This calibration method is defined by calculating $$s = B/n \sum_i (P_i - n/B)^2$$ where $$B$$ is number of 'buckets', $$n$$ is the number of predictions, and $$P_i$$ is the predicted number of deaths in the $$i$$th interval [0, 100/B), [100/B, 50/B),....,[(B - 100)/B, 1).

A model is well-calibrated if s ~ Unif(B), tested with chisq.test (p > 0.05 if well-calibrated). Model i is better calibrated than model j if s_i < s_j.

## 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-calibration. If chisq = FALSE and m is the predicted value then you can manually compute the p.value with pchisq(m, 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")


## Meta Information

• Type: "surv"

• Range: $$[0, \infty)$$

• Minimize: TRUE

• Required prediction: distr

## 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.

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.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.schmid

## Super classes

mlr3::Measure -> mlr3proba::MeasureSurv -> MeasureSurvDCalibration

## Active bindings

B

(integer(1))
Number of buckets to test for uniform predictions over. Default of 10 is recommended by Haider et al. (2020).

chisq

(logical(1))
If TRUE returns the p.value of the corresponding chisq.test instead of the measure. Otherwise this can be performed manually with pchisq(m, B - 1, lower.tail = FALSE). p > 0.05 indicates well-calibrated.

## Methods

### Public methods

Inherited methods

### Method new()

Creates a new instance of this R6 class.

#### Arguments

deep

Whether to make a deep clone.