Description Usage Format Details See Also

A list of length two containing a one stage jointmeta1 fit and corresponding bootstrapped standard errors.

1 |

A list of 2 objects:

`onestagefit2`

an object of class

`jointmeta1`

`onestagefit2SE`

an object of class

`jointmeta1SE`

These are the results of using the `jointmeta1`

function to fit
a one stage joint meta model for multi-study data, and also the bootstrap
results of applying the `jointmetaSE`

function to the resulting model
fit. The data used is the `simdat2`

data available in the
`joineRmeta`

package. 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 format of this model is as follows. The structure of the longitudinal sub-model is:

*Y_{kij} = β_{10} + β_{11}time + β_{12}treat +
b^{(2)}_{0ki} + b^{(2)}_{1ki}time + b^{(3)}_{0k} + b^{(3)}_{1k}treat +
ε_{kij}*

Where *Y_{kij}* represents the continuous longitudinal outcome for the
*i*th individual in the *k*th study at the *j*th time point,
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 individual level, or
level 2 random effects. This means they take can take a unique value for
each individual in the dataset. A superscript of 3 indicates study level
random effects, or level 3 random effects. This means that they can take a
unique value for each study 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^{(2)}(b^{(2)}_{0ki} + b^{(2)}_{1ki}time) + α^{(3)}(b^{(2)}_{0k}
+ b^{(3)}_{1k}treat)) *

In the above equation, *λ_{ki}(t)* represents the survival time
of the individual *i* in study *k*, and *λ_{0}(t)*
represents the unspecified baseline hazard. This baseline was not
stratified by study. The fixed effect coefficients are represented by
*β* terms. A proportional random effects only association
structure links the sub-models, with *α^{(2)}* representing the
association between the longitudinal and survival outcomes attributable to
the deviation of the individual in question from the population mean
longitudinal trajectory, and *α^{(3)}* representing the
association between the longitudinal and survival outcomes attributable to
the deviation

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.

This model accounts for between study heterogeneity using study level random effects.

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

The code used to fit this one stage model was:

```
onestagefit2<-jointmeta1(data = jointdat, long.formula = Y ~ 1 +
time + treat, long.rand.ind = c('int', 'time'), long.rand.stud = c('study',
'treat'), sharingstrct = 'randprop', surv.formula = Surv(survtime, cens) ~
treat, study.name = 'study', strat = F)
```

And the code used to bootstrap the model was:

` onestagefit2SE<-jointmetaSE(fitted = onestagefit2, n.boot = 200) `

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