Type: Package
Title: Joint Model of Heterogeneous Repeated Measures and Survival Data
Version: 1.0.3
Date: 2024-02-19
Maintainer: Shanpeng Li <lishanpeng0913@ucla.edu>
Description: Maximum likelihood estimation for the semi-parametric joint modeling of competing risks and longitudinal data in the presence of heterogeneous within-subject variability, proposed by Li and colleagues (2023) <doi:10.48550/arXiv.2301.06584>. The proposed method models the within-subject variability of the biomarker and associates it with the risk of the competing risks event. The time-to-event data is modeled using a (cause-specific) Cox proportional hazards regression model with time-fixed covariates. The longitudinal outcome is modeled using a mixed-effects location and scale model. The association is captured by shared random effects. The model is estimated using an Expectation Maximization algorithm.
License: GPL (≥ 3)
NeedsCompilation: yes
Imports: Rcpp (≥ 1.0.7), parallel, dplyr, stats, caret, timeROC
LinkingTo: Rcpp, RcppEigen
Depends: R (≥ 3.5.0), survival, nlme, utils, MASS, statmod
RoxygenNote: 7.2.3
Suggests: testthat (≥ 3.0.0), spelling
Language: en-US
LazyData: true
Packaged: 2024-02-20 06:22:18 UTC; shanpengli
Author: Shanpeng Li [aut, cre], Jin Zhou [ctb], Hua Zhou [ctb], Gang Li [ctb]
Repository: CRAN
Date/Publication: 2024-02-20 06:40:02 UTC

Time-dependent AUC for joint models

Description

Time-dependent AUC for joint models

Usage

AUCJMMLSM(
  object,
  seed = 100,
  landmark.time = NULL,
  horizon.time = NULL,
  obs.time = NULL,
  method = c("Laplace", "GH"),
  quadpoint = NULL,
  maxiter = 1000,
  n.cv = 3,
  survinitial = TRUE,
  ...
)

Arguments

object

object of class 'JMMLSM'.

seed

a numeric value of seed to be specified for cross validation.

landmark.time

a numeric value of time for which dynamic prediction starts..

horizon.time

a numeric vector of future times for which predicted probabilities are to be computed.

obs.time

a character string of specifying a longitudinal time variable.

method

estimation method for predicted probabilities. If Laplace, then the empirical empirical estimates of random effects is used. If GH, then the pseudo-adaptive Gauss-Hermite quadrature is used.

quadpoint

the number of pseudo-adaptive Gauss-Hermite quadrature points if method = "GH".

maxiter

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

n.cv

number of folds for cross validation. Default is 3.

survinitial

Fit a Cox model to obtain initial values of the parameter estimates. Default is TRUE.

...

Further arguments passed to or from other methods.

Value

a list of matrices with conditional probabilities for subjects.

Author(s)

Shanpeng Li lishanpeng0913@ucla.edu

See Also

JMMLSM, survfitJMMLSM

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"
)

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.

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.

Examples

require(JMH)
data(ydata)
data(cdata)
## fit a joint model
## Not run: 
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)

## End(Not run)

A metric of prediction accuracy of joint model by comparing the predicted risk with the empirical risks stratified on different predicted risk group.

Description

A metric of prediction accuracy of joint model by comparing the predicted risk with the empirical risks stratified on different predicted risk group.

Usage

MAEQJMMLSM(
  seed = 100,
  object,
  landmark.time = NULL,
  horizon.time = NULL,
  obs.time = NULL,
  method = c("Laplace", "GH"),
  quadpoint = NULL,
  maxiter = 1000,
  survinitial = TRUE,
  n.cv = 3,
  quantile.width = 0.25,
  opt = "nlminb",
  initial.para = FALSE,
  ...
)

Arguments

seed

a numeric value of seed to be specified for cross validation.

object

object of class 'JMMLSM'.

landmark.time

a numeric value of time for which dynamic prediction starts..

horizon.time

a numeric vector of future times for which predicted probabilities are to be computed.

obs.time

a character string of specifying a longitudinal time variable.

method

estimation method for predicted probabilities. If Laplace, then the empirical empirical estimates of random effects is used. If GH, then the standard Gauss-Hermite quadrature is used.

quadpoint

the number of standard Gauss-Hermite quadrature points if method = "GH".

maxiter

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

survinitial

Fit a Cox model to obtain initial values of the parameter estimates. Default is TRUE.

n.cv

number of folds for cross validation. Default is 3.

quantile.width

a numeric value of width of quantile to be specified. Default is 0.25.

opt

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

initial.para

Initial guess of parameters for cross validation. Default is FALSE.

