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.

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) (57). 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.

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/m2), overweight (25 ≤ BMI < 30 kg/m2), and obese (BMI ≥30 kg/m2).

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 (G0 and I0, respectively) and 120 min after undergoing a 75-g OGTT (G120 and I120, respectively); the measures of insulin secretion and sensitivity used were 120-min corrected insulin response (CIR120 = [I120/(G120 ∗ [G120 − 70 mg/dL])]) and insulin sensitivity index (ISI0 = [104/(I0 ∗ G0)]), respectively, and their DI was calculated as DIO = ISI0 ∗ CIR120. Several surrogate indices of insulin secretion and sensitivity can be calculated from OGTTs. However, we used CIR120 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 ISI0 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 DIIV = M ∗ AIR.

Statistical Analysis

The relationship between baseline insulin secretion and sensitivity was studied by estimating ln (CIR120 or AIR) as a function of ln (ISI0 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).

Figure 1

Illustration of distances away from the SMA line and distances along the SMA line. Pink dot represents centroid of the data (mean of ln[insulin sensitivity], mean of ln[insulin secretion]), where the SMA line and its orthogonal line intercept. A: Distances away from the SMA lines ln(secretion) = a + b ∗ ln(sensitivity) to a point (x0, y0) were calculated using the formula d = (y0 − [a + bx0])/√(1 + b2); by not taking the absolute value of the numerator in this formula, we allowed distances to be negative or positive, taking on the same direction as the residuals. Distances from the points to the line orthogonal to the SMA line were calculated using the same procedure. Points that are below and to the left of the SMA line have negative distances away from the SMA line, and points above and to the right of the SMA line have positive distances away from line. Points that are below and to the right of the orthogonal line have negative distances along the SMA line, and points above and to the left of the orthogonal line have positive distances along the SMA line. Distances away from the SMA line increase as points go from below and to the left of the SMA line to above and to the right of the SMA line (they increase as they go from negative to positive), and insulin secretion compensation increases as distances away from the SMA line increase. Distances along the SMA line increase as points go from below and to the right of the orthogonal line to above and to the left of the orthogonal line, and insulin secretion demand increases as distances along the SMA line increase. B: Participants who are below and to the left of the SMA line have lower insulin secretion compensation than participants above the SMA line. Participants who are below and to the right of the orthogonal line have lower insulin secretion demand than participants who are above and to the right of the orthogonal line. The participant represented by the red dot with a positive distance away from the SMA line and a negative distance along the SMA line has lower risk of diabetes than the participant represented by the green dot with a negative distance from the SMA line and a positive distance along the SMA line (i.e., participant represented by the red dot has higher secretion compensation and lower secretion demand than participant represented by the green dot).

Figure 1

Illustration of distances away from the SMA line and distances along the SMA line. Pink dot represents centroid of the data (mean of ln[insulin sensitivity], mean of ln[insulin secretion]), where the SMA line and its orthogonal line intercept. A: Distances away from the SMA lines ln(secretion) = a + b ∗ ln(sensitivity) to a point (x0, y0) were calculated using the formula d = (y0 − [a + bx0])/√(1 + b2); by not taking the absolute value of the numerator in this formula, we allowed distances to be negative or positive, taking on the same direction as the residuals. Distances from the points to the line orthogonal to the SMA line were calculated using the same procedure. Points that are below and to the left of the SMA line have negative distances away from the SMA line, and points above and to the right of the SMA line have positive distances away from line. Points that are below and to the right of the orthogonal line have negative distances along the SMA line, and points above and to the left of the orthogonal line have positive distances along the SMA line. Distances away from the SMA line increase as points go from below and to the left of the SMA line to above and to the right of the SMA line (they increase as they go from negative to positive), and insulin secretion compensation increases as distances away from the SMA line increase. Distances along the SMA line increase as points go from below and to the right of the orthogonal line to above and to the left of the orthogonal line, and insulin secretion demand increases as distances along the SMA line increase. B: Participants who are below and to the left of the SMA line have lower insulin secretion compensation than participants above the SMA line. Participants who are below and to the right of the orthogonal line have lower insulin secretion demand than participants who are above and to the right of the orthogonal line. The participant represented by the red dot with a positive distance away from the SMA line and a negative distance along the SMA line has lower risk of diabetes than the participant represented by the green dot with a negative distance from the SMA line and a positive distance along the SMA line (i.e., participant represented by the red dot has higher secretion compensation and lower secretion demand than participant represented by the green dot).

