R/data.R
In mesudell/joineRmeta: Joint Modelling for Meta-Analytic (Multi-Study) Data
#' Simulated joint longitudinal and survival dataset containing 5 studies
#'
#' A simulated dataset containing a single continuous longitudinal outcome and a
#' single survival outcome, with data available from 5 studies.
#'
#' @format A list of three objects: \describe{ \item{\code{longitudinal}}{A list
#' of long format longitudinal datasets one for each of the 5 studies included
#' in the dataset. Each of these datasets contains the following variables:
#' \describe{ \item{\code{id}}{long version of the id variable for the data.
#' Identical ids between the longitudinal and the survival datasets identify
#' the same individual} \item{\code{Y}}{a continuous longitudinal outcome}
#' \item{\code{time}}{the longitudinal time variable} \item{\code{study}}{a
#' long version of the study membership indicator} \item{\code{intercept}}{a
#' long version of the intercept, always takes a value of 1}
#' \item{\code{treat}}{a long version of the binary treatment group indicator}
#' \item{\code{ltime}}{a duplicate of the longitudinal time variable,
#' duplicated as part of the longitudinal data simulation process} }}
#'
#' \item{\code{survival}}{A list of survival datasets, one for each of the 5
#' studies included in the dataset. Each of these datasets contains the
#' following variables: \describe{ \item{\code{id}}{the id variable for the
#' data. Identical ids between the longitudinal and the survival datasets
#' identify the same individual} \item{\code{survtime}}{the survival time for
#' each individual at which they experienced the event or were censored. This
#' is on the same scale as the longitudinal time measurements.}
#' \item{\code{cens}}{censoring indicator for the survival data where 1
#' indicates an event and 0 indicates censoring} \item{\code{study}}{study
#' membership indicator} \item{\code{treat}}{binary treatment group indicator}
#' }}
#'
#' \item{\code{percentevent}}{A list of the percentage of events experienced
#' in each datasets. The first element contains the percentage of events
#' observed for the first simulated study and so on.} }
#'
#' @details This is a simulated dataset generated using the
#' \code{\link{simjointmeta}} function using the following function call:
#'
#' \code{ simdat<-simjointmeta(k = 5, n = rep(500, 5), sepassoc = FALSE, ntms
#' = 5, longmeasuretimes = c(0, 1, 2, 3, 4), beta1 = c(1, 2, 3), beta2 = 3,
#' rand_ind = 'intslope', rand_stud = 'inttreat', gamma_ind = 1, gamma_stud =
#' 1, sigb_ind = matrix(c(1,0.5,0.5,1.5),nrow=2), sigb_stud =
#' matrix(c(1,0.5,0.5,1.5),nrow=2), vare = 0.01, theta0 = -3, theta1 = 1,
#' censoring = TRUE, censlam = exp(-3), truncation = TRUE, trunctime = 6) }
#'
#' Note that this will not give you identical data to that held in
#' \code{simdat} due to the differences in starting seed.
#'
#' @seealso \code{\link{simjointmeta}}
#'
"simdat"
#' Simulated joint longitudinal and survival dataset containing 3 studies
#'
#' A simulated dataset containing a single continuous longitudinal outcome and a
#' single survival outcome, with data available from 3 studies.
#'
#' @format A list of three objects: \describe{ \item{\code{longitudinal}}{A list
#' of long format longitudinal datasets one for each of the 3 studies included
#' in the dataset. Each of these datasets contains the following variables:
#' \describe{ \item{\code{id}}{long version of the id variable for the data.
#' Identical ids between the longitudinal and the survival datasets identify
#' the same individual} \item{\code{Y}}{a continuous longitudinal outcome}
#' \item{\code{time}}{the longitudinal time variable} \item{\code{study}}{a
#' long version of the study membership indicator} \item{\code{intercept}}{a
#' long version of the intercept, always takes a value of 1}
#' \item{\code{treat}}{a long version of the binary treatment group indicator}
#' \item{\code{ltime}}{a duplicate of the longitudinal time variable,
#' duplicated as part of the longitudinal data simulation process} }}
#'
#' \item{\code{survival}}{A list of survival datasets, one for each of the 5
#' studies included in the dataset. Each of these datasets contains the
#' following variables: \describe{ \item{\code{id}}{the id variable for the
#' data. Identical ids between the longitudinal and the survival datasets
#' identify the same individual} \item{\code{survtime}}{the survival time for
#' each individual at which they experienced the event or were censored. This
#' is on the same scale as the longitudinal time measurements.}
#' \item{\code{cens}}{censoring indicator for the survival data where 1
#' indicates an event and 0 indicates censoring} \item{\code{study}}{study
#' membership indicator} \item{\code{treat}}{binary treatment group indicator}
#' }}
#'
#' \item{\code{percentevent}}{A list of the percentage of events experienced
#' in each datasets. The first element contains the percentage of events
#' observed for the first simulated study and so on.} }
#'
#' @details This is a simulated dataset generated by subsetting the \code{simdat}
#' dataset to leave only three studies with 100 individuals in each study.
#' This dataset is for demonstration purposes only within the package.
#'
#' @seealso \code{\link{simjointmeta}}
#'
"simdat2"
#' Simulated joint longitudinal and survival dataset containing 5 studies
#'
#' A simulated dataset containing a single continuous longitudinal outcome and a
#' single survival outcome, with data available from 5 studies. This dataset
#' does not have longitudinal measurements capped at each individual's survival
#' time.
#'
#' @format A list of three objects: \describe{ \item{\code{longitudinal}}{A list
#' of long format longitudinal datasets one for each of the 5 studies included
#' in the dataset. Each of these datasets contains the following variables:
#' \describe{ \item{\code{id}}{long version of the id variable for the data.
#' Identical ids between the longitudinal and the survival datasets identify
#' the same individual} \item{\code{Y}}{a continuous longitudinal outcome}
#' \item{\code{time}}{the longitudinal time variable} \item{\code{study}}{a
#' long version of the study membership indicator} \item{\code{intercept}}{a
#' long version of the intercept, always takes a value of 1}
#' \item{\code{treat}}{a long version of the binary treatment group indicator}
#' \item{\code{ltime}}{a duplicate of the longitudinal time variable,
#' duplicated as part of the longitudinal data simulation process} }}
#'
#' \item{\code{survival}}{A list of survival datasets, one for each of the 5
#' studies included in the dataset. Each of these datasets contains the
#' following variables: \describe{ \item{\code{id}}{the id variable for the
#' data. Identical ids between the longitudinal and the survival datasets
#' identify the same individual} \item{\code{survtime}}{the survival time for
#' each individual at which they experienced the event or were censored. This
#' is on the same scale as the longitudinal time measurements.}
#' \item{\code{cens}}{censoring indicator for the survival data where 1
#' indicates an event and 0 indicates censoring} \item{\code{study}}{study
#' membership indicator} \item{\code{treat}}{binary treatment group indicator}
#' }}
#'
#' \item{\code{percentevent}}{A list of the percentage of events experienced
#' in each datasets. The first element contains the percentage of events
#' observed for the first simulated study and so on.} }
#'
#' @details This is a simulated dataset generated in order to show how the
#' function \code{\link{removeafter}} works, as it does not cap longitudinal
#' outcomes at each individual's survival time. This data was generated by
#' manually stepping through the code available in simjointmeta and retaining
#' instead of discarding any simulated longitudinal measurements recorded
#' after the individual in question's survival time.
