category, we first tested whether the SMA regression lines for NGR and IGR participants shared a common slope using likelihood ratio tests (17). Not sharing a common slope indicated that the relationship was associated with glucose tolerance category. We followed the same procedure to determine whether BMI category was associated with this relationship. All SMA regression lines and tests for common slope were calculated using the *smatr* package in R (20).

In both data sets, we fit an overall SMA regression line to the whole data set and obtained a line orthogonal to it that intercepted the SMA line at the mean of the natural logarithm of both insulin sensitivity and secretion measures; thus, both lines passed through the centroid of the data. We then calculated perpendicular distances from the data points to the SMA line and to its orthogonal line, allowing them be positive or negative to take on the same direction as the residuals. This is illustrated in Fig. 1. The same procedure was followed for NGR and IGR participants. The distances were calculated with the purpose of treating data points in a continuous way in the insulin secretion by insulin sensitivity representation, following a similar approach to that of Stumvoll et al. (10). We describe the distances from the SMA line as distances away from the SMA line, and the distances from the orthogonal line as distances along the SMA line. Distances away from the SMA line are analogous to the DI (and represent adequacy of insulin secretion compensation in response to changes in insulin sensitivity), while distances along the SMA line are related to the Β-cell demand index in the Stumvoll et al. (10) approach (and represent insulin secretion demand imposed by any decrease in insulin sensitivity). The use of distances along the SMA line (secretion demand) allowed us to quantify increase in insulin secretion per decrease in insulin sensitivity for participants with the same distances away from the SMA line (same level of secretion compensation).

We formed groups of participants based on the distances away from the SMA line and along the SMA line. For the OGTT data set, participants were placed into nine groups based on tertile of distance away from line and along the line (tertile 1 low, tertile 2 medium, and tertile 3 high secretion compensation and secretion demand); in the IV/CLAMP data set, because of the smaller sample, four groups were formed (below median low and above median high secretion compensation and secretion demand). Using Cox proportional hazards models, we investigated whether the development of diabetes was associated with the group in which participants were classified. We also studied how distances away from the line and along the line were associated with diabetes development in the whole data set and the datasets with NGR and IGR participants only. These models adjusted for sex, age, and fraction of American Indian heritage. We estimated incidence rates of diabetes using Poisson regression models to determine whether participants with the same DI, but different values of insulin secretion and sensitivity, had the same risk of diabetes.

We compared the performance of different Cox proportional hazards models for predicting diabetes in the OGTT data set and the IV/CLAMP data set. In both data sets, comparisons were made with respect to a baseline model with sex, age, and fraction of American Indian heritage. All continuous variables were standardized to mean of 0 and SD of 1. Models that added new variables to the baseline model were compared using the following statistics: area under the receiver-operating curve (AUC), difference in AUC (ΔAUC), integrated discrimination improvement (IDI), relative IDI, and net reclassification improvement (NRI) with respect to the baseline model. We compared AUCs between two models to determine which models had significantly higher AUCs than other models. AUCs were calculated using the C-statistic of Pencina and D’Agostino (21). IDI and relative IDI were calculated using the method proposed by Chambless et al. (22), while NRI was calculated using the method of Pencina et al. (23); these three statistics were calculated at the average follow-up time. Comparisons between the two models (e.g., significance of ΔAUC) were made by the DeLong et al. (24) method. The higher these five statistics were, the better a model performed in predicting diabetes development. A relative IDI >0.33 (1/*n* of variables in baseline model) indicated that a model with added variables predicted diabetes better than the baseline model (23). An NRI >0.6 indicated strong performance in predicting diabetes, while an NRI of ∼0.4 indicated intermediate performance and an NRI <0.2 was considered weak (25).

### Data and Resource Availability

The data sets generated and/or analyzed during the current study are not publicly available because of privacy concerns.

## Results

### Descriptive Statistics

Table 1 presents descriptive statistics for both data sets by glucose tolerance group. In the OGTT data set, 255 participants had normal weight, 410 were overweight, 896 were obese, and five had missing data on BMI. In the IV/CLAMP data set, 52 participants had normal weight, 94 were overweight, and 274 were obese.

Demographic . | OGTT data set (n = 1,566)
. | IV/CLAMP data set (n = 420)
. | ||
---|---|---|---|---|

NGR . | IGR* . | NGR . | IGR* . | |

N of participants (male/female) | 1,207 (403/804) | 359 (121/238) | 318 (202/116) | 102 (43/59) |

Age, years | 23.7 (20.1–31.2) | 31.8 (23.8–44.8) | 24.5 (21.3–30.3) | 26.9 (23.6–32.6) |

BMI, kg/m^{2} | 30.4 (26.0–35.1) | 33.1 (29.4–38.2) | 32.1 (27.4–37.4) | 34.4 (30.4–39.0) |

Fasting glucose, mg/dL | 91 (86–96) | 102 (94–109) | 87 (82–93) | 93 (88–100) |

2-h glucose, mg/dL | 111 (100–122) | 154 (144–170) | 108 (94–122) | 159 (145–172) |

Fasting insulin, μU/mL | 24 (16–35) | 35 (23–51) | 33.1 (23.1–45.8) | 46.6 (33.2–65) |

2-h insulin, μU/mL | 112 (76–166) | 195 (128–310) | 121.8 (69.3–180) | 285.9 (208.1–386) |

HOMA-IR, (mg · μU)/(mL · dL) | 5.3 (3.5–8.2) | 9.0 (5.6–13.5) | — | — |

CIR_{120}, (μU · dL)/(mg · mL) | 0.026 (0.018–0.037) | 0.015 (0.009–0.023) | — | — |

