merge

Latex/Paper/Main.tex

@@ -52,10 +52,10 @@
 \subfile{sections/10_CausalStory}
 \subfile{sections/02_data}
 
-%---------------------------------------------------------------
+% %---------------------------------------------------------------
-\section{Causal Identification}\label{SEC:CausalIdentification}
+% \section{Causal Identification}\label{SEC:CausalIdentification}
-%---------------------------------------------------------------
+% %---------------------------------------------------------------
-\subfile{sections/03_CausalIdentification}
+% \subfile{sections/03_CausalIdentification}
 
 %---------------------------------------------------------------
 \section{Econometric Model}\label{SEC:EconometricModel}

Latex/Paper/sections/03_CausalIdentification.tex

@@ -62,7 +62,7 @@ investment directly, causing a trial to terminate early if the return is
 not high enough.
 
 \begin{figure}[H] %use [H] to fix the figure here.
-	\includegraphics[width=\textwidth]{../assets/img/dagitty-model.jpg}
+    \scalebox{0.6}{\tikzfig{../assets/tikzit/CausalGraph2}}
     \caption{Causal Model}
     \label{Fig:CausalModel}
 \end{figure}

Latex/Paper/sections/04_EconometricModel.tex

@@ -47,8 +47,8 @@ The betas are distributed
 \end{align}
 With hyperparameters
 \begin{align}
-    \mu_k \sim \text{Normal}(0,1) \\
+    \mu_k \sim \text{Normal}(0,0.05) \\
-    \sigma_k \sim \text{Gamma}(2,1)
+    \sigma_k \sim \text{Gamma}(4,20)
 \end{align}
 
 

Latex/Paper/sections/06_Results.tex

@@ -19,97 +19,101 @@ written or requires reparameterization.
 %TODO: and info about how I learned about these diagnostics
 
 
-\subsubsection{Diagnostics}
+% \subsubsection{Diagnostics}
-%Examine trank plots
+% %Examine trank plots
-To identify which parameters were problematic, I first looked at trace rank 
+% To identify which parameters were problematic, I first looked at trace rank 
-histograms.
+% histograms.
-Under idea circumstances, each line (representing a chain) should exchange 
+% Under idea circumstances, each line (representing a chain) should exchange 
-places with the other lines frequently.
+% places with the other lines frequently.
-In both \cref{fig:mu_trank} and \cref{fig:sigma_trank}, most parameters seem
+% In both \cref{fig:mu_trank} and \cref{fig:sigma_trank}, most parameters seem
-to mix well but there are a couple of exceptions.
+% to mix well but there are a couple of exceptions.
-This warrants further investigation.
+% This warrants further investigation.
+%
+% \begin{figure}[H]
+%     \includegraphics[width=\textwidth]{../assets/img/mu_trank.png}
+%     \caption{Trace Rank Histogram: Mu values}
+% 	\label{fig:mu_trank}
+% \end{figure}
+%
+% \begin{figure}[H]
+%     \includegraphics[width=\textwidth]{../assets/img/sigma_trank.png}
+%     \caption{Trace Rank Histogram: Sigma values}
+% 	\label{fig:sigma_trank}
+% \end{figure}
+%
+% %Take a look at batman and points for mu
+% In the case of the Mu values, a parallel coordinates plot 
+% doesn't seem to indicate any parameters as likely candidates
+% for causing the issues with divergent transitions.
+% \begin{figure}[H]
+%     \includegraphics[width=\textwidth]{../assets/img/mu_batman.png}
+%     \caption{Parallel Coordinate Plot: Mu values}
+% 	\label{fig:mu_batman}
+% \end{figure}
+% Note that at each parameter, there is some level of dispersion between 
+% values that diverged.
+%
+% On the other hand, in the parallel coordinates plot for sigma values,
+% it appears that most divergent transitions occur with values of 
+% sigma[1], sigma[3], sigma[6], and sigma[7] close to zero.
+% \begin{figure}[H]
+%     \includegraphics[width=\textwidth]{../assets/img/sigma_batman.png}
+%     \caption{Parallel Coordinate Plot: Sigma values}
+% 	\label{fig:sigma_batman}
+% \end{figure}
+% Overall this suggests that there is an issue with the specification
+% of the covariance structures of the hyperparameters.
+%
+% Additional evidence that the covariance structure is incorrect comes from 
+% plotting pairs of parameter values and examining the chains with divergent
+% transitions.
+%
+% \begin{figure}[H]
+%     \includegraphics[width=\textwidth]{../assets/img/sigma_pairs_5-9.png}
+% 	\caption{Parameter Pairs plots: Sigma[5] through Sigma[9]}
+% 	\label{fig:sigma_pairs_5-9.png}
+% \end{figure}
+% From this we can see that divergent pairs are highly correlated with the cases
+% where sigma[6] or sigma[7] are equal to zero.
+% This has an impact on the shape of both of those estimated parameters, causing
+% both to be bimodal.
 
