plot: Plot of a fitted model

Description

This function produces different plots (residuals, goodness-of-fit, estimated link functions, estimated baseline risk/survival and posterior probabilities distributions) of a fitted object of class hlme, lcmm, multlcmm or Jointlcmm.

Usage

# S3 method for hlme
plot(x, which = "residuals", var.time, break.times, marg, subset, shades, ...)
# S3 method for lcmm
plot(x, which = "residuals", var.time, break.times, marg, subset, shades, ...)
# S3 method for multlcmm
plot(
  x,
  which = "residuals",
  var.time,
  break.times,
  marg,
  outcome,
  subset,
  shades,
  ...
)
# S3 method for Jointlcmm
plot(
  x,
  which = "residuals",
  var.time,
  break.times,
  marg,
  event,
  subset,
  shades,
  ...
)
# S3 method for mpjlcmm
plot(x, which, event, ...)
# S3 method for externSurv
plot(x, which = "hazard", event, ...)
# S3 method for externX
plot(x, which = "postprob", event, ...)

Arguments

x: an object inheriting from classes hlme, lcmm, multlcmm or Jointlcmm, representing respectively a fitted latent class linear mixed model, a more general latent class mixed model or a joint latent class model
which: a character string indicating the type of plot to produce. For hlme objects, are available "residuals", "postprob","fit". For lcmm and multlcmm objects, are available "residuals", "postprob", "link", "linkfunction", "fit". For Jointlcmm objects, are avaiable "residuals", "postprob", "link", "linkfunction", "fit", "hazard", "baselinerisk", "survival". Default to "residuals"
var.time: for which="fit" only, a character string containing the name of the variable that corresponds to time in the longitudinal model.
break.times: for which="fit" only, either a numeric vector containing the cuts-off defining the time-intervals or an integer giving the number of cut-offs. In the latter case, the cut-offs are placed at the quantiles of the observed times distribution.
marg: for which="fit" only, a logical indicating the type of prediction. If marg=TRUE (the default), the marginal predictions are provided. If marg=FALSE, the subject-specific predictions are provided.
subset: for which="fit" only, a subset of the data used to estimate the model, defining the data on which the fit is evaluated. By default, all the data are used.
shades: logical indicating if confidence intervals should be represented with shades. Default to FALSE, confidence intervals are represented as dotted lines.
...: other parameters to be passed through to plotting functions. This includes graphical parameters described in par function and further arguments legend (character or expression to appear in the legend. If no legend should be added, "legend" should be NULL. ), legend.loc (keyword for the position of the legend from the list "bottomright", "bottom", "bottomleft", "left", "topleft","top", "topright", "right" and "center". By default, the legend is located in the top left of the plot. ) and add (logical indicating if the curves should be added to an existing plot. Default to FALSE.).
outcome: for which="fit" and multlcmm objects only, the outcome to consider.
event: for which="baselinerisk" or which="hazard" only, an integer corresponding to the numeric code (in the indicator variable) of the event for which the baseline risk functions are to be plotted. By default, the first event is considered.

Author

Cecile Proust-Lima, Viviane Philipps and Benoit Liquet

Details

With which="residuals", this function provides the marginal residuals against the marginal predictions, the subject-specific residuals against the subject-specific predictions, a normal QQ-plot with confidence bands for the marginal residuals and a normal QQ-plot with confidence bands for the subject-specific residuals.

With which="postprob", the function provides the histograms of the posterior class-membership probabilities stemmed from a Jointlcmm, lcmm, hlme or multlcmm object.

With which="link" or which="linkfunction", the function displays the estimated transformation(s) specified in the option link of lcmm and multlcmm functions. It corresponds to the (non)linear parameterized link estimated between the oberved longitudinal outcome and the underlying latent process.

With which="fit", the function provides the class-specific weighted marginal and subject-specific mean predicted trajectories with time and the class-specific weighted mean observed trajectories and their 95% confidence bounds. The predicted and observed class-specific values are weighted means within each time interval; For each observation or prediction (in the transformed scale if appropriate), the weights are the class-specific (posterior with subject-specific or marginal otherwise) probabilities to belong to the latent class.

With which="baselinerisk" or which="hazard", the function displays the estimated baseline risk functions for the time-to-event of interest in each latent class.

With which="survival", the function displays the estimated event-free probabilities (survival functions) for the time-to-event of interest in each latent class.

