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\onecolumn  
\title{Addressing Treatment Switching Bias with
G-methods: Exploring the Impact of Model
Specification}
\author[1,2]{Amani Al Tawil\thanks{Correspondence: altawil@ibe.med.uni-muenchen.de}}
\author[3]{Sean McGrath}
\author[4]{Robin Ristl\thanks{Equally contributed}}
\author[1,2]{Ulrich Mansmann\textsuperscript{†}}
\affil[1]{Institute for Medical Information Processing, Biometry, and Epidemiology (IBE), Faculty of Medicine, Ludwig-Maximilians-Universität München}
\affil[2]{Pettenkofer School of Public Health, Faculty of Medicine, Ludwig-Maximilians-Universität München}
\affil[3]{Department of Biostatistics, Harvard T.H. Chan School of Public Health}
\affil[4]{Center for Medical Data Science, Medical University of Vienna}

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\begin{document}
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\vspace{-5em} % Increase the space between title and author names
\vspace{3em}  % Increase the space between author names and "Electronic Supplementary Material"
\begin{center}
\section*{\centering \LARGE Electronic Supplementary Material 4}
\vspace{1.5em} % Increase the space between "Electronic Supplementary Material 1" and "Data Dictionary"
%\large \textbf{List of Covariates Included in the Parametric G-formula Analysis}
\centering
\large \textbf{List of Covariates Included in the Parametric G-formula Analysis}
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\onecolumn
\begin{minipage}[h]{\linewidth} % Align the title at the top of the page
\centering
\large \textbf{List of Covariates Included in the Parametric G-formula Analysis}
\vspace{30pt}
% Spec 1
%\begin{landscape}
\begin{table}[H]
\centering
\begin{adjustwidth}{-2.5cm}{-2.5cm} % Adjust the values of X as needed
\centering
\begin{threeparttable}
\caption{Description of the covariates included in specification 1 of the parametric g-formula analysis}
\begingroup
\renewcommand{\arraystretch}{1.5}
\begin{tabular}{>{\raggedright\arraybackslash}p{2cm}p{3cm}p{6cm}p{6cm}}
\hline
\textbf{Specification}\tnote{\ding{61}} & & \textbf{Control} &\textbf{Experimental}\\
\cmidrule(lr){3-3}
\cmidrule(lr){4-4}
& \textbf{Dependent Variable} & \textbf{Independent Variables} & \textbf{Independent Variables} \\
\cmidrule(lr){2-4}
\multirow{5}{*}{\textbf{}} & Progression & time, quadratic time, race, baseline ECOG, smoking history, intracranial progression (lagged), target lesion size (lagged) & time, sex, race, baseline ECOG, smoking history, strata at randomization, intracranial progression (lagged), target lesion size (lagged)  \\
\cmidrule(lr){2-4}
& ECOG & time, age, quadratic age, sex, race, baseline ECOG, smoking history, measurable intracranial CNS disease, prior radiation therapy, strata at randomization, progression (lagged), progression, intracranial progression (lagged), target lesion size (lagged), treatment(lagged) &  time, quadratic time, age, quadratic age, sex, race, baseline ECOG, smoking history, measurable intracranial CNS disease, prior radiation therapy, strata at randomization, intracranial progression (lagged), target lesion size (lagged) \\
\cmidrule(lr){2-4}
\textbf{1} & Intracranial progression & time, age, race, prior radiation therapy, strata at randomization, progression (lagged), progression, target lesion size (lagged), treatment(lagged)  & time, quadratic time, baseline ECOG, strata at randomization, progression (lagged), progression, target lesion size (lagged)\\
\cmidrule(lr){2-4}
& Target lesion size & time, quadratic time, age, sex, race, baseline ECOG, measurable intracranial central nervous system(CNS) disease, prior radiation therapy, strata at randomization, progression (lagged), progression, ECOG(lagged), ECOG, intracranial progression (lagged), intracranial progression, treatment(lagged) &  time, quadratic time, age, quadratic age, sex, race, baseline ECOG,  strata at randomization, progression (lagged), progression, ECOG(lagged), ECOG, intracranial progression (lagged), intracranial progression\\
\cmidrule(lr){2-4}
& Death & time, quadratic time, age, quadratic age, smoking history, strata at randomization, ECOG(lagged), ECOG, treatment (lagged), treatment, progression time & time, sex, measurable intracranial CNS disease, strata at randomization, ECOG(lagged), ECOG, intracranial progression (lagged), intracranial progression, progression time\\ 
\hline
\end{tabular}
\begin{tablenotes}
\item \textbf{Abbreviations}: ECOG, Eastern Cooperative Oncology Group score; CNS, Central Nervous System 
\item[\ding{61}] Specification 4 from g-formula analysis is the same as specification 1 but replacing 2 categories of ECOG with 3 categories.\\ Specification 5 from g-formula analysis is the same as specification 1 but without progression time.
\end{tablenotes}
\endgroup
\end{threeparttable}
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\end{table}
\end{minipage}
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% Spec 2
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\begin{table}[H]
\centering
\begin{adjustwidth}{-2.5cm}{-2.5cm} % Adjust the values of X as needed
\centering
\begin{threeparttable}
\caption{Description of the covariates included in specification 2 of the parametric g-formula analysis}
\begingroup
\renewcommand{\arraystretch}{1.5}
\begin{tabular}{>{\raggedright\arraybackslash}p{2cm}p{3cm}p{5cm}p{5cm}}
\hline
\textbf{Specification}\tnote{\ding{61}} & & \textbf{Control} &\textbf{Experimental}\\
\cmidrule(lr){3-3}
\cmidrule(lr){4-4}
& \textbf{Dependent Variable} & \textbf{Independent Variables} & \textbf{Independent Variables} \\
\cmidrule(lr){2-4}
\multirow{5}{*}{\textbf{}} & Progression & time, race, baseline ECOG, intracranial progression (lagged), target lesion size (lagged) & time, race, baseline ECOG, smoking history, strata at randomization, intracranial progression (lagged), target lesion size (lagged)  \\
\cmidrule(lr){2-4}
& ECOG & time, age, quadratic age, race, baseline ECOG, smoking history, measurable intracranial CNS disease, prior radiation therapy, strata at randomization, progression (lagged), intracranial progression (lagged), target lesion size (lagged), treatment(lagged) &  time, quadratic time, age, quadratic age, sex, race, baseline ECOG, smoking history, measurable intracranial CNS disease, prior radiation therapy, strata at randomization, intracranial progression (lagged), target lesion size (lagged) \\
\cmidrule(lr){2-4}
\textbf{2} & Intracranial progression & time, age, race, prior radiation therapy, strata at randomization, progression (lagged), progression & time, baseline ECOG, strata at randomization, progression (lagged), progression\\
\cmidrule(lr){2-4}
& Target lesion size & time, quadratic time, age, sex, race, baseline ECOG, measurable intracranial central nervous system(CNS) disease, prior radiation therapy, strata at randomization, progression, treatment(lagged) &  time, quadratic time, age, quadratic age, sex, race, baseline ECOG,  strata at randomization, progression\\
\cmidrule(lr){2-4}
& Death & time, quadratic time, age, quadratic age, smoking history, strata at randomization, treatment (lagged), treatment, progression time & time, sex, measurable intracranial CNS disease, strata at randomization, intracranial progression (lagged), intracranial progression, progression time\\ 
\hline
\end{tabular}
\begin{tablenotes}
\item \textbf{Abbreviations}: ECOG, Eastern Cooperative Oncology Group score; CNS, Central Nervous System  
%\item[\ding{61}] Specification 4 from g-formula analysis is the same as specification 1 but replacing 2 categories of ECOG with 3 categories. Specification 5 from g-formula analysis is the same as specification 1 but without progression time.
\end{tablenotes}
\endgroup
\end{threeparttable}
\end{adjustwidth}
\end{table}
%\end{landscape}