-\begin{figure}[H]
-    \includegraphics[width=\textwidth]{../assets/img/mu_trank.png}
-    \caption{Trace Rank Histogram: Mu values}
-	\label{fig:mu_trank}
-\end{figure}
 
-\begin{figure}[H]
+\subsection{Interpretation}
-    \includegraphics[width=\textwidth]{../assets/img/sigma_trank.png}
-    \caption{Trace Rank Histogram: Sigma values}
-	\label{fig:sigma_trank}
-\end{figure}
 
-%Take a look at batman and points for mu
+The key results so far are related to the distribution of differences in $p$.
-In the case of the Mu values, a parallel coordinates plot 
+
-doesn't seem to indicate any parameters as likely candidates
+In figure \ref{fig:pred_dist_dif_delay} we see that there while most trials do not see any increased risk 
-for causing the issues with divergent transitions.
+from a delay in closing enrollment, there is a small group that does experience this.
-\begin{figure}[H]
-    \includegraphics[width=\textwidth]{../assets/img/mu_batman.png}
-    \caption{Parallel Coordinate Plot: Mu values}
-	\label{fig:mu_batman}
-\end{figure}
-Note that at each parameter, there is some level of dispersion between 
-values that diverged.
 
-On the other hand, in the parallel coordinates plot for sigma values,
-it appears that most divergent transitions occur with values of 
-sigma[1], sigma[3], sigma[6], and sigma[7] close to zero.
 \begin{figure}[H]
-    \includegraphics[width=\textwidth]{../assets/img/sigma_batman.png}
+    \includegraphics[width=\textwidth]{../assets/img/current/pred_dist_diff-delay}
-    \caption{Parallel Coordinate Plot: Sigma values}
+	\caption{}
-	\label{fig:sigma_batman}
+	\label{fig:pred_dist_diff_delay}
 \end{figure}
-Overall this suggests that there is an issue with the specification
-of the covariance structures of the hyperparameters.
-
-Additional evidence that the covariance structure is incorrect comes from 
-plotting pairs of parameter values and examining the chains with divergent
-transitions.
 
+Figure \ref{fig:pred_dist_dif_delay2} shows how this varies across disease categories
 \begin{figure}[H]
-    \includegraphics[width=\textwidth]{../assets/img/sigma_pairs_5-9.png}
+    \includegraphics[width=\textwidth]{../assets/img/current/pred_dist_diff-delay-group}
-	\caption{Parameter Pairs plots: Sigma[5] through Sigma[9]}
+	\caption{}
-	\label{fig:sigma_pairs_5-9.png}
+	\label{fig:pred_dist_dif_delay2}
 \end{figure}
-From this we can see that divergent pairs are highly correlated with the cases
-where sigma[6] or sigma[7] are equal to zero.
-This has an impact on the shape of both of those estimated parameters, causing
-both to be bimodal.
-
-
-\subsection{Interpretation}
-
-Ignoring the diagnosed issues with the model, we do see some interesting
-preliminary results.
-
-%in mu, mu[5] shifted strongly
-In \cref{fig:mu_posterior} we see that mu[5], the parameter corresponding
-to enrollment appears to be strongly negative.
-This is consistent with the idea that enrollment close to planned enrollment
-decreases the probability of terminating the trial.
-In \cref{fig:sigma_posterior}, sigma[2] (corresponding to the number of brands
-selling the drug of interest) has a large variance covers some relatively 
-high values.
-This suggests that the impact of how frequently the drug is sold varies greatly
-across different ICD-10 categories of disease.
 
+We can also examine the direct effect from adding a single generic competitior drug.
 
 \begin{figure}[H]
-    \includegraphics[width=\textwidth]{../assets/img/mu_posterior.png}
+    \includegraphics[width=\textwidth]{../assets/img/current/pred_dist_diff-generic}
-	\caption{Posterior Parameter Estimates: Mu}
+	\caption{}
-	\label{fig:mu_posterior}
+	\label{fig:pred_dist_diff_generic}
 \end{figure}
 
-% Sigma[2] suggests there is a high variance in the impact that the number of drugs on the market has.
+Figure \ref{fig:pred_dist_dif_generic2} shows how this varies across disease categories
 \begin{figure}[H]
-    \includegraphics[width=\textwidth]{../assets/img/sigma_posterior.png}
+    \includegraphics[width=\textwidth]{../assets/img/current/pred_dist_diff-generic-group}
-	\caption{Posterior Hyperparameter Estimates: Sigma}
+	\caption{}
-	\label{fig:sigma_posterior}
+	\label{fig:pred_dist_dif_generic2}
 \end{figure}
 
-Due to the deficiencies in the data and model, this is the limit of the 
+
-analysis I will perform at this time.
 
 \end{document}

Latex/Paper/sections/10_CausalStory.tex

@@ -62,7 +62,7 @@ investment directly, causing a trial to terminate early if the return is
 not high enough.
 
 \begin{figure}[H] %use [H] to fix the figure here.
-	\includegraphics[width=\textwidth]{../assets/img/dagitty-model.jpg}
+    \scalebox{0.6}{\tikzfig{../assets/tikzit/CausalGraph2}}
     \caption{Causal Model}
     \label{Fig:CausalModel}
 \end{figure}

Latex/Presentation/presentation.tex

@@ -27,6 +27,7 @@
 \input{../assets/preambles/BibPreamble.tex}
 \input{../assets/preambles/GeneralPreamble.tex}
 
+\addbibresource{/home/will/research/ClinicalTrialsPaper/Latex/assets/preambles/References.bib}
 
 %----------------------------------------------------------------------------------------
 %    TITLE PAGE
@@ -445,19 +446,20 @@ Washington State University \\ % Your institution for the title page
 
     Thus the required adjustment set depends on the effects of interest.
 