...

Further arguments passed to or from other methods.

Value

a list of matrices with conditional probabilities for subjects.

Author(s)

Shanpeng Li lishanpeng0913@ucla.edu

See Also

JMMLSM, survfitJMMLSM

A metric of prediction accuracy of joint model by comparing the predicted risk with the counting process.

Description

A metric of prediction accuracy of joint model by comparing the predicted risk with the counting process.

Usage

PEJMMLSM(
  seed = 100,
  object,
  landmark.time = NULL,
  horizon.time = NULL,
  obs.time = NULL,
  method = c("Laplace", "GH"),
  quadpoint = NULL,
  maxiter = 1000,
  n.cv = 3,
  survinitial = TRUE,
  ...
)

Arguments

seed

a numeric value of seed to be specified for cross validation.

object

object of class 'JMMLSM'.

landmark.time

a numeric value of time for which dynamic prediction starts..

horizon.time

a numeric vector of future times for which predicted probabilities are to be computed.

obs.time

a character string of specifying a longitudinal time variable.

method

estimation method for predicted probabilities. If Laplace, then the empirical empirical estimates of random effects is used. If GH, then the pseudo-adaptive Gauss-Hermite quadrature is used.

quadpoint

the number of pseudo-adaptive Gauss-Hermite quadrature points if method = "GH".

maxiter

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

n.cv

number of folds for cross validation. Default is 3.

survinitial

Fit a Cox model to obtain initial values of the parameter estimates. Default is TRUE.

...

Further arguments passed to or from other methods.

Value

a list of matrices with conditional probabilities for subjects.

Author(s)

Shanpeng Li lishanpeng0913@ucla.edu

See Also

JMMLSM, survfitJMMLSM

Simulated competing risks data

Description

The cdata data frame has 200 rows and 6 columns.

Usage

data(cdata)

Format

This data frame contains the following columns:

ID

patient identifier.

survtime

event time.

cmprsk

event indicator. 0 denotes censoring, 1 risk 1, and 2 risk 2.

var1

treatment indicator. 0 denotes the placebo group and 1 the treatment group.

var2

continuous variable.

var3

continuous variable.

Plot conditional probabilities for new subjects

Description

Plot conditional probabilities for new subjects. If CompetingRisk = FALSE, print the survival probabilities. Otherwise, print the cumulative incidence probabilities for each failure type.

Usage

## S3 method for class 'survfitJMMLSM'
plot(
  x,
  include.y = FALSE,
  xlab = NULL,
  ylab = NULL,
  xlim = NULL,
  ylim.long = NULL,
  ylim.surv = NULL,
  ...
)

Arguments

x

x of class survfitJMMLSM.

include.y

include longitudinal responses of this subject versus time. Default is FALSE.

xlab

X axis label.

ylab

Y axis label.

xlim

X axis support.

ylim.long

Y axis support for the longitudinal outcome.

ylim.surv

Y axis support for the event / survival probability.

...

further arguments passed to or from other methods.

Value

plots of conditional probabilities over different pre-specified time points for subjects. If single failure type, then survival probabilities will be returned. Otherwise, cumulative incidence probabilities for each failure type will be returned.

Author(s)

Shanpeng Li lishanpeng0913@ucla.edu

See Also

survfitJMMLSM

Print JMMLSM

Description

Print contents of JMMLSM object.

Usage

## S3 method for class 'JMMLSM'
print(x, digits = 4, ...)

Arguments

x

Object of class 'JMMLSM'.

digits

number of digits of decimal to be printed.

...

Further arguments passed to or from other methods.

Value

a summary of data, joint model, log likelihood, and parameter estimates.

Author(s)

Shanpeng Li

See Also

JMMLSM

Print survfitJMMLSM

Description

Print survfitJMMLSM

Usage

## S3 method for class 'survfitJMMLSM'
print(x, ...)

Arguments

x

x of class 'survfitJMMLSM'.

