# Difference of expected prognostic cross-entropy (EPOCE) estimators and its 95% tracking interval between two joint latent class models estimated with Jointlcmm

### Description

This function computes the difference of 2 EPOCE estimates (CVPOL or MPOL) and its 95% tracking interval between two joint latent class models estimated using `Jointlcmm`

and evaluated using `epoce`

function. Difference in CVPOL is computed when the EPOCE was previously estimated on the same dataset as used for estimation (using an approximated cross-validation), and difference in MPOL is computed when the EPOCE was previously estimated on an external dataset.

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

### Usage

1 | ```
Diffepoce(epoceM1,epoceM2)
``` |

### Arguments

`epoceM1` |
a first object inheriting from class |

`epoceM2` |
a second object inheriting from class |

### Details

From the EPOCE estimates and the individual contributions to the prognostic observed log-likelihood obtained with `epoce`

function on the same dataset from two different estimated joint latent class models, the difference of CVPOL (or MPOL) and its 95% tracking interval is computed. The 95% tracking interval is:

Delta(MPOL) +/- qnorm(0.975)*sqrt(VARIANCE) for an external dataset

Delta(CVPOL) +/- qnorm(0.975)*sqrt(VARIANCE) for the dataset used in `Jointlcmm`

where Delta(CVPOL) (or Delta(MPOL)) is the difference of CVPOL (or MPOL) of the two joint latent class models, and VARIANCE is the empirical variance of the difference of individual contributions to the prognostic observed log-likelihoods of the two joint latent class models.

See Commenges et al. (2012) and Proust-Lima et al. (2012) for further details.

### Value

`call.Jointlcmm1` |
the |

`call.Jointlcmm2` |
the |

`call` |
the matched call |

`DiffEPOCE` |
Dataframe containing, for each prediction time s, the difference in either MPOL or CVPOL depending on the dataset used, and the 95% tracking bands (TIinf and TIsup) |

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

### See Also

`Jointlcmm`

,`epoce`

,`summary.Diffepoce`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ```
## Not run:
#### estimation with 2 latent classes (ng=2)
m2 <- 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,
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),logscale=TRUE)
m1 <- Jointlcmm(fixed= Ydep1~Time*X1,random=~Time,subject='ID'
,survival = Surv(Tevent,Event)~ X1+X2 ,hazard="Weibull"
,hazardtype="PH",ng=1,data=data_lcmm,
B=c(-7.6634, 0.9136, 0.1002, 0.6641, 10.5675, -1.6589, 1.4767, -0.0806,
0.9240,0.5643, 1.2277, 1.5004))
## EPOCE computation for predictions times from 1 to 6 on the dataset used
## for estimation of m.
VecTime <- c(1,3,5,7,9,11,13,15)
cvpol1 <- epoce(m1,var.time="Time",pred.times=VecTime)
cvpol1
cvpol2 <- epoce(m2,var.time="Time",pred.times=VecTime)
cvpol2
DeltaEPOCE <- Diffepoce(cvpol1,cvpol2)
summary(DeltaEPOCE)
plot(DeltaEPOCE,bty="l")
## End(Not run)
``` |