Insulin release indices: formulas and interpretation

insulin_release() computes eight surrogate indices of beta-cell insulin secretion from fasting and 75 g oral glucose tolerance test (OGTT) data. This article gives the exact formula, units and interpretation of each, and the references they come from.

Units and conversions

The source formulae mix conventional and SI units, so insulin_release() converts internally before applying each equation:

Quantity	Input unit	Converted to	Factor
Glucose (`G0`, `G30`, `G120`)	mmol/L	mg/dL	`x 18`
Insulin (`I0`, `I30`, `I120`)	pmol/L	microU/mL	`x 0.1667` (that is, `/ 6`)

sex enters the BIGTT equations as a male indicator (male = 1, otherwise female), and bmi is in kg/m^2. The subscripts 0, 30 and 120 denote minutes after the glucose load.

Fasting index

Index	Formula (converted units)	Reference
`Homa_beta`	`(20 x I0_uU) / (G0 - 3.5)`	Matthews 1985

HOMA-beta estimates steady-state basal beta-cell function. Higher values mean greater fasting insulin output; markedly high values often reflect compensatory hypersecretion in the face of insulin resistance, while low values suggest beta-cell insufficiency. It is undefined as G0 approaches 3.5 mmol/L.

OGTT indices

Index	Formula (converted units)	Reference
`Cir`	`(100 x I30_uU) / (G30_mg x (G30_mg - 70))`	Sluiter 1976
`Stumvoll`	`1283 + 1.829 x I30 - 138.7 x G30 + 3.772 x I0` (pmol/L, mmol/L)	Stumvoll 2000
`Xinsdg30`	`((I30 - I0)_uU) / ((G30 - G0)_mg)`	insulinogenic index
`Xinsg30`	`((I30 - I0)_uU) / G30` (mmol/L)	insulinogenic index
`Di`	`Xinsg30 x 1000 / (sqrt(G0_mg x I0_uU) x meanG_mg x meanI_uU)`	Madsen 2024 (see note)
`Bigtt_air`	`exp(8.20 + 0.00178 I0 + 0.00168 I30 - 0.000383 I120 - 0.314 G0 - 0.109 G30 + 0.0781 G120 + 0.180 sex + 0.032 bmi)`	Hansen 2007
`Dibig`	`Bigtt_air x exp(4.90 - 0.00402 I0 - 0.000556 I30 - 0.00127 I120 - 0.152 G0 - 0.00871 G30 - 0.0373 G120 - 0.145 sex - 0.0376 bmi)`	Madsen 2024

where meanG and meanI are the row means of glucose and insulin across 0, 30 and 120 min.

Interpretation.

Cir (corrected insulin response) and the insulinogenic indices (Xinsdg30, Xinsg30) capture the early-phase insulin response to glucose; higher is greater early secretion.
Stumvoll and Bigtt_air estimate first-phase / acute insulin release; higher means a larger burst.
Di and Dibig are disposition indices: insulin secretion scaled by insulin sensitivity. Because a healthy beta cell secretes more when the body is more resistant, the disposition index is the key measure of whether secretion is adequate for the prevailing sensitivity. Lower values indicate beta-cell failure to compensate and are a strong predictor of progression to type 2 diabetes.

Note on the `Di` formula

The Di equation is transcribed exactly as reported in the Madsen (2024) index table: the square root covers only G0_mg x I0_uU, with the mean terms outside the root and a numerator of 1000. This is not identical to the canonical Matsuda-based disposition index (a single square root over all four terms, numerator 10000). We keep the as-reported form so results reproduce the source exactly; if you need the Matsuda-standard disposition index, compute it separately.

Worked example

data(example_data)
res <- insulin_release(example_data, category = c("fasting", "ogtt"))
round(head(res[, c("Homa_beta", "Cir", "Stumvoll", "Xinsg30",
                   "Di", "Bigtt_air", "Dibig")], 5), 3)
#>   Homa_beta   Cir Stumvoll Xinsg30    Di Bigtt_air    Dibig
#> 1    85.085 0.386  850.569   4.512 0.043  1161.789 13100.08
#> 2    84.846 0.205  542.216   2.253 0.045  1650.537 16881.84
#> 3   267.638 0.849 1462.166   9.032 0.049  3477.854 24216.88
#> 4   133.546 0.679 1196.181   6.875 0.058  2609.218 24179.56
#> 5    64.021 0.259  587.807   3.048 0.071  1734.967 17734.61

References