-    For the total effect these are controls for:
+    For the total effect:
     \begin{itemize}
         \item Proceed with Phase III
         \item Condition
         \item Population
     \end{itemize}
 
-    For the direct effect these are controls for:
+    For the direct effect:
     \begin{itemize}
         \item Proceed with Phase III
         \item Condition
         \item Population (optional)
-        \item Enrollment
+        \item Enrollment Status
+        \item Elapsed Duration
     \end{itemize}
 
 \end{frame}
@@ -736,24 +738,53 @@ Washington State University \\ % Your institution for the title page
 \begin{frame}
     \frametitle{Total Effects Model}
     %TODO: describe X\beta
+    \begin{itemize}
+        \item asinh(brands with identical ingredients)
+        \item asinh(brands in USP-DC category)
+        \item asinh(high sdi DALY estimate)
+        \item asinh(high-medium sdi DALY estimate)
+        \item asinh(medium sdi DALY estimate)
+        \item asinh(low-medium sdi DALY estimate)
+        \item asinh(low sdi DALY estimate)
+    \end{itemize}
+    Units of observation: Snapshots
 \end{frame}
 %-------------------------------
 \begin{frame}
     \frametitle{Direct Effects Model}
     %TODO: describe X\beta
+    \begin{itemize}
+        \item elapsed duration 
+        \item enrollment status
+        \item asinh(brands with identical ingredients)
+        \item asinh(brands in USP-DC category)
+        \item asinh(high sdi DALY estimate)
+        \item asinh(high-medium sdi DALY estimate)
+        \item asinh(medium sdi DALY estimate)
+        \item asinh(low-medium sdi DALY estimate)
+        \item asinh(low sdi DALY estimate)
+    \end{itemize}
+    Units of Observation: Snapshot
 \end{frame}
 
 %-------------------------------
 \begin{frame}
     \frametitle{Analysis}
 
-    Review:
+    For each effect, we will look at:
     \begin{itemize}
-        \item Hyperparameters
+        \item Distribution of Parameters of Interest
-        \item Parameters of Interest
         \item Distrbution of Predicted Differences (Hypothetical Causal Intervention)
     \end{itemize}
 
+    \vspace{12pt}
+
+    The interventions are:
+    \begin{itemize}
+        \item Adding a single brand to the generic market competitors
+        \item Adding a single brand to the USP DC market competitors
+    \end{itemize}
+
 \end{frame}
 %-------------------------------
 \begin{frame}
@@ -767,29 +798,30 @@ Washington State University \\ % Your institution for the title page
 %--------------------------------
 %-------------------------------
 \begin{frame}
-    \frametitle{Priors - Mu}
+    \frametitle{Data Summaries}
     \begin{figure}
-%        \includegraphics[height=0.8\textheight]{../assets/img/Images/}
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/HistTrialDurations_Faceted.png}
-        \label{FIG:Prior:Mu}
-        \caption{Prior - Mu}
     \end{figure}
 \end{frame}
 %-------------------------------
 \begin{frame}
-    \frametitle{Priors - Sigma}
+    \frametitle{Data Summaries}
     \begin{figure}
-%        \includegraphics[height=0.8\textheight]{../assets/img/Images/}
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/HistSnapshots.png}
-        \label{FIG:Prior:Sigma}
-        \caption{Prior - Sigma}
     \end{figure}
 \end{frame}
 %-------------------------------
 \begin{frame}
-    \frametitle{Priors - $p$}
+    \frametitle{Data Summaries}
     \begin{figure}
-%        \includegraphics[height=0.8\textheight]{../assets/img/Images/}
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/SnapshotsVsDurationVsTermination.png}
-        \label{FIG:Prior:p}
+    \end{figure}
-        \caption{Prior - $p$}
+\end{frame}
+%-------------------------------
+\begin{frame}
+    \frametitle{Data Summaries}
+    \begin{figure}
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/CategoryCounts.png}
     \end{figure}
 \end{frame}
 %--------------------------------
@@ -803,29 +835,96 @@ Washington State University \\ % Your institution for the title page
 %        - Distributions
 % - Review Posterior Prediction for interventions
 %--------------------------------
+%%-------------------------------
+%\begin{frame}
+%    \frametitle{Priors - Mu}
+%    \begin{figure}
+%%        \includegraphics[height=0.8\textheight]{../assets/img/Images/}
+%        \label{FIG:Prior:Mu}
+%        \caption{Prior - Mu}
+%    \end{figure}
+%\end{frame}
+%%-------------------------------
+%\begin{frame}
+%    \frametitle{Priors - Sigma}
+%    \begin{figure}
+%%        \includegraphics[height=0.8\textheight]{../assets/img/Images/}
+%        \label{FIG:Prior:Sigma}
+%        \caption{Prior - Sigma}
+%    \end{figure}
+%\end{frame}
 %-------------------------------
 \begin{frame}
-    \frametitle{Results}
+    \frametitle{Priors - $p$}
-    Because Bayesian estimation is typically done numerically, we will first 
+    \begin{figure}
-    validate convergence.
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/TotalEffects/prior_p.png}
-
+        \label{FIG:Prior:p}
-    Then we will take a look at preliminary results.
+        \caption{Prior prediction - $p$}
-
+    \end{figure}
-    Sampling details
+\end{frame}
-
+%-------------------------------
-    %TODO: Update
+\begin{frame}
-    \begin{itemize}
+    \frametitle{Posteriors - $\beta$ Competing Brands}
-        \item 4 chains
+    \begin{figure}
-        \item 2,500 warm-up, 2,500 sampling runs
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/TotalEffects/Parameters/1&2_generics_and_uspdc.png}
-        \item seed = 11021585
+        \label{FIG:Posterior:beta-brands-total}
-    \end{itemize}
+    \end{figure}
+\end{frame}
+%-------------------------------
+\begin{frame}
+    \frametitle{Predictive Posteriors - $p$ - no intervention}
+    \begin{figure}
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/TotalEffects/posterior_p.png}
+        \label{FIG:Prior:p}
+        \caption{Posterior prediction - $p$}
+    \end{figure}
+\end{frame}
+%-------------------------------
+\begin{frame}
+    \frametitle{Posteriors - $p$ with intervention (generics)}
+    \begin{figure}
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/TotalEffects/default_p_generic_intervention_interv.png}
+        \label{FIG:Prior:p-intervention_total}
+    \end{figure}
+\end{frame}
+%-------------------------------
+\begin{frame}
+    \frametitle{Distribution of Differences - Generics Intervention}
+    \begin{figure}
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/TotalEffects/default_p_generic_intervention_distdiff.png}
+        \label{FIG:Prior:p-intervention_total}
+    \end{figure}
+\end{frame}
+%-------------------------------
+\begin{frame}
+    \frametitle{Distribution of Differences - Generics Intervention | By group}
+    \begin{figure}
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/TotalEffects/p_generic_intervention_histdiff_by_group.png}
+        \label{FIG:Prior:p-intervention_total}
+    \end{figure}
+\end{frame}
+%-------------------------------
+\begin{frame}
+    \frametitle{Posteriors - $p$ with intervention (USP DC)}
+    \begin{figure}
+%        \includegraphics[height=0.8\textheight]{../assets/img/Images/}
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/TotalEffects/p_uspdc_intervention_distdiff_styled.png}
+        \label{FIG:Prior:p-intervention_total}
+    \end{figure}
+\end{frame}
+%-------------------------------
+\begin{frame}
+    \frametitle{Posteriors - $p$ with intervention (USP DC) by group}
+    \begin{figure}
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/TotalEffects/p_uspdc_intervention_distdiff_by_group.png}
+        \label{FIG:Prior:p-intervention_total}
+    \end{figure}
 \end{frame}
 %-------------------------------
 \begin{frame}
     \frametitle{Questions?}
 