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.

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.

Table 1

Descriptive statistics at baseline

DemographicOGTT data set (n = 1,566)IV/CLAMP data set (n = 420)
NGRIGR*NGRIGR*
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/m2 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) — — 
CIR120, (μU · dL)/(mg · mL) 0.026 (0.018–0.037) 0.015 (0.009–0.023) — — 
CIR30, (μU · dL)/(mg · mL) — — 0.023 (0.016–0.036) 0.019 (0.012–0.029) 
ISI0, (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) 
DIO, CIR120 ∗ ISI0 0.005 (0.003–0.008) 0.002 (0.001–0.003) — — 
DI30, CIR30 ∗ ISI0 — — 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) 
DIIV, AIR ∗ M value — — 848.7 (575.1–1194.5) 622.2 (349.8–902.9) 
DemographicOGTT data set (n = 1,566)IV/CLAMP data set (n = 420)
NGRIGR*NGRIGR*
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/m2 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) — — 
CIR120, (μU · dL)/(mg · mL) 0.026 (0.018–0.037) 0.015 (0.009–0.023) — — 
CIR30, (μU · dL)/(mg · mL) — — 0.023 (0.016–0.036) 0.019 (0.012–0.029) 
ISI0, (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) 
DIO, CIR120 ∗ ISI0 0.005 (0.003–0.008) 0.002 (0.001–0.003) — — 
DI30, CIR30 ∗ ISI0 — — 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) 
DIIV, 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(CIR120) as a function of ln(ISI0) 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 CIR120 and ISI0 was almost hyperbolic in NGR participants and was hyperbolic in IGR participants and that when combining both samples, the relationship was essentially hyperbolic.

Figure 2

Differences in the relationship between insulin secretion and sensitivity by glucose tolerance and weight category. Left panels represent comparisons in logarithmic scale by glucose tolerance and weight group; right panels represent comparisons in original scale. A: Glucose tolerance group graphs for the OGTT data set. B: Glucose tolerance group graphs for the IV/CLAMP data set. C: Weight group graphs for the OGTT data set. D: Weight group graphs for the IV/CLAMP data set. EMBS, estimated metabolic body size.

Figure 2

Differences in the relationship between insulin secretion and sensitivity by glucose tolerance and weight category. Left panels represent comparisons in logarithmic scale by glucose tolerance and weight group; right panels represent comparisons in original scale. A: Glucose tolerance group graphs for the OGTT data set. B: Glucose tolerance group graphs for the IV/CLAMP data set. C: Weight group graphs for the OGTT data set. D: Weight group graphs for the IV/CLAMP data set. EMBS, estimated metabolic body size.

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(CIR120) as a function of ln(ISI0) 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(CIR120) as a function of ln(ISI0) 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.

Figure 3

Groups formed in the OGTT data set and the IV/CLAMP data set with hazard ratios (HRs) for risk of type 2 diabetes. A: Groups in the OGTT data set are formed based on low, medium, and high secretion compensation for changes in sensitivity (tertiles 1, 2, and 3 of distances away from the line, respectively) and secretion demand imposed by decreased insulin sensitivity (tertiles 1, 2, and 3 of distances along the line, respectively) (i.e., those in the low compensation, medium demand group have low secretion compensation for changes in sensitivity and medium secretion demand for decreased sensitivity; the reference group in the OGTT data set is the medium compensation, medium demand group). B: Groups in the IV/CLAMP data set are formed based on low and high secretion compensation for changes in sensitivity (distances away from the line below and above the median) and secretion demand imposed by decreased sensitivity (distances along the line below and above the median) (i.e., those in the low compensation, high demand group have low secretion compensation for changes in sensitivity and high secretion demand imposed by decreased sensitivity; in this data set, the reference group is the high compensation, low demand group). In both data sets, Cox proportional hazards models were adjusted for age, sex, and fraction of American Indian heritage. EMBS, estimated metabolic body size.

