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. $$L(S) = \frac{1}{NT} \sum_{i=1}^N \sum_{j=1}^T L(S_i,t_i|t^*_j)$$

Format

R6::R6Class() inheriting from MeasureSurvIntegrated/MeasureSurv.

Construction

MeasureSurvIntLogloss$new(integrated = TRUE, times, eps = 1e-15, method = 2)
mlr_measures$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.

Meta Information

  • Type: "surv"

  • Range: \([0, \infty)\)

  • Minimize: TRUE

  • Required prediction: distr

Fields

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.

References

Graf E, Schmoor C, Sauerbrei W, Schumacher M (1999). “Assessment and comparison of prognostic classification schemes for survival data.” Statistics in Medicine, 18(17-18), 2529--2545. doi: 10.1002/(sici)1097-0258(19990915/30)18:17/18<2529::aid-sim274>3.0.co;2-5 .

See also