CIR_{30}, (μU · dL)/(mg · mL) | — | — | 0.023 (0.016–0.036) | 0.019 (0.012–0.029) |

ISI_{0}, (mL · dL)/(mg · μU) | 0.188 (0.122–0.287) | 0.111 (0.074–0.179) | 3.548 (2.464–5.148) | 2.357 (1.672–3.226) |

DI_{O}, CIR_{120} ∗ ISI_{0} | 0.005 (0.003–0.008) | 0.002 (0.001–0.003) | — | — |

DI_{30}, CIR_{30} ∗ ISI_{0} | — | — | 0.081 (0.052–0.127) | 0.043 (0.028–0.065) |

Follow-up, years | 15.7 (8.9–21.7) | 7.6 (3.4–14.7) | 10.6 (6.9–13.5) | 8.5 (5.0–12.0) |

Type 2 diabetes diagnosis, n (%) | 543 (45) | 257 (72) | 89 (28) | 57 (56) |

PFAT, % | — | — | 31.1 (24.4–37.3) | 36.1 (30.2–41.6) |

AIR, μU/mL | — | — | 209.2 (146.8–329.9) | 197.5 (105.6–276.5) |

M value, mg · kg EMBS^{−1} · min^{−1} | — | — | 3.7 (3.1–4.5) | 3.0 (2.7–3.4) |

DI_{IV}, AIR ∗ M value | — | — | 848.7 (575.1–1194.5) | 622.2 (349.8–902.9) |

Demographic . | OGTT data set (n = 1,566)
. | IV/CLAMP data set (n = 420)
. | ||
---|---|---|---|---|

NGR . | IGR* . | NGR . | IGR* . | |

N of participants (male/female) | 1,207 (403/804) | 359 (121/238) | 318 (202/116) | 102 (43/59) |

Age, years | 23.7 (20.1–31.2) | 31.8 (23.8–44.8) | 24.5 (21.3–30.3) | 26.9 (23.6–32.6) |

BMI, kg/m^{2} | 30.4 (26.0–35.1) | 33.1 (29.4–38.2) | 32.1 (27.4–37.4) | 34.4 (30.4–39.0) |

Fasting glucose, mg/dL | 91 (86–96) | 102 (94–109) | 87 (82–93) | 93 (88–100) |

2-h glucose, mg/dL | 111 (100–122) | 154 (144–170) | 108 (94–122) | 159 (145–172) |

Fasting insulin, μU/mL | 24 (16–35) | 35 (23–51) | 33.1 (23.1–45.8) | 46.6 (33.2–65) |

2-h insulin, μU/mL | 112 (76–166) | 195 (128–310) | 121.8 (69.3–180) | 285.9 (208.1–386) |

HOMA-IR, (mg · μU)/(mL · dL) | 5.3 (3.5–8.2) | 9.0 (5.6–13.5) | — | — |

CIR_{120}, (μU · dL)/(mg · mL) | 0.026 (0.018–0.037) | 0.015 (0.009–0.023) | — | — |

CIR_{30}, (μU · dL)/(mg · mL) | — | — | 0.023 (0.016–0.036) | 0.019 (0.012–0.029) |

ISI_{0}, (mL · dL)/(mg · μU) | 0.188 (0.122–0.287) | 0.111 (0.074–0.179) | 3.548 (2.464–5.148) | 2.357 (1.672–3.226) |

DI_{O}, CIR_{120} ∗ ISI_{0} | 0.005 (0.003–0.008) | 0.002 (0.001–0.003) | — | — |

DI_{30}, CIR_{30} ∗ ISI_{0} | — | — | 0.081 (0.052–0.127) | 0.043 (0.028–0.065) |

Follow-up, years | 15.7 (8.9–21.7) | 7.6 (3.4–14.7) | 10.6 (6.9–13.5) | 8.5 (5.0–12.0) |

Type 2 diabetes diagnosis, n (%) | 543 (45) | 257 (72) | 89 (28) | 57 (56) |

PFAT, % | — | — | 31.1 (24.4–37.3) | 36.1 (30.2–41.6) |

AIR, μU/mL | — | — | 209.2 (146.8–329.9) | 197.5 (105.6–276.5) |

M value, mg · kg EMBS^{−1} · min^{−1} | — | — | 3.7 (3.1–4.5) | 3.0 (2.7–3.4) |

DI_{IV}, AIR ∗ M value | — | — | 848.7 (575.1–1194.5) | 622.2 (349.8–902.9) |

Data are presented as median (interquartile range [quartile 1–3]) unless otherwise indicated. One NGR participant in the IV/CLAMP data set was missing measurement of insulin 30 min after OGTT. — indicates not measured.

EMBS, estimated metabolic body size; HOMA-IR, HOMA of insulin resistance; PFAT, percentage body fat.

Breakdown of participants with impaired fasting glucose and impaired glucose tolerance shown in Supplementary Tables 3 and 4.

### Relationship Between Insulin Secretion and Insulin Sensitivity

#### Glucose tolerance

Figure 2A and B present SMA lines describing the relationship between insulin secretion and sensitivity for NGR and IGR participants in the OGTT and IV/CLAMP data sets. In the OGTT data set, the slopes for the model of ln(CIR_{120}) as a function of ln(ISI_{0}) were marginally different from −1 in the whole sample (95% CI −0.999 to −0.908) and in NGR participants (95% CI −0.948 to −0.854) but not in IGR participants (95% CI −1.093 to −0.918). This suggested that the relationship between CIR_{120} and ISI_{0} was almost hyperbolic in NGR participants and was hyperbolic in IGR participants and that when combining both samples, the relationship was essentially hyperbolic.

