Estimation of multi-process joint latent class mixed models
Estimation of multi-process joint latent class mixed models
mpjlcmm(longitudinal, subject, classmb, ng, survival, hazard = "Weibull", hazardtype = "Specific", hazardnodes = NULL, TimeDepVar = NULL, data, B, convB = 1e-04, convL = 1e-04, convG = 1e-04, maxiter = 100, nsim = 100, prior, logscale = FALSE, subset = NULL, na.action = 1, posfix = NULL, partialH = FALSE, verbose = TRUE)
longitudinal |
list of longitudinal models of the type hlme, lcmm or multlcmm |
subject |
name of the covariate representing the grouping structure (called subject identifier) |
classmb |
optional one-sided formula describing the covariates in the class-membership multinomial logistic model |
ng |
number of latent classes considered |
survival |
two-sided formula object specifying the survival part of the model |
hazard |
optional family of hazard function assumed for the survival model (Weibull, piecewise or splines) |
hazardtype |
optional indicator for the type of baseline risk function (Specific, PH or Common) |
hazardnodes |
optional vector containing interior nodes if
|
TimeDepVar |
optional vector specifying the name of the time-depending covariate in the survival model |
data |
data frame containing all the variables used in the model |
B |
optional specification for the initial values for the parameters.
Three options are allowed: (1) a vector of initial values is entered (the
order in which the parameters are included is detailed in |
convB |
optional threshold for the convergence criterion based on the parameter stabilit |
convL |
optional threshold for the convergence criterion based on the log-likelihood stability |
convG |
optional threshold for the convergence criterion based on the derivatives |
maxiter |
optional maximum number of iterations for the Marquardt iterative algorithm |
nsim |
optional number of points for the predicted survival curves and predicted baseline risk curves |
prior |
optional name of a covariate containing a prior information about the latent class membership |
logscale |
optional boolean indicating whether an exponential (logscale=TRUE) or a square (logscale=FALSE -by default) transformation is used to ensure positivity of parameters in the baseline risk functions |
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. |
posfix |
Optional vector specifying the indices in vector B of the parameters that should not be estimated. Default to NULL, all parameters are estimated |
partialH |
optional logical for Piecewise and Splines baseline risk functions only. Indicates whether the parameters of the baseline risk functions can be dropped from the Hessian matrix to define convergence criteria. |
verbose |
logical indicating if information about computation should be reported. Default to TRUE. |
Cecile Proust Lima and Viviane Philipps
## Not run:
paquid$age65 <- (paquid$age-65)/10
##############################################################################
### EXAMPLE 1 : ###
###two outcomes measuring the same latent process along with dementia onset###
##############################################################################
## multlcmm model for MMSE and BVRT for 1 class
mult1 <- multlcmm(MMSE+BVRT~age65+I(age65^2)+CEP+male,random=~age65+I(age65^2),
subject="ID",link=c("5-quant-splines","4-quant-splines"),data=paquid)
summary(mult1)
## joint model for 1 class
m1S <- mpjlcmm(longitudinal=list(mult1),subject="ID",ng=1,data=paquid,
survival=Surv(age_init,agedem,dem)~1)
summary(m1S)
##### joint model for 2 classes #####
## specify longitudinal model for 2 classes, without estimation
mult2 <- multlcmm(MMSE+BVRT~age65+I(age65^2)+CEP+male,random=~age65+I(age65^2),
