onestage2: One stage jointmeta1 fit and bootstrapped standard errors
In joineRmeta: Joint Modelling for Meta-Analytic (Multi-Study) Data

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

onestage2

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 ith individual in the kth study at the jth 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)

jointmeta1, jointmetaSE

joineRmeta documentation built on Jan. 24, 2020, 5:10 p.m.