diff --git a/biblio.bib b/biblio.bib
index eb9642ffa25e3a819b68f4d5eb7e8d041c2181d3..9fbb400ab581d77b29270b14ff230d2dfbfe93c2 100644
--- a/biblio.bib
+++ b/biblio.bib
@@ -10,7 +10,6 @@ year = {2017}
}
-
@article{morr:etal:19,
author = {Morris, Tim P. and White, Ian R. and Crowther, Michael J.},
title = {Using simulation studies to evaluate statistical methods},
@@ -33,7 +32,8 @@ year = {2007},
publisher = {Taylor \& Francis},
doi = {10.1198/016214506000001437},
}
-@Article{ruck:etal:08,
+
+@article{ruck:etal:08,
author={R{\"u}cker, Gerta and Schwarzer, Guido and Carpenter, James R. and Schumacher, Martin},
title={Undue reliance on I2 in assessing heterogeneity may mislead},
journal={BMC Medical Research Methodology},
@@ -183,3 +183,28 @@ url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.4029},
year = {2010}
}
+@book{fisher:34,
+ author = {Fisher, R. A.},
+ year = {1934},
+ title = {{S}tatistical {M}ethods for {R}esearch {W}orkers},
+ publisher = {{O}liver \& {B}oyd},
+ address = {Edinburgh},
+ edition = {4}
+}
+
+
+@article{edgington:72,
+ title = {An {Additive} {Method} for {Combining} {Probability} {Values} from {Independent} {Experiments}},
+ volume = {80},
+ issn = {0022-3980},
+ url = {https://doi.org/10.1080/00223980.1972.9924813},
+ doi = {10.1080/00223980.1972.9924813},
+ number = {2},
+ urldate = {2023-11-01},
+ journal = {The Journal of Psychology},
+ author = {Edgington, Eugene S.},
+ month = mar,
+ year = {1972},
+ note = {Publisher: Routledge \_eprint: https://doi.org/10.1080/00223980.1972.9924813},
+ pages = {351--363},
+}
diff --git a/protocol.pdf b/protocol.pdf
index 16fc4a40495d939434836d6633aed85f0a7a7878..f57700f68a41bd1f9d66a14c3b244360a9cd220b 100644
Binary files a/protocol.pdf and b/protocol.pdf differ
diff --git a/protocol.tex b/protocol.tex
index 5c1a19ab99ddfcd28283a2559de46cb412d59e69..e6329d103baa9f37ccc7d316ceff453a818ff580 100644
--- a/protocol.tex
+++ b/protocol.tex
@@ -1,4 +1,4 @@
-\documentclass[letterpaper, 9pt]{article}
+\documentclass[letterpaper, 12pt]{article}
%\usepackage[nomarkers]{endfloat} %%%%%%%%%
\usepackage{calc}
\usepackage{color}
@@ -12,7 +12,7 @@
\floatstyle{plaintop}
\restylefloat{listing}
-%\usepackage{natbib}
+\usepackage{natbib}
%\usepackage{multind}
\usepackage{booktabs}
\usepackage{enumerate}
@@ -24,14 +24,12 @@
%% \linenumber
\renewcommand{\baselinestretch}{1} %% 2
-\usepackage{natbib}
-
\usepackage{color,xcolor}
\definecolor{link}{HTML}{004C80}
\usepackage[labelfont=bf]{caption}
\usepackage[english]{babel}
-\usepackage[pdftex,plainpages=false,pdfpagelabels,pagebackref=true,colorlinks=true, citecolor=link,linkcolor=link]{hyperref}
+\usepackage[pdftex,plainpages=false,pdfpagelabels,pagebackref=true,colorlinks=true,citecolor=link,linkcolor=link]{hyperref}
\hypersetup{colorlinks,urlcolor=link}
\usepackage{array, lipsum}
@@ -67,51 +65,29 @@
uncertainty of the combined estimate of a meta-analysis
}\\
\bigskip
-{\noindent \Large Florian Gerber, Leonhard Held, Lisa Hofer, Felix Hofmann, Philip Heesen
+{\noindent \Large Leonhard Held, Felix Hofmann
}\end{center}
\bigskip
\vspace*{.5cm}
-
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}.
-
\tableofcontents
\newpage
\section{Aims and objectives}\label{ref:aims}
-% TODO:
-% 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?)
-% Standard REML is missing (DONE)
-% Add k-Trials (DONE)
-%\color{red}
-%Changes to the last version:
-%\begin{itemize}
-%\color{red}
- %\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}.
-
+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 p-value functions that
+implement the methods from \citet{edgington:72} and \citet{fisher:34}. 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}