Synthetic binary outcome data with a smooth calibration misfit

A small, fully synthetic dataset for demonstrating the goodness-of-fit and calibration battery. It was generated reproducibly (see data-raw/make_gof_demo.R) from a logistic data-generating process whose true linear predictor includes a quadratic term in (standardized) age. A model that regresses outcome on age linearly (together with bmi, sex and treatment) is therefore mildly misspecified, through a smooth, low-dimensional calibration distortion. This is the regime in which the directed Ebrahim–Farrington / EDGE test (edge.gof, def.gof) is designed to have more power than classical omnibus tests such as Hosmer–Lemeshow.

Usage

gof_demo

Format

A data frame with 800 rows and 5 variables:

outcome

binary response, 0/1 (event rate about 0.27).

age

continuous covariate, years (range about 20–70). The true model depends on age quadratically.

bmi

continuous covariate, body mass index in kg/m^2.

sex

binary covariate, 0 = female, 1 = male.

treatment

binary covariate, 0 = control, 1 = treated.

Source

Simulated; see data-raw/make_gof_demo.R in the package sources.

Details

The true data-generating linear predictor is $$\eta = -0.6 + 0.8 z_a - 0.7 z_a^2 + 0.5 z_b + 0.4\,\mathrm{sex} - 0.3\,\mathrm{treatment},$$ where \(z_a = (\mathrm{age} - 45)/14\) and \(z_b = (\mathrm{bmi} - 27)/4\), and \(\Pr(\mathrm{outcome} = 1) = \mathrm{plogis}(\eta)\).

Examples

data("gof_demo", package = "ebrahim.gof")
fit <- glm(outcome ~ age + bmi + sex + treatment,
           data = gof_demo, family = binomial)
edge.gof(fit)
#>   Test Basis Test_Statistic       df        Method    p_value
#> 1 EDGE poly3       8.329512 2.072814 satterthwaite 0.01496412