subject="ID",link=c("5-quant-splines","4-quant-splines"),ng=2,
mixture=~age65+I(age65^2),data=paquid,B=random(mult1),maxiter=0)
## estimation of the associated joint model
m2S <- mpjlcmm(longitudinal=list(mult2),subject="ID",ng=2,data=paquid,
survival=Surv(age_init,agedem,dem)~1)
## estimation by a grid search with 50 replicates, initial values
## randomly generated from m1S
m2S_b <- gridsearch(mpjlcmm(longitudinal=list(mult2),subject="ID",ng=2,
data=paquid,survival=Surv(age_init,agedem,dem)~1), minit=m1S, rep=50, maxiter=30)
##### joint model for 3 classes #####
mult3 <- multlcmm(MMSE+BVRT~age65+I(age65^2)+CEP+male,random=~age65+I(age65^2),
subject="ID",link=c("5-quant-splines","4-quant-splines"),ng=3,
mixture=~age65+I(age65^2),data=paquid,B=random(mult1),maxiter=0)
m3S <- mpjlcmm(longitudinal=list(mult3),subject="ID",ng=3,data=paquid,
survival=Surv(age_init,agedem,dem)~1)
m3S_b <- gridsearch(mpjlcmm(longitudinal=list(mult3),subject="ID",ng=3,
data=paquid,survival=Surv(age_init,agedem,dem)~1), minit=m1S, rep=50, maxiter=30)
##### summary of the models #####
summarytable(m1S,m2S,m2S_b,m3S,m3S_b)
##### post-fit #####
## update longitudinal models :
mod2 <- update(m2S)
mult2_post <- mod2[[1]]
## -> use the available functions for multlcmm on the mult2_post object
## fit of the longitudinal trajectories
par(mfrow=c(2,2))
plot(mult2_post,"fit","age65",marg=TRUE,shades=TRUE,outcome=1)
plot(mult2_post,"fit","age65",marg=TRUE,shades=TRUE,outcome=2)
plot(mult2_post,"fit","age65",marg=FALSE,shades=TRUE,outcome=1)
plot(mult2_post,"fit","age65",marg=FALSE,shades=TRUE,outcome=2)
## predicted trajectories
dpred <- data.frame(age65=seq(0,3,0.1),male=0,CEP=0)
predL <- predictL(mult2_post,newdata=dpred,var.time="age65",confint=TRUE)
plot(predL,shades=TRUE) # in the latent process scale
predY <- predictY(mult2_post,newdata=dpred,var.time="age65",draws=TRUE)
plot(predY,shades=TRUE,ylim=c(0,30),main="MMSE") #in the 0-30 scale for MMSE
plot(predY,shades=TRUE,ylim=c(0,15),outcome=2,main="BVRT") #in 0-15 for BVRT
## baseline hazard and survival curves :
plot(m2S,"hazard")
plot(m2S,"survival")
## posteriori probabilities and classification :
postprob(m2S)
####################################################################################
### EXAMPLE 2 : ###
### two latent processes measured each by one outcome along with dementia onset ###
####################################################################################
## define the two longitudinal models
mMMSE1 <- lcmm(MMSE~age65+I(age65^2)+CEP,random=~age65+I(age65^2),subject="ID",
link="5-quant-splines",data=paquid)
mCESD1 <- lcmm(CESD~age65+I(age65^2)+male,random=~age65+I(age65^2),subject="ID",
link="5-quant-splines",data=paquid)
## joint estimation
mm1S <- mpjlcmm(longitudinal=list(mMMSE1,mCESD1),subject="ID",ng=1,data=paquid,
survival=Surv(age_init,agedem,dem)~CEP+male)
## with 2 latent classes
mMMSE2 <- lcmm(MMSE~age65+I(age65^2)+CEP,random=~age65+I(age65^2),subject="ID",
link="5-quant-splines",data=paquid,ng=2,mixture=~age65+I(age65^2),
B=random(mMMSE1),maxiter=0)
mCESD2 <- lcmm(CESD~age65+I(age65^2)+male,random=~age65+I(age65^2),subject="ID",
link="5-quant-splines",data=paquid,ng=2,mixture=~age65+I(age65^2),
B=random(mCESD1),maxiter=0)
mm2S <- mpjlcmm(longitudinal=list(mMMSE2,mCESD2),subject="ID",ng=2,data=paquid,
survival=Surv(age_init,agedem,dem)~CEP+mixture(male),classmb=~CEP+male)
mm2S_b <- gridsearch(mpjlcmm(longitudinal=list(mMMSE2,mCESD2),subject="ID",ng=2,
data=paquid,survival=Surv(age_init,agedem,dem)~CEP+mixture(male),
classmb=~CEP+male),minit=mm1S,rep=50,maxiter=50)
summarytable(mm1S,mm2S,mm2S_b)
mod1_biv <- update(mm1S)
mod2_biv <- update(mm2S)
## -> use post-fit functions as in exemple 1
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