JMMLSM: Joint Modeling for Continuous outcomes

Description

Joint modeling of longitudinal continuous data and competing risks

Usage

JMMLSM(
  cdata,
  ydata,
  long.formula,
  surv.formula,
  variance.formula,
  random,
  maxiter = 1000,
  epsilon = 1e-04,
  quadpoint = NULL,
  print.para = FALSE,
  survinitial = TRUE,
  initial.para = NULL,
  method = "adaptive",
  opt = "nlminb",
  initial.optimizer = "BFGS"
)

Value

Object of class JMMLSM with elements

ydata: the input longitudinal dataset for fitting a joint model. It has been re-ordered in accordance with descending observation times in cdata.
cdata: the input survival dataset for fitting a joint model. It has been re-ordered in accordance with descending observation times.
PropEventType: a frequency table of number of events.
beta: the vector of fixed effects for the mean trajectory in the mixed effects location and scale model.
tau: the vector of fixed effects for the within-subject variability in the mixed effects location and scale model.
gamma1: the vector of fixed effects for type 1 failure for the survival model.
gamma2: the vector of fixed effects for type 2 failure for the survival model. Valid only if CompetingRisk = TRUE.
alpha1: the vector of association parameter(s) for the mean trajectory for type 1 failure.
alpha2: the vector of association parameter(s) for the mean trajectory for type 2 failure. Valid only if CompetingRisk = TRUE.
vee1: the vector of association parameter(s) for the within-subject variability for type 1 failure.
vee2: the vector of association parameter(s) for the within-subject variability for type 2 failure. Valid only if CompetingRisk = TRUE.
H01: the matrix that collects baseline hazards evaluated at each uncensored event time for type 1 failure. The first column denotes uncensored event times, the second column the number of events, and the third columns the hazards obtained by Breslow estimator.
H02: the matrix that collects baseline hazards evaluated at each uncensored event time for type 2 failure. The data structure is the same as H01. Valid only if CompetingRisk = TRUE.
Sig: the variance-covariance matrix of the random effects.
iter: the total number of iterations until convergence.
convergence: convergence identifier: 1 corresponds to successful convergence, whereas 0 to a problem (i.e., when 0, usually more iterations are required).
vcov: the variance-covariance matrix of all the fixed effects for both models.
sebeta: the standard error of beta.
setau: the standard error of tau.
segamma1: the standard error of gamma1.
segamma2: the standard error of gamma2. Valid only if CompetingRisk = TRUE.
sealpha1: the standard error of alpha1.
sealpha2: the standard error of alpha2. Valid only if CompetingRisk = TRUE.
sevee1: the standard error of vee1.
sevee2: the standard error of vee2. Valid only if CompetingRisk = TRUE.
seSig: the vector of standard errors of covariance of random effects.
loglike: the log-likelihood value.
EFuntheta: a list with the expected values of all the functions of random effects.
CompetingRisk: logical value; TRUE if a competing event are accounted for.
quadpoint: the number of Gauss Hermite quadrature points used for numerical integration.
LongitudinalSubmodelmean: the component of the long.formula.
LongitudinalSubmodelvariance: the component of the variance.formula.
SurvivalSubmodel: the component of the surv.formula.
random: the component of the random.
call: the matched call.

Arguments

cdata: a survival data frame with competing risks or single failure. Each subject has one data entry.
ydata: a longitudinal data frame in long format.
long.formula: a formula object with the response variable and fixed effects covariates to be included in the longitudinal sub-model.
surv.formula: a formula object with the survival time, event indicator, and the covariates to be included in the survival sub-model.
variance.formula: an one-sided formula object with the fixed effects covariates to model the variance of longitudinal sub-model.
random: a one-sided formula object describing the random effects part of the longitudinal sub-model. For example, fitting a random intercept model takes the form ~ 1|ID. Alternatively. Fitting a random intercept and slope model takes the form ~ x1 + ... + xn|ID.
maxiter: the maximum number of iterations of the EM algorithm that the function will perform. Default is 10000.
epsilon: Tolerance parameter. Default is 0.0001.
quadpoint: the number of Gauss-Hermite quadrature points to be chosen for numerical integration. Default is 15 which produces stable estimates in most dataframes.
print.para: Print detailed information of each iteration. Default is FALSE, i.e., not to print the iteration details.
survinitial: Fit a Cox model to obtain initial values of the parameter estimates. Default is TRUE.
initial.para: a list of initialized parameters for EM iteration. Default is NULL.
method: Method for proceeding numerical integration in the E-step. Default is adaptive.
opt: Optimization method to fit a linear mixed effects model, either nlminb (default) or optim.
initial.optimizer: Method for numerical optimization to be used. Default is BFGS.

Examples

Run this code

require(JMH)
data(ydata)
data(cdata)
## fit a joint model
if (FALSE) {
fit <- JMMLSM(cdata = cdata, ydata = ydata, 
              long.formula = Y ~ Z1 + Z2 + Z3 + time,
              surv.formula = Surv(survtime, cmprsk) ~ var1 + var2 + var3,
              variance.formula = ~ Z1 + Z2 + Z3 + time, 
              quadpoint = 6, random = ~ 1|ID, print.para = FALSE)
              
## make dynamic prediction of two subjects
cnewdata <- cdata[cdata$ID %in% c(122, 152), ]
ynewdata <- ydata[ydata$ID %in% c(122, 152), ]
survfit <- survfitJMMLSM(fit, seed = 100, ynewdata = ynewdata, cnewdata = cnewdata, 
                         u = seq(5.2, 7.2, by = 0.5), Last.time = "survtime",
                         obs.time = "time", method = "GH")
oldpar <- par(mfrow = c(2, 2), mar = c(5, 4, 4, 4))
plot(survfit, include.y = TRUE)
par(oldpar)
}

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