 \end{frame}
-%-------------------------------
 %--------------------------------
 \subsubsection{Direct Effects}
 % - Review Parameter Values
@@ -839,14 +938,62 @@ Washington State University \\ % Your institution for the title page
 %--------------------------------
 %-------------------------------
 \begin{frame}
-    \frametitle{Convergence}
+    \frametitle{Posteriors - $\beta$ Competing Brands}
-    Sampling details
+    \begin{figure}
-    %TODO: UPDATE
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/DirectEffects/Parameters/2+3_generic_and_uspdc.png}
-    \begin{itemize}
+        \label{FIG:Posterior:beta-brands-total}
-        \item 6 chains
+        \caption{Posterior prediction - $\beta$}
-        \item 2,500 warm-up, 2,500 sampling runs
+    \end{figure}
-        \item seed = 11021585
+\end{frame}
-    \end{itemize}
+%-------------------------------
+\begin{frame}
+    \frametitle{Predictive Posteriors - $p$ - no intervention}
+    \begin{figure}
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/DirectEffects/posterior_p.png}
+        \label{FIG:Prior:p}
+        \caption{Posterior prediction - $p$}
+    \end{figure}
+\end{frame}
+%-------------------------------
+\begin{frame}
+    \frametitle{Posteriors - $p$ with intervention (generics)}
+    \begin{figure}
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/DirectEffects/default_p_generic_intervention_interv.png}
+        \label{FIG:Prior:p-intervention_total}
+    \end{figure}
+\end{frame}
+%-------------------------------
+\begin{frame}
+    \frametitle{Distribution of Differences - Generics Intervention}
+    \begin{figure}
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/DirectEffects/default_p_generic_intervention_distdiff.png}
+        \label{FIG:Prior:p-intervention_total}
+    \end{figure}
+\end{frame}
+%-------------------------------
+\begin{frame}
+    \frametitle{Distribution of Differences - Generics Intervention | By group}
+    \begin{figure}
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/DirectEffects/p_generic_intervention_histdiff_by_group.png}
+        \label{FIG:Prior:p-intervention_total}
+    \end{figure}
+\end{frame}
+%-------------------------------
+\begin{frame}
+    \frametitle{Posteriors - $p$ with intervention (USP DC)}
+    \begin{figure}
+%        \includegraphics[height=0.8\textheight]{../assets/img/Images/}
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/DirectEffects/p_uspdc_intervention_distdiff_styled.png}
+        \label{FIG:Prior:p-intervention_total}
+    \end{figure}
+\end{frame}
+%-------------------------------
+\begin{frame}
+    \frametitle{Posteriors - $p$ with intervention (USP DC) by group}
+    \begin{figure}
+        \includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/DirectEffects/p_uspdc_intervention_histdiff_by_group.png}
+        \label{FIG:Prior:p-intervention_total}
+    \end{figure}
 \end{frame}
 %-------------------------------
 \begin{frame}
@@ -865,13 +1012,27 @@ Washington State University \\ % Your institution for the title page
     \begin{enumerate}
         \item Match more trials to ICD-10 codes and Formularies
         \item Add more formularies
-        \item Remove disease categories that don't exist in the data from the priors
+        \item Remove disease categories that don't exist in the data.
         \item Imputing Enrollment
+        \item Add covariance terms to $\beta$.
     \end{enumerate}
+
+    Suggestions?
 \end{frame}
 %-------------------------------
 \begin{frame}
     \frametitle{Summary}
+
+    Results Summary
+    \begin{enumerate}
+        \item A trial's response to adding a competitor drug depends on:
+            \begin{itemize}
+                \item Whether the drug is a generic or not
+                \item The disease category that applies to the trial
+            \end{itemize}
+            The effects suggest that the enrollment pathway had a strong regulating effect.
+        \item
+    \end{enumerate}
 \end{frame}
 %-------------------------------
 \begin{frame}
@@ -885,75 +1046,49 @@ Washington State University \\ % Your institution for the title page
