Van Houwelingen's Calibration Alpha Survival Measure

This calibration method is defined by estimating $$\hat{\alpha} = \frac{\sum_{i=1}^n \delta_i}{\sum_{i=1}^n H_i(T_i)}$$ where \(\delta\) is the observed censoring indicator from the test data \(n\) observations), \(H_i\) is the predicted cumulative hazard, and \(T_i\) is the observed survival time (event or censoring).

The standard error is given by $$\hat{\alpha_{se}} = e^{1/\sqrt{\sum \delta_i}}$$

The model is well calibrated if the estimated \(\hat{\alpha}\) coefficient (returned score) is equal to 1.

Dictionary

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

MeasureSurvCalibrationAlpha$new()
mlr_measures$get("surv.calib_alpha")
msr("surv.calib_alpha")

Parameters

Id	Type	Default	Levels	Range
eps	numeric	0.001		\([0, 1]\)
se	logical	FALSE	TRUE, FALSE	-
method	character	ratio	ratio, diff	-
truncate	numeric	Inf		\((-\infty, \infty)\)

Meta Information

• Type: "surv"

• Range: \((-\infty, \infty)\)

• Minimize: FALSE

• Required prediction: distr

Parameter details

• eps (numeric(1))
  Very small number to substitute near-zero values in order to prevent errors in e.g. log(0) and/or division-by-zero calculations. Default value is 0.001.

• se (logical(1))
  If TRUE then return standard error of the measure, otherwise the score itself (default).

• method (character(1))
  Returns \(\hat{\alpha}\) if equal to ratio (default) and \(|1-\hat{\alpha}|\) if equal to diff. With diff, the output score can be minimized and for example be used for tuning purposes. This parameter takes effect only if se is FALSE.

• truncate (double(1))
  This parameter controls the upper bound of the output score. We use truncate = Inf by default (so no truncation) and it's up to the user to set this up reasonably given the chosen method. Note that truncation may severely limit automated tuning with this measure using method = diff.

References

Van Houwelingen, C. H (2000). “Validation, calibration, revision and combination of prognostic survival models.” Statistics in Medicine, 19(24), 3401–3415. doi:10.1002/1097-0258(20001230)19:24<3401::AID-SIM554>3.0.CO;2-2 .

See also

Other survival measures: mlr_measures_surv.calib_beta, mlr_measures_surv.calib_index, mlr_measures_surv.chambless_auc, mlr_measures_surv.cindex, mlr_measures_surv.dcalib, mlr_measures_surv.graf, mlr_measures_surv.hung_auc, mlr_measures_surv.intlogloss, mlr_measures_surv.logloss, mlr_measures_surv.mae, mlr_measures_surv.mse, mlr_measures_surv.nagelk_r2, mlr_measures_surv.oquigley_r2, mlr_measures_surv.rcll, mlr_measures_surv.rmse, mlr_measures_surv.schmid, mlr_measures_surv.song_auc, mlr_measures_surv.song_tnr, mlr_measures_surv.song_tpr, mlr_measures_surv.uno_auc, mlr_measures_surv.uno_tnr, mlr_measures_surv.uno_tpr, mlr_measures_surv.xu_r2

Other calibration survival measures: mlr_measures_surv.calib_beta, mlr_measures_surv.calib_index, mlr_measures_surv.dcalib

Other distr survival measures: mlr_measures_surv.calib_index, mlr_measures_surv.dcalib, mlr_measures_surv.graf, mlr_measures_surv.intlogloss, mlr_measures_surv.logloss, mlr_measures_surv.rcll, mlr_measures_surv.schmid

Super classes

mlr3::Measure -> mlr3proba::MeasureSurv -> MeasureSurvCalibrationAlpha

Methods

Public methods

• MeasureSurvCalibrationAlpha$new()

• MeasureSurvCalibrationAlpha$clone()

Inherited methods

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

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Method new()

Creates a new instance of this R6 class.

Usage

MeasureSurvCalibrationAlpha$new(method = "ratio")

Arguments

method

defines which output score to return, see "Parameter details" section.

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Method clone()

The objects of this class are cloneable with this method.

Usage

MeasureSurvCalibrationAlpha$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.