Examples

Run this code



###################### fit, residuals and postprob 

# estimation of the model
m<-lcmm(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3,
subject='ID',ng=2,data=data_hlme,B=c(0.41,0.55,-0.18,-0.41,
-14.26,-0.34,1.33,13.51,24.65,2.98,1.18,26.26,0.97))  

# fit
plot(m,which="fit",marg=FALSE,var.time="Time",bty="n")
# residuals plot
plot(m)
# postprob plot
plot(m,which="postprob") 


###################### fit, linkfunctions

#### Estimation of homogeneous mixed models with different assumed link
#### functions, a quadratic mean trajectory for the latent process with 
#### independent random intercept, slope and quadratic slope
#### (comparison of linear, Beta and 3 and 5 splines link functions)
if (FALSE) {

# linear link function
m10<-lcmm(Ydep2~Time+I(Time^2),random=~Time+I(Time^2),subject='ID',ng=1,
          data=data_lcmm,link="linear",
          B=c(-0.7454, -0.2031,  0.2715,  0.2916 , 0.6114, -0.0064,  0.0545,
              0.0128, 25.3795, 2.2371))
            
# Beta link function
m11<-lcmm(Ydep2~Time+I(Time^2),random=~Time+I(Time^2),subject='ID',ng=1,
          data=data_lcmm,link="beta",B=c(-0.9109, -0.0831,  0.5194,  0.1910 ,
          0.8984, -0.0179, -0.0636,  0.0045,  0.5514, -0.7692,  0.7037,  0.0899))
          
# fit 
par(mfrow=c(2,1),mar=c(4,4,1,1))
plot(m11,which="fit",var.time="Time",bty="l",ylim=c(-3,0))
plot(m11,which="fit",var.time="Time",marg=FALSE,bty="l",ylim=c(-3,0))

# I-splines with 3 equidistant nodes
m12<-lcmm(Ydep2~Time+I(Time^2),random=~Time+I(Time^2),subject='ID',ng=1,
          data=data_lcmm,link="3-equi-splines",B=c(-0.9272, -0.0753 , 0.5304, 
          0.1950,  0.9260, -0.0204, -0.0739 , 0.0059, -7.8369,  0.9228 ,-1.4689,
          2.0396,  1.8102))

# I-splines with 5 nodes, and interior nodes entered manually
m13<-lcmm(Ydep2~Time+I(Time^2),random=~Time+I(Time^2),subject='ID',ng=1,
          data=data_lcmm,link="5-manual-splines",intnodes=c(10,20,25),
          B=c(-0.9315, -0.0739 , 0.5254 , 0.1933,  0.9418, -0.0206, -0.0776,
          0.0064, -7.8645, 0.7470,  1.2080,  1.5537 , 1.7558 , 1.3386 , 1.0982))

# Plot of estimated different link functions:
# (applicable for models that only differ in the "link function" used. 
# Otherwise, the latent process scale is different and a rescaling
# is necessary)
plot(m10,which="linkfunction",bty="l")
plot(m11,which="linkfunction",bty="l",add=TRUE,col=2)
plot(m12,which="linkfunction",bty="l",add=TRUE,col=3)
plot(m13,which="linkfunction",bty="l",add=TRUE,col=4)
legend("topleft",legend=c("linear","beta","3-Isplines","5-Isplines"),
col=1:4,lty=1,bty='n')
}


###################### fit, baselinerisk and survival
if (FALSE) {
#### estimation with 3 latent classes (ng=3) - see Jointlcmm 
#### help for details on the model
m3 <- Jointlcmm(fixed= Ydep1~Time*X1,mixture=~Time,random=~Time,
classmb=~X3,subject='ID',survival = Surv(Tevent,Event)~ X1+mixture(X2),
hazard="3-quant-splines",hazardtype="PH",ng=3,data=data_lcmm,
B=c(0.7576, 0.4095, -0.8232, -0.2737, 0, 0, 0, 0.2838, -0.6338, 
2.6324, 5.3963, -0.0273, 1.3979, 0.8168, -15.041, 10.164, 10.2394, 
11.5109, -2.6219, -0.4553, -0.6055, 1.473, -0.0383, 0.8512, 0.0389, 
0.2624, 1.4982))

# fit
plot(m3,which="fit",var.time="Time",bty="l")
plot(m3,which="fit",var.time="Time",marg=FALSE,bty="l",ylim=c(0,15))


# Class-specific predicted baseline risk & survival functions in the 
# 3-class model retained (for the reference value of the covariates) 
plot(m3,which="baselinerisk",bty="l")
plot(m3,which="baselinerisk",ylim=c(0,5),bty="l")
plot(m3,which="survival",bty="l")
}