Inverse Probability of Censoring Weights (Graf et al.)

Computes the weights time-dependent survival metrics need so that subjects lost to follow-up don't bias the score: at evaluation time \(t\), a subject still under observation (\(T > t\)) gets \(1/G(t)\); a subject with an event by \(t\) gets \(1/G(T^-)\); a subject censored by \(t\) gets 0, as their status at \(t\) is unknown.

Usage

graf_weights(truth, eval_time, censoring, trunc = 0.05)

Arguments

truth: A right-censored [survival::Surv()] object, one element per subject (see [surv_subject_truth()]).
eval_time: Numeric vector of evaluation times.
censoring: A [censoring_km()] object, estimated on the training data.
trunc: Lower bound for \(G\), capping weights at `1 / trunc` (default 0.05, as in tidymodels' `parsnip`).

Value

A numeric matrix with one row per element of `truth` and one column per `eval_time`.

Details

The weights assume follow-up starts at time 0 for every subject: they do not correct for delayed entry (left truncation).

References

Graf E, Schmoor C, Sauerbrei W, Schumacher M (1999). Assessment and comparison of prognostic classification schemes for survival data. *Statistics in Medicine*, 18(17-18), 2529-2545.

Examples

if (requireNamespace("survival", quietly = TRUE)) {
  train <- survival::Surv(c(2, 4, 6, 8), c(0, 1, 0, 1))
  test <- survival::Surv(c(5, 7), c(1, 0))
  graf_weights(test, eval_time = c(3, 6), censoring = censoring_km(train))
}
#>             3        6
#> [1,] 1.333333 1.333333
#> [2,] 1.333333 2.666667