jmcs {FastJM}

Joint modeling of longitudinal continuous data and competing risks

Description

Joint modeling of longitudinal continuous data and competing risks

Usage

jmcs(
  ydata,
  cdata,
  long.formula,
  random = NULL,
  surv.formula,
  REML = TRUE,
  quadpoint = NULL,
  maxiter = 10000,
  print.para = FALSE,
  survinitial = TRUE,
  tol = 1e-04,
  method = "pseudo-adaptive",
  opt = "nlminb"
)

Arguments

ydata

a longitudinal data frame in long format.

cdata

a survival data frame with competing risks or single failure. Each subject has one data entry.

long.formula

a formula object with the response variable and fixed effects covariates to be included in the 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.

surv.formula

a formula object with the survival time, event indicator, and the covariates to be included in the survival sub-model.

REML

a logic object that indicates the use of REML estimator. Default is TRUE.

quadpoint

the number of pseudo-adaptive Gauss-Hermite quadrature points. to be chosen for numerical integration. Default is 6 which produces stable estimates in most dataframes.

maxiter

the maximum number of iterations of the EM algorithm that the function will perform. Default is 10000.

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.

tol

Tolerance parameter. Default is 0.0001.

method

Method for proceeding numerical integration in the E-step. Default is pseudo-adaptive.

opt

Optimization method to fit a linear mixed effects model, either nlminb (default) or optim.

Value

Object of class jmcs with elements

beta

the vector of fixed effects for the linear mixed effects 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.

nu1

the vector of association parameter(s) for type 1 failure.

nu2

the vector of association parameter(s) 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.

sigma

the variance of the measurement error for the linear mixed effects model.

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.

segamma1

the standard error of gamma1.

segamma2

the standard error of gamma2. Valid only if CompetingRisk = TRUE.

senu1

the standard error of nu1.

senu2

the standard error of nu2. Valid only if CompetingRisk = TRUE.

seSig

the vector of standard errors of covariance of random effects.

sesigma

the standard error of variance of measurement error for the linear mixed effects model.

loglike

the log-likelihood value.

fitted

a list with the fitted values:

resid

the vector of estimated residuals for the linear mixed effects model.

fitted

the vector of fitted values for the linear mixed effects model.

fittedmar

the vector of marginal fitted values for the linear mixed effects model.

residmar

the vector of estimated marginal residuals for the linear mixed effects model.

fittedSurv

the estimated survival rate evaluated at each uncensored event time.

FUNB

the estimated random effects for each subject.

CompetingRisk

logical value; TRUE if a competing event are accounted for.

quadpoint

the number of Gauss Hermite quadrature points used for numerical integration.

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.

LongitudinalSubmodel

the component of the long.formula.

SurvivalSubmodel

the component of the surv.formula.

random

the component of the random.

call

the matched call.

Quad.method

the quadrature rule used for integration. If pseudo-adaptive quadrature rule is used, then return pseudo-adaptive. Otherwise return standard.

id

the grouping vector for the longitudinal outcome.

Author(s)

Shanpeng Li [e-mail]

See Also

ranef, fixef, fitted.jmcs, residuals.jmcs, survfitjmcs, plot.jmcs, vcov.jmcs

Examples

require(FastJM)
require(survival)
# Load a simulated longitudinal dataset
data(ydata)
# Load a simulated survival dataset with two competing events
data(cdata)

# Fit a joint model
fit <- jmcs(ydata = ydata, cdata = cdata, 
            long.formula = response ~ time + gender + x1 + race, 
            surv.formula = Surv(surv, failure_type) ~ x1 + gender + x2 + race, 
            random =  ~ time| ID)
fit
# Extract the parameter estimates of longitudinal sub-model fixed effects
fixef(fit, process = "Longitudinal")
# Extract the parameter estimates of survival sub-model fixed effects
fixef(fit, process = "Event")
# Obtain the random effects estimates for first 6 subjects 
head(ranef(fit))
# Obtain the variance-covariance matrix of all parameter estimates 
vcov(fit)
# Obtain the result summaries of the joint model fit
summary(fit, process = "Longitudinal")
summary(fit, process = "Event")
# Prediction of cumulative incidence for competing risks data
# Predict the conditional probabilities for two patients who are alive (censored)
ND <- ydata[ydata$ID %in% c(419, 218), ]
ID <- unique(ND$ID)
NDc <- cdata[cdata$ID  %in% ID, ]
survfit <- survfitjmcs(fit, 
                       ynewdata = ND, 
                       cnewdata = NDc, 
                       u = seq(3, 4.8, by = 0.2), 
                       method = "GH",
                       obs.time = "time")
survfit
PE <- PEjmcs(fit, seed = 100, landmark.time = 3, horizon.time = c(3.6, 4, 4.4), 
             obs.time = "time", method = "GH", 
             quadpoint = NULL, maxiter = 1000, n.cv = 3, 
             survinitial = TRUE)
Brier <- summary(PE, error = "Brier")
Brier

MAEQ <- MAEQjmcs(fit, seed = 100, landmark.time = 3, horizon.time = c(3.6, 4, 4.4), 
                 obs.time = "time", method = "GH", 
                 quadpoint = NULL, maxiter = 1000, n.cv = 3, 
                 survinitial = TRUE)
APE <- summary(MAEQ, digits = 3)
APE

## evaluate prediction accuracy of fitted joint model using cross-validated mean AUC
AUC <- AUCjmcs(fit, seed = 100, landmark.time = 3, horizon.time = c(3.6, 4, 4.4),
               obs.time = "time", method = "GH",
               quadpoint = NULL, maxiter = 1000, n.cv = 3)
summary(AUC, digits = 3)