 %-------------------------------------------------------------------------------------
 %----------------------------------
 %%%%%%%%%%%%%%%%%%%% Convergence Tests
-\subsection{Convergence}
+%\subsection{Convergence}
 %----------------------------------
 %-------------------------------
-\begin{frame}
-    \frametitle{Warnings}
-    %TODO: UPDATE
-
-    \begin{itemize}
-        \item There were no diverging transitions.
-        \item There were 15,000 transitions that exceeded max treedepth. 
-            Sampling efficiency is poor.
-        \item All chains had low Bayesian Fraction of Missing Information. 
-            Some areas of the distribution were poorly explored.
-        \item R-hat = $1.23$, ideal is around 1, chains did not mix well.
-        \item Bulk and Tail Effective Sample sizes were low, 
-            suggesting mean and variance/quantile estimates will be unreliable.
-    \end{itemize}
-    \cite{mc-stan}
-\end{frame}
-%-------------------------------
-\begin{frame}
-    \frametitle{Convergence: Mu}
-    \begin{figure}
-        %TODO: UPDATE
-        %\includegraphics[height=0.9\textheight]{../assets/img/2023-04-11_mu_points.png}
-        \label{FIG:caption}
-        \caption{Hyperparameter Points Plots: Mu}
-    \end{figure}
-\end{frame}
-%-------------------------------
-\begin{frame}
-    \frametitle{Convergence: Sigma}
-    \begin{figure}
-        %TODO: UPDATE
-        %\includegraphics[height=0.9\textheight]{../assets/img/2023-04-11_mu_points.png}
-        \label{FIG:caption}
-        \caption{Hyperparameter Points Plots: Sigma}
-    \end{figure}
-\end{frame}
-%-------------------------------
-\begin{frame}[allowframebreaks]
-    \frametitle{Bibliography}
-    \printbibliography
-\end{frame}
-%-------------------------------
-\end{document} 
-%=========================================
 %\begin{frame}
-%    \frametitle{MarginalRevenue}
+%    \frametitle{Warnings}
+%    %TODO: UPDATE
+%
+%    \begin{itemize}
+%        \item There were no diverging transitions.
+%        \item There were 15,000 transitions that exceeded max treedepth. 
+%            Sampling efficiency is poor.
+%        \item All chains had low Bayesian Fraction of Missing Information. 
+%            Some areas of the distribution were poorly explored.
+%        \item R-hat = $1.23$, ideal is around 1, chains did not mix well.
+%        \item Bulk and Tail Effective Sample sizes were low, 
+%            suggesting mean and variance/quantile estimates will be unreliable.
+%    \end{itemize}
+%    \cite{mc-stan}
+%\end{frame}
+%%-------------------------------
+%\begin{frame}
+%    \frametitle{Convergence: Mu}
 %    \begin{figure}
-%        \tikzfig{../Assets/owned/ch8_MarginalRevenue}
+%        %TODO: UPDATE
-%        \includegraphics[height=\textheight]{../Assets/copyrighted/KrugmanObsterfeldMeliz_fig8-7.jpg}
+%        %\includegraphics[height=0.9\textheight]{../assets/img/2023-04-11_mu_points.png}
-%        \label{FIG:costs}
+%        \label{FIG:caption}
-%        \caption{Average Cost Curve as firms enter.}
+%        \caption{Hyperparameter Points Plots: Mu}
 %    \end{figure}
 %\end{frame}
-%-------------------------------
+%%-------------------------------
 %\begin{frame}
-%    \frametitle{Columns}
+%    \frametitle{Convergence: Sigma}
-%     \begin{columns}
-%        \begin{column}{0.5\textwidth}
-%        \end{column}
-%        \begin{column}{0.5\textwidth}
 %    \begin{figure}
-%                   \tikzfig{../Assets/owned/ch7_EstablishedAdvantageExample2}
+%        %TODO: UPDATE
-%                   \label{FIG:costs}
+%        %\includegraphics[height=0.9\textheight]{../assets/img/2023-04-11_mu_points.png}
-%                   \caption{Setting the Stage}
+%        \label{FIG:caption}
+%        \caption{Hyperparameter Points Plots: Sigma}
 %    \end{figure}
-%        \end{column}
-%     \end{columns}
 %\end{frame}
-% %---------------------------------------------------------------
+%%-------------------------------
+\begin{frame}[allowframebreaks]
+    \frametitle{Bibliography}
+    \printbibliography
+\end{frame}
+%-------------------------------
+\end{document} 