In the IV/CLAMP data set, the slopes for the models describing the relationship between ln(AIR) and ln(*M*) were significantly different from −1 in NGR participants (95% CI −2.333 to −1.898) and IGR participants (95% CI −4.146 to −2.803) and in the whole data set (95% CI −2.442 to −2.027). This suggested that the relationship between AIR and *M* value was not hyperbolic in either NGR or IGR participants or in the combined sample.

In the OGTT data set, the slopes for the models of ln(CIR_{120}) as a function of ln(ISI_{0}) between NGR and IGR participants were significantly different (*P* = 0.010). In the IV/CLAMP data set, the slopes describing the relationship between ln(AIR) and ln(*M*) in NGR and IGR participants were also significantly different (*P* < 0.0001). Thus, participants with NGR would experience a different decrease in insulin secretion than those with IGR, even if they had the same level of insulin sensitivity. In both data sets, IGR curves were leftward and downward shifted compared with NGR curves.

#### BMI

Figures 2C and D present the SMA lines describing the relationship between insulin secretion and sensitivity in normal weight, overweight, and obese participants in the OGTT and IV/CLAMP data sets. In the OGTT data set, the slope of ln(CIR_{120}) as a function of ln(ISI_{0}) differed significantly across weight categories (*P* = 0.0265). In the IV/CLAMP data set, the slope of ln(AIR) as a function of ln(*M*) also differed significantly across weight categories (*P* < 0.0001). For both data sets, the curves for obese participants were generally leftward and downward shifted compared with curves for overweight participants, which in turn were leftward and downward shifted compared with curves for normal weight participants.

### Cox Proportional Hazards Models With Distances Away From the Line and Along the Line

Participants in the OGTT data set were classified into nine groups based on their distances away from the line and their distances along the line; results for proportional hazards models comparing these groups are shown in Fig. 3A. Figure 3B presents results for the four groups formed in the IV/CLAMP data set. In both data sets, distances away from the line (secretion compensation) were highly correlated with ln(DI) (*R* > 0.850), while distances along the line (secretion demand) were highly correlated with the natural logarithm of Β-cell demand index (*R* > 0.980), the ratio of insulin secretion divided by insulin sensitivity (10) (Supplementary Table 5). In both data sets, when controlled for sex, age, and fraction of American Indian heritage, both distance away from the line and distance along the line were associated significantly with the hazard of diabetes for all participants and for NGR participants only, but distance along the line was not significantly associated with risk of diabetes in IGR participants for either data set (Table 2). Thus, in general, in both data sets, participants with similar levels of secretion compensation (distance away from the line) had different hazards of diabetes that changed with the level of secretion demand (distance along the line). This suggests that even when two participants have the same secretion compensation, their risk of diabetes will differ if they have different secretion demand. Such situations can be studied by checking whether risk of diabetes for participants with the same DI differs according to whether their insulin secretion and sensitivity are different.

. | OGTT data set . | IV/CLAMP data set . | ||
---|---|---|---|---|

Hazard ratio (95% CI) . | P
. | Hazard ratio (95% CI) . | P
. | |

Whole data set | ||||

Distance away from line | 0.586 (0.545–0.631) | <0.0001 | 0.395 (0.309–0.505) | <0.0001 |

Distance along the line | 1.252 (1.166–1.345) | <0.0001 | 1.432 (1.134–1.808) | 0.003 |

NGR | ||||

Distance away from line | 0.744 (0.684–0.808) | <0.0001 | 0.432 (0.316–0.590) | <0.0001 |

Distance along the line | 1.350 (1.237–1.472) | <0.0001 | 1.430 (1.072–1.908) | 0.015 |

IGR | ||||

Distance away from line | 0.643 (0.559–0.739) | <0.0001 | 0.627 (0.445–0.883) | 0.008 |

Distance along the line | 1.118 (0.987–1.268) | 0.080 | 1.027 (0.719–1.466) | 0.884 |

. | OGTT data set . | IV/CLAMP data set . | ||
---|---|---|---|---|

Hazard ratio (95% CI) . | P
. | Hazard ratio (95% CI) . | P
. | |

Whole data set | ||||

Distance away from line | 0.586 (0.545–0.631) | <0.0001 | 0.395 (0.309–0.505) | <0.0001 |

Distance along the line | 1.252 (1.166–1.345) | <0.0001 | 1.432 (1.134–1.808) | 0.003 |

NGR | ||||

Distance away from line | 0.744 (0.684–0.808) | <0.0001 | 0.432 (0.316–0.590) | <0.0001 |

Distance along the line | 1.350 (1.237–1.472) | <0.0001 | 1.430 (1.072–1.908) | 0.015 |

IGR | ||||

Distance away from line | 0.643 (0.559–0.739) | <0.0001 | 0.627 (0.445–0.883) | 0.008 |

Distance along the line | 1.118 (0.987–1.268) | 0.080 | 1.027 (0.719–1.466) | 0.884 |

Hazard ratios are presented per SD of each variable. SDs are considered separately in each group. Models also include age, sex, and fraction of American Indian heritage. Distance away from the line refers to perpendicular distance from the SMA line, a measure of insulin secretion compensation in response to changes in insulin sensitivity. Distance along the line refers to perpendicular distance from the line orthogonal to the SMA line, a measure of insulin secretion demand imposed by decreased insulin sensitivity.

