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

The standard error is given by $$\hat{\alpha_{se}} = exp(1/\sqrt{\sum \delta_i})$$

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

IdTypeDefaultLevelsRange
epsnumeric0.001\([0, 1]\)
selogicalFALSETRUE, FALSE-
methodcharacterratioratio, diff-
truncatenumericInf\((-\infty, \infty)\)

Meta Information

  • Type: "surv"

  • Range: \((-\infty, \infty)\)

  • Minimize: FALSE

  • Required prediction: distr

Parameter details

  • eps (numeric(1))
    Very small number to substitute 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 .

Super classes

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

Methods

Inherited methods


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.


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.