# Joint Modelling of Multivariate Longitudinal Data and Time-to-Event Outcomes

Fits the joint model proposed by Henderson and colleagues (2000) , but extended to the case of multiple continuous longitudinal measures. The time-to-event data is modelled using a Cox proportional hazards regression model with time-varying covariates. The multiple longitudinal outcomes are modelled using a multivariate version of the Laird and Ware linear mixed model. The association is captured by a multivariate latent Gaussian process. The model is estimated using a Monte Carlo Expectation Maximization algorithm. This project was funded by the Medical Research Council (Grant number MR/M013227/1).

`joineRML` is an extension of the joineR package for fitting joint models of time-to-event data and multivariate longitudinal data. The model fitted in joineRML is an extension of the Wulfsohn and Tsiatis (1997) and Henderson et al. (2000) models, which is comprised of (K + 1)-sub-models: a Cox proportional hazards regression model (Cox, 1972) and a K-variate linear mixed-effects model - a direct extension of the Laird and Ware (1982) regression model. The model is fitted using a Monte Carlo Expectation-Maximization (MCEM) algorithm, which closely follows the methodology presented by Lin et al. (2002).

## Why use joineRML?

As noted in Hickey et al. (2016), there is a lack of statistical software available for fitting joint models to multivariate longitudinal data. This is contrary to a growing methodology in the statistical literature. `joineRML` is intended to fill this void.

# Example

The main workhorse function is `mjoint`. As a simple example, we use the `heart.valve` dataset from the package and fit a bivariate joint model.

The fitted model is assigned to `fit`. We can apply a number of functions to this object, e.g. `coef`, `logLik`, `plot`, `print`, `ranef`, `fixef`, `summary`, `AIC`, `getVarCov`, `vcov`, `confint`, `sigma`, `update`, `formula`, `resid`, and `fitted`. In addition, several special functions have been added, including `dynSurv`, `dynLong`, and `baseHaz`, as well as plotting functions for objects inheriting from the `dynSurv`, `dynLong`, `ranef`, and `mjoint` functions. For example,

`mjoint` automatically estimates approximate standard errors using the empirical information matrix (Lin et al., 2002), but the `bootSE` function can be used as an alternative.

If you spot any errors or wish to see a new feature added, please file an issue at https://github.com/graemeleehickey/joineRML/issues or email Graeme Hickey.

# Further learning

For an overview of the model estimation being performed, please see the technical vignette, which can be accessed by

For a demonstration of the package, please see the introductory vignette, which can be accessed by

# Funding

This project is funded by the Medical Research Council (Grant number MR/M013227/1).

# Using the latest developmental version

To install the latest developmental version, you will need R version (version 3.3.0 or higher) and some additional software depending on what platform you are using.

## Windows

If not already installed, you will need to install Rtools. Choose the version that corresponds to the version of R that you are using.

## Mac OSX

If not already installed, you will need to install Xcode Command Line Tools. To do this, open a new terminal and run

## From R

The latest developmental version will not yet be available on CRAN. Therefore, to install it, you will need `devtools`. You can check you are using the correct version by running

Once the prerequisite software is installed, you can install `joineRML` by running the following command in an R console

# 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. Lin H, McCulloch CE, Mayne ST. Maximum likelihood estimation in the joint analysis of time-to-event and multiple longitudinal variables. Stat Med. 2002; 21: 2369-2382.

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

# joineRML 0.4.2

## Bug patches

• Fixed issue with citation date due to DATE not being present in the DESCRIPTION file.

## Housekeeping

• Added ORCID IDs for authors.

• Remove unused objects once finished with them to try and reduce memory overheads.

• Changed maintainer to Pete Philipson.

# joineRML 0.4.1

## New features

• Added smoothed predicted survival curves to the `plot.dynSuv()`. Smoothing is based on the contrainsed B-splines method.

• `dynSurv()` now includes an argument to specify a horizon time from the last known observation time.

• `simData()` now includes an argument to choose multivariate t-distributed random effects with varying degrees of freedom, thus allowing for sensitivity analyses of heavier tail distributions.

## Housekeeping

• Minor corrections to documentation.

• Minor bug fixes to plotting functions.

• Added MRC to DESCRIPTION as funder.

# joineRML 0.4.0

## New features

• The MCEM algorithm can be implemented with vanilla Monte Carlo and quasi-Monte Carlo (using either the scrambled Sobol sequence or the Halton sequence). This is implemented through the `type` argument passed to the list of `control` parameters in `mjoint()`.

• `bootSE()` now has option to use parallel computing via the `foreach` package.

## Bug patches

• Fixed some small errors in the `epileptic.qol` dataset.

• Fixed situation where a tibble might be given as the dataset (#55 @ellessenne).

• Catches errors in bootstrap due to "bad" data and automatically restarts the bootstrap (#57 @ellessenne)

## Housekeeping

• Moved the make files and raw data for `qol` and `renal` datasets into the `~/data-raw/` directory.

• Added @ellessenne as package contributor for testing and bug corrections (PRs #55 and #57).

# joineRML 0.3.0

## New features

• Added new functions `dynSurv()` and `dynLong()`, which generates survival probabilities and xpected longitudinal predictions, respectively, for a new subject conditional on their last measurement time and longitudial history. Prediction can be implemented using either a first order approximation or a Monte Carlo simulation approach.

• Added an associated `print()` method for `dynSurv` and `dynLong` objects.

• Added an associated `plot()` method for `dynSurv` and `dynLong` objects.

• Added a function `baseHaz()` for extracting the centered and uncetered estimates of the baseline hazard function.