### Incidence Rates of Diabetes

We fit a Poisson regression model to the OGTT data set that adjusted for sex, age, and fraction of American Indian heritage and included CIR_{120} and ISI_{0} in logarithmic scale. We then estimated incidence of diabetes for a grid of values of CIR_{120} and ISI_{0} based on this model (Fig. 4A). Among participants with the same DI_{O} (CIR_{120} ∗ ISI_{0}), those with higher ISI_{0} had lower risk of diabetes. Similarly, we estimated incidence of diabetes for a grid of AIR and *M* values for the IV/CLAMP data set (Fig. 4B). Among participants with the same DI_{IV} (AIR ∗ *M*), those with higher *M* values had lower incidence of diabetes. In general, results in both data sets suggest that in assessing risk of developing diabetes, one should consider a person’s levels of insulin secretion and insulin sensitivity instead of simply considering the DI.

### Predictive Accuracy of Models for Diabetes Development

We compared the performance of various Cox proportional hazards models in predicting future diabetes development. For both data sets, the baseline model included age, sex, and fraction of American Indian heritage. Models compared included insulin secretion and sensitivity measures in logarithmic scale (ln[CIR_{120}] and ln[ISI_{0}] in OGTT data set and ln[AIR] and ln[*M*] in IV/CLAMP data set), DI in logarithmic scale (ln[DI_{O} = CIR_{120} ∗ ISI_{0}] in OGTT data set and ln[DI_{IV} = AIR ∗ *M*] in IV/CLAMP data set), distances away from the line and along the line, and different combinations of these variables. Tables 3 and 4 present statistics of predictive performance of future diabetes development for models fit to all participants, NGR participants only, and IGR participants only in the OGTT data set and the IV/CLAMP data set, respectively. Supplementary Tables 6–11 show AUC comparisons between several models in the OGTT and IV/CLAMP data sets for all participants and NGR and IGR participants only.

Model . | Hazard ratio per 1 SD (P)
. | Predictive performance statistics . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

ln(DI) . | ln(CIR_{120})
. | ln(ISI_{0})
. | Distance away . | Distance along . | AUC . | ΔAUC . | IDI . | Relative IDI . | NRI . | |

OGTT data set: all participants (baseline model AUC 0.579) | ||||||||||

ln(DI) | 0.574 (P < 0.0001) | — | — | — | — | 0.695 | 0.116 | 0.093 | 4.692 | 0.608 |

ln(CIR_{120}) | — | 0.882 (P = 0.0011) | — | — | — | 0.596 | 0.017 | 0.004 | 0.216 | 0.132 |

ln(ISI_{0}) | — | — | 0.607 (P < 0.0001) | — | — | 0.673 | 0.094 | 0.081 | 4.093 | 0.55 |

ln(CIR_{120}) and ln(ISI_{0}) | — | 0.738 (P < 0.0001) | 0.556 (P < 0.0001) | — | — | 0.703 | 0.124 | 0.106 | 5.343 | 0.645 |

Distance away | — | — | — | 0.578 (P < 0.0001) | — | 0.693 | 0.114 | 0.091 | 4.578 | 0.604 |

Distance along | — | — | — | — | 1.301 (P < 0.0001) | 0.601 | 0.022 | 0.024 | 1.22 | 0.295 |

Distances away and along | — | — | — | 0.586 (P < 0.0001) | 1.252 (P < 0.0001) | 0.703 | 0.124 | 0.106 | 5.343 | 0.645 |

OGTT data set: NGR participants only (baseline model AUC 0.547) | ||||||||||

ln(DI) | 0.715 (P < 0.0001) | — | — | — | — | 0.628 | 0.081 | 0.032 | 6.152 | 0.417 |

ln(CIR_{120}) | — | 1.062 (P = 0.18) | — | — | — | 0.544 | −0.003 | 0.001 | 0.259 | 0.001 |

ln(ISI_{0}) | — | — | 0.652 (P < 0.0001) | — | — | 0.642 | 0.095 | 0.055 | 10.659 | 0.457 |

ln(CIR_{120}) and ln(ISI_{0}) | — | 0.902 (P = 0.03) | 0.629 (P < 0.0001) | — | — | 0.647 | 0.1 | 0.057 | 10.965 | 0.475 |

Distance away | — | — | — | 0.730 (P < 0.0001) | — | 0.622 | 0.075 | 0.03 | 5.384 | 0.415 |

Distance along | — | — | — | — | 1.376 (P < 0.0001) | 0.607 | 0.06 | 0.031 | 6.048 | 0.32 |

Distances away and along | — | — | — | 0.744 (P < 0.0001) | 1.350 (P < 0.0001) | 0.647 | 0.1 | 0.057 | 10.965 | 0.475 |

OGTT data set: IGR participants only (baseline model AUC 0.535) | ||||||||||

ln(DI) | 0.632 (P < 0.0001) | — | — | — | — | 0.644 | 0.109 | 0.079 | 17.586 | 0.578 |

ln(CIR_{120}) | — | 0.953 (P = 0.47) | — | — | — | 0.583 | 0.048 | 0.037 | 8.285 | 0.292 |

ln(ISI_{0}) | — | — | 0.748 (P < 0.0001) | — | — | 0.564 | 0.029 | 0.001 | 0.167 | 0.267 |

ln(CIR_{120}) and ln(ISI_{0}) | — | 0.671 (P < 0.0001) | 0.591 (P < 0.0001) | — | — | 0.641 | 0.106 | 0.082 | 18.306 | 0.468 |

Distance away | — | — | — | 0.639 (P < 0.0001) | — | 0.644 | 0.109 | 0.079 | 17.602 | 0.578 |

Distance along | — | — | — | — | 1.155 (P = 0.02) | 0.527 | −0.008 | 0.01 | 2.287 | 0.027 |

