predict: Predictions for Joint Models
In drizopoulos/JMbayes: Joint Modeling of Longitudinal and Time-to-Event Data under a Bayesian Approach

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Calculates predicted values for the longitudinal part of a joint model.

## S3 method for class 'JMbayes'
predict(object, newdata, type = c("Marginal", "Subject"),
    interval = c("none", "confidence", "prediction"), level = 0.95, idVar = "id", 
    FtTimes = NULL, last.time = NULL, LeftTrunc_var = NULL, 
    M = 300, returnData = FALSE, scale = 1.6, 
    weight = rep(1, nrow(newdata)), invlink = NULL, seed = 1, ...)

`object`	an object inheriting from class `JMBayes`.
`newdata`	a data frame in which to look for variables with which to predict.
`type`	a character string indicating the type of predictions to compute, marginal or subject-specific. See Details.
`interval`	a character string indicating what type of intervals should be computed.
`level`	a numeric scalar denoting the tolerance/confidence level.
`idVar`	a character string indicating the name of the variable in `newdata` that corresponds to the subject identifier; required when `type = "Subject"`.
`FtTimes`	a list with components numeric vectors denoting the time points for which we wish to compute subject-specific predictions after the last available measurement provided in `newdata`. For each subject in `newdata` the default is a sequence of 25 equally spaced time points from the last available measurement to the maximum follow-up time of all subjects (plus a small quantity). This argument is only used when `type = "Subject"`.
`last.time`	a numeric vector. This specifies the known time at which each of the subjects in `newdata` was known to be alive. If `NULL`, then this is automatically taken as the last time each subject provided a longitudinal measurement. If a numeric vector, then it is assumed to contain this last time point for each subject.
`LeftTrunc_var`	character string indicating the name of the variable in `newdata` that denotes the left-truncation time.
`M`	numeric scalar denoting the number of Monte Carlo samples. See Details.
`returnData`	logical; if `TRUE` the data frame supplied in `newdata` is returned augmented with the outputs of the function.
`scale`	a numeric value setting the scaling of the covariance matrix of the empirical Bayes estimates in the Metropolis step during the Monte Carlo sampling.
`weight`	a numeric vector of weights to be applied to the predictions of each subject.
`invlink`	a function to tranform the linear predictor of the mixed model to fitted means; relevant when the user has specified her own density for the longitudinal outcome in `jointModelBayes`.
`seed`	numeric scalar, the random seed used to produce the results.
`...`	additional arguments; currently none is used.

When type = "Marginal", this function computes predicted values for the fixed-effects part of the longitudinal submodel. In particular, let X denote the fixed-effects design matrix calculated using newdata. The predict() calculates \hat{y} = X \hat{β}, and if interval = "confidence", then it calculates the confidence intervals based on the percentiles of the MCMC sample for β.

When type = "Subject", this functions computes subject-specific predictions for the longitudinal outcome based on the joint model. This accomplished with a Monte Carlo simulation scheme, similar to the one described in survfitJM. The only difference is in Step 3, where for interval = "confidence" y_i^* = X_i β^* + Z_i b_i^*, whereas for interval = "prediction" y_i^* is a random vector from a normal distribution with mean X_i β^* + Z_i b_i^* and standard deviation σ^*. Based on this Monte Carlo simulation scheme we take as estimate of \hat{y}_i the average of the M estimates y_i^* from each Monte Carlo sample. Confidence intervals are constructed using the percentiles of y_i^* from the Monte Carlo samples.

If se.fit = FALSE a numeric vector of predicted values, otherwise a list with components pred the predicted values, se.fit the standard error for the fitted values, and low and upp the lower and upper limits of the confidence interval. If returnData = TRUE, it returns the data frame newdata with the previously mentioned components added.

The user is responsible to appropriately set the invlink argument when a user-specified mixed effects model has been fitted.

Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl

Rizopoulos, D. (2016). The R package JMbayes for fitting joint models for longitudinal and time-to-event data using MCMC. Journal of Statistical Software 72(7), 1–45. doi:10.18637/jss.v072.i07.

Rizopoulos, D. (2012) Joint Models for Longitudinal and Time-to-Event Data: with Applications in R. Boca Raton: Chapman and Hall/CRC.

survfitJM.JMbayes, jointModelBayes

## Not run: 
# linear mixed model fit
fitLME <- lme(log(serBilir) ~ drug * year, data = pbc2,
    random = ~ year | id)
# survival regression fit
fitSURV <- coxph(Surv(years, status2) ~ drug, data = pbc2.id, 
    x = TRUE)
# joint model fit, under the (default) Weibull model
fitJOINT <- jointModelBayes(fitLME, fitSURV, timeVar = "year")

DF <- with(pbc2, expand.grid(drug = levels(drug),
    year = seq(min(year), max(year), len = 100)))
Ps <- predict(fitJOINT, DF, interval = "confidence", return = TRUE)
require(lattice)
xyplot(pred + low + upp ~ year | drug, data = Ps,
    type = "l", col = c(2,1,1), lty = c(1,2,2), lwd = 2,
    ylab = "Average log serum Bilirubin")


# Subject-specific predictions
ND <- pbc2[pbc2$id == 2, ]
Ps.ss <- predict(fitJOINT, ND, type = "Subject",
  interval = "confidence", return = TRUE)
xyplot(pred + low + upp ~ year | id, data = Ps.ss,
    type = "l", col = c(2,1,1), lty = c(1,2,2), lwd = 2,
    ylab = "Average log serum Bilirubin")

## End(Not run)