uncertainty of the combined estimate of a meta-analysis
uncertainty of the combined estimate of a meta-analysis
}\\
}\\
\bigskip
\bigskip
{\noindent\LargeFlorian Gerber, Leonhard Held, Lisa Hofer, Felix Hofmann, Philip Heesen
{\noindent\Large Leonhard Held, Felix Hofmann
}\end{center}
}\end{center}
\bigskip
\bigskip
\vspace*{.5cm}
\vspace*{.5cm}
For the present protocol is inspired by \citet{burt:etal:06} and \citet{morr:etal:19}.
For the present protocol is inspired by \citet{burt:etal:06} and \citet{morr:etal:19}.
The simulation is implemented in \texttt{simulate\_all.R}.
The simulation is implemented in \texttt{simulate\_all.R}.
\tableofcontents
\tableofcontents
\newpage
\newpage
\section{Aims and objectives}\label{ref:aims}
\section{Aims and objectives}\label{ref:aims}
% TODO:
The aim of this simulation study is the comparison of confidence intervals
% Add paragraph for distribution of the test statistic (F and Chi-square) for harmonic mean methods (or did we decide to ditch the F-distribution?)
(CIs) summarizing the uncertainty of the combined estimate of a meta-analysis.
% Standard REML is missing (DONE)
Specifically, we focus on CIs constructed using p-value functions that
% Add k-Trials (DONE)
implement the methods from \citet{edgington:72} and \citet{fisher:34}. The
%\color{red}
underlying data sets are simulated as described in Section~\ref{sec:simproc}
%Changes to the last version:
and Section~\ref{sec:scenario}. The resulting intervals are then compared to CIs
%\begin{itemize}
constructed using the other methods listed in Section~\ref{sec:method} using the
%\color{red}
measures defined in Section~\ref{sec:meas}.
%\item The protocol mentioned the DerSimonian-Laird method to construct confidence intervals. However, there is no method called ``DerSimonian-Laird'' in the simulation. The paper indicates that this also uses a random effects model with REML. Is this the same as the method called ``REML'' that we already have in the simulation?
%\item Removed harmonic mean with alternative \texttt{two.sided}
%\item Added entries for k-Trials rule
% \item Added a subsection about the distribution of the minimum of the p-value function in ``Aims and objectives''
%\item Updated criteria for evaluation of CIs
%\item Updated number of studies $k$
%\end{itemize}
%\vspace*{.5cm}
%Notes:
%\begin{itemize}
%\color{red}
% \item{Should we mention that we tried F-distribution for the harmonic mean test statistic?}
%\end{itemize}
%\color{black}
The aim of this simulation study is the comparison of confidence intervals (CIs) summarizing the uncertainty of the combined estimate of a meta-analysis. Specifically, we focus on CIs constructed using the harmonic mean method, which is described in \citet{Held2020b}, and the $k$-trials rule, which is defined in Subsection~\ref{sec:ktrial}. The underlying data sets are simulated as described in Section~\ref{sec:simproc} and Section~\ref{sec:scenario}. The resulting intervals are then compared to CIs constructed using the other methods listed in Section~\ref{sec:method} using the measures defined in Section~\ref{sec:meas}.
\section{Simulation of the data sets}\label{sec:simproc}
\section{Simulation of the data sets}\label{sec:simproc}