Distances away and along | — | — | — | 0.643 (P < 0.0001) | 1.118 (P = 0.08) | 0.641 | 0.106 | 0.082 | 18.306 | 0.468 |

Model . | Hazard ratio per 1 SD (P)
. | Predictive performance statistics . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

ln(DI) . | ln(CIR_{120})
. | ln(ISI_{0})
. | Distance away . | Distance along . | AUC . | ΔAUC . | IDI . | Relative IDI . | NRI . | |

OGTT data set: all participants (baseline model AUC 0.579) | ||||||||||

ln(DI) | 0.574 (P < 0.0001) | — | — | — | — | 0.695 | 0.116 | 0.093 | 4.692 | 0.608 |

ln(CIR_{120}) | — | 0.882 (P = 0.0011) | — | — | — | 0.596 | 0.017 | 0.004 | 0.216 | 0.132 |

ln(ISI_{0}) | — | — | 0.607 (P < 0.0001) | — | — | 0.673 | 0.094 | 0.081 | 4.093 | 0.55 |

ln(CIR_{120}) and ln(ISI_{0}) | — | 0.738 (P < 0.0001) | 0.556 (P < 0.0001) | — | — | 0.703 | 0.124 | 0.106 | 5.343 | 0.645 |

Distance away | — | — | — | 0.578 (P < 0.0001) | — | 0.693 | 0.114 | 0.091 | 4.578 | 0.604 |

Distance along | — | — | — | — | 1.301 (P < 0.0001) | 0.601 | 0.022 | 0.024 | 1.22 | 0.295 |

Distances away and along | — | — | — | 0.586 (P < 0.0001) | 1.252 (P < 0.0001) | 0.703 | 0.124 | 0.106 | 5.343 | 0.645 |

OGTT data set: NGR participants only (baseline model AUC 0.547) | ||||||||||

ln(DI) | 0.715 (P < 0.0001) | — | — | — | — | 0.628 | 0.081 | 0.032 | 6.152 | 0.417 |

ln(CIR_{120}) | — | 1.062 (P = 0.18) | — | — | — | 0.544 | −0.003 | 0.001 | 0.259 | 0.001 |

ln(ISI_{0}) | — | — | 0.652 (P < 0.0001) | — | — | 0.642 | 0.095 | 0.055 | 10.659 | 0.457 |

ln(CIR_{120}) and ln(ISI_{0}) | — | 0.902 (P = 0.03) | 0.629 (P < 0.0001) | — | — | 0.647 | 0.1 | 0.057 | 10.965 | 0.475 |

Distance away | — | — | — | 0.730 (P < 0.0001) | — | 0.622 | 0.075 | 0.03 | 5.384 | 0.415 |

Distance along | — | — | — | — | 1.376 (P < 0.0001) | 0.607 | 0.06 | 0.031 | 6.048 | 0.32 |

Distances away and along | — | — | — | 0.744 (P < 0.0001) | 1.350 (P < 0.0001) | 0.647 | 0.1 | 0.057 | 10.965 | 0.475 |

OGTT data set: IGR participants only (baseline model AUC 0.535) | ||||||||||

ln(DI) | 0.632 (P < 0.0001) | — | — | — | — | 0.644 | 0.109 | 0.079 | 17.586 | 0.578 |

ln(CIR_{120}) | — | 0.953 (P = 0.47) | — | — | — | 0.583 | 0.048 | 0.037 | 8.285 | 0.292 |

ln(ISI_{0}) | — | — | 0.748 (P < 0.0001) | — | — | 0.564 | 0.029 | 0.001 | 0.167 | 0.267 |

ln(CIR_{120}) and ln(ISI_{0}) | — | 0.671 (P < 0.0001) | 0.591 (P < 0.0001) | — | — | 0.641 | 0.106 | 0.082 | 18.306 | 0.468 |

Distance away | — | — | — | 0.639 (P < 0.0001) | — | 0.644 | 0.109 | 0.079 | 17.602 | 0.578 |

Distance along | — | — | — | — | 1.155 (P = 0.02) | 0.527 | −0.008 | 0.01 | 2.287 | 0.027 |

Distances away and along | — | — | — | 0.643 (P < 0.0001) | 1.118 (P = 0.08) | 0.641 | 0.106 | 0.082 | 18.306 | 0.468 |

For all participants, IDI, relative IDI, and NRI calculated at average follow-up of 8.03 years. For NGR participants only, IDI, relative IDI, and NRI calculated at average follow-up of 15.49 years. For IGR participants only, IDI, relative IDI, and NRI calculated at average follow-up of 9.55 years. All models adjusted for age, sex, and fraction of American Indian heritage. — indicates not applicable.

Model . | Hazard ratio per 1 SD (P)
. | Predictive performance statistics . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

ln(DI) . | ln(AIR) . | ln(M)
. | Distance away . | Distance along . | AUC . | ΔAUC . | IDI . | Relative IDI . | NRI . | |

IV/CLAMP data set: all participants (baseline AUC 0.567) | ||||||||||

ln(DI) | 0.606 (P < 0.0001) | — | — | — | — | 0.655 | 0.088 | 0.074 | 4.945 | 0.443 |

ln(AIR) | — | 0.761 (P = 0.0017) | — | — | — | 0.601 | 0.034 | 0.02 | 1.35 | 0.24 |

ln(M) | — | — | 0.491 (P < 0.0001) | — | — | 0.691 | 0.124 | 0.097 | 6.514 | 0.583 |

ln(AIR) and ln(M) | — | 0.661 (P < 0.0001) | 0.441 (P < 0.0001) | — | — | 0.721 | 0.154 | 0.161 | 10.791 | 0.598 |

