Calculates the integrated logarithmic (log), loss, aka integrated cross entropy.

For an individual who dies at time \(t\), with predicted Survival function, \(S\), the probabilistic log loss at time \(t^*\) is given by $$L(S,t|t^*) = - [log(1 - S(t^*))I(t \le t^*, \delta = 1)(1/G(t))] - [log(S(t^*))I(t > t^*)(1/G(t^*))]$$ where \(G\) is the Kaplan-Meier estimate of the censoring distribution.

If `integrated == FALSE`

then the sample mean is taken for the single specified `times`

, \(t^*\), and the returned
score is given by
$$L(S,t|t^*) = \frac{1}{N} \sum_{i=1}^N L(S_i,t_i|t^*)$$
where \(N\) is the number of observations, \(S_i\) is the predicted survival function for
individual \(i\) and \(t_i\) is their true survival time.

If `integrated == TRUE`

then an approximation to integration is made by taking the mean over all
\(T\) unique time-points, and then the sample mean over all \(N\) observations.
$$L(S) = \frac{1}{NT} \sum_{i=1}^N \sum_{j=1}^T L(S_i,t_i|t^*_j)$$

`R6::R6Class()`

inheriting from `MeasureSurvIntegrated`

/MeasureSurv.

MeasureSurvIntLogloss$new(integrated = TRUE, times, eps = 1e-15) mlr_measures$get("surv.intlogloss") msr("surv.intlogloss")

`integrated`

::`logical(1)`

If`TRUE`

(default), returns the integrated score; otherwise, not integrated.`times`

::`vector()`

If`integrate == TRUE`

then a vector of time-points over which to integrate the score. If`integrate == FALSE`

then a single time point at which to return the score.`eps`

::`numeric(1)`

Very small number to set zero-valued predicted probabilities to, in order to prevent errors in log(0) calculation.

Type:

`"surv"`

Range: \([0, \infty)\)

Minimize:

`TRUE`

Required prediction:

`distr`

See MeasureSurv, as well as all variables passed to the constructor.

As well as

eps :: numeric(1)

Very small number to set zero-valued predicted probabilities to, in order to prevent errors in log(0) calculation.

Graf, E., Schmoor, C., Sauerbrei, W. and Schumacher, M. (1999).

Assessment and comparison of prognostic classification schemes for survival data.

Statistics in Medicine, 18(17), 2529-2545.

doi: 10.1002/(SICI)1097-0258(19990915/30)18:17/18<2529::AID-SIM274>3.0.CO;2-5

Other survival measures:
`MeasureSurvBeggC`

,
`MeasureSurvChamblessAUC`

,
`MeasureSurvGonenC`

,
`MeasureSurvGrafSE`

,
`MeasureSurvGraf`

,
`MeasureSurvHarrellC`

,
`MeasureSurvHungAUC`

,
`MeasureSurvIntLoglossSE`

,
`MeasureSurvLoglossSE`

,
`MeasureSurvLogloss`

,
`MeasureSurvNagelkR2`

,
`MeasureSurvOQuigleyR2`

,
`MeasureSurvSongAUC`

,
`MeasureSurvSongTNR`

,
`MeasureSurvSongTPR`

,
`MeasureSurvUnoAUC`

,
`MeasureSurvUnoC`

,
`MeasureSurvUnoTNR`

,
`MeasureSurvUnoTPR`

,
`MeasureSurvXuR2`

Other Probabilistic survival measures:
`MeasureSurvGrafSE`

,
`MeasureSurvGraf`

,
`MeasureSurvIntLoglossSE`

,
`MeasureSurvLoglossSE`

,
`MeasureSurvLogloss`