#'
#' @seealso \code{\link{simjointmeta}}, \code{\link{removeafter}}
#'
"simdat3"
#' Study specific joint model fits using the joineR package
#'
#' A dataset containing a list of the model fits for joint models fitted to the
#' data for each study in the \code{simdat2} dataset using the joineR package.
#' Further details of model fits supplied below.
#'
#' @format A list of 6 objects: \describe{ \item{\code{joineRfit1}}{an object
#' of class \code{joint}, the result of using the \code{joint} function to fit
#' a joint model to the data from the first study in the \code{simdat2}
#' dataset.} \item{\code{joineRfit1SE}}{an object of class \code{data.frame},
#' the result of applying the function \code{jointSE} to the joint model fit
#' \code{joineRfit1}.} \item{\code{joineRfit2}}{ an object of class
#' \code{joint}, the result of using the \code{joint} function to fit a joint
#' model to the data from the second study in the \code{simdat2} dataset.}
#' \item{\code{joineRfit2SE}}{an object of class \code{data.frame}, the result
#' of applying the function \code{jointSE} to the joint model fit
#' \code{joineRfit2}.} \item{\code{joineRfit3}}{an object of class
#' \code{joint}, the result of using the \code{joint} function to fit a joint
#' model to the data from the third study in the \code{simdat2} dataset.}
#' \item{\code{joineRfit3SE}}{an object of class \code{data.frame}, the result
#' of applying the function \code{jointSE} to the joint model fit
#' \code{joineRfit3}.} }
#'
#' @details These are the results of fitting a joint model using the
#' \code{joineR} package separately to the data from the first three studies
#' present in the \code{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,
#' and random intercept and slope. The survival sub-model contained a fixed
#' treatment assignment term. A proportional association structure was used
#' to link the sub-models. More formally, the longitudinal sub-model
#' had the following format:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' b^{(2)}_{0ki} + b^{(2)}_{1ki}time + \epsilon_{kij}}
#'
#' Where \eqn{Y} represents the continuous longitudinal outcome, fixed effect
#' coefficients are represented by \eqn{\beta}, random effects coefficients by
#' \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment variable (a binary
#' factor) is represented by \eqn{treat}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0}(t)exp(\beta_{21}treat +
#' \alpha(b^{(2)}_{0ki} + b^{(2)}_{1ki}time)) }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0}(t)}
#' represents the baseline hazard. The fixed effect coefficient is
#' represented by \eqn{\beta_{21}}. The association parameter quantifying the
#' link between the sub-models is represented by \eqn{\alpha}. Again
#' \eqn{treat} represents the binary factor treatment assignment variable, and
#' \eqn{b^{(2)}_{0ki}} and \eqn{b^{(2)}_{1ki}} are the zero mean random
#' effects shared 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.
#'
#' @seealso \code{\link[joineR]{jointdata}}, \code{\link[joineR]{joint}},
#' \code{\link[joineR]{jointSE}}
#'
"joineRfits"
#' Study specific joint model fits using the joineR package
#'
#' A dataset containing a list of the model fits for joint models fitted to the
#' data for each study in the \code{simdat2} dataset using the joineR package.
#' Further details of model fits supplied below.
#'
#' @format A list of 6 objects: \describe{ \item{\code{joineRfit6}}{an object
#' of class \code{joint}, the result of using the \code{joint} function to fit
#' a joint model to the data from the first study in the \code{simdat2}
#' dataset.} \item{\code{joineRfit6SE}}{an object of class \code{data.frame},
#' the result of applying the function \code{jointSE} to the joint model fit
#' \code{joineRfit6}.} \item{\code{joineRfit7}}{ an object of class
#' \code{joint}, the result of using the \code{joint} function to fit a joint
#' model to the data from the second study in the \code{simdat2} dataset.}
#' \item{\code{joineRfit7SE}}{an object of class \code{data.frame}, the result
#' of applying the function \code{jointSE} to the joint model fit
#' \code{joineRfit7}.} \item{\code{joineRfit8}}{an object of class
#' \code{joint}, the result of using the \code{joint} function to fit a joint
#' model to the data from the third study in the \code{simdat2} dataset.}
#' \item{\code{joineRfit8SE}}{an object of class \code{data.frame}, the result
#' of applying the function \code{jointSE} to the joint model fit
#' \code{joineRfit8}.} }
#'
#' @details These are the results of fitting a joint model using the
#' \code{joineR} package separately to the data from the first three studies
#' present in the \code{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,
#' and random intercept. The survival sub-model contained a fixed treatment
#' assignment term. A proportional association structure was used to link the
#' sub-models. More formally, the longitudinal sub-model had the following
#' format:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' b^{(2)}_{0ki} + \epsilon_{kij}}
#'
#' Where \eqn{Y} represents the continuous longitudinal outcome, fixed effect
#' coefficients are represented by \eqn{\beta}, random effects coefficients by
#' \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment variable (a binary
#' factor) is represented by \eqn{treat}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0}(t)exp(\beta_{21}treat +
#' \alpha(b^{(2)}_{0ki})) }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0}(t)}
#' represents the baseline hazard. The fixed effect coefficient is
#' represented by \eqn{\beta_{21}}. The association parameter quantifying the
#' link between the sub-models is represented by \eqn{\alpha}. Again
#' \eqn{treat} represents the binary factor treatment assignment variable, and
#' \eqn{b^{(2)}_{0ki}} are the zero mean random effects shared 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.
#'
#' @seealso \code{\link[joineR]{jointdata}}, \code{\link[joineR]{joint}},
#' \code{\link[joineR]{jointSE}}
#'
"joineRfits2"
#' Study specific joint model fits using the JM package
#'
#' A dataset containing a list of the model fits for joint models fitted to the
#' data for each study in the \code{simdat2} dataset using the JM package.
#' Further details of model fits supplied below.
#'
#' @format A list of 3 \code{jointModel} objects, the result of fitting a joint
#' model using the JM package to the data for the first three studies in the
#' \code{simdat2} dataset in turn.
#'
#' @details These are the results of fitting a joint model using the \code{JM}
#' package separately to the data the first three studies present in the
#' \code{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, and random intercept
#' and slope. The survival sub-model contained a fixed treatment assignment
#' term. A current value association structure was used to link the
#' sub-models. More formally, the longitudinal sub-model had the following
#' format:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' b^{(2)}_{0ki} + b^{(2)}_{1ki}time + \epsilon_{kij}}
#'
#' Where \eqn{Y} represents the continuous longitudinal outcome, fixed effect
#' coefficients are represented by \eqn{\beta}, random effects coefficients by
#' \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment variable (a binary
#' factor) is represented by \eqn{treat}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0}(t)exp(\beta_{21}treat +
#' \alpha(\beta_{10} + \beta_{11}time + \beta_{12}treat + b^{(2)}_{0ki} +
#' b^{(2)}_{1ki}time)) }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0}(t)}
#' represents the baseline hazard, which was modelled using splines. The fixed
#' effect coefficient is represented by \eqn{\beta_{21}}. The association
#' parameter quantifying the link between the sub-models is represented by
#' \eqn{\alpha}. Again \eqn{treat} represents the binary factor treatment
#' assignment variable, and \eqn{b^{(2)}_{0ki}} and \eqn{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.