Latex/Presentation/presentation.tex.bak

@@ -1,573 +0,0 @@
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Beamer Presentation
-% LaTeX Template
-% Version 1.0 (10/11/12)
-%
-% This template has been downloaded from:
-% http://www.LaTeXTemplates.com
-%
-% License:
-% CC BY-NC-SA 3.0 (http://creativecommons.org/licenses/by-nc-sa/3.0/)
-%
-% Changed theme to WSU by William King
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%----------------------------------------------------------------------------------------
-%	PACKAGES AND THEMES
-%----------------------------------------------------------------------------------------
-
-\documentclass[xcolor=dvipsnames,aspectratio=169]{beamer}
-
-
-%Import Preamble bits
-\input{../assets/preambles/FormattingPreamble.tex}
-\input{../assets/preambles/TikzitPreamble.tex}
-\input{../assets/preambles/MathPreamble.tex}
-\input{../assets/preambles/BibPreamble.tex}
-\input{../assets/preambles/GeneralPreamble.tex}
-
-
-
-
-%----------------------------------------------------------------------------------------
-%	TITLE PAGE
-%----------------------------------------------------------------------------------------
-
-\title[Clinical Trials]{The Effects of Market Conditions on Recruitment and Completion of Clinical Trials} 
-
-\author{Will King} % Your name
-\institute[WSU] % Your institution as it will appear on the bottom of every slide, may be shorthand to save space
-{
-Washington State University \\ % Your institution for the title page
-\medskip
-\textit{william.f.king@wsu.edu} % Your email address
-}
-\date{\today} % Date, can be changed to a custom date
-
-
-
-
-
-\begin{document}
-\begin{frame}
-\titlepage % Print the title page as the first slide
-\end{frame}
-%----------------------------------
-\begin{frame} %Allow frame breaks
-\frametitle{Clincial Trials} % Table of contents slide, comment this out to remove it
-    % - Intro and hook (Clinical Trials are key part of pharmacological pipeline)
-    Pharmaceuticals are a frequently discussed aspect of health care cost managment.
-    Their development is dictated by scientific and regulatory hurdles 
-    including passing clinical trials
-    (\cite{noauthor_fda_nodate}), 
-    while their market is characterized by strategic competition and ambiguous 
-    patent protection
-    (\cite{van_der_gronde_addressing_2017}).
-
-    \vspace{12pt}
-
-    This research investigates the pathways by which market conditions
-    affect clinical trial completion.
-\end{frame}
-%-------------------------------
-\begin{frame}
-    \frametitle{This research}
-    \textbf{Questions:} 
-    \begin{enumerate}
-        \item Does the existence of alternative drugs on the market make it
-            harder for clinical trials to complete successfully? 
-        \item How much of this is occurs due to increased recruitment difficulty?
-    \end{enumerate}
-    
-\end{frame}
-%--------------------------------
-\begin{frame}
-\frametitle{Thanks} % Table of contents slide, comment this out to remove it
-    Thanks to Chris Adams and Rebecca Sachs of the Congressional Budget Office.
-\end{frame}
-%--------------------------------
-\begin{frame}[allowframebreaks] %Allow frame breaks
-\frametitle{Overview} % Table of contents slide, comment this out to remove it
-\tableofcontents 
-% - Intro and hook
-% - Literature review
-% - Causal Identification
-% - Data
-% - Econometric model
-% - Results
-% - Improvements
-\end{frame}
-%-------------------------------------------------------------------------------------
-%%%%%%%%%%%%%%%%%%%% Lit Review %%%%%%%%%%%%%%%%%%%%%%%%
-\section{Lit Review}
-% First slide:
-%-------------------------------------------------------------------------------------
-%-------------------------------
-\begin{frame}
-    \frametitle{Literature Highlights}
-    \begin{itemize}
-        \item \cite{van_der_gronde_addressing_2017}: 
-            High level synthesis of overall discussion regarding drug costs. 
-            Both academic and non-academic sources.
-        \item \cite{hwang_failure_2016}:
-            Answered the question "Why do late-stage (phase III) trials fail?"
-            Found that efficacy, safety, and competition reasons accounted for 
-            57\%, 17\%, and 22\% respectively.
-        \item \cite{abrantes-metz_pharmaceutical_2004}:
-            Described how drugs progress through the 3 phases of clinical trials
-            and correllations between various trial characteristics and the 
-            clinical trial failures.
-        \item \cite{khmelnitskaya_competition_2021}: 
-            Modeled clinical trial lifecycle of drugs, found method to separate
-            scientific from competitive reasons for failure to progress to the 
-            next phase.
-%        \item \cite{}: 
-
-    \end{itemize}
-\end{frame}
-%-------------------------------
-\begin{frame}
-    \frametitle{This research, in context}
-
-    In contrast to previous work looking at multiple phases of trials,
-    I seek to figure out what causes individual trials to fail.
-
-    \vspace{12pt}
-
-    Instead of focusing on the drug development pipeline, I attempt to 
-    investigate the population of drug-based, phase III trials.
