`gmvjoint`

`gmvjoint`

?- “
**g**eneralised” **m**ulti**v**ariate**Joint**models.

`gmvjoint`

allows the user to fit joint models of survival
and multivariate longitudinal data, where the longitudinal sub-models
are specified by generalised linear mixed models (GLMMs). The joint
models are fit via maximum likelihood using an approximate EM algorithm
first proposed by Bernhardt *et al*. (2015). The GLMMs are
specified using the same syntax as for package `glmmTMB`

(Brooks *et al*., 2017). The joint models themselves are then the
flexible extensions to those in e.g. Wulfsohn and Tsiatis (1997). The
user is able to simulate data under many different response types.

Currently, six families can be fit: Gaussian; Poisson; binomial; Gamma; negative binomial; and generalised Poisson.

You can install the latest ‘official’ release from CRAN in the usual way:

`install.packages('gmvjoint')`

or the latest development version using `devtools`

:

`::install_github('jamesmurray7/gmvjoint') devtools`

MacOS users may be interested in swapping
their BLAS library to one which provides an optimal BLAS
implementation for Mac hardware (`vecLib`

).

To fit a joint model, we first need to specify the longitudinal and survival sub-models.

The longitudinal sub-model **must** be a list which
contains the specification of the longitudinal process along with its
random effects structure in the same syntax as a glmmTMB model
(which itself is the same as the widely-used `lme4`

). As an
example, suppose we want to fit a trivariate model on the oft-used PBC
data, with a linear time-drug interaction term on albumin, a spline term
on (logged) serum bilirubin and a linear fit on spiders, we specify

```
data(PBC)
<- subset(PBC, select = c('id', 'survtime', 'status', 'drug', 'time',
PBC 'serBilir', 'albumin', 'spiders'))
<- na.omit(PBC)
PBC <- list(
long.formulas ~ drug * time + (1 + time|id),
albumin log(serBilir) ~ drug * splines::ns(time, 3) + (1 + splines::ns(time, 3)|id),
~ drug * time + (1|id)
spiders )
```

where we note interactions and spline-time fits are possible.

The survival sub-model must be set-up using `Surv()`

from
the survival
package e.g.

`<- Surv(survtime, status) ~ drug surv.formula `

Currently interaction terms in the survival sub-model specification are unsupported.

Now we can do the joint model call through the main workhorse
function `joint`

. This notably take a *list* of family
arguments which **must** match-up in the desired order as
the longitudinal process list. We then fit our joint model via

```
<- joint(long.formulas = long.formulas, surv.formula = surv.formula, data = PBC,
fit family = list("gaussian", "gaussian", "binomial"))
summary(fit)
```

where extra control arguments are documented in `?joint`

.
For certain families, we could additionally supply
`disp.formulas`

which specify the dispersion model for the
corresponding longitudinal process. Numerous S3 methods exist for the
class of object `joint`

creates: `summary()`

,
`logLik()`

, `fixef()`

, `ranef()`

,
`fitted()`

, `resid()`

, and `vcov()`

.
LaTeX-ready tables can also be generated by S3 method
`xtable()`

. Data can be simulated under a host of different
parameter set-ups using the `simData()`

function.

We bridge from a set of joint model parameter estimates to a
prognostic one by dynamic predictions `dynPred`

. We can
assess discriminatory capabilities of the `joint()`

model fit
by the `ROC`

function, too.

Currently the largest limitation exists with the relatively strict
data structure necessary and the corresponding calls to the
`joint`

function. The below lists these (known) limitations
and plans for relaxing.

- Longitudinal information: The longitudinal time argument
**must**be named`time`

and the subject identifier (which we ‘split’ random effects by)`id`

. Unsure if I will ever change these; I think a little more user pre-processing is no bad thing, when alternative would be a more crowded call to`joint`

, which I wouldn’t be a fan of. - Misc.: data must be balanced (i.e. no
`NA`

values); this will be fixed in a future update. For now I don’t think this is the biggest issue, and recommend using`na.omit`

for example. Additionally, the id variable**must**increment by no more than one. That is,`data$id=1,1,1,2,2,2,3,3,3`

is fine, but`data$id=1,1,1,1,3,3,3,4,4`

is not. This is due to how data matrices are created internally and will be fixed in the future.

Update June 2023: Since calls and data are passed straight to`glmmTB`

, possible to assign these unique indices`1:n`

, nothing currently done with this, though. - Pretty-ing of progress bars using cli package (maybe…).

Note I’m a PhD student, and the S3 methods (and some functions themselves) have largely arisen out of things I needed, or thought would be a good idea at some point!

Bernhardt PW, Zhang D and Wang HJ. A fast EM Algorithm for Fitting
Joint Models of a Binary Response to Multiple Longitudinal Covariates
Subject to Detection Limits. *Computational Statistics and Data
Analysis* 2015; **85**; 37–53

Mollie E. Brooks, Kasper Kristensen, Koen J. van Benthem, Arni
Magnusson, Casper W. Berg, Anders Nielsen, Hans J. Skaug, Martin
Maechler and Benjamin M. Bolker (2017). glmmTMB Balances Speed and
Flexibility Among Packages for Zero-inflated Generalized Linear Mixed
Modeling. *The R Journal*, **9(2)**, 378-400.

Murray, J and Philipson P. A fast approximate EM algorithm for joint
models of survival and multivariate longitudinal data. *Computational
Statistics and Data Analysis* 2022

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