Distance away | — | — | — | 0.505 (P < 0.0001) | — | 0.699 | 0.132 | 0.13 | 8.747 | 0.613 |

Distance along | — | — | — | — | 0.848 (P = 0.0595) | 0.579 | 0.012 | 0.007 | 0.457 | 0.185 |

Distances away and along | — | — | — | 0.395 (P < 0.0001) | 1.432 (P = 0.0025) | 0.721 | 0.154 | 0.161 | 10.791 | 0.598 |

IV/CLAMP data set: NGR participants only (baseline AUC 0.541) | ||||||||||

ln(DI) | 0.663 (P = 0.0003) | — | — | — | — | 0.613 | 0.072 | 0.04 | 6.832 | 0.318 |

ln(AIR) | — | 0.840 (P = 0.12) | — | — | — | 0.557 | 0.016 | 0.006 | 0.991 | 0.066 |

ln(M) | — | — | 0.540 (P < 0.0001) | — | — | 0.669 | 0.128 | 0.067 | 11.46 | 0.493 |

ln(AIR) and ln(M) | — | 0.660 (P = 0.001) | 0.443 (P < 0.0001) | — | — | 0.685 | 0.144 | 0.129 | 22.032 | 0.546 |

Distance away | — | — | — | 0.539 (P < 0.0001) | — | 0.663 | 0.122 | 0.095 | 16.346 | 0.521 |

Distance along | — | — | — | — | 0.929 (P = 0.51) | 0.543 | 0.002 | 0.001 | 0.143 | 0.002 |

Distances away and along | — | — | — | 0.432 (P < 0.0001) | 1.430 (P = 0.02) | 0.685 | 0.144 | 0.129 | 22.032 | 0.546 |

IV/CLAMP data set: IGR participants only (baseline AUC 0.571) | ||||||||||

ln (DI) | 0.682 (P = 0.01) | — | — | — | — | 0.652 | 0.081 | 0.049 | 3.478 | 0.488 |

ln(AIR) | — | 0.757 (P = 0.05) | — | — | — | 0.625 | 0.054 | 0.027 | 1.914 | 0.468 |

ln(M) | — | — | 0.713 (P = 0.03) | — | — | 0.618 | 0.047 | 0.032 | 2.327 | 0.018 |

ln(AIR) and ln(M) | — | 0.721 (P = 0.02) | 0.701 (P = 0.01) | — | — | 0.675 | 0.104 | 0.064 | 4.568 | 0.545 |

Distance away | — | — | — | 0.637 (P = 0.001) | — | 0.676 | 0.105 | 0.064 | 4.588 | 0.544 |

Distance along | — | — | — | — | 0.786 (P = 0.08) | 0.616 | 0.045 | 0.02 | 1.461 | 0.468 |

Distances away and along | — | — | — | 0.627 (P = 0.01) | 1.027 (P = 0.88) | 0.675 | 0.104 | 0.064 | 4.568 | 0.545 |

Model . | Hazard ratio per 1 SD (P)
. | Predictive performance statistics . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

ln(DI) . | ln(AIR) . | ln(M)
. | Distance away . | Distance along . | AUC . | ΔAUC . | IDI . | Relative IDI . | NRI . | |

IV/CLAMP data set: all participants (baseline AUC 0.567) | ||||||||||

ln(DI) | 0.606 (P < 0.0001) | — | — | — | — | 0.655 | 0.088 | 0.074 | 4.945 | 0.443 |

ln(AIR) | — | 0.761 (P = 0.0017) | — | — | — | 0.601 | 0.034 | 0.02 | 1.35 | 0.24 |

ln(M) | — | — | 0.491 (P < 0.0001) | — | — | 0.691 | 0.124 | 0.097 | 6.514 | 0.583 |

ln(AIR) and ln(M) | — | 0.661 (P < 0.0001) | 0.441 (P < 0.0001) | — | — | 0.721 | 0.154 | 0.161 | 10.791 | 0.598 |

Distance away | — | — | — | 0.505 (P < 0.0001) | — | 0.699 | 0.132 | 0.13 | 8.747 | 0.613 |

Distance along | — | — | — | — | 0.848 (P = 0.0595) | 0.579 | 0.012 | 0.007 | 0.457 | 0.185 |

Distances away and along | — | — | — | 0.395 (P < 0.0001) | 1.432 (P = 0.0025) | 0.721 | 0.154 | 0.161 | 10.791 | 0.598 |

IV/CLAMP data set: NGR participants only (baseline AUC 0.541) | ||||||||||

ln(DI) | 0.663 (P = 0.0003) | — | — | — | — | 0.613 | 0.072 | 0.04 | 6.832 | 0.318 |

ln(AIR) | — | 0.840 (P = 0.12) | — | — | — | 0.557 | 0.016 | 0.006 | 0.991 | 0.066 |

ln(M) | — | — | 0.540 (P < 0.0001) | — | — | 0.669 | 0.128 | 0.067 | 11.46 | 0.493 |

ln(AIR) and ln(M) | — | 0.660 (P = 0.001) | 0.443 (P < 0.0001) | — | — | 0.685 | 0.144 | 0.129 | 22.032 | 0.546 |

Distance away | — | — | — | 0.539 (P < 0.0001) | — | 0.663 | 0.122 | 0.095 | 16.346 | 0.521 |

Distance along | — | — | — | — | 0.929 (P = 0.51) | 0.543 | 0.002 | 0.001 | 0.143 | 0.002 |

