Blanche's AUC Competing Risks Measure

Calculates the cause-specific time-dependent ROC-AUC at a specific time point, as described in Blanche et al. (2013).

By default, this measure returns a cause-independent AUC(t) score, calculated as a weighted average of the cause-specific AUCs. The weights correspond to the relative event frequencies of each cause, following Equation (7) in Heyard et al. (2020).

Details

Calls riskRegression::Score() with:

• metric = "auc"

• cens.method = "ipcw"

• cens.model = "km"

Notes on the riskRegression implementation:

1. IPCW weights are estimated using the test data only.

2. No extrapolation is supported: if time_horizon exceeds the maximum observed time on the test data, an error is thrown.

3. The choice of time_horizon is critical: if, at that time, no events of a given cause have occurred and all predicted CIFs are zero, riskRegression will return NaN for that cause-specific AUC (and subsequently for the summary AUC).

Dictionary

This Measure can be instantiated via the dictionary mlr_measures or with the associated sugar function msr():

MeasureCompRisksAUC$new()
mlr_measures$get("cmprsk.auc")
msr("cmprsk.auc")

Parameters

Id	Type	Default	Range
cause	integer	-	\([1, \infty)\)
time_horizon	numeric	NULL	\([0, \infty)\)

Meta Information

• Type: "cmprsk"

• Range: \([0, 1]\)

• Minimize: FALSE

• Required prediction: cif

Parameter details

• cause (numeric(1)|"mean")
  Integer number indicating which cause to use. Default value is "mean" which returns a weighted mean of the cause-specific AUCs.

• time_horizon (numeric(1))
  Single time point at which to return the score. If NULL, the median time point from the test set is used.

References

Blanche, Paul, Dartigues, Francois J, Jacqmin-Gadda, Helene (2013). “Estimating and comparing time-dependent areas under receiver operating characteristic curves for censored event times with competing risks.” Statistics in Medicine, 32(30), 5381–5397. ISSN 1097-0258, doi:10.1002/SIM.5958 , https://onlinelibrary.wiley.com/doi/10.1002/sim.5958.

Heyard, Rachel, Timsit, Jean-Francois, Held, Leonhard (2020). “Validation of discrete time-to-event prediction models in the presence of competing risks.” Biometrical Journal, 62(3), 643–657. https://doi.org/10.1002/BIMJ.201800293.

Super classes

mlr3::Measure -> mlr3proba::MeasureCompRisks -> MeasureCompRisksAUC

Methods

Public methods

• MeasureCompRisksAUC$new()

• MeasureCompRisksAUC$clone()

Inherited methods

• mlr3::Measure$aggregate()
• mlr3::Measure$format()
• mlr3::Measure$help()
• mlr3::Measure$print()
• mlr3::Measure$score()

---

Method new()

Creates a new instance of this R6 class.

Usage

MeasureCompRisksAUC$new()

---

Method clone()

The objects of this class are cloneable with this method.

Usage

MeasureCompRisksAUC$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

library(mlr3)

# Define the Learner
learner = lrn("cmprsk.aalen")
learner
#> 
#> ── <LearnerCompRisksAalenJohansen> (cmprsk.aalen): Aalen Johansen Estimator ────
#> • Model: -
#> • Parameters: list()
#> • Packages: mlr3, mlr3proba, and survival
#> • Predict Types: [cif]
#> • Feature Types: logical, integer, numeric, and factor
#> • Encapsulation: none (fallback: -)
#> • Properties: weights
#> • Other settings: use_weights = 'use'

# Define a Task
task = tsk("pbc")

# Stratification based on event
task$set_col_roles(cols = "status", add_to = "stratum")

# Create train and test set
part = partition(task)

# Train the learner on the training set
learner$train(task, row_ids = part$train)
learner$model
#> Call: survfit(formula = task$formula(1), data = task$data(cols = task$target_names))
#> 
#>        n nevent    rmean se(rmean)*
#> (s0) 184      0 90.68602   4.209205
#> 1    184     12  7.97298   2.218065
#> 2    184     74 49.34100   4.196810
#>    *restricted mean time in state (max time = 148 )

# Make predictions for the test set
predictions = learner$predict(task, row_ids = part$test)
predictions
#> 
#> ── <PredictionCompRisks> for 92 observations: ──────────────────────────────────
#>  row_ids time event       CIF
#>        1   13     2 <list[2]>
#>        3   33     2 <list[2]>
#>        8   78     2 <list[2]>
#>      ---  ---   ---       ---
#>      213   47     1 <list[2]>
#>      230   50     1 <list[2]>
#>      256   29     1 <list[2]>

# Score the predictions

# AUC(t = 100), weighted mean score across causes (default)
predictions$score(msr("cmprsk.auc", cause = "mean", time_horizon = 100))
#> cmprsk.auc 
#>        0.5 

# AUC(t = 100), 1st cause
predictions$score(msr("cmprsk.auc", cause = 1, time_horizon = 100))
#> cmprsk.auc 
#>        0.5 

# AUC(t = 100), 2nd cause
predictions$score(msr("cmprsk.auc", cause = 2, time_horizon = 100))
#> cmprsk.auc 
#>        0.5