-\end{frame}
-%-------------------------------
-\begin{frame} %Allow frame breaks
-\frametitle{Why this approach?} % Table of contents slide, comment this out to remove it
-
-    \begin{figure}
-        \includegraphics[height=0.8\textheight]{../assets/img/methodology_trial.png}
-        \label{FIG:xkcd2726}
-        \caption{``If you think THAT'S unethical, you should see the stuff we approved via our Placebo IRB.'' 
-        - \url{https://xkcd.com/2726}
-        }
-    \end{figure}
-\end{frame}
-%-------------------------------------------------------------------------------------
-%%%%%%%%%%%%%%%%%%%% Causal Identification / DGP%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Causal Model}
-% Data Generating process
-% - Agents and their decisions
-% - Factors that influence each decision
-% - 
-% - 
-%-------------------------------------------------------------------------------------
-%-------------------------------
-\begin{frame}
-    \frametitle{Data Generating Process}
-    % study sponsors
-    Study Sponsors Decide to start a Phase 3 trial and whether to terminate it.
-    \\
-    They ask themselves:
-    \begin{itemize}
-        \item Do safety incidents require terminating a trial?
-        \item Do efficacy results indicate the trial is worth continuing?
-        \item Is recruiting sufficient to achieve our results and contain costs?
-        \item Do expectations about future returns justify our expenditures?
-    \end{itemize}
-    
-\end{frame}
-%-------------------------------
-\begin{frame}
-    \frametitle{Data Generating Process}
-    % participants
-    Participants decide to enroll (and disenroll) themselves in a trial based 
-    \begin{itemize}
-        \item Disease severity
-        \item Relative safety/efficacy compared to other treatments
-    \end{itemize}
-
-    Study sponsors plan their enrollment considering
-    \begin{itemize}
-        \item Total population affected
-        \item Likely participant response rates
-    \end{itemize}
-
-\end{frame}
-%-------------------------------
-\begin{frame}
-    \frametitle{Data Generating Process}
-    % Trial Snapshots and dependencies.
-    During a trial, the study sponsor reports snapshots of their trial.
-    This includes updates to:
-
-    \begin{itemize}
-        \item enrollment (actual or anticipated)
-        \item current recruitment status (Recruiting, Active not recruiting, etc)
-        \item study sponsor
-        \item planned completion dates
-        \item elapsed duration
-    \end{itemize}
-
-    Note that final enrollment and the final status (Completed or Terminated) 
-    of the trial are jointly determined.
-\end{frame}
-%-------------------------------
-\begin{frame}
-    \frametitle{Causal Diagram: Key Pathways}
-    % Estimating Direct vs Total Effects
-    \begin{figure}
-        \resizebox{!}{0.5\textheight}{
-            \tikzfig{../assets/tikzit/CausalGraph}
-        }
-        \label{FIG:CausalDiagram}
-        \caption{Causal Diagram highlighting direct and total pathways}
-    \end{figure}
-\end{frame}
-%-------------------------------
-\begin{frame}
-    \frametitle{Causal Diagram: Backdoor Crieterion}
-    \small
-    \begin{block}{$d$-separation}
-        A set $S$ of nodes blocks a path $p$ if either
-        \begin{enumerate}
-            \item $p$ contains at least one arrow-emitting node in $S$
-            \item $p$ contains at least one collision node $c$ that is outside $S$ 
-                and has no descendants in $S$.
-        \end{enumerate}
-        If $S$ blocks all paths from X to Y, then it is said to ``$d$-separate'' 
-        $X$ and $Y$, and then $X \perp Y | S$.
-    \end{block}
-    \begin{block}{Back-Door Criterion}
-        A set $S$ of covariates is admisible as controls on the 
-        causal relationship $X \rightarrow Y$ if:
-        \begin{enumerate}
-            \item No element of $S$ is a decendant of $X$
-            \item The elements of $S$ d-separate all paths from $X$ to $Y$ that include
-                parents of $X$.
-        \end{enumerate}
-    \end{block}
-    \cite{pearl_causality_2000}
-\end{frame}
-%-------------------------------
-\begin{frame}
-    \frametitle{Causal Diagram}
-    Key takeaways
-    \begin{itemize}
-        \item Measuring enrollment prior to trial completion is necessary for causal identification.
-        \item The backdoor criterion gives us the following adjustment sets:
-            \begin{itemize}
-                \item Total Effect for Market on Termination; Population, Condition, Phase III
-                \item Direct Effects for Enrollment, Market on Termination; Population, Condition Phase III, 
-                    Elapsed Duration, Planned Enrollment
-            \end{itemize}
-        \item Enrollment requires imputation
-    \end{itemize}
-\end{frame}
-%-------------------------------------------------------------------------------------
-%%%%%%%%%%%%%%%%%%%% Data %%%%%%%%%%%%%%%%%%%%%%%%
-\section{Data}
-%-------------------------------------------------------------------------------------
-%----------------------------------
-%%%%%%%%%%%%%%%%%%%% Sources
-\subsection{Sources}