Distances away and along | — | — | — | 0.432 (P < 0.0001) | 1.430 (P = 0.02) | 0.685 | 0.144 | 0.129 | 22.032 | 0.546 |

IV/CLAMP data set: IGR participants only (baseline AUC 0.571) | ||||||||||

ln (DI) | 0.682 (P = 0.01) | — | — | — | — | 0.652 | 0.081 | 0.049 | 3.478 | 0.488 |

ln(AIR) | — | 0.757 (P = 0.05) | — | — | — | 0.625 | 0.054 | 0.027 | 1.914 | 0.468 |

ln(M) | — | — | 0.713 (P = 0.03) | — | — | 0.618 | 0.047 | 0.032 | 2.327 | 0.018 |

ln(AIR) and ln(M) | — | 0.721 (P = 0.02) | 0.701 (P = 0.01) | — | — | 0.675 | 0.104 | 0.064 | 4.568 | 0.545 |

Distance away | — | — | — | 0.637 (P = 0.001) | — | 0.676 | 0.105 | 0.064 | 4.588 | 0.544 |

Distance along | — | — | — | — | 0.786 (P = 0.08) | 0.616 | 0.045 | 0.02 | 1.461 | 0.468 |

Distances away and along | — | — | — | 0.627 (P = 0.01) | 1.027 (P = 0.88) | 0.675 | 0.104 | 0.064 | 4.568 | 0.545 |

For all participants, IDI, relative IDI, and NRI calculated at average follow-up of 10.19 years. For NGR participants only, IDI, relative IDI, and NRI calculated at average follow-up of 10.68 years. For IGR participants only, IDI, relative IDI, and NRI calculated at average follow-up of 8.65 years. All models adjusted for age, sex, and fraction of American Indian heritage. — indicates not applicable.

For both data sets, the predictive performance statistics for the model with insulin secretion and sensitivity measures in logarithmic scale were equal to those for the model with distances away from the line and distances along the line in all cases (all participants, NGR only, and IGR only). For both data sets, the predictive performance statistics for the model with insulin secretion and sensitivity measures in logarithmic scale were higher than those for the model with ln(DI) in all cases, except for IGR participants in the OGTT data set, where values were almost equal. Most models, including those with insulin secretion and sensitivity measures and DI in logarithmic scale, had relative IDIs >0.33 and predicted diabetes development better than the baseline model in both data sets.

In the OGTT data set, the AUC for the model with ln(CIR_{120}) and ln(ISI_{0}) was significantly higher than that of the model with ln(DI_{O}) for NGR participants only (0.647 vs. 0.628; *P* = 0.04), but not for all participants (0.703 vs. 0.695; *P* = 0.08) or IGR participants only (0.641 vs. 0.644; *P* = 0.67). In the IV/CLAMP data set, the AUC for the model with ln(AIR) and ln(*M*) was significantly higher than that of the model with ln(DI_{IV}) for all participants (0.721 vs. 0.655; *P* = 0.001) and NGR participants only (0.685 vs. 0.613; *P* = 0.01), but not for IGR participants only (0.675 vs. 0.652; *P* = 0.34). According to the NRI criterion, in the OGTT data set, the models with ln(DI_{O}) and with both ln(CIR_{120}) and ln(ISI_{0}) had strong predictive performance in all participants (0.608 vs. 0.645).

## Discussion

In people with normal glucose regulation, insulin secretion and insulin sensitivity are linked through a negative feedback loop such that as insulin sensitivity decreases insulin secretion increases and vice versa (5,8). For surrogate measures derived from the OGTT in the current study, the relationship between CIR_{120} and ISI_{0} was close to hyperbolic in NGR participants (with a slope that was modestly but significantly different from −1) and was not significantly different from hyperbolic in IGR participants; when combining NGR and IGR participants, the overall relationship between CIR_{120} and ISI_{0} was essentially hyperbolic. However, the intravenous measures of first-phase insulin secretion and insulin sensitivity did not have a hyperbolic relationship; the relationship between AIR and *M* was markedly and significantly different from hyperbolic for the NGR, IGR, and combined samples of participants. CIR_{120} and ISI_{0} were obtained from the same OGTTs, which may have resulted in some intrinsic interdependence between them, causing their relationship to be close to hyperbolic (26,27). The intravenous measures were estimated from independent tests, which might be the reason for their nonhyperbolic relationship (26). Our results agree with previous findings that the relationship between insulin sensitivity and insulin secretion is not necessarily hyperbolic, and whether it is may depend on which measures are used and how they are determined, from the same test or independently (7,9,26–29). Although this relationship was not always hyperbolic in our study, it was still a curvilinear function, in which insulin secretion changed relatively little over a wide range of insulin sensitivity values and then increased markedly with small changes of sensitivity.

The relationship between insulin secretion and sensitivity was different across glucose tolerance categories. For both oral and intravenous measures of insulin sensitivity and secretion, the curves for IGR participants were below and to the left of the curves for NGR participants. This shows that individuals with NGR are more insulin sensitive and have better β-cell function than those with IGR. This is consistent with the observation that insulin secretion and sensitivity both decrease in the transition from NGR to IGR status in the development of type 2 diabetes (2).

The relationship between oral and intravenous measures of insulin secretion and sensitivity was also associated with BMI category. The curves for obese participants were almost always to the left of and below the curves for overweight participants, which were to the left of and below the curves for normal weight participants. This is consistent with the finding that higher levels of BMI are associated with decreased insulin sensitivity (5) and with findings from the Diabetes Prevention Program, where participants in the weight-loss intervention group had improved insulin sensitivity and β-cell function (30).

