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\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 6}
%\vspace{1.5em} % Increase the space between "Electronic Supplementary Material 1" and "Data Dictionary"
\vspace{30pt}
\large \textbf{
Survival and Forest Plots
}
\end{center}
\vspace{30pt}
\maketitle
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\begin{figure}[t]
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    \hfill
    %\begin{subfigure}[b]{0.60\textwidth}
        \raggedright \includegraphics[width=\textwidth,height=8cm]{FigureS1.pdf}
         \caption{Forest plot of RR and their 95\% CI for the effect of brigatinib versus crizotinib on OS investigated through various modelling approaches. RRs for the ITT, exclude switchers censor at switching and including treatment as a TVC analyses were estimated from a pooled logistic regression model. RR for the IPCW approach was estimated using a weighted pooled logistic regression model using the product of the two weights for LTFU/AC (specifications 4 in Table 4) and switching (specifications 4 in Table 5). RR from the parametric g-formula were estimated from specification 1 in Table 7. 95\% CIs were estimated using a non-parametric bootstrap procedure based on 1000 samples for all approaches and 500 samples for the parametric g-formula}
        \label{forest_all}
    %\end{subfigure}
\end{figure}
}





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    \begin{subfigure}[b]{0.75\textwidth}
        \raggedright
        \includegraphics[width=\textwidth]{FigureS2a_merged.pdf}
        \caption{\textbf{Kaplan-Meier survival curves comparing overall survival between \enquote{assign to brigatinib} and \enquote{assign to crizotinib} and assuming non-informative censoring; Survival probabilities are derived from the KM estimator, Cumulative Hazard Ratios (cHRs) and Risk Ratios(RRs) are estimated from a pooled logistic regression model}}
        \label{survplot_ITT}
    \end{subfigure}%
    \hfill
    \begin{subfigure}[b]{0.75\textwidth}
        \raggedright
        \includegraphics[width=\textwidth]{FigureS2b_merged.pdf}
        \caption{\textbf{Parametric survival curves standardized for baseline covariate distribution from a pooled logistic regression comparing overall survival between \enquote{assign to brigatinib} and \enquote{assign to crizotinib} and assuming non-informative censoring; Cumulative Hazard Ratios (cHRs), Risk Ratios(RRs) and survival probabilities are estimated from a pooled logistic regression model standardized for baseline covariate distribution}}
        \label{survplot_itt_param}
    \end{subfigure}
\caption{\textbf{Overall survival: ITT}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% IPCW Forest Plot LTFU       %
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\begin{figure}[t]
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    %\begin{subfigure}[b]{0.60\textwidth}
        \raggedright \includegraphics[width=\textwidth,height=8cm]{FigureS3.pdf}
         \caption{Forest plot of RR and 95\% CI for the Causal effect of \enquote{assign to brigatinib} versus \enquote{assign to crizotinib} on OS investigated through specifications 1 to 6 using IPCW. Death is censored by LTFU/AC. RRs were estimated from a weighted pooled logistic regression using weights for LTFU/AC and formulated as the ratio of the cumulative risks by month 48. Reported CIs were estimated using a non-parametric bootstrap procedure based on 1000 samples. cHR, cumulative hazard ratio; CI, confidence interval; OS, overall survival, IPCW, inverse probability of censoring weights; LTFU, loss to follow up; AC, administrative censoring}
        \label{forest_lofu}
    %\end{subfigure}
\end{figure}
}







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\begin{figure}[b]
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    \begin{subfigure}[b]{0.75\textwidth}
        \raggedright
        \includegraphics[width=\textwidth]{FigureS4a_merged.pdf}
        \caption{\textbf{Overall survival: Censoring at switching}}
        \label{survplot_rs}
    \end{subfigure}
    \hfill
    \begin{subfigure}[b]{0.75\textwidth}
        \raggedright
        \includegraphics[width=\textwidth]{FigureS4b_merged.pdf}
        \caption{\textbf{Overall survival: Excluding switchers}}
        \label{survplot_cs}
    \end{subfigure}
\caption{\textbf{Kaplan-Meier survival curves comparing overall survival between \enquote{always Treat with Crizotinib} and \enquote{always Treat with brigatinib} and assuming non-informative censoring; Survival probabilities are derived from the KM estimator, Cumulative Hazard Ratios (cHRs) and Risk Ratios(RRs) are estimated from a pooled logistic regression model; In panel (a) switchers were excluded; In panel (b) switchers were censored at switching }}
\label{fig4}
\end{figure}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% IPCW Forest Plot XO         %
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    \hfill
    %\begin{subfigure}[b]{0.60\textwidth}
        \raggedright \includegraphics[width=\textwidth,height=8cm]{FigureS5.pdf}
         \caption{Forest plot of RR and 95\% CI for the causal effect of \enquote{always treat with brigatinib} versus \enquote{always treat with crizotinib} on OS investigated through specifications 1 to 8 using IPCW. LTFU is assumed at random; Death is censored by a minimum of treatment switching and LTFU/AC and formulated as the ratio of the cumulative risks by month 48. Reported CIs were estimated using a non-parametric bootstrap procedure based on 1000 samples. cHR, cumulative hazard ratio; CI, confidence interval; OS, overall survival, IPCW, inverse probability of censoring weights}
        \label{forest_lofu}
    %\end{subfigure}
\end{figure}
}








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\begin{figure}\captionsetup{justification=justified, singlelinecheck=false}
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        \raggedright
        \includegraphics[width=\textwidth,height=8cm]{FigureS6.pdf}
        \caption{Forest plot of RR and their 95\% CI for the causal effect of \enquote{always treat with brigatinib} versus \enquote{always treat with crizotinib} on OS investigated through specifications 1 to 5 using the parametric g-formula. Reported CIs were calculated using a non-parametric bootstrap procedure based on 500 samples ( with 60 replicate failures observed for specification 4)}
        \label{forest_g}
    %\end{subfigure}
\end{figure}















\end{document}