D-Calibration Survival Measure

This calibration method is defined by calculating the following statistic: $$s = B/n \sum_i (P_i - n/B)^2$$ where \(B\) is number of 'buckets' (that equally divide \([0,1]\) into intervals), \(n\) is the number of predictions, and \(P_i\) is the observed proportion of observations in the \(i\)th interval. An observation is assigned to the \(i\)th bucket, if its predicted survival probability at the time of event falls within the corresponding interval. This statistic assumes that censoring time is independent of death time.

A model is well D-calibrated if \(s \sim Unif(B)\), tested with chisq.test (\(p > 0.05\) if well-calibrated, i.e. higher p-values are preferred). Model \(i\) is better calibrated than model \(j\) if \(s(i) < s(j)\), meaning that lower values of this measure are preferred.

Details

This measure can either return the test statistic or the p-value from the chisq.test. The former is useful for model comparison whereas the latter is useful for determining if a model is well-calibrated. If chisq = FALSE and s is the predicted value then you can manually compute the p.value with pchisq(s, B - 1, lower.tail = FALSE).

NOTE: This measure is still experimental both theoretically and in implementation. Results should therefore only be taken as an indicator of performance and not for conclusive judgements about model calibration.

Dictionary

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

MeasureSurvDCalibration$new()
mlr_measures$get("surv.dcalib")
msr("surv.dcalib")

Parameters

Id	Type	Default	Levels	Range
B	integer	10		\([1, \infty)\)
chisq	logical	FALSE	TRUE, FALSE	-
truncate	numeric	Inf		\([0, \infty)\)

Meta Information

• Type: "surv"

• Range: \([0, \infty)\)

• Minimize: TRUE

• Required prediction: distr

Parameter details

• B (integer(1))
  Number of buckets to test for uniform predictions over. Default of 10 is recommended by Haider et al. (2020). Changing this parameter affects truncate.

• chisq (logical(1))
  If TRUE returns the p-value of the corresponding chisq.test instead of the measure. Default is FALSE and returns the statistic s. You can manually get the p-value by executing pchisq(s, B - 1, lower.tail = FALSE). The null hypothesis is that the model is D-calibrated.

• truncate (double(1))
  This parameter controls the upper bound of the output statistic, when chisq is FALSE. We use truncate = Inf by default but values between \(10-16\) are sufficient for most purposes, which correspond to p-values of \(0.35-0.06\) for the chisq.test using the default \(B = 10\) buckets. Values \(B > 10\) translate to even lower p-values and thus less D-calibrated models. If the number of buckets \(B\) changes, you probably will want to change the truncate value as well to correspond to the same p-value significance. Note that truncation may severely limit automated tuning with this measure.

References

Haider, Humza, Hoehn, Bret, Davis, Sarah, Greiner, Russell (2020). “Effective Ways to Build and Evaluate Individual Survival Distributions.” Journal of Machine Learning Research, 21(85), 1–63. https://jmlr.org/papers/v21/18-772.html.

See also

Other survival measures: mlr_measures_surv.calib_alpha, mlr_measures_surv.calib_beta, mlr_measures_surv.chambless_auc, mlr_measures_surv.cindex, 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_alpha, mlr_measures_surv.calib_beta

Other distr survival measures: mlr_measures_surv.calib_alpha, 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 -> MeasureSurvDCalibration

Methods

Public methods

• MeasureSurvDCalibration$new()

• MeasureSurvDCalibration$clone()

Inherited methods

• mlr3::Measure$aggregate()
• mlr3::Measure$format()
• mlr3::Measure$help()
• mlr3::Measure$score()
• mlr3proba::MeasureSurv$print()

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Method new()

Creates a new instance of this R6 class.

Usage

MeasureSurvDCalibration$new()

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Method clone()

The objects of this class are cloneable with this method.

Usage

MeasureSurvDCalibration$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.