# Estimators of the Expected Prognostic Observed Cross-Entropy (EPOCE) for evaluating predictive accuracy of joint latent class models estimated using Jointlcmm

### Description

This function computes estimators of the Expected Prognostic Observed Cross-Entropy (EPOCE) for evaluating the predictive accuracy of joint latent class models estimated using `Jointlcmm`

. On the same data as used for estimation of the `Jointlcmm`

object, this function computes both the Mean Prognostic Observed Log-Likelihood (MPOL) and the Cross-Validated Observed Log-Likelihood (CVPOL), two estimators of EPOCE. The latter corrects the MPOL estimate for over-optimism by approximated cross-validation. On external data, this function only computes the Mean Prognostic Observed Log-Likelihood (MPOL).

This function does not apply for the moment with multiple causes of event (competing risks).

### Usage

1 |

### Arguments

`model` |
an object inheriting from class |

`pred.times` |
Vector of times of prediction, from which predictive accuracy is evaluated (only subjects still at risk at the time of prediction are included in the computation, and only information before the time of prediction is considered. |

`var.time` |
Name of the variable indicating time in the dataset |

`fun.time` |
an optional function. This is only required if the time scales in the longitudinal part of the model and the survival part are different. In that case, |

`newdata` |
optional. When missing, the data used for estimating the |

`subset` |
a specification of the rows to be used: defaults to all rows. This can be any valid indexing vector for the rows of data or if that is not supplied, a data frame made up of the variable used in formula. |

`na.action` |
Integer indicating how NAs are managed. The default is 1 for 'na.omit'. The alternative is 2 for 'na.fail'. Other options such as 'na.pass' or 'na.exclude' are not implemented in the current version. |

### Details

EPOCE assesses the prognostic information of a joint latent class model. It relies on information theory.

MPOL computed at time s equals minus the mean individual contribution to the conditional log-likelihood of the time to event given the longitudinal data up to the time of prediction s and given the subject is still at risk of event in s.

CVPOL computed at time s equals MPOL at time s plus a penalty term that corrects for over-optimism when computing predictive accuracy measures on the same dataset as used for estimation. This penalty term is computed from the inverse of the Hessian of the joint log-likelihood and the product of the gradients of the contributions to respectively the joint log-likelihood and the conditional log-likelihood.

The theory of EPOCE and its estimators MPOL and CVPOL is given in Commenges et al. (2012), and further detailed and illustrated for joint models in Proust-Lima et al. (2013).

### Value

`call.Jointlcmm` |
the |

`call.epoce` |
the matched call |

`EPOCE` |
Dataframe containing, for each prediction time s, the number of subjects still at risk at s (and with at least one measure before s), the number of events after time s, the MPOL, and the CVPOL when computation is done on the dataset used for |

`IndivContrib` |
Individual contributions to the prognostic observed log-likelihood at each time of prediction. Used for computing tracking intervals of EPOCE differences between models. |

`new.data` |
a boolean for internal use only, which is FALSE if computation is done on the same data as for |

### Author(s)

Cecile Proust-Lima and Amadou Diakite

### References

Commenges, Liquet and Proust-Lima (2012). Choice of prognostic estimators in joint models by estimating differences of expected conditional Kullback-Leibler risks. Biometrics 68(2), 380-7.

Proust-Lima, Sene, Taylor and Jacqmin-Gadda (2014). Joint latent class models of longitudinal and time-to-event data: a review. Statistical Methods in Medical Research 23, 74-90.

### See Also

`Jointlcmm`

,`print.epoce`

,`summary.epoce`

,`plot.epoce`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
## Not run:
## estimation of a joint latent class model with 2 latent classes (ng=2)
# (see the example section of Jointlcmm for details about
# the model specification)
m <- Jointlcmm(fixed= Ydep1~Time*X1,random=~Time,mixture=~Time,subject='ID'
,survival = Surv(Tevent,Event)~ X1+X2 ,hazard="Weibull"
,hazardtype="PH",ng=2,data=data_lcmm,logscale=TRUE,
B=c(0.7608, -9.4974 , 1.0242, 1.4331 , 0.1063 , 0.6714, 10.4679, 11.3178,
-2.5671, -0.5386, 1.4616, -0.0605, 0.9489, 0.1020 , 0.2079, 1.5045))
summary(m)
## Computation of the EPOCE on the same dataset as used for
# estimation of m with times at predictions from 1 to 15
VecTime <- c(1,3,5,7,9,11,13,15)
cvpl <- epoce(m,var.time="Time",pred.times=VecTime)
summary(cvpl)
plot(cvpl,bty="l",ylim=c(0,2))
## End(Not run)
``` |

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