Plot prediction stability across bootstrap replicates

A prediction (in)stability plot shows estimated risk probabilities from models developed on resampled data evaluated on the original development data as a function of the 'apparent' prediction (prediction from original/development model evaluated on original data). A stable model should produce points that exhibit minimal dispersion. See Riley and Collins (2023).

Usage

prediction_stability(
  x,
  bounds = 0.95,
  smooth_bounds = FALSE,
  xlab,
  ylab,
  pch,
  cex,
  col,
  lty,
  span
)

Arguments

x

an object produced by validate with method = "boot_\*" (or boot_optimism with method="boot")

bounds

width of the 'stability interval' (percentiles of the bootstrap model predictions). NULL = do not add bounds to plot.

smooth_bounds

if TRUE, use loess to smooth the bounds (default = FALSE)

xlab

a title for the x axis

ylab

a title for the y axis

pch

plotting character (default = 16)

cex

controls point size (default = 0.4)

col

color of points (default = grDevices::grey(.5, .5))

lty

line type for bounds (default = 2)

span

controls the degree of smoothing (see loess; default = 0.75)

Value

plots prediction (in)stability. The stability bounds are not smoothed. Invisibly returns stability matrix (where column 1 are original predictions) that can be used for creating plots with other packages/software.

References

Riley RD, Collins GS. (2023). Stability of clinical prediction models developed using statistical or machine learning methods. Biom J. doi:10.1002/bimj.202200302. Epub ahead of print.

Examples

set.seed(456)
# simulate data with two predictors that interact
dat <- pmcalibration::sim_dat(N = 2000, a1 = -2, a3 = -.3)
mean(dat$y)
#> [1] 0.1985
dat$LP <- NULL # remove linear predictor

# fit a (misspecified) logistic regression model
m1 <- glm(y ~ ., data=dat, family="binomial")

# internal validation of m1 via bootstrap optimism with 10 resamples
# B = 10 for example but should be >= 200 in practice
m1_iv <- validate(m1, method="boot_optimism", B=10)
#> It is recommended that B >= 200 for bootstrap validation

prediction_stability(m1_iv)