Integrated Brier score for right censored data

Compute the integrated Brier score for right censored data, which is an overall calculation of model performance for all values of .eval_time.

Usage

brier_survival_integrated(data, ...)

# S3 method for class 'data.frame'
brier_survival_integrated(data, truth, ..., na_rm = TRUE, case_weights = NULL)

brier_survival_integrated_vec(
  truth,
  estimate,
  na_rm = TRUE,
  case_weights = NULL,
  ...
)

Arguments

data: A data.frame containing the columns specified by truth and ....
...: The column identifier for the survival probabilities this should be a list column of data.frames corresponding to the output given when predicting with censored model. This should be an unquoted column name although this argument is passed by expression and supports quasiquotation (you can unquote column names). For _vec() functions, the dots are not used.
truth: The column identifier for the true survival result (that is created using survival::Surv().). This should be an unquoted column name although this argument is passed by expression and supports quasiquotation (you can unquote column names). For _vec() functions, an survival::Surv() object.
na_rm: A logical value indicating whether NA values should be stripped before the computation proceeds.
case_weights: The optional column identifier for case weights. This should be an unquoted column name that evaluates to a numeric column in data. For _vec() functions, a numeric vector, hardhat::importance_weights(), or hardhat::frequency_weights().
estimate: A list column of data.frames corresponding to the output given when predicting with censored model. See the details for more information regarding format.

Value

A tibble with columns .metric, .estimator, and .estimate.

For an ungrouped data frame, the result has one row of values. For a grouped data frame, the number of rows returned is the same as the number of groups.

For brier_survival_integrated_vec(), a numeric vector same length as the input argument eval_time. (or NA).

Details

The integrated time-dependent brier score is calculated in an "area under the curve" fashion. The brier score is calculated for each value of .eval_time. The area is calculated via the trapezoidal rule. The area is divided by the largest value of .eval_time to bring it into the same scale as the traditional brier score.

Smaller values of the score are associated with better model performance.

This formulation takes survival probability predictions at one or more specific evaluation times and, for each time, computes the Brier score. To account for censoring, inverse probability of censoring weights (IPCW) are used in the calculations.

The column passed to ... should be a list column with one element per independent experiential unit (e.g. patient). The list column should contain data frames with several columns:

.eval_time: The time that the prediction is made.
.pred_survival: The predicted probability of survival up to .eval_time
.weight_censored: The case weight for the inverse probability of censoring.

The last column can be produced using parsnip::.censoring_weights_graf(). This corresponds to the weighting scheme of Graf et al (1999). The internal data set lung_surv shows an example of the format.

This method automatically groups by the .eval_time argument.

References

E. Graf, C. Schmoor, W. Sauerbrei, and M. Schumacher, “Assessment and comparison of prognostic classification schemes for survival data,” Statistics in Medicine, vol. 18, no. 17-18, pp. 2529–2545, 1999.

Author

Emil Hvitfeldt

Examples

library(dplyr)

lung_surv %>%
  brier_survival_integrated(
    truth = surv_obj,
    .pred
  )
#> # A tibble: 1 × 3
#>   .metric                   .estimator .estimate
#>   <chr>                     <chr>          <dbl>
#> 1 brier_survival_integrated standard       0.158