...

Further arguments passed to or from other methods.

Value

a list of matrices with conditional probabilities for subjects.

Author(s)

Shanpeng Li lishanpeng0913@ucla.edu

See Also

JMMLSM, survfitJMMLSM

Print AUCJMMLSM

Description

Print AUCJMMLSM

Usage

## S3 method for class 'AUCJMMLSM'
summary(object, digits = 4, ...)

Arguments

object

object of class 'AUCJMMLSM'.

digits

number of digits of decimal to be printed.

...

Further arguments passed to or from other methods.

Value

a list of matrices with conditional probabilities for subjects.

Author(s)

Shanpeng Li lishanpeng0913@ucla.edu

See Also

JMMLSM, survfitJMMLSM

Print MAEQJMMLSM

Description

Print MAEQJMMLSM

Usage

## S3 method for class 'MAEQJMMLSM'
summary(object, digits = 3, ...)

Arguments

object

object of class 'MAEQJMMLSM'.

digits

number of decimal points to be rounded.

...

Further arguments passed to or from other methods.

Value

a list of matrices with conditional probabilities for subjects.

Author(s)

Shanpeng Li lishanpeng0913@ucla.edu

See Also

JMMLSM, survfitJMMLSM

Print PEJMMLSM

Description

Print PEJMMLSM

Usage

## S3 method for class 'PEJMMLSM'
summary(object, error = c("MAE", "Brier"), ...)

Arguments

object

object of class 'PEJMMLSM'.

error

a character string that specifies the loss function.

...

Further arguments passed to or from other methods.

Value

a list of matrices with conditional probabilities for subjects.

Author(s)

Shanpeng Li lishanpeng0913@ucla.edu

See Also

JMMLSM, survfitJMMLSM

Prediction in Joint Models

Description

This function computes the conditional probability of surviving later times than the last observed time for which a longitudinal measurement was available.

Usage

survfitJMMLSM(
  object,
  seed = 100,
  ynewdata = NULL,
  cnewdata = NULL,
  u = NULL,
  Last.time = NULL,
  obs.time = NULL,
  method = c("Laplace", "GH"),
  quadpoint = NULL,
  ...
)

Arguments

object

an object inheriting from class JMMLSM.

seed

a random seed number to proceed non-parametric bootstrap. Default is 100.

ynewdata

a data frame that contains the longitudinal and covariate information for the subjects for which prediction of survival probabilities is required.

cnewdata

a data frame that contains the survival and covariate information for the subjects for which prediction of survival probabilities is required.

u

a numeric vector of times for which prediction survival probabilities are to be computed.

Last.time

a numeric vector or character string. This specifies the known time at which each of the subjects in cnewdata was known to be alive. If NULL, then this is automatically taken as the survival time of each subject. If a numeric vector, then it is assumed to be greater than or equals to the last available longitudinal time point for each subject. If a character string, then it should be a variable in cnewdata.

obs.time

a character string of specifying a longitudinal time variable in ynewdata.

method

a character string specifying the type of probability approximation; if Laplace, then a first order estimator is computed. If GH, then the standard Gauss-Hermite quadrature is used instead.

quadpoint

number of quadrature points used for estimating conditional probabilities when method = "GH". Default is NULL. If method = "GH", then 15 is used.

...

further arguments passed to or from other methods.

Value

a list of matrices with conditional probabilities for subjects.

Author(s)

Shanpeng Li lishanpeng0913@ucla.edu

See Also

JMMLSM

Variance-covariance matrix of the estimated parameters for joint models

Description

Extract variance-covariance matrix for joint models.

Usage

## S3 method for class 'JMMLSM'
vcov(object, ...)

Arguments

object

an object inheriting from class JMMLSM.

...

further arguments passed to or from other methods.

Value

a matrix of variance covariance of all parameter estimates.

Author(s)

Shanpeng Li lishanpeng0913@ucla.edu

See Also

JMMLSM

Simulated longitudinal data

Description

The ydata data frame has 1353 rows and 6 columns.

Usage

data(ydata)

Format

This data frame contains the following columns:

ID

patient identifier.

Y

response variable.

time

visit time.

Z1

treatment indicator. 0 denotes the placebo group and 1 the treatment group.

Z2

continuous variable..

Z3

continuous variable..