Figure 3

Groups formed in the OGTT data set and the IV/CLAMP data set with hazard ratios (HRs) for risk of type 2 diabetes. A: Groups in the OGTT data set are formed based on low, medium, and high secretion compensation for changes in sensitivity (tertiles 1, 2, and 3 of distances away from the line, respectively) and secretion demand imposed by decreased insulin sensitivity (tertiles 1, 2, and 3 of distances along the line, respectively) (i.e., those in the low compensation, medium demand group have low secretion compensation for changes in sensitivity and medium secretion demand for decreased sensitivity; the reference group in the OGTT data set is the medium compensation, medium demand group). B: Groups in the IV/CLAMP data set are formed based on low and high secretion compensation for changes in sensitivity (distances away from the line below and above the median) and secretion demand imposed by decreased sensitivity (distances along the line below and above the median) (i.e., those in the low compensation, high demand group have low secretion compensation for changes in sensitivity and high secretion demand imposed by decreased sensitivity; in this data set, the reference group is the high compensation, low demand group). In both data sets, Cox proportional hazards models were adjusted for age, sex, and fraction of American Indian heritage. EMBS, estimated metabolic body size.

Table 2

Proportional hazards analysis: distance away from the line (secretion compensation) and distance along the line (secretion demand) as predictors of type 2 diabetes

OGTT data setIV/CLAMP data set
Hazard ratio (95% CI)PHazard 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 setIV/CLAMP data set
Hazard ratio (95% CI)PHazard 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 CIR120 and ISI0 in logarithmic scale. We then estimated incidence of diabetes for a grid of values of CIR120 and ISI0 based on this model (Fig. 4A). Among participants with the same DIO (CIR120 ∗ ISI0), those with higher ISI0 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 DIIV (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.

Figure 4

Risk of type 2 diabetes and the DI. A: Incidence of diabetes calculated based on Poisson model fit to the OGTT data set for women age 29.74 years, with fraction of American Indian heritage of 8/8 and length of follow-up of 11.02 years, with different levels of CIR120 and ISI0. The incidence ranges of cases per 100 person-years (PY) for each of the risk bands in the OGTT data set were as follows: lowest risk 7.71–12.37, very low risk 12.39–14.11, low risk 14.11–16.32, moderate risk 16.33–19.47, high risk 19.47–24.05, very high risk 24.07–32.10, and highest risk 32.20–49.82 cases/100 PY. B: Incidence of diabetes calculated based on Poisson model fit to the IV/CLAMP data set for women age 26.62 years, with fraction of American Indian heritage of 8/8 and length of follow-up of 8.33 years, with different levels of AIR and M values. The incidence ranges of cases per 100 PY for each of the risk bands in the IV/CLAMP data set were as follows: lowest risk 0.79–2.11, very low risk 2.11–3.37, low risk 3.37–4.97, moderate risk 4.97–7.44, high risk 7.44–11.98, very high risk 11.98–20.98, and highest risk 20.98–49.98 cases/100 PY.

