# Negative Log-Likelihood Survival Measure

Source:`R/MeasureSurvLogloss.R`

`mlr_measures_surv.logloss.Rd`

Calculates the cross-entropy, or negative log-likelihood (NLL) or logarithmic (log), loss.

## Details

The Log Loss, in the context of probabilistic predictions, is defined as the negative log probability density function, \(f\), evaluated at the observation time (event or censoring), \(t\), $$L_{NLL}(f, t) = -log(f(t))$$

The standard error of the Log Loss, L, is approximated via, $$se(L) = sd(L)/\sqrt{N}$$ where \(N\) are the number of observations in the test set, and \(sd\) is the standard deviation.

The **Re-weighted Negative Log-Likelihood** (RNLL) or IPCW Log Loss is defined by
$$L_{RNLL}(f, t, \Delta) = -\Delta log(f(t))/G(t)$$
where \(\Delta\) is the censoring indicator and G is the Kaplan-Meier estimator of the
censoring distribution.
So only observations that have experienced the event are taking into account
for RNLL and both \(f(t), G(t)\) are calculated only at the event times.
If only censored observations exist in the test set, `NaN`

is returned.

If `task`

and `train_set`

are passed to `$score`

then \(G(t)\) is fit on training data,
otherwise testing data. The first is likely to reduce any bias caused by calculating
parts of the measure on the test data it is evaluating. The training data is automatically
used in scoring resamplings.

## Dictionary

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

## Parameters

Id | Type | Default | Levels | Range |

eps | numeric | 1e-15 | \([0, 1]\) | |

se | logical | FALSE | TRUE, FALSE | - |

IPCW | logical | TRUE | TRUE, FALSE | - |

ERV | logical | FALSE | TRUE, FALSE | - |

## 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 1e-15.

`se`

(`logical(1)`

)

If`TRUE`

then returns standard error of the measure otherwise returns the mean across all individual scores, e.g. the mean of the per observation scores. Default is`FALSE`

(returns the mean).

`ERV`

(`logical(1)`

)

If`TRUE`

then the Explained Residual Variation method is applied, which means the score is standardized against a Kaplan-Meier baseline. Default is`FALSE`

.

`IPCW`

(`logical(1)`

)

If`TRUE`

(default) then returns the \(L_{RNLL}\) score (which is proper), otherwise the \(L_{NLL}\) score (improper).

## 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.dcalib`

,
`mlr_measures_surv.graf`

,
`mlr_measures_surv.hung_auc`

,
`mlr_measures_surv.intlogloss`

,
`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 Probabilistic survival measures:
`mlr_measures_surv.graf`

,
`mlr_measures_surv.intlogloss`

,
`mlr_measures_surv.rcll`

,
`mlr_measures_surv.schmid`

Other distr survival measures:
`mlr_measures_surv.calib_alpha`

,
`mlr_measures_surv.dcalib`

,
`mlr_measures_surv.graf`

,
`mlr_measures_surv.intlogloss`

,
`mlr_measures_surv.rcll`

,
`mlr_measures_surv.schmid`

## Super classes

`mlr3::Measure`

-> `mlr3proba::MeasureSurv`

-> `MeasureSurvLogloss`