Calculate integrated Brier score

This function calculates the integrated Brier score metric for a survival model.

integrated_brier_score(y_true = NULL, risk = NULL, surv = NULL, times = NULL)

loss_integrated_brier_score(
  y_true = NULL,
  risk = NULL,
  surv = NULL,
  times = NULL
)

Arguments

y_true

a survival::Surv object containing the times and statuses of observations for which the metric will be evaluated

risk

ignored, left for compatibility with other metrics

surv

a matrix containing the predicted survival functions for the considered observations, each row represents a single observation, whereas each column one time point

times

a vector of time points at which the survival function was evaluated

Value

numeric from 0 to 1, lower values indicate better performance

Details

It is useful to see how a model performs as a whole, not at specific time points, for example for easier comparison. This function allows for calculating the integral of Brier score metric numerically using the trapezoid method.

References

• [1] Brier, Glenn W. "Verification of forecasts expressed in terms of probability." Monthly Weather Review 78.1 (1950): 1-3.

• [2] Graf, Erika, et al. "Assessment and comparison of prognostic classification schemes for survival data." Statistics in Medicine 18.17‐18 (1999): 2529-2545.

See also

brier_score() integrated_cd_auc() loss_one_minus_integrated_cd_auc()

Examples

library(survival)
library(survex)

cph <- coxph(Surv(time, status) ~ ., data = veteran, model = TRUE, x = TRUE, y = TRUE)
cph_exp <- explain(cph)
#> Preparation of a new explainer is initiated 
#>   -> model label       :  coxph (  default  ) 
#>   -> data              :  137  rows  6  cols (  extracted from the model  ) 
#>   -> target variable   :  137  values ( 128 events and 9 censored , censoring rate = 0.066 ) (  extracted from the model  ) 
#>   -> times             :  50 unique time points , min = 1.5 , median survival time = 80 , max = 999 
#>   -> times             :  (  generated from y as uniformly distributed survival quantiles based on Kaplan-Meier estimator  ) 
#>   -> predict function  :  predict.coxph with type = 'risk' will be used (  default  ) 
#>   -> predict survival function  :  predictSurvProb.coxph will be used (  default  ) 
#>   -> predict cumulative hazard function  :  -log(predict_survival_function) will be used (  default  ) 
#>   -> model_info        :  package survival , ver. 3.5.8 , task survival (  default  ) 
#>   A new explainer has been created!  

y <- cph_exp$y
times <- cph_exp$times
surv <- cph_exp$predict_survival_function(cph, cph_exp$data, times)

# calculating directly
integrated_brier_score(y, surv = surv, times = times)
#> [1] 0.0574109