JMbayes (version 0.8-85)

predict: Predictions for Joint Models

Description

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

Usage

# S3 method for 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, …)

Arguments

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.

Value

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.

Details

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 \(\hat{y} = X \hat{\beta}\), and if interval = "confidence", then it calculates the confidence intervals based on the percentiles of the MCMC sample for \(\beta\).

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" \(y_i^* = X_i \beta^* + Z_i b_i^*\), whereas for interval = "prediction" \(y_i^*\) is a random vector from a normal distribution with mean \(X_i \beta^* + Z_i b_i^*\) and standard deviation \(\sigma^*\). 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.

References

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.

See Also

survfitJM.JMbayes, jointModelBayes

Examples

# 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")
# }