Figure 4

Risk of type 2 diabetes and the DI. A: Incidence of diabetes calculated based on Poisson model fit to the OGTT data set for women age 29.74 years, with fraction of American Indian heritage of 8/8 and length of follow-up of 11.02 years, with different levels of CIR120 and ISI0. The incidence ranges of cases per 100 person-years (PY) for each of the risk bands in the OGTT data set were as follows: lowest risk 7.71–12.37, very low risk 12.39–14.11, low risk 14.11–16.32, moderate risk 16.33–19.47, high risk 19.47–24.05, very high risk 24.07–32.10, and highest risk 32.20–49.82 cases/100 PY. B: Incidence of diabetes calculated based on Poisson model fit to the IV/CLAMP data set for women age 26.62 years, with fraction of American Indian heritage of 8/8 and length of follow-up of 8.33 years, with different levels of AIR and M values. The incidence ranges of cases per 100 PY for each of the risk bands in the IV/CLAMP data set were as follows: lowest risk 0.79–2.11, very low risk 2.11–3.37, low risk 3.37–4.97, moderate risk 4.97–7.44, high risk 7.44–11.98, very high risk 11.98–20.98, and highest risk 20.98–49.98 cases/100 PY.

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[CIR120] and ln[ISI0] in OGTT data set and ln[AIR] and ln[M] in IV/CLAMP data set), DI in logarithmic scale (ln[DIO = CIR120 ∗ ISI0] in OGTT data set and ln[DIIV = 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.

Table 3

Comparison of different models predicting type 2 diabetes in the OGTT data set for all participants, NGR participants only, and IGR participants only

ModelHazard ratio per 1 SD (P)Predictive performance statistics
ln(DI)ln(CIR120)ln(ISI0)Distance awayDistance alongAUCΔAUCIDIRelative IDINRI
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(CIR120— 0.882 (P = 0.0011) — — — 0.596 0.017 0.004 0.216 0.132 
 ln(ISI0— — 0.607 (P < 0.0001) — — 0.673 0.094 0.081 4.093 0.55 
 ln(CIR120) and ln(ISI0— 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(CIR120— 1.062 (P = 0.18) — — — 0.544 −0.003 0.001 0.259 0.001 
 ln(ISI0— — 0.652 (P < 0.0001) — — 0.642 0.095 0.055 10.659 0.457 
 ln(CIR120) and ln(ISI0— 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(CIR120— 0.953 (P = 0.47) — — — 0.583 0.048 0.037 8.285 0.292 
 ln(ISI0— — 0.748 (P < 0.0001) — — 0.564 0.029 0.001 0.167 0.267 
 ln(CIR120) and ln(ISI0— 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 
ModelHazard ratio per 1 SD (P)Predictive performance statistics
ln(DI)ln(CIR120)ln(ISI0)Distance awayDistance alongAUCΔAUCIDIRelative IDINRI
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(CIR120— 0.882 (P = 0.0011) — — — 0.596 0.017 0.004 0.216 0.132 
 ln(ISI0— — 0.607 (P < 0.0001) — — 0.673 0.094 0.081 4.093 0.55 
 ln(CIR120) and ln(ISI0— 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(CIR120— 1.062 (P = 0.18) — — — 0.544 −0.003 0.001 0.259 0.001 
 ln(ISI0— — 0.652 (P < 0.0001) — — 0.642 0.095 0.055 10.659 0.457 
 ln(CIR120) and ln(ISI0— 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(CIR120— 0.953 (P = 0.47) — — — 0.583 0.048 0.037 8.285 0.292 
 ln(ISI0— — 0.748 (P < 0.0001) — — 0.564 0.029 0.001 0.167 0.267 
 ln(CIR120) and ln(ISI0— 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.

Table 4

Comparison of different models predicting type 2 diabetes in the IV/CLAMP data set for all participants, NGR participants only, and IGR participants only

ModelHazard ratio per 1 SD (P)Predictive performance statistics
ln(DI)ln(AIR)ln(M)Distance awayDistance alongAUCΔAUCIDIRelative IDINRI
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 
ModelHazard ratio per 1 SD (P)Predictive performance statistics
ln(DI)ln(AIR)ln(M)Distance awayDistance alongAUCΔAUCIDIRelative IDINRI
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(CIR120) and ln(ISI0) was significantly higher than that of the model with ln(DIO) 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(DIIV) 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(DIO) and with both ln(CIR120) and ln(ISI0) had strong predictive performance in all participants (0.608 vs. 0.645).

