Description Usage Format Details See Also

A dataset containing a list of the model fits for joint models fitted to the
data the first three studies in the `simdat2`

dataset using the JM
package. Further details of model fits supplied below.

1 |

A list of 3 `jointModel`

objects, the result of fitting a joint
model using the JM package to the data from the first three studies in the
`simdat2`

dataset in turn.

These are the results of fitting a joint model using the `JM`

package separately to the data from the first three studies present in the
`simdat2`

dataset. This data has three levels, namely the longitudinal
measurements at level 1, nested within individuals (level 2) who are
themselves nested within studies (level 3). The joint models fitted to each
study's data had the same format. The longitudinal sub-model contained a
fixed intercept, time and treatment assignment term, as well as a fixed
time by treatment assignment interaction term, and random intercept and
slope. The survival sub-model contained a fixed treatment assignment term.
The sub-models were linked by inserting both the current value of the
longitudinal trajectory and its first derivative with respect to time into
the survival sub-model. More formally, the longitudinal sub-model had the
following format:

*Y_{kij} = β_{10} + β_{11}time + β_{12}treat +
β_{13}time*treat+ b^{(2)}_{0ki} + b^{(2)}_{1ki}time + ε_{kij}*

Where *Y* represents the continuous longitudinal outcome, fixed effect
coefficients are represented by *β*, random effects coefficients by
*b* and the measurement error by *ε*. For the random
effects the superscript of 2 indicates that these are individual level, or
level 2 random effects. This means they take can take a unique value for
each individual in the dataset. The longitudinal time variable is
represented by *time*, and the treatment assignment variable (a binary
factor) is represented by *treat*.

The survival sub-model had format:

*λ_{ki}(t) = λ_{0}(t)exp(β_{21}treat +
α_{1}(β_{10} + β_{11}time + β_{12}treat + +
β_{13}time*treat b^{(2)}_{0ki} + b^{(2)}_{1ki}time)+
α_{2}(β_{11} + β_{13}treat + b^{(2)}_{1ki})) *

In the above equation, *λ_{ki}(t)* represents the survival time
of the individual *i* in study *k*, and *λ_{0}(t)*
represents the baseline hazard, which was modelled using splines. The fixed
effect coefficient is represented by *β_{21}*. Association
parameters representing the link between the sub-models are represented by
*α* terms, where *α_{1}* represents the effect of the
current value of the longitudinal outcome on the risk of an event, whilst
*α_{2}* represents the effect of the slope, or rate of change of
the longitudinal trajectory (the value of the first derivative of the
longitudinal trajectory with respect to time) on the risk of an event.
Again *treat* represents the binary facator treatment assignment
variable, and *b^{(2)}_{0ki}* and *b^{(2)}_{1ki}* are the zero mean
random effects from the longitudinal sub-model.

We differentiate between the fixed effect coefficients in the longitudinal and the survival sub-models by varying the first number present in the subscript of the fixed effect, which takes a 1 for coefficients from the longitudinal sub-model and a 2 for coefficients from the survival sub-model.

These fits have been provided in this package for use with the package vignette, see the vignette for more information.

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