#'
#' @seealso \code{\link[JM]{jointModel}}, \code{\link[JM]{jointModelObject}}
#'
"JMfits"
#' Study specific joint model fits using the JM package
#'
#' A dataset containing a list of the model fits for joint models fitted to the
#' data the first three studies in the \code{simdat2} dataset using the JM
#' package. Further details of model fits supplied below.
#'
#' @format A list of 3 \code{jointModel} objects, the result of fitting a joint
#' model using the JM package to the data from the first three studies in the
#' \code{simdat2} dataset in turn.
#'
#' @details These are the results of fitting a joint model using the \code{JM}
#' package separately to the data from the first three studies present in the
#' \code{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:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' \beta_{13}time*treat+ b^{(2)}_{0ki} + b^{(2)}_{1ki}time + \epsilon_{kij}}
#'
#' Where \eqn{Y} represents the continuous longitudinal outcome, fixed effect
#' coefficients are represented by \eqn{\beta}, random effects coefficients by
#' \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment variable (a binary
#' factor) is represented by \eqn{treat}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0}(t)exp(\beta_{21}treat +
#' \alpha_{1}(\beta_{10} + \beta_{11}time + \beta_{12}treat + +
#' \beta_{13}time*treat b^{(2)}_{0ki} + b^{(2)}_{1ki}time)+
#' \alpha_{2}(\beta_{11} + \beta_{13}treat + b^{(2)}_{1ki})) }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0}(t)}
#' represents the baseline hazard, which was modelled using splines. The fixed
#' effect coefficient is represented by \eqn{\beta_{21}}. Association
#' parameters representing the link between the sub-models are represented by
#' \eqn{\alpha} terms, where \eqn{\alpha_{1}} represents the effect of the
#' current value of the longitudinal outcome on the risk of an event, whilst
#' \eqn{\alpha_{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 \eqn{treat} represents the binary facator treatment assignment
#' variable, and \eqn{b^{(2)}_{0ki}} and \eqn{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.
#'
#' @seealso \code{\link[JM]{jointModel}}, \code{\link[JM]{jointModelObject}}
#'
"JMfits2"
#' One stage jointmeta1 fit and bootstrapped standard errors
#'
#' A list of length two containing a one stage jointmeta1 fit and corresponding
#' bootstrapped standard errors.
#'
#' @format A list of 2 objects: \describe{ \item{\code{onestagefit0}}{an object
#' of class \code{jointmeta1}} \item{\code{onestagefit0SE}}{an object of class
#' \code{jointmeta1SE}} }
#'
#' @details These are the results of using the \code{jointmeta1} function to fit
#' a one stage joint meta model for multi-study data, and also the bootstrap
#' results of applying the \code{jointmetaSE} function to the resulting model
#' fit. The data used is the \code{simdat2} data available in the
#' \code{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:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' b^{(2)}_{0ki} + b^{(2)}_{1ki}time + \epsilon_{kij}}
#'
#' \eqn{Y_{kij}} represents the continuous longitudinal outcome for the
#' \eqn{i}th individual in the \eqn{k}th study at the \eqn{j}th time point,
#' fixed effect coefficients are represented by \eqn{\beta}, random effects
#' coefficients by \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment
#' variable (a binary factor) is represented by \eqn{treat}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0}(t)exp(\beta_{21}treat +
#' \alpha^{(2)}(b^{(2)}_{0ki} + b^{(2)}_{1ki}time)) }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0}(t)}
#' represents the unspecified baseline hazard. This baseline was not
#' stratified by study. The fixed effect coefficient is represented by
#' \eqn{\beta_{21}}. A proportional random effects only association structure
#' links the sub-models, with \eqn{\alpha^{(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.
#'
#' 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 is a naive model as it analyses data from all the studies in the
#' dataset but does not account for between study heterogeneity (differences
#' between the studies included in the dataset) in any way.
#'
#' 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:
#'
#' \code{ onestagefit0<-jointmeta1(data = jointdat, long.formula = Y ~ 1 +
#' time + treat, long.rand.ind = c('int', 'time'), sharingstrct = 'randprop',
#' surv.formula = Surv(survtime, cens) ~ treat, study.name = 'study', strat =
#' F) }
#'
#' And the code used to bootstrap the model was:
#'
#' \code{ onestagefit0SE<-jointmetaSE(fitted = onestagefit0, n.boot = 200) }
#'
#'
#' @seealso \code{\link{jointmeta1}}, \code{\link{jointmetaSE}}
#'
"onestage0"
#' One stage jointmeta1 fit and bootstrapped standard errors
#'
#' A list of length two containing a one stage jointmeta1 fit and corresponding
#' bootstrapped standard errors.
#'
#' @format A list of 2 objects: \describe{ \item{\code{onestagefit1}}{an object
#' of class \code{jointmeta1}} \item{\code{onestagefit1SE}}{an object of class
#' \code{jointmeta1SE}} }
#'
#' @details These are the results of using the \code{jointmeta1} function to fit
#' a one stage joint meta model for multi-study data, and also the bootstrap
#' results of applying the \code{jointmetaSE} function to the resulting model
#' fit. The data used is the \code{simdat2} data available in the
#' \code{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:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' \beta_{13}study + \beta_{14}treat*study + b^{(2)}_{0ki} + b^{(2)}_{1ki}time
#' + \epsilon_{kij}}
#'
#' \eqn{Y_{kij}} represents the continuous longitudinal outcome for the
#' \eqn{i}th individual in the \eqn{k}th study at the \eqn{j}th time point,
#' fixed effect coefficients are represented by \eqn{\beta}, random effects
#' coefficients by \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment
#' variable (a binary factor) is represented by \eqn{treat}. The study
#' membership variable, a factor variable, is represented by \eqn{study}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0}(t)exp(\beta_{21}treat + \beta_{22}study
#' + \beta_{23}treat*study + \alpha^{(2)}(b^{(2)}_{0ki} + b^{(2)}_{1ki}time))
#' }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0}(t)}
#' represents the unspecified baseline hazard. This baseline was not
#' stratified by study. The fixed effect coefficients are represented by
#' \eqn{\beta} terms. A proportional random effects only association
#' structure links the sub-models, with \eqn{\alpha^{(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.
#'
#' 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 by including study
#' membership and interactions between the study membership and the treatment
#' assignment in the fixed effects of both sub-models.
#'
#' 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:
#'
#' \code{ onestagefit1<-jointmeta1(data = jointdat, long.formula = Y ~ 1 +
#' time + treat*study, long.rand.ind = c('int', 'time'), sharingstrct =
#' 'randprop', surv.formula = Surv(survtime, cens) ~ treat*study, study.name =
#' 'study', strat = F) }
#'
#' And the code used to bootstrap the model was:
#'
#' \code{ onestagefit1SE<-jointmetaSE(fitted = onestagefit1, n.boot = 200,
#' overalleffects = list(long = list(c('treat1', 'treat1:study2'), c('treat1',
#' 'treat1:study3'), c('treat1', 'treat1:study4'), c('treat1',
#' 'treat1:study5')), surv = list(c('treat1', 'treat1:study2'), c('treat1',
#' 'treat1:study3'), c('treat1', 'treat1:study4'), c('treat1',
#' 'treat1:study5')))) }
#'
#' @seealso \code{\link{jointmeta1}}, \code{\link{jointmetaSE}}
#'
"onestage1"
#' One stage jointmeta1 fit and bootstrapped standard errors
#'
#' A list of length two containing a one stage jointmeta1 fit and corresponding
#' bootstrapped standard errors.
