Extract an approximate variance-covariance matrix of estimated parameters from an mjoint object

Returns the variance-covariance matrix of the main parameters of a fitted mjoint model object.

Usage

# S3 method for class 'mjoint'
vcov(object, correlation = FALSE, ...)

Arguments

object: an object inheriting from class mjoint for a joint model of time-to-event and multivariate longitudinal data.
correlation: logical: if TRUE returns the correlation matrix, otherwise returns the variance-covariance matrix (default).
...: additional arguments; currently none are used.

Value

A variance-covariance matrix.

Details

This is a generic function that extracts the variance-covariance matrix of parameters from an mjoint model fit. It is based on a profile likelihood, so no estimates are given for the baseline hazard function, which is generally considered a nuisance parameter. It is based on the empirical information matrix (see Lin et al. 2002, and McLachlan and Krishnan 2008 for details), so is only approximate.

Note

This function is not to be confused with getVarCov, which returns the extracted variance-covariance matrix for the random effects distribution.

References

Lin H, McCulloch CE, Mayne ST. Maximum likelihood estimation in the joint analysis of time-to-event and multiple longitudinal variables. Stat Med. 2002; 21: 2369-2382.

McLachlan GJ, Krishnan T. The EM Algorithm and Extensions. Second Edition. Wiley-Interscience; 2008.

Author

Graeme L. Hickey (graemeleehickey@gmail.com)

Examples

if (FALSE) { # \dontrun{
# Fit a classical univariate joint model with a single longitudinal outcome
# and a single time-to-event outcome

data(heart.valve)
hvd <- heart.valve[!is.na(heart.valve$log.grad) & !is.na(heart.valve$log.lvmi), ]

set.seed(1)
fit1 <- mjoint(formLongFixed = log.lvmi ~ time + age,
    formLongRandom = ~ time | num,
    formSurv = Surv(fuyrs, status) ~ age,
    data = hvd,
    timeVar = "time",
    control = list(nMCscale = 2, burnin = 5)) # controls for illustration only

vcov(fit1)
} # }

if (FALSE) { # \dontrun{
# Fit a joint model with bivariate longitudinal outcomes

data(heart.valve)
hvd <- heart.valve[!is.na(heart.valve$log.grad) & !is.na(heart.valve$log.lvmi), ]

fit2 <- mjoint(
    formLongFixed = list("grad" = log.grad ~ time + sex + hs,
                         "lvmi" = log.lvmi ~ time + sex),
    formLongRandom = list("grad" = ~ 1 | num,
                          "lvmi" = ~ time | num),
    formSurv = Surv(fuyrs, status) ~ age,
    data = list(hvd, hvd),
    inits = list("gamma" = c(0.11, 1.51, 0.80)),
    timeVar = "time",
    verbose = TRUE)

vcov(fit2)
} # }

Extract an approximate variance-covariance matrix of estimated parameters from an `mjoint` object