Calculate integrated C/D AUC loss

This function subtracts integrated the C/D AUC metric from one to obtain a loss function whose lower values indicate better model performance (useful for permutational feature importance)

loss_one_minus_integrated_cd_auc(
  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

#' @section References:

• [1] Uno, Hajime, et al. "Evaluating prediction rules for t-year survivors with censored regression models." Journal of the American Statistical Association 102.478 (2007): 527-537.

• [2] Hung, Hung, and Chin‐Tsang Chiang. "Optimal composite markers for time‐dependent receiver operating characteristic curves with censored survival data." Scandinavian Journal of Statistics 37.4 (2010): 664-679.

See also

integrated_cd_auc() cd_auc() loss_one_minus_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
loss_one_minus_integrated_cd_auc(y, surv = surv, times = times)
#> [1] 0.1894802