#'
#' @format A list of 2 objects: \describe{ \item{\code{onestagefit2}}{an object
#' of class \code{jointmeta1}} \item{\code{onestagefit2SE}}{an object of class
#' \code{jointmeta1SE}} }
#'
#' @details These are the results of using the \code{jointmeta1} function to fit
#' a one stage joint meta model for multi-study data, and also the bootstrap
#' results of applying the \code{jointmetaSE} function to the resulting model
#' fit. The data used is the \code{simdat2} data available in the
#' \code{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:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' b^{(2)}_{0ki} + b^{(2)}_{1ki}time + b^{(3)}_{0k} + b^{(3)}_{1k}treat +
#' \epsilon_{kij}}
#'
#' Where \eqn{Y_{kij}} represents the continuous longitudinal outcome for the
#' \eqn{i}th individual in the \eqn{k}th study at the \eqn{j}th time point,
#' fixed effect coefficients are represented by \eqn{\beta}, random effects
#' coefficients by \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment variable (a
#' binary factor) is represented by \eqn{treat}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0}(t)exp(\beta_{21}treat +
#' \alpha^{(2)}(b^{(2)}_{0ki} + b^{(2)}_{1ki}time) + \alpha^{(3)}(b^{(2)}_{0k}
#' + b^{(3)}_{1k}treat)) }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0}(t)}
#' represents the unspecified baseline hazard. This baseline was not
#' stratified by study. The fixed effect coefficients are represented by
#' \eqn{\beta} terms. A proportional random effects only association
#' structure links the sub-models, with \eqn{\alpha^{(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 \eqn{\alpha^{(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:
#'
#' \code{ 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:
#'
#' \code{ onestagefit2SE<-jointmetaSE(fitted = onestagefit2, n.boot = 200) }
#'
#' @seealso \code{\link{jointmeta1}}, \code{\link{jointmetaSE}}
#'
"onestage2"
#' One stage jointmeta1 fit and bootstrapped standard errors
#'
#' A list of length two containing a one stage jointmeta1 fit and corresponding
#' bootstrapped standard errors.
#'
#' @format A list of 2 objects: \describe{ \item{\code{onestagefit3}}{an object
#' of class \code{jointmeta1}} \item{\code{onestagefit3SE}}{an object of class
#' \code{jointmeta1SE}} }
#'
#' @details These are the results of using the \code{jointmeta1} function to fit
#' a one stage joint meta model for multi-study data, and also the bootstrap
#' results of applying the \code{jointmetaSE} function to the resulting model
#' fit. The data used is the \code{simdat2} data available in the
#' \code{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:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' \beta_{13}study + \beta_{14}treat*study + b^{(2)}_{0ki} + b^{(2)}_{1ki}time
#' + \epsilon_{kij}}
#'
#' \eqn{Y_{kij}} represents the continuous longitudinal outcome for the
#' \eqn{i}th individual in the \eqn{k}th study at the \eqn{j}th time point,
#' fixed effect coefficients are represented by \eqn{\beta}, random effects
#' coefficients by \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment
#' variable (a binary factor) is represented by \eqn{treat}. The study
#' membership variable, a factor variable, is represented by \eqn{study}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0k}(t)exp(\beta_{21}treat +
#' \alpha^{(2)}(b^{(2)}_{0ki} + b^{(2)}_{1ki}time)) }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0k}(t)}
#' represents the unspecified baseline hazard which is stratified by study.
#' The fixed effect coefficients are represented by \eqn{\beta} terms. A
#' proportional random effects only association structure links the
#' sub-models, with \eqn{\alpha^{(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.
#'
#' 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 by including study
#' membership and interactions between the study membership and the treatment
#' assignment in the fixed effects of the longitudinal sub-model, and by
#' stratifying the baseline hazard by study in the survival sub-model.
#'
#' 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:
#'
#' \code{ onestagefit3<-jointmeta1(data = jointdat, long.formula = Y ~ 1 +
#' time + treat*study, long.rand.ind = c('int', 'time'), sharingstrct =
#' 'randprop', surv.formula = Surv(survtime, cens) ~ treat, study.name =
#' 'study', strat = T) }
#'
#' And the code used to bootstrap the model was:
#'
#' \code{ onestagefit3SE<-jointmetaSE(fitted = onestagefit3, n.boot = 200,
#' overalleffects = list(long = list(c('treat1', 'treat1:study2'), c('treat1',
#' 'treat1:study3'), c('treat1', 'treat1:study4'), c('treat1',
#' 'treat1:study5')))) }
#'
#' @seealso \code{\link{jointmeta1}}, \code{\link{jointmetaSE}}
#'
"onestage3"
#' One stage jointmeta1 fit and bootstrapped standard errors
#'
#' A list of length two containing a one stage jointmeta1 fit and corresponding
#' bootstrapped standard errors.
#'
#' @format A list of 2 objects: \describe{ \item{\code{onestagefit4}}{an object
#' of class \code{jointmeta1}} \item{\code{onestagefit4SE}}{an object of class
#' \code{jointmeta1SE}} }
#'
#' @details These are the results of using the \code{jointmeta1} function to fit
#' a one stage joint meta model for multi-study data, and also the bootstrap
#' results of applying the \code{jointmetaSE} function to the resulting model
#' fit. The data used is the \code{simdat2} data available in the
#' \code{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:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' \beta_{13}study + b^{(2)}_{0ki} + b^{(2)}_{1ki}time + b^{(3)}_{1k}treat +
#' \epsilon_{kij}}
#'
#' Where \eqn{Y_{kij}} represents the continuous longitudinal outcome for the
#' \eqn{i}th individual in the \eqn{k}th study at the \eqn{j}th time point,
#' fixed effect coefficients are represented by \eqn{\beta}, random effects
#' coefficients by \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment variable (a
#' binary factor) is represented by \eqn{treat}. The study membership, a
#' factor variable, is represented by \eqn{study}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0k}(t)exp(\beta_{21}treat +
#' \alpha^{(2)}(b^{(2)}_{0ki} + b^{(2)}_{1ki}time) + \alpha^{(3)}(b^{(2)}_{0k}
#' + b^{(3)}_{1k}treat)) }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0k}(t)}
#' represents the unspecified baseline hazard which is stratified by study.
#' The fixed effect coefficients are represented by \eqn{\beta} terms. A
#' proportional random effects only association structure links the
#' sub-models, with \eqn{\alpha^{(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 \eqn{\alpha^{(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:
#'
#' \code{ onestagefit4<-jointmeta1(data = jointdat, long.formula = Y ~ 1 +
#' time + treat + study, long.rand.ind = c('int', 'time'), long.rand.stud =
#' c('treat'), sharingstrct = 'randprop', surv.formula = Surv(survtime, cens)
#' ~ treat, study.name = 'study', strat = T) }
#'
#' And the code used to bootstrap the model was:
#'
#' \code{ onestagefit4SE<-jointmetaSE(fitted = onestagefit4, n.boot = 200) }
#'
#' @seealso \code{\link{jointmeta1}}, \code{\link{jointmetaSE}}
#'
"onestage4"
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#' Simulated joint longitudinal and survival dataset containing 5 studies
#'
#' A simulated dataset containing a single continuous longitudinal outcome and a
#' single survival outcome, with data available from 5 studies.
