Joint Modelling of Repeated Measurements and Time-to-Event Data.

joineR

The joineR package implements methods for analyzing data from longitudinal studies in which the response from each subject consists of a time-sequence of repeated measurements and a possibly censored time-to-event outcome. The modelling framework for the repeated measurements is the linear model with random effects and/or correlated error structure (Laird and Ware, 1982). The model for the time-to-event outcome is a Cox proportional hazards model with log-Gaussian frailty (Cox, 1972). Stochastic dependence is captured by allowing the Gaussian random effects of the linear model to be correlated with the frailty term of the Cox proportional hazards model. The methodology used to fit the model is described in Henderson et al. (2002) and Wulfsohn and Tsiatis (1997).

The joineR package also allows competing risks data to be jointly modelled through a cause-specific hazards model. The importance of accounting for competing risks is detailed in Williamson et al. (2007a,b). The methodology used to fit this model is described in Williamson et al. (2008).

Example

The joineR package comes with several data sets including one the describes the survival of patients who underwent aortic valve replacement surgery. The patients were routinely followed up in clinic, where the left ventricular mass index (LVMI) was calculated. To fit a joint model, we must first create a jointdata object, which holds the survival, longitudinal, and baseline covariate data, along with the names of the columns that identify the patient identifiers and repeated time outcomes.

library(joineR)
#> Loading required package: survival
data(heart.valve)
heart.surv <- UniqueVariables(heart.valve, 
                              var.col = c("fuyrs", "status"),
                              id.col = "num")
heart.long <- heart.valve[, c("num", "time", "log.lvmi")]
heart.cov <- UniqueVariables(heart.valve, 
                             c("age", "hs", "sex"), 
                             id.col = "num")
heart.valve.jd <- jointdata(longitudinal = heart.long, 
                            baseline = heart.cov, 
                            survival = heart.surv, 
                            id.col = "num", 
                            time.col = "time")

With the creation of the heart.valve.jd object, we can fit a joint model using the joint function. For this, we need 4 arguments:

• jointdata: the data object we created above
• long.formula: the linear mixed effects model formula for the longitudinal sub-model
• surv.formula: the survival formula the survival sub-model
• model: the latent association structure.

fit <- joint(data = heart.valve.jd, 
             long.formula = log.lvmi ~ 1 + time + hs, 
             surv.formula = Surv(fuyrs, status) ~ hs, 
             model = "intslope")

summary(fit)
#> 
#> Call:
#> joint(data = heart.valve.jd, long.formula = log.lvmi ~ 1 + time + 
#>     hs, surv.formula = Surv(fuyrs, status) ~ hs, model = "intslope")
#> 
#> Random effects joint model
#>  Data: heart.valve.jd 
#>  Log-likelihood: -424.7084 
#> 
#> Longitudinal sub-model fixed effects: log.lvmi ~ 1 + time + hs                              
#> (Intercept)        4.993080959
#> time              -0.007045486
#> hsStentless valve  0.055831384
#> 
#> Survival sub-model fixed effects: Surv(fuyrs, status) ~ hs                           
#> hsStentless valve 0.7934551
#> 
#> Latent association:                 
#> gamma_0 0.8211701
#> 
#> Variance components:
#>         U_0         U_1    Residual 
#> 0.113577498 0.001766164 0.037071195 
#> 
#> Convergence at iteration: 9 
#> 
#> Number of observations: 988 
#> Number of groups: 256

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 ease and speed in fitting the models.

Multivariate data

joineR only models a single repeated measurement and a single event time. If multiple longitudinal outcomes are available (see Hickey et al., 2016), a separate package is available: joineRML.

Funding

This project was funded by the Medical Research Council (Grant numbers G0400615 and MR/M013227/1).

Using the latest developmental version

To install the latest developmental version, you will need the R package devtools and to run the following code

library('devtools')
install_github('graemeleehickey/joineR', build_vignettes = FALSE)

References

1. Cox DR. Regression models and life-tables. J R Stat Soc Ser B Stat Methodol. 1972; 34(2): 187-220.

2. Henderson R, Diggle PJ, Dobson A. Joint modelling of longitudinal measurements and event time data. Biostatistics. 2000; 1(4): 465-480.

3. Hickey GL, Philipson P, Jorgensen A, Kolamunnage-Dona R. Joint modelling of time-to-event and multivariate longitudinal outcomes: recent developments and issues. BMC Med Res Methodol. 2016; 16(1): 117.

4. Laird NM, Ware JH. Random-effects models for longitudinal data. Biometrics. 1982; 38(4): 963-974.

5. Williamson PR, Kolamunnage-Dona R, Tudur-Smith C. The influence of competing-risks setting on the choice of hypothesis test for treatment effect. Biostatistics. 2007; 8(4): 689–694.

6. Williamson PR., Tudur-Smith C, Sander JW, Marson AG. Importance of competing risks in the analysis of anti-epileptic drug failure. Trials. 2007; 8: 12.

7. Williamson PR, Kolamunnage-Dona R, Philipson P, Marson AG. Joint modelling of longitudinal and competing risks data. Stat Med. 2008; 27: 6426–6438.

8. Wulfsohn MS, Tsiatis AA. A joint model for survival and longitudinal data measured with error. Biometrics. 1997; 53(1): 330-339.