% Spec 3
\onecolumn
\begin{table}[H]
\centering
\begin{adjustwidth}{-2.5cm}{-2.5cm} % Adjust the values of X as needed
\centering
\begin{threeparttable}
\caption{Description of the covariates included in specification 3 of the parametric g-formula analysis}
\begingroup
\renewcommand{\arraystretch}{1.5}
\begin{tabular}{>{\raggedright\arraybackslash}p{2cm}p{3cm}p{5cm}p{5cm}}
\hline
\textbf{Specification}\tnote{\ding{61}} & & \textbf{Control} &\textbf{Experimental}\\
\cmidrule(lr){3-3}
\cmidrule(lr){4-4}
& \textbf{Dependent Variable} & \textbf{Independent Variables} & \textbf{Independent Variables} \\
\cmidrule(lr){2-4}
\multirow{5}{*}{\textbf{}} & Progression & time, race, baseline ECOG, intracranial progression (lagged), target lesion size (lagged) & time, race, baseline ECOG, strata at randomization, intracranial progression (lagged), target lesion size (lagged)  \\
\cmidrule(lr){2-4}
& ECOG & time, age, quadratic age, race, baseline ECOG, smoking history, measurable intracranial CNS disease, prior radiation therapy, strata at randomization, progression (lagged), intracranial progression (lagged), target lesion size (lagged), treatment(lagged) &  time, age, quadratic age, sex, race, baseline ECOG, smoking history, measurable intracranial CNS disease, prior radiation therapy, strata at randomization, intracranial progression (lagged)\\
\cmidrule(lr){2-4}
\textbf{3} & Intracranial progression & time, age, prior radiation therapy, strata at randomization, progression (lagged), progression & time, baseline ECOG, strata at randomization, progression (lagged), progression\\
\cmidrule(lr){2-4}
& Target lesion size & time, quadratic time, age, sex, race, baseline ECOG, measurable intracranial central nervous system(CNS) disease, prior radiation therapy, strata at randomization, progression, treatment(lagged) &  time, quadratic time, age, quadratic age, sex, race, baseline ECOG,  strata at randomization, progression\\
\cmidrule(lr){2-4}
& Death & time, age, quadratic age, strata at randomization, treatment (lagged), treatment, progression time & time, intracranial progression (lagged), intracranial progression, progression time\\ 
\hline
\end{tabular}
\begin{tablenotes}
\item \textbf{Abbreviations}: ECOG, Eastern Cooperative Oncology Group score; CNS, Central Nervous System  
%\item[\ding{61}] Specification 4 from g-formula analysis is the same as specification 1 but replacing 2 categories of ECOG with 3 categories. Specification 5 from g-formula analysis is the same as specification 1 but without progression time.
\end{tablenotes}
\endgroup
\end{threeparttable}
\end{adjustwidth}
\end{table}
%\end{landscape}

\end{document}