#'
#' @format A list of three objects: \describe{ \item{\code{longitudinal}}{A list
#' of long format longitudinal datasets one for each of the 5 studies included
#' in the dataset. Each of these datasets contains the following variables:
#' \describe{ \item{\code{id}}{long version of the id variable for the data.
#' Identical ids between the longitudinal and the survival datasets identify
#' the same individual} \item{\code{Y}}{a continuous longitudinal outcome}
#' \item{\code{time}}{the longitudinal time variable} \item{\code{study}}{a
#' long version of the study membership indicator} \item{\code{intercept}}{a
#' long version of the intercept, always takes a value of 1}
#' \item{\code{treat}}{a long version of the binary treatment group indicator}
#' \item{\code{ltime}}{a duplicate of the longitudinal time variable,
#' duplicated as part of the longitudinal data simulation process} }}
#'
#' \item{\code{survival}}{A list of survival datasets, one for each of the 5
#' studies included in the dataset. Each of these datasets contains the
#' following variables: \describe{ \item{\code{id}}{the id variable for the
#' data. Identical ids between the longitudinal and the survival datasets
#' identify the same individual} \item{\code{survtime}}{the survival time for
#' each individual at which they experienced the event or were censored. This
#' is on the same scale as the longitudinal time measurements.}
#' \item{\code{cens}}{censoring indicator for the survival data where 1
#' indicates an event and 0 indicates censoring} \item{\code{study}}{study
#' membership indicator} \item{\code{treat}}{binary treatment group indicator}
#' }}
#'
#' \item{\code{percentevent}}{A list of the percentage of events experienced
#' in each datasets. The first element contains the percentage of events
#' observed for the first simulated study and so on.} }
#'
#' @details This is a simulated dataset generated using the
#' \code{\link{simjointmeta}} function using the following function call:
#'
#' \code{ simdat<-simjointmeta(k = 5, n = rep(500, 5), sepassoc = FALSE, ntms
#' = 5, longmeasuretimes = c(0, 1, 2, 3, 4), beta1 = c(1, 2, 3), beta2 = 3,
#' rand_ind = 'intslope', rand_stud = 'inttreat', gamma_ind = 1, gamma_stud =
#' 1, sigb_ind = matrix(c(1,0.5,0.5,1.5),nrow=2), sigb_stud =
#' matrix(c(1,0.5,0.5,1.5),nrow=2), vare = 0.01, theta0 = -3, theta1 = 1,
#' censoring = TRUE, censlam = exp(-3), truncation = TRUE, trunctime = 6) }
#'
#' Note that this will not give you identical data to that held in
#' \code{simdat} due to the differences in starting seed.
#'
#' @seealso \code{\link{simjointmeta}}
#'
"simdat"
#' Simulated joint longitudinal and survival dataset containing 3 studies
#'
#' A simulated dataset containing a single continuous longitudinal outcome and a
#' single survival outcome, with data available from 3 studies.
#'
#' @format A list of three objects: \describe{ \item{\code{longitudinal}}{A list
#' of long format longitudinal datasets one for each of the 3 studies included
#' in the dataset. Each of these datasets contains the following variables:
#' \describe{ \item{\code{id}}{long version of the id variable for the data.
#' Identical ids between the longitudinal and the survival datasets identify
#' the same individual} \item{\code{Y}}{a continuous longitudinal outcome}
#' \item{\code{time}}{the longitudinal time variable} \item{\code{study}}{a
#' long version of the study membership indicator} \item{\code{intercept}}{a
#' long version of the intercept, always takes a value of 1}
#' \item{\code{treat}}{a long version of the binary treatment group indicator}
#' \item{\code{ltime}}{a duplicate of the longitudinal time variable,
#' duplicated as part of the longitudinal data simulation process} }}
#'
#' \item{\code{survival}}{A list of survival datasets, one for each of the 5
#' studies included in the dataset. Each of these datasets contains the
#' following variables: \describe{ \item{\code{id}}{the id variable for the
#' data. Identical ids between the longitudinal and the survival datasets
#' identify the same individual} \item{\code{survtime}}{the survival time for
#' each individual at which they experienced the event or were censored. This
#' is on the same scale as the longitudinal time measurements.}
#' \item{\code{cens}}{censoring indicator for the survival data where 1
#' indicates an event and 0 indicates censoring} \item{\code{study}}{study
#' membership indicator} \item{\code{treat}}{binary treatment group indicator}
#' }}
#'
#' \item{\code{percentevent}}{A list of the percentage of events experienced
#' in each datasets. The first element contains the percentage of events
#' observed for the first simulated study and so on.} }
#'
#' @details This is a simulated dataset generated by subsetting the \code{simdat}
#' dataset to leave only three studies with 100 individuals in each study.
#' This dataset is for demonstration purposes only within the package.
#'
#' @seealso \code{\link{simjointmeta}}
#'
"simdat2"
#' Simulated joint longitudinal and survival dataset containing 5 studies
#'
#' A simulated dataset containing a single continuous longitudinal outcome and a
#' single survival outcome, with data available from 5 studies. This dataset
#' does not have longitudinal measurements capped at each individual's survival
#' time.
#'
#' @format A list of three objects: \describe{ \item{\code{longitudinal}}{A list
#' of long format longitudinal datasets one for each of the 5 studies included
#' in the dataset. Each of these datasets contains the following variables:
#' \describe{ \item{\code{id}}{long version of the id variable for the data.
#' Identical ids between the longitudinal and the survival datasets identify
#' the same individual} \item{\code{Y}}{a continuous longitudinal outcome}
#' \item{\code{time}}{the longitudinal time variable} \item{\code{study}}{a
#' long version of the study membership indicator} \item{\code{intercept}}{a
#' long version of the intercept, always takes a value of 1}
#' \item{\code{treat}}{a long version of the binary treatment group indicator}
#' \item{\code{ltime}}{a duplicate of the longitudinal time variable,
#' duplicated as part of the longitudinal data simulation process} }}
#'
#' \item{\code{survival}}{A list of survival datasets, one for each of the 5
#' studies included in the dataset. Each of these datasets contains the
#' following variables: \describe{ \item{\code{id}}{the id variable for the
#' data. Identical ids between the longitudinal and the survival datasets
#' identify the same individual} \item{\code{survtime}}{the survival time for
#' each individual at which they experienced the event or were censored. This
#' is on the same scale as the longitudinal time measurements.}
#' \item{\code{cens}}{censoring indicator for the survival data where 1
#' indicates an event and 0 indicates censoring} \item{\code{study}}{study
#' membership indicator} \item{\code{treat}}{binary treatment group indicator}
#' }}
#'
#' \item{\code{percentevent}}{A list of the percentage of events experienced
#' in each datasets. The first element contains the percentage of events
#' observed for the first simulated study and so on.} }
#'
#' @details This is a simulated dataset generated in order to show how the
#' function \code{\link{removeafter}} works, as it does not cap longitudinal
#' outcomes at each individual's survival time. This data was generated by
#' manually stepping through the code available in simjointmeta and retaining
#' instead of discarding any simulated longitudinal measurements recorded
#' after the individual in question's survival time.
#'
#' @seealso \code{\link{simjointmeta}}, \code{\link{removeafter}}
#'
"simdat3"
#' Study specific joint model fits using the joineR package
#'
#' A dataset containing a list of the model fits for joint models fitted to the
#' data for each study in the \code{simdat2} dataset using the joineR package.
