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

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.

Usage

Diffepoce(epoceM1, epoceM2)

Arguments

epoceM1: a first object inheriting from class epoce
epoceM2: a second object inheriting from class epoce

Value

call.Jointlcmm1: the Jointlcmm call for epoceM1
call.Jointlcmm2: the Jointlcmm call for epoceM2
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 Jointlcmm estimation, and TRUE otherwise.

Details

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

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.

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.

Author

Cecile Proust-Lima and Amadou Diakite

Examples


# \dontrun{
#### 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)
#> Be patient, epoce function is running ... 
#> The program took 0.26 seconds 
cvpol1
#> Expected Prognostic Observed Cross-Entropy (EPOCE) of the joint latent class model: 
#>  
#> Jointlcmm(fixed = Ydep1 ~ Time * X1, random = ~Time, subject = "ID", 
#>     ng = 1, survival = Surv(Tevent, Event) ~ X1 + X2, hazard = "Weibull", 
#>     hazardtype = "PH", data = data_lcmm)
#>  
#> EPOCE estimators on data used for estimation: 
#>     Mean Prognostic Observed Log-likelihood (MPOL) 
#>     and Cross-validated Prognostic Observed Log-likelihood (CVPOL) 
#>     (CVPOL is the bias-corrected MPOL obtained by approximated cross-validation) 
#>  
#>   pred. times  N at risk  N events     MPOL    CVPOL
#>             1        300       150 1.892619 1.906395
#>             3        299       150 1.889432 1.903253
#>             5        291       149 1.899210 1.913254
#>             7        258       127 1.785964 1.799345
#>             9        205       107 1.850733 1.865251
#>            11        158        81 1.793531 1.809033
#>            13        129        68 1.772987 1.789439
#>            15         99        49 1.656587 1.673814
#>  
cvpol2 <- epoce(m2,var.time="Time",pred.times=VecTime)
#> Be patient, epoce function is running ... 
#> The program took 0.48 seconds 
cvpol2
#> Expected Prognostic Observed Cross-Entropy (EPOCE) of the joint latent class model: 
#>  
#> Jointlcmm(fixed = Ydep1 ~ Time * X1, mixture = ~Time, random = ~Time, 
#>     subject = "ID", ng = 2, survival = Surv(Tevent, Event) ~ 
#>         X1 + X2, hazard = "Weibull", hazardtype = "PH", data = data_lcmm, 
#>     logscale = TRUE)
#>  
#> EPOCE estimators on data used for estimation: 
#>     Mean Prognostic Observed Log-likelihood (MPOL) 
#>     and Cross-validated Prognostic Observed Log-likelihood (CVPOL) 
#>     (CVPOL is the bias-corrected MPOL obtained by approximated cross-validation) 
#>  
#>   pred. times  N at risk  N events     MPOL    CVPOL
#>             1        300       150 1.869272 1.886070
#>             3        299       150 1.840027 1.860890
#>             5        291       149 1.853149 1.874388
#>             7        258       127 1.735359 1.756333
#>             9        205       107 1.773111 1.795867
#>            11        158        81 1.672144 1.695271
#>            13        129        68 1.628349 1.653144
#>            15         99        49 1.463446 1.487694
#>  
DeltaEPOCE <- Diffepoce(cvpol1,cvpol2)
summary(DeltaEPOCE)
#> Difference in Expected Prognostic Observed Cross-Entropy (EPOCE) estimates 
#>  from the two following joint latent class models: 
#>  
#> Jointlcmm(fixed = Ydep1 ~ Time * X1, random = ~Time, subject = "ID", 
#>     ng = 1, survival = Surv(Tevent, Event) ~ X1 + X2, hazard = "Weibull", 
#>     hazardtype = "PH", data = data_lcmm)
#> Jointlcmm(fixed = Ydep1 ~ Time * X1, mixture = ~Time, random = ~Time, 
#>     subject = "ID", ng = 2, survival = Surv(Tevent, Event) ~ 
#>         X1 + X2, hazard = "Weibull", hazardtype = "PH", data = data_lcmm, 
#>     logscale = TRUE)
#>  
#> Difference in the Cross-Validated Prognostic Observed Log-likelihood (CVPOL) 
#>       and its 95% tracking interval 
#>  
#>   pred. times Diff CVPOL      95%TIinf   95%TIsup
#>             1 0.02032484 -0.0134220325 0.05407170
#>             3 0.04236342  0.0002114357 0.08451541
#>             5 0.03886617 -0.0041803390 0.08191268
#>             7 0.04301238 -0.0045571082 0.09058187
#>             9 0.06938394  0.0137801969 0.12498769
#>            11 0.11376117  0.0507038450 0.17681850
#>            13 0.13629482  0.0642955138 0.20829412
#>            15 0.18612023  0.1103956560 0.26184480
#>  
plot(DeltaEPOCE,bty="l")

# }

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