• `print()` and `summary()` now report the total computation time in addition to just the EM algorithm time. This was deemed useful after some examples showed that the time to get initial values was more expensive than the time for the MCEM algorithm to converge.

## Bug patches

• Fixed a bug that prevented models being fitted with no covariates in the survival sub-model, i.e. `Surv() ~ 1`.

• Correction to the vignette description of `mjoint()` arguments.

• Removed `enumintem` package for Sweave vignette to satisfy CRAN checks on macOS (release).

## Housekeeping

• Updated `Makevars` and `Markvars.win` to allow for OpenMP, which can be used by RcppArmadillo.

• Minor tidy-up of in-code comments.

• Minor updates and corrections to documentation.

• Added unit tests for new features.

# joineRML 0.2.2

• This update is an attempt to overcome a FAIL status on the CRAN checks for macOS.

## Housekeeping

• Changed the technical vignette to Rnw (with engine = Sweave) from ltx (with engine = R.rsp) in attempt to remove some CMD check warnings.

• Shortened the vignette to make it compile quicker (removed execution of bootstrapping).

• Lots of tweaks of minor formatting tweaks in the documentation.

# joineRML 0.2.1

## Bug patches

• Fixed a bug that prevented factors with >2 levels being included in the time-to-event sub-model.

• Fixed package registration, which strangely broke on R 3.4.0 for OSX platform.

## Housekeeping

• `joineRML` version 0.2.1 will depend on R version >=3.3.0 to remedy issue with `sigma.mjoint()` S3 issue.

# joineRML 0.2.0

## New features

• Add `residual()` and `fitted()` functions for `mjoint` objects.

• Added a plot function -- `plot.ranef.mjoint()` -- for `ranef.mjoint` objects.

• `bootSE()` now uses control parameters from fitted model and allows for individual parameter overwrite.

• Added a check that any initial covariance matrix given is positive-definite.

• Added a check that dimensions of any `inits` given match the calculated dimensions from the model formulae.

• Added a check that if multiple repeated longitudinal outcoems were given, that each subject contributes at least one measurement per outcome.

• Changed the API so that `postRE` and `approx.se` arguments are now replaced by a single `pfs` argument, which stands for post fit statistics. If `TRUE`, then both the approximate SEs and the BLUPs (and SEs) are calculated and returned. This change is to facilitate other post fit statistics, e.g. residuals.

• `sampleData()` now allows for sampling without replacement.

• `plot()` and `plotConvergence()` now have the option to discard burn-in phase iterations from the MCEM algorithm.

• `plot()` and `plotConvergence()` now plot the log-likelihood trace.

• `vcov()` now calculates the variance-covariance matrix rather than inside `mjoint()` and then extracting it. It also utilises the QR-decomposition inverse function and the Moore-Penrose matrix inverse, as in some cases the matrix was nearly singular.

• `hessian()` (and therefore `vcov()`) now calculate the contribution for the random effect variance terms rather than the random effect precision (1 divided by the variance) terms. The correct contribution to the score for off-diagonal terms is now also impleted.

• The left-hand side of the `formLongFixed` now handles transformations.

## Bug patches

• `vcov()` now returns the variance-covariance matrix as intended. Previously it was only returning the profile empirical information matrix.

• Patched a major bug in `gammaUpdate()` where ties in failure times were not being properly handled. The code for `gammaUpdate_approx()` always worked fine, as it was based only on the score vector. This bug manifested when `bootSE()` was called due to the resampling with replacement yielding datasets with many more ties than in the original dataset used to fit the model. To fix it, the information matrix required scaling at each failure time by the number of failures in the data. The formula for the information matrix in the Technical Details vignette has also been updated.

• Patched a minor bug with prevented univariate random-intercept models for being fitted.

• Patched a minor bug in plotting convergence traces.

• Patched a minor bug with bootstrapping univariate joint models without passing the MLEs as the initial values to the `mjoint()` call.

## Housekeeping

• Renamed `approxSE()` function to `hessian()`.

• Renamed `control` argument `earlyPhase` to `burnin`.

• Default settings for `control` parameters updated based on practical experience.

• Package now `Depends` on `survival` and `nlme` rather than `Imports` to allow `require()` statements to be removed from code.

• Prevented `roxygen` from exporting all functions.

• Fixed Imports following CRAN Checks of v0.1.1.

• Minor documentation edits and corrections.

• Minor code tidy-up with slight speed-ups and stabilisations where found.

• LICENSE upgraded to GPL-3 to be compatible with `joineR` v1.1.0.

• Removed internal function `fast_nearPD()` from package code as was unused.

• Removed internal function `EexpArma()` from package code as was unused.

• Registered native C++ routines and disabled symbol search to satisfy CRAN CMD checks.

# joineRML 0.1.1

• Patched sigma.R roxygen documentation to handle sigma S3 method changing from lme4 to stats in R v3.3.0.

# joineRML 0.1.0

• First package release.

# Reference manual

install.packages("joineRML")

0.4.5 by Graeme L. Hickey, 3 months ago

https://github.com/graemeleehickey/joineRML

Report a bug at https://github.com/graemeleehickey/joineRML/issues

Browse source code at https://github.com/cran/joineRML

Authors: Graeme L. Hickey [cre, aut] , Pete Philipson [aut] , Andrea Jorgensen [ctb] , Ruwanthi Kolamunnage-Dona [aut] , Paula Williamson [ctb] , Dimitris Rizopoulos [ctb, dtc] (data/renal.rda , R/hessian.R , R/vcov.R) , Alessandro Gasparini [aut] , Medical Research Council [fnd] (Grant number: MR/M013227/1)

Documentation:   PDF Manual