#' Further details of model fits supplied below.
#'
#' @format A list of 6 objects: \describe{ \item{\code{joineRfit1}}{an object
#' of class \code{joint}, the result of using the \code{joint} function to fit
#' a joint model to the data from the first study in the \code{simdat2}
#' dataset.} \item{\code{joineRfit1SE}}{an object of class \code{data.frame},
#' the result of applying the function \code{jointSE} to the joint model fit
#' \code{joineRfit1}.} \item{\code{joineRfit2}}{ an object of class
#' \code{joint}, the result of using the \code{joint} function to fit a joint
#' model to the data from the second study in the \code{simdat2} dataset.}
#' \item{\code{joineRfit2SE}}{an object of class \code{data.frame}, the result
#' of applying the function \code{jointSE} to the joint model fit
#' \code{joineRfit2}.} \item{\code{joineRfit3}}{an object of class
#' \code{joint}, the result of using the \code{joint} function to fit a joint
#' model to the data from the third study in the \code{simdat2} dataset.}
#' \item{\code{joineRfit3SE}}{an object of class \code{data.frame}, the result
#' of applying the function \code{jointSE} to the joint model fit
#' \code{joineRfit3}.} }
#'
#' @details These are the results of fitting a joint model using the
#' \code{joineR} package separately to the data from the first three studies
#' present in the \code{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,
#' and random intercept and slope. The survival sub-model contained a fixed
#' treatment assignment term. A proportional association structure was used
#' to link the sub-models. More formally, the longitudinal sub-model
#' had the following format:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' b^{(2)}_{0ki} + b^{(2)}_{1ki}time + \epsilon_{kij}}
#'
#' Where \eqn{Y} represents the continuous longitudinal outcome, fixed effect
#' coefficients are represented by \eqn{\beta}, random effects coefficients by
#' \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment variable (a binary
#' factor) is represented by \eqn{treat}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0}(t)exp(\beta_{21}treat +
#' \alpha(b^{(2)}_{0ki} + b^{(2)}_{1ki}time)) }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0}(t)}
#' represents the baseline hazard. The fixed effect coefficient is
#' represented by \eqn{\beta_{21}}. The association parameter quantifying the
#' link between the sub-models is represented by \eqn{\alpha}. Again
#' \eqn{treat} represents the binary factor treatment assignment variable, and
#' \eqn{b^{(2)}_{0ki}} and \eqn{b^{(2)}_{1ki}} are the zero mean random
#' effects shared 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.
#'
#' @seealso \code{\link[joineR]{jointdata}}, \code{\link[joineR]{joint}},
#' \code{\link[joineR]{jointSE}}
#'
"joineRfits"
#' Study specific joint model fits using the joineR package
#'
#' A dataset containing a list of the model fits for joint models fitted to the
#' data for each study in the \code{simdat2} dataset using the joineR package.
#' Further details of model fits supplied below.
#'
#' @format A list of 6 objects: \describe{ \item{\code{joineRfit6}}{an object
#' of class \code{joint}, the result of using the \code{joint} function to fit
#' a joint model to the data from the first study in the \code{simdat2}
#' dataset.} \item{\code{joineRfit6SE}}{an object of class \code{data.frame},
#' the result of applying the function \code{jointSE} to the joint model fit
#' \code{joineRfit6}.} \item{\code{joineRfit7}}{ an object of class
#' \code{joint}, the result of using the \code{joint} function to fit a joint
#' model to the data from the second study in the \code{simdat2} dataset.}
#' \item{\code{joineRfit7SE}}{an object of class \code{data.frame}, the result
#' of applying the function \code{jointSE} to the joint model fit
#' \code{joineRfit7}.} \item{\code{joineRfit8}}{an object of class
#' \code{joint}, the result of using the \code{joint} function to fit a joint
#' model to the data from the third study in the \code{simdat2} dataset.}
#' \item{\code{joineRfit8SE}}{an object of class \code{data.frame}, the result
#' of applying the function \code{jointSE} to the joint model fit
#' \code{joineRfit8}.} }
#'
#' @details These are the results of fitting a joint model using the
#' \code{joineR} package separately to the data from the first three studies
#' present in the \code{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,
#' and random intercept. The survival sub-model contained a fixed treatment
#' assignment term. A proportional association structure was used to link the
#' sub-models. More formally, the longitudinal sub-model had the following
#' format:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' b^{(2)}_{0ki} + \epsilon_{kij}}
#'
#' Where \eqn{Y} represents the continuous longitudinal outcome, fixed effect
#' coefficients are represented by \eqn{\beta}, random effects coefficients by
#' \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment variable (a binary
#' factor) is represented by \eqn{treat}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0}(t)exp(\beta_{21}treat +
#' \alpha(b^{(2)}_{0ki})) }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0}(t)}
#' represents the baseline hazard. The fixed effect coefficient is
#' represented by \eqn{\beta_{21}}. The association parameter quantifying the
#' link between the sub-models is represented by \eqn{\alpha}. Again
#' \eqn{treat} represents the binary factor treatment assignment variable, and
#' \eqn{b^{(2)}_{0ki}} are the zero mean random effects shared 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.
#'
#' @seealso \code{\link[joineR]{jointdata}}, \code{\link[joineR]{joint}},
#' \code{\link[joineR]{jointSE}}
#'
"joineRfits2"
#' Study specific joint model fits using the JM package
#'
#' A dataset containing a list of the model fits for joint models fitted to the
#' data for each study in the \code{simdat2} dataset using the JM package.
#' Further details of model fits supplied below.
#'
#' @format A list of 3 \code{jointModel} objects, the result of fitting a joint
#' model using the JM package to the data for the first three studies in the
#' \code{simdat2} dataset in turn.
#'
#' @details These are the results of fitting a joint model using the \code{JM}
#' package separately to the data the first three studies present in the
#' \code{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, and random intercept
#' and slope. The survival sub-model contained a fixed treatment assignment
#' term. A current value association structure was used to link the
#' sub-models. More formally, the longitudinal sub-model had the following
#' format:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' b^{(2)}_{0ki} + b^{(2)}_{1ki}time + \epsilon_{kij}}
#'
#' Where \eqn{Y} represents the continuous longitudinal outcome, fixed effect
#' coefficients are represented by \eqn{\beta}, random effects coefficients by
#' \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment variable (a binary
#' factor) is represented by \eqn{treat}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0}(t)exp(\beta_{21}treat +
#' \alpha(\beta_{10} + \beta_{11}time + \beta_{12}treat + b^{(2)}_{0ki} +
#' b^{(2)}_{1ki}time)) }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0}(t)}
#' represents the baseline hazard, which was modelled using splines. The fixed
#' effect coefficient is represented by \eqn{\beta_{21}}. The association
#' parameter quantifying the link between the sub-models is represented by
#' \eqn{\alpha}. Again \eqn{treat} represents the binary factor treatment
#' assignment variable, and \eqn{b^{(2)}_{0ki}} and \eqn{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.
#'
#' @seealso \code{\link[JM]{jointModel}}, \code{\link[JM]{jointModelObject}}
#'
"JMfits"
#' Study specific joint model fits using the JM package
#'
#' A dataset containing a list of the model fits for joint models fitted to the
#' data the first three studies in the \code{simdat2} dataset using the JM
#' package. Further details of model fits supplied below.