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 CIR120 and ISI0 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 CIR120 and ISI0 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. CIR120 and ISI0 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 (7,9,2629). 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 CIR120 and ISI0 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 (CIR30 and ISI0), 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, CIR120 and ISI0, 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.

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.

1
DeFronzo
RA
.
Lilly lecture 1987. The triumvirate: beta-cell, muscle, liver. A collusion responsible for NIDDM
.
Diabetes
1988
;
37
:
667
687
2
Weyer
C
,
Bogardus
C
,
Mott
DM
,
Pratley
RE
.
The natural history of insulin secretory dysfunction and insulin resistance in the pathogenesis of type 2 diabetes mellitus
.
J Clin Invest
1999
;
104
:
787
794
3
Cersosimo
E
,
Triplitt
C
,
Solis-Herrera
C
,
Mandarino
LJ
,
DeFronzo
RA
.
Pathogenesis of type 2 diabetes mellitus
. In
Endotext.
Feingold
KR
,
Anawalt
B
,
Boyce
A
, et al
., Eds.
South Dartmouth, MA
,
MDText.com, Inc.
,
2000
,
12
16
4
Bergman
RN
.
Lilly lecture 1989. Toward physiological understanding of glucose tolerance. Minimal-model approach
.
Diabetes
1989
;
38
:
1512
1527
5
Kahn
SE
,
Prigeon
RL
,
McCulloch
DK
, et al
.
Quantification of the relationship between insulin sensitivity and beta-cell function in human subjects. Evidence for a hyperbolic function
.
Diabetes
1993
;
42
:
1663
1672
6
Utzschneider
KM
,
Prigeon
RL
,
Carr
DB
, et al
.
Impact of differences in fasting glucose and glucose tolerance on the hyperbolic relationship between insulin sensitivity and insulin responses
.
Diabetes Care
2006
;
29
:
356
362
7
Utzschneider
KM
,
Prigeon
RL
,
Faulenbach
MV
, et al
.
Oral disposition index predicts the development of future diabetes above and beyond fasting and 2-h glucose levels
.
Diabetes Care
2009
;
32
:
335
341
8
Bergman
RN
,
Ader
M
,
Huecking
K
,
Van Citters
G
.
Accurate assessment of beta-cell function: the hyperbolic correction
.
Diabetes
2002
;
51
(
Suppl. 1
):
S212
S220
9
Pacini
G
.
The hyperbolic equilibrium between insulin sensitivity and secretion
.
Nutr Metab Cardiovasc Dis
2006
;
16
(
Suppl. 1
):
S22
S27
10
Stumvoll
M
,
Tataranni
PA
,
Stefan
N
,
Vozarova
B
,
Bogardus
C
.
Glucose allostasis
.
Diabetes
2003
;
52
:
903
909
11
Lorenzo
C
,
Wagenknecht
LE
,
Rewers
MJ
, et al
.
Disposition index, glucose effectiveness, and conversion to type 2 diabetes: the Insulin Resistance Atherosclerosis Study (IRAS)
.
Diabetes Care
2010
;
33
:
2098
2103
12
Knowler
WC
,
Bennett
PH
,
Hamman
RF
,
Miller
M
.
Diabetes incidence and prevalence in Pima Indians: a 19-fold greater incidence than in Rochester, Minnesota
.
Am J Epidemiol
1978
;
108
:
497
505
13
World Health Organization
.
Definition and diagnosis of diabetes mellitus and intermediate hyperglycaemia: report of a WHO/IDF consultation
.
14
Hanson
RL
,
Pratley
RE
,
Bogardus
C
, et al
.
Evaluation of simple indices of insulin sensitivity and insulin secretion for use in epidemiologic studies
.
Am J Epidemiol
2000
;
151
:
190
198
15
Lillioja
S
,
Mott
DM