The degree of glucose homeostasis strongly determines glycemia, and our prospective analyses showed that participants with lower secretion compensation at baseline were more likely to develop diabetes than those with higher secretion compensation (i.e., risk was associated with distance from the average curve, increasing with distances below and to the left of the curve and decreasing with distances above and to the right of the curve). Our analyses also show that participants with higher secretion demand at baseline (reflecting allostatic load/physiologic stress of β-cell compensation for diminished insulin sensitivity) were at higher risk of diabetes, regardless of their secretion compensation levels (i.e., risk was associated with distance along the curve, increasing with distances to the left and upward along the curve and decreasing with distances to the right and downward along the curve). Previous analyses using intravenous measures in this same population showed that participants with low DI and high Β-cell demand index had increased risk of diabetes (10); these measures reflect low homeostatic response and high allostatic load, respectively, under the assumption that the relationship between insulin sensitivity and secretion is hyperbolic. The present results build on the previous findings in that they indicate that participants with similar homeostatic responses at baseline have different risks depending on their allostatic loads, even if the relationship is not hyperbolic, and for oral as well as intravenous measures.

The prospective analyses also show that joint analysis of insulin sensitivity and secretion provides better prediction of diabetes than analysis of DI alone; participants with the same DI have different risks of diabetes depending on their insulin secretion and sensitivity levels. One might expect this finding in situations where the relationship between insulin sensitivity and insulin secretion is not hyperbolic, and using the DI as a summary of their relationship may not appropriately capture the information about glucose tolerance (7). However, we observed such findings not only in the IV/CLAMP data set, where the estimated relationship between AIR and *M* was far from hyperbolic, but also in participants with NGR in the OGTT data set, where the relationship between CIR_{120} and ISI_{0} was essentially hyperbolic. These results suggest that the individual components of the DI, insulin sensitivity and insulin secretion, provide information about risk of diabetes that is not captured by the DI itself.

Previous studies have shown that the DI is better or has similar predictive performance than measures of insulin secretion or insulin sensitivity in logarithmic scale, alone or combined (7,11). However, the predictive models developed in these studies were only compared using the AUC, and the AUC is relatively insensitive to differences in individual risk prediction (25,31). Our analyses show that the combination of insulin sensitivity and insulin secretion measures (or, equivalently, of orthogonal distances from and along the curve) provides better prediction of diabetes than DI alone by comparison of AUCs; these models also substantially outperform DI alone when compared by measures such as NRI and IDI, which are more sensitive to differences in individual risk. We replicated all these results when analyzing OGTT-based surrogate indices of insulin secretion and sensitivity in the IV/CLAMP data set (CIR_{30} and ISI_{0}), finding that the relationship between these two indices is closer to hyperbolic than that between AIR and *M* and that together they predict diabetes better than the DI (i.e., their product) (results not shown).

Including insulin secretion and insulin sensitivity measures in logarithmic scale when predicting diabetes provides the same information as measuring secretion compensation and secretion demand by SMA regression; however, the interpretation of the parameter estimates is different. Therefore, if the interest is in predicting future diabetes development or assessing the relative roles of insulin sensitivity and secretion, we recommend including measures of insulin secretion and insulin sensitivity in logarithmic scale rather than the DI. If the interest is in assessing the roles of secretion compensation in response to changes in sensitivity (homeostatic response) and secretion demand resulting from decreased sensitivity (allostatic load), the distances from a regression procedure that accounts for variability in both insulin secretion and sensitivity are required. Most importantly, our results apply both when the relationship between insulin secretion and sensitivity is hyperbolic and when it is not. This suggests that to accurately evaluate insulin secretion in relation to insulin sensitivity in studies assessing risk of diabetes, one should include both measures instead of summarizing such a relationship with the DI (i.e., their product).

A limitation of our study is that, because participants belonged to an American Indian community with high risk of type 2 diabetes, our findings might not be generalizable to the general population or other ethnic groups. Also, our OGTT measures, CIR_{120} and ISI_{0}, do not describe the entire dynamics of the OGTT, because the stimulus for secretion is continually changing. When studying secretion after oral glucose, it may be important to account for changes in glycemia and to analyze the different modes of response of β-cells (29). Although AIR is the gold-standard measure of glucose-stimulated acute insulin secretion, it is still a surrogate index, because it only measures the first phase of insulin secretion, a biphasic process, and does not account for all the cellular mechanisms that mediate insulin release during a meal (29).

In conclusion, while the relationship between insulin sensitivity and insulin secretion is nonlinear, whether it is hyperbolic or not may depend on which measures are analyzed. Regardless of the exact form of the relationship, joint analysis of insulin sensitivity and insulin secretion measures provides information about risk of developing diabetes that is not fully captured in the DI. On a physiologic basis, this may reflect long-term risk associated with increased allostatic load resulting from the stimulation of insulin hypersecretion by increased glycemia.

This article contains supplementary material online at https://doi.org/10.2337/figshare.16811152.

## Article Information

**Acknowledgments.** The authors are grateful to the volunteers from the Southwestern American Indian community for their participation in the study.

**Funding.** This study was supported by the Intramural Research Program, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health.

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

**Author Contributions.** E.V.A. managed the data, conducted statistical analysis, and wrote the first draft of the manuscript. R.L.H. and W.C.K. designed the study. C.B., R.L.H. and W.C.K. accessed and verified the data in the study. All authors contributed to the interpretation of the data, reviewed and edited the manuscript and approved the final version, and had final responsibility for the decision to submit for publication. E.V.A. 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.

**Prior Presentation.** These results were presented in part at the 81st Annual Scientific Meeting of the American Diabetes Association, 25–29 June 2021.