#'
#' @format A list of 3 \code{jointModel} objects, the result of fitting a joint
#' model using the JM package to the data from the first three studies in the
#' \code{simdat2} dataset in turn.
#'
#' @details These are the results of fitting a joint model using the \code{JM}
#' package separately to the data from the first three studies present in the
#' \code{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:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' \beta_{13}time*treat+ b^{(2)}_{0ki} + b^{(2)}_{1ki}time + \epsilon_{kij}}
#'
#' Where \eqn{Y} represents the continuous longitudinal outcome, fixed effect
#' coefficients are represented by \eqn{\beta}, random effects coefficients by
#' \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment variable (a binary
#' factor) is represented by \eqn{treat}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0}(t)exp(\beta_{21}treat +
#' \alpha_{1}(\beta_{10} + \beta_{11}time + \beta_{12}treat + +
#' \beta_{13}time*treat b^{(2)}_{0ki} + b^{(2)}_{1ki}time)+
#' \alpha_{2}(\beta_{11} + \beta_{13}treat + b^{(2)}_{1ki})) }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0}(t)}
#' represents the baseline hazard, which was modelled using splines. The fixed
#' effect coefficient is represented by \eqn{\beta_{21}}. Association
#' parameters representing the link between the sub-models are represented by
#' \eqn{\alpha} terms, where \eqn{\alpha_{1}} represents the effect of the
#' current value of the longitudinal outcome on the risk of an event, whilst
#' \eqn{\alpha_{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 \eqn{treat} represents the binary facator treatment assignment
#' variable, and \eqn{b^{(2)}_{0ki}} and \eqn{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.
#'
#' @seealso \code{\link[JM]{jointModel}}, \code{\link[JM]{jointModelObject}}
#'
"JMfits2"
#' One stage jointmeta1 fit and bootstrapped standard errors
#'
#' A list of length two containing a one stage jointmeta1 fit and corresponding
#' bootstrapped standard errors.
#'
#' @format A list of 2 objects: \describe{ \item{\code{onestagefit0}}{an object
#' of class \code{jointmeta1}} \item{\code{onestagefit0SE}}{an object of class
#' \code{jointmeta1SE}} }
#'
#' @details These are the results of using the \code{jointmeta1} function to fit
#' a one stage joint meta model for multi-study data, and also the bootstrap
#' results of applying the \code{jointmetaSE} function to the resulting model
#' fit. The data used is the \code{simdat2} data available in the
#' \code{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:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' b^{(2)}_{0ki} + b^{(2)}_{1ki}time + \epsilon_{kij}}
#'
#' \eqn{Y_{kij}} represents the continuous longitudinal outcome for the
#' \eqn{i}th individual in the \eqn{k}th study at the \eqn{j}th time point,
#' fixed effect coefficients are represented by \eqn{\beta}, random effects
#' coefficients by \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment
#' variable (a binary factor) is represented by \eqn{treat}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0}(t)exp(\beta_{21}treat +
#' \alpha^{(2)}(b^{(2)}_{0ki} + b^{(2)}_{1ki}time)) }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0}(t)}
#' represents the unspecified baseline hazard. This baseline was not
#' stratified by study. The fixed effect coefficient is represented by
#' \eqn{\beta_{21}}. A proportional random effects only association structure
#' links the sub-models, with \eqn{\alpha^{(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.
#'
#' 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 is a naive model as it analyses data from all the studies in the
#' dataset but does not account for between study heterogeneity (differences
#' between the studies included in the dataset) in any way.
#'
#' 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:
#'
#' \code{ onestagefit0<-jointmeta1(data = jointdat, long.formula = Y ~ 1 +
#' time + treat, long.rand.ind = c('int', 'time'), sharingstrct = 'randprop',
#' surv.formula = Surv(survtime, cens) ~ treat, study.name = 'study', strat =
#' F) }
#'
#' And the code used to bootstrap the model was:
#'
#' \code{ onestagefit0SE<-jointmetaSE(fitted = onestagefit0, n.boot = 200) }
#'
#'
#' @seealso \code{\link{jointmeta1}}, \code{\link{jointmetaSE}}
#'
"onestage0"
#' One stage jointmeta1 fit and bootstrapped standard errors
#'
#' A list of length two containing a one stage jointmeta1 fit and corresponding
#' bootstrapped standard errors.
#'
#' @format A list of 2 objects: \describe{ \item{\code{onestagefit1}}{an object
#' of class \code{jointmeta1}} \item{\code{onestagefit1SE}}{an object of class
#' \code{jointmeta1SE}} }
#'
#' @details These are the results of using the \code{jointmeta1} function to fit
#' a one stage joint meta model for multi-study data, and also the bootstrap
#' results of applying the \code{jointmetaSE} function to the resulting model
#' fit. The data used is the \code{simdat2} data available in the
#' \code{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:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' \beta_{13}study + \beta_{14}treat*study + b^{(2)}_{0ki} + b^{(2)}_{1ki}time
#' + \epsilon_{kij}}
#'
#' \eqn{Y_{kij}} represents the continuous longitudinal outcome for the
#' \eqn{i}th individual in the \eqn{k}th study at the \eqn{j}th time point,
#' fixed effect coefficients are represented by \eqn{\beta}, random effects
#' coefficients by \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment
#' variable (a binary factor) is represented by \eqn{treat}. The study
#' membership variable, a factor variable, is represented by \eqn{study}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0}(t)exp(\beta_{21}treat + \beta_{22}study
#' + \beta_{23}treat*study + \alpha^{(2)}(b^{(2)}_{0ki} + b^{(2)}_{1ki}time))
#' }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0}(t)}
#' represents the unspecified baseline hazard. This baseline was not
#' stratified by study. The fixed effect coefficients are represented by
#' \eqn{\beta} terms. A proportional random effects only association
#' structure links the sub-models, with \eqn{\alpha^{(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.
#'
#' 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 by including study
#' membership and interactions between the study membership and the treatment
#' assignment in the fixed effects of both sub-models.
#'
#' 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:
#'
#' \code{ onestagefit1<-jointmeta1(data = jointdat, long.formula = Y ~ 1 +
#' time + treat*study, long.rand.ind = c('int', 'time'), sharingstrct =
#' 'randprop', surv.formula = Surv(survtime, cens) ~ treat*study, study.name =
#' 'study', strat = F) }
#'
#' And the code used to bootstrap the model was:
#'
#' \code{ onestagefit1SE<-jointmetaSE(fitted = onestagefit1, n.boot = 200,
#' overalleffects = list(long = list(c('treat1', 'treat1:study2'), c('treat1',
#' 'treat1:study3'), c('treat1', 'treat1:study4'), c('treat1',
#' 'treat1:study5')), surv = list(c('treat1', 'treat1:study2'), c('treat1',
#' 'treat1:study3'), c('treat1', 'treat1:study4'), c('treat1',
#' 'treat1:study5')))) }
#'
#' @seealso \code{\link{jointmeta1}}, \code{\link{jointmetaSE}}
#'
"onestage1"
#' One stage jointmeta1 fit and bootstrapped standard errors
#'
#' A list of length two containing a one stage jointmeta1 fit and corresponding
#' bootstrapped standard errors.
