Fits joint models of the type proposed by Henderson and colleagues
joineRmeta package implements methods to analyse multi-study joint data consisting of a single continuous longitudinal outcome, and a single possible censored time-to-event outcome. The modelling framework for the longitudinal data is a linear mixed effects model (Laird and Ware, 1982). The modelling framework for the time-to-event outcome is a Cox proportional hazards model with an unspecified baseline hazard (Cox, 1972). The longitudinal and time-to-event sub-model are linked through an association structure. Currently only the random effects only proportional association is available (see Gould et al, 2015). The methodology used to fit the model is described in Henderson et al (2000) and Wulfsohn and Tsiatis (1997).
joineRmeta package contains methods to perform the second stage of a two stage meta-analysis (MA) of study specific joint modelling fits, and one stage MA of multi-study joint data where between study heterogeneity can be accounted for using interaction terms with study membership variables, study level random effects, or baseline hazard stratified by study. The package also contains plotting and simulation functions.
joineRmeta package contains several simulated datasets. One of these is
simdat which contains data from 5 studies, each containing 500 simulated individuals. This data first must be transformed into a joint data object
library(joineRmeta)data(simdat)jointdat<-tojointdata(longitudinal = simdat$longitudinal,survival = simdat$survival, id = "id", longoutcome = "Y",timevarying = c("time","ltime"), survtime = "survtime", cens = "cens",time = "time")jointdat$baseline$study <- as.factor(jointdat$baseline$study)jointdat$baseline$treat <- as.factor(jointdat$baseline$treat)
Using the data held in the
jointdat we can then fit a one stage multi-study joint model.
data: the data object we created above
long.formula: the linear mixed effects model formula for the longitudinal sub-model
long.rand.ind: vector of character strings denoting variables to assign individual level random effects to
long.rand.stud: vector of character strings denoting variables to assign study level random effects to
sharingstrct: the association structure linking the sub-models - currently this must be set to
surv.formula: the survival formula the survival sub-model.
study.name: character string denoting the variable name of the study membership variable.
strat: logical value denoting whether or not the baseline hazard is to be stratified by study.
fit <- jointmeta1(data = jointdat,long.formula = Y ~ 1 + time + treat,long.rand.ind = c("int", "time"),long.rand.stud = "treat",sharingstrct = "randprop",surv.formula = Surv(survtime, cens) ~ treat,study.name = "study",strat = T)
Full details on the data and the functions are provided in the help documentation and package vignette. The purpose of this code is to simply illustrate the model fitting.
This work was supported by the Health eResearch Centre (HeRC) funded by the Medical Research Council Grant MR/K006665/1.
To install the latest developmental version, you will need the R package
devtools and to run the following code
library('devtools')install_github('mesudell/joineRmeta', build_vignettes = FALSE)
Cox DR. Regression models and life-tables. J R Stat Soc Ser B Stat Methodol. 1972; 34(2): 187-220.
Gould LA, Boye M, Bois F, et al. Joint modeling of survival and longitudinal non-survival data: current methods and issues. Report of the DIA Bayesian joint modeling working group. Stat Med. 2015; 34(14): 2181-2195.
Henderson R, Diggle PJ, Dobson A. Joint modelling of longitudinal measurements and event time data. Biostatistics. 2000; 1(4): 465-480.
Laird NM, Ware JH. Random-effects models for longitudinal data. Biometrics. 1982; 38(4): 963-974.
Wulfsohn MS, Tsiatis AA. A joint model for survival and longitudinal data measured with error. Biometrics. 1997; 53(1): 330-339.