,
Zawadzki
JK
, et al
.
In vivo insulin action is familial characteristic in nondiabetic Pima Indians
.
Diabetes
1987
;
36
:
1329
1335
16
Lillioja
S
,
Mott
DM
,
Howard
BV
, et al
.
Impaired glucose tolerance as a disorder of insulin action. Longitudinal and cross-sectional studies in Pima Indians
.
N Engl J Med
1988
;
318
:
1217
1225
17
Warton
DI
,
Wright
IJ
,
Falster
DS
,
Westoby
M
.
Bivariate line-fitting methods for allometry
.
Biol Rev Camb Philos Soc
2006
;
81
:
259
291
18
Smith
RJ
.
Use and misuse of the reduced major axis for line-fitting
.
Am J Phys Anthropol
2009
;
140
:
476
486
19
Patzer
ABC
,
Bauer
H
,
Chang
C
,
Bolte
J
,
Sulzle
D
.
Revisiting the scale-invariant, two-dimensional linear regression method
.
J Chem Educ
2018
;
95
:
978
984
20
Warton
DI
,
Duursma
RA
,
Falster
DS
,
Taskinen
S
.
smatr 3-an R package for estimation and inference about allometric lines
.
Methods Ecol Evol
2012
;
3
:
257
259
21
Pencina
MJ
,
D’Agostino
RB
.
Overall C as a measure of discrimination in survival analysis: model specific population value and confidence interval estimation
.
Stat Med
2004
;
23
:
2109
2123
22
Chambless
LE
,
Cummiskey
CP
,
Cui
G
.
Several methods to assess improvement in risk prediction models: extension to survival analysis
.
Stat Med
2011
;
30
:
22
38
23
Pencina
MJ
,
D’Agostino
RB
Sr
,
D’Agostino
RB
Jr
,
Vasan
RS
.
Evaluating the added predictive ability of a new marker: from area under the ROC curve to reclassification and beyond
.
Stat Med
2008
;
27
:
157
172
;
discussion 207–212
24
DeLong
ER
,
DeLong
DM
,
Clarke-Pearson
DL
.
Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach
.
Biometrics
1988
;
44
:
837
845
25
Pencina
MJ
,
D’Agostino
RB
,
Pencina
KM
,
Janssens
AC
,
Greenland
P
.
Interpreting incremental value of markers added to risk prediction models
.
Am J Epidemiol
2012
;
176
:
473
481
26
Kim
SH
,
Silvers
A
,
Viren
J
,
Reaven
GM
.
Relationship between insulin sensitivity and insulin secretion rate: not necessarily hyperbolic
.
Diabet Med
2016
;
33
:
961
967
27
Mari
A
,
Ahrén
B
,
Pacini
G
.
Assessment of insulin secretion in relation to insulin resistance
.
Curr Opin Clin Nutr Metab Care
2005
;
8
:
529
533
28
Aizawa
T
,
Yamada
M
,
Katakura
M
,
Funase
Y
,
Yamashita
K
,
Yamauchi
K
.
Hyperbolic correlation between insulin sensitivity and insulin secretion fades away in lean subjects with superb glucose regulation
.
Endocr J
2012
;
59
:
127
136
29
Ferrannini
E
,
Mari
A
.
Beta cell function and its relation to insulin action in humans: a critical appraisal
.
Diabetologia
2004
;
47
:
943
956
30
Kitabchi
AE
,
Temprosa
M
,
Knowler
WC
, et al.;
Diabetes Prevention Program Research Group
.
Role of insulin secretion and sensitivity in the evolution of type 2 diabetes in the diabetes prevention program: effects of lifestyle intervention and metformin
.
Diabetes
2005
;
54
:
2404
2414
31
Cook
NR
.
Use and misuse of the receiver operating characteristic curve in risk prediction
.
Circulation
2007
;
115
:
928
935
Readers may use this article as long as the work is properly cited, the use is educational and not for profit, and the work is not altered. More information is available at https://www.diabetesjournals.org/journals/pages/license.