#'
#' @format A list of 2 objects: \describe{ \item{\code{onestagefit2}}{an object
#' of class \code{jointmeta1}} \item{\code{onestagefit2SE}}{an object of class
#' \code{jointmeta1SE}} }
#'
#' @details These are the results of using the \code{jointmeta1} function to fit
#' a one stage joint meta model for multi-study data, and also the bootstrap
#' results of applying the \code{jointmetaSE} function to the resulting model
#' fit. The data used is the \code{simdat2} data available in the
#' \code{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:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' b^{(2)}_{0ki} + b^{(2)}_{1ki}time + b^{(3)}_{0k} + b^{(3)}_{1k}treat +
#' \epsilon_{kij}}
#'
#' Where \eqn{Y_{kij}} represents the continuous longitudinal outcome for the
#' \eqn{i}th individual in the \eqn{k}th study at the \eqn{j}th time point,
#' fixed effect coefficients are represented by \eqn{\beta}, random effects
#' coefficients by \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment variable (a
#' binary factor) is represented by \eqn{treat}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0}(t)exp(\beta_{21}treat +
#' \alpha^{(2)}(b^{(2)}_{0ki} + b^{(2)}_{1ki}time) + \alpha^{(3)}(b^{(2)}_{0k}
#' + b^{(3)}_{1k}treat)) }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0}(t)}
#' represents the unspecified baseline hazard. This baseline was not
#' stratified by study. The fixed effect coefficients are represented by
#' \eqn{\beta} terms. A proportional random effects only association
#' structure links the sub-models, with \eqn{\alpha^{(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 \eqn{\alpha^{(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:
#'
#' \code{ 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:
#'
#' \code{ onestagefit2SE<-jointmetaSE(fitted = onestagefit2, n.boot = 200) }
#'
#' @seealso \code{\link{jointmeta1}}, \code{\link{jointmetaSE}}
#'
"onestage2"
#' One stage jointmeta1 fit and bootstrapped standard errors
#'
#' A list of length two containing a one stage jointmeta1 fit and corresponding
#' bootstrapped standard errors.
#'
#' @format A list of 2 objects: \describe{ \item{\code{onestagefit3}}{an object
#' of class \code{jointmeta1}} \item{\code{onestagefit3SE}}{an object of class
#' \code{jointmeta1SE}} }
#'
#' @details These are the results of using the \code{jointmeta1} function to fit
#' a one stage joint meta model for multi-study data, and also the bootstrap
#' results of applying the \code{jointmetaSE} function to the resulting model
#' fit. The data used is the \code{simdat2} data available in the
#' \code{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:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' \beta_{13}study + \beta_{14}treat*study + b^{(2)}_{0ki} + b^{(2)}_{1ki}time
#' + \epsilon_{kij}}
#'
#' \eqn{Y_{kij}} represents the continuous longitudinal outcome for the
#' \eqn{i}th individual in the \eqn{k}th study at the \eqn{j}th time point,
#' fixed effect coefficients are represented by \eqn{\beta}, random effects
#' coefficients by \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment
#' variable (a binary factor) is represented by \eqn{treat}. The study
#' membership variable, a factor variable, is represented by \eqn{study}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0k}(t)exp(\beta_{21}treat +
#' \alpha^{(2)}(b^{(2)}_{0ki} + b^{(2)}_{1ki}time)) }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0k}(t)}
#' represents the unspecified baseline hazard which is stratified by study.
#' The fixed effect coefficients are represented by \eqn{\beta} terms. A
#' proportional random effects only association structure links the
#' sub-models, with \eqn{\alpha^{(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.
#'
#' 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 by including study
#' membership and interactions between the study membership and the treatment
#' assignment in the fixed effects of the longitudinal sub-model, and by
#' stratifying the baseline hazard by study in the survival sub-model.
#'
#' 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:
#'
#' \code{ onestagefit3<-jointmeta1(data = jointdat, long.formula = Y ~ 1 +
#' time + treat*study, long.rand.ind = c('int', 'time'), sharingstrct =
#' 'randprop', surv.formula = Surv(survtime, cens) ~ treat, study.name =
#' 'study', strat = T) }
#'
#' And the code used to bootstrap the model was:
#'
#' \code{ onestagefit3SE<-jointmetaSE(fitted = onestagefit3, n.boot = 200,
#' overalleffects = list(long = list(c('treat1', 'treat1:study2'), c('treat1',
#' 'treat1:study3'), c('treat1', 'treat1:study4'), c('treat1',
#' 'treat1:study5')))) }
#'
#' @seealso \code{\link{jointmeta1}}, \code{\link{jointmetaSE}}
#'
"onestage3"
#' One stage jointmeta1 fit and bootstrapped standard errors
#'
#' A list of length two containing a one stage jointmeta1 fit and corresponding
#' bootstrapped standard errors.
#'
#' @format A list of 2 objects: \describe{ \item{\code{onestagefit4}}{an object
#' of class \code{jointmeta1}} \item{\code{onestagefit4SE}}{an object of class
#' \code{jointmeta1SE}} }
#'
#' @details These are the results of using the \code{jointmeta1} function to fit
#' a one stage joint meta model for multi-study data, and also the bootstrap
#' results of applying the \code{jointmetaSE} function to the resulting model
#' fit. The data used is the \code{simdat2} data available in the
#' \code{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:
#'
#' \deqn{Y_{kij} = \beta_{10} + \beta_{11}time + \beta_{12}treat +
#' \beta_{13}study + b^{(2)}_{0ki} + b^{(2)}_{1ki}time + b^{(3)}_{1k}treat +
#' \epsilon_{kij}}
#'
#' Where \eqn{Y_{kij}} represents the continuous longitudinal outcome for the
#' \eqn{i}th individual in the \eqn{k}th study at the \eqn{j}th time point,
#' fixed effect coefficients are represented by \eqn{\beta}, random effects
#' coefficients by \eqn{b} and the measurement error by \eqn{\epsilon}. 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 \eqn{time}, and the treatment assignment variable (a
#' binary factor) is represented by \eqn{treat}. The study membership, a
#' factor variable, is represented by \eqn{study}.
#'
#' The survival sub-model had format:
#'
#' \deqn{\lambda_{ki}(t) = \lambda_{0k}(t)exp(\beta_{21}treat +
#' \alpha^{(2)}(b^{(2)}_{0ki} + b^{(2)}_{1ki}time) + \alpha^{(3)}(b^{(2)}_{0k}
#' + b^{(3)}_{1k}treat)) }
#'
#' In the above equation, \eqn{\lambda_{ki}(t)} represents the survival time
#' of the individual \eqn{i} in study \eqn{k}, and \eqn{\lambda_{0k}(t)}
#' represents the unspecified baseline hazard which is stratified by study.
#' The fixed effect coefficients are represented by \eqn{\beta} terms. A
#' proportional random effects only association structure links the
#' sub-models, with \eqn{\alpha^{(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 \eqn{\alpha^{(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:
#'
#' \code{ onestagefit4<-jointmeta1(data = jointdat, long.formula = Y ~ 1 +
#' time + treat + study, long.rand.ind = c('int', 'time'), long.rand.stud =
#' c('treat'), sharingstrct = 'randprop', surv.formula = Surv(survtime, cens)
#' ~ treat, study.name = 'study', strat = T) }
#'
#' And the code used to bootstrap the model was:
#'
#' \code{ onestagefit4SE<-jointmetaSE(fitted = onestagefit4, n.boot = 200) }
#'
#' @seealso \code{\link{jointmeta1}}, \code{\link{jointmetaSE}}
#'
"onestage4"
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