-%----------------------------------
-%-------------------------------
-\begin{frame} %Allow frame breaks
-    \frametitle{Data Sources}
-    \begin{itemize}
-        \item ClinicalTrials.gov - AACT \& custom scripts
-            \begin{itemize}
-                \item Select trials of interest
-                \item Trial details: 
-                    \begin{itemize}
-                        \item conditions
-                        \item final status
-                        \item drugs/interventions
-                    \end{itemize}
-                \item Trial snapshots:
-                    \begin{itemize}
-                        \item enrollment (anticipated, planned, or actual)
-                        \item elapsed duration
-                        \item current status
-                    \end{itemize}
-            \end{itemize}
-        \item Medical Subject Headings (MeSH) Thesaurus
-            \begin{itemize}
-                \item A standardized nomenclature used to classify interventions 
-                    and conditions in the clinical trials database.
-            \end{itemize}
-    \end{itemize}
-\end{frame}
-%-------------------------------
-\begin{frame} %Allow frame breaks
-    \frametitle{Data Sources}
-    \begin{itemize}
-        \item NSDE Files (New drug code Structured product labels Data Element)
-            \begin{itemize}
-                \item Contains information about when a given drug was on the market.
-            \end{itemize}
-        \item RxNorm
-            \begin{itemize}
-                \item Links pharmaceuticals between MeSH standardized terms and 
-                    NSDE files.
-            \end{itemize}
-        \item Global Disease Burden Survey (2019)
-            \begin{itemize}
-                \item Estimates of DALYs for categories of disease
-                \item Links of Categories to ICD-10 Codes
-            \end{itemize}
-        \item ICD-10 (2019)
-            \begin{itemize}
-                \item WHO version
-                \item CMS version (Clinical Managment)
-                \item Used to group disease conditions in hierarchal model
-            \end{itemize}
-        \item Unified Medical Language System Thesaurus
-            \begin{itemize}
-                \item Used to link MeSH standardized terms and ICD-10 conditions
-                \item Manual matching process
-            \end{itemize}
-    \end{itemize}
-\end{frame}
-%----------------------------------
-%%%%%%%%%%%%%%%%%%%% Integration
-\subsection{Integration}
-%----------------------------------
-%-------------------------------
-\begin{frame}
-    \frametitle{Data Summaries}
-    %put summaries now
-    \begin{itemize}
-        \item Number of Phase III, FDA monitored Drug Trials: 1,981
-        \item Number of Trials matched to ICD-10: 186
-        \item Number of Trials matched to ICD-10 with population measures: 67 
-            (51 completed, 16 terminated)
-        \item Number of Snapshots: 616
-    \end{itemize}
-\end{frame}
-%-------------------------------
-\begin{frame}
-    \frametitle{Data used}
-    The following data points were used.
-    \begin{itemize}
-        \item elapsed duration 
-        \item asinh(number of brands)
-        \item asinh(high sdi DALY estimate)
-        \item asinh(high-medium sdi DALY estimate)
-        \item asinh(medium sdi DALY estimate)
-        \item asinh(low-medium sdi DALY estimate)
-        \item asinh(low sdi DALY estimate)
-    \end{itemize}
-    The asinh operator was used because it parallells $\text{ln}(x)$ for 
-    large values of $x$ but also handles $\text{asinh}(0)=0$.
-\end{frame}
-%----------------------------------
-\begin{frame}
-    \frametitle{Summaries: Trial Durations}
-    \begin{figure}
-        \includegraphics[height=0.8\textheight]{../assets/img/2023-04-12_durations_hist.png}
-        \label{FIG:durations}
-        \caption{Trial Durations (days)}
-    \end{figure}
-\end{frame}
-%----------------------------------
-\begin{frame}
-    \frametitle{Summaries: snapshots}
-    \begin{figure}
-        \includegraphics[height=0.8\textheight]{../assets/img/2023-04-12_snapshots_hist.png}
-        \label{FIG:snapshots}
-        \caption{Number of Snapshots per matched trial}
-    \end{figure}
-\end{frame}
-%----------------------------------
-\begin{frame}
-    \frametitle{Summaries: snapshots}
-    \begin{figure}
-        \includegraphics[height=0.8\textheight]{../assets/img/2023-04-12_status_duration_snapshots_points.png}
-        \label{FIG:snapshot_duration_scatter}
-        \caption{Scatterplot of snapshot count and durations}
-    \end{figure}
-\end{frame}
-%-------------------------------------------------------------------------------------
-%%%%%%%%%%%%%%%%%%%% Econometric Model %%%%%%%%%%%%%%%%%%%%%%%%
-\section{Econometric model}
-%-------------------------------------------------------------------------------------
-%-------------------------------
-\begin{frame}
-    \frametitle{Econometric Model}
-    Estimating the total effect of brands on market
-    \begin{align}
-        y_n &\sim \text{Bernoulli}(p_n) \\
-        p_n &= \text{logisticfn}(x_n * \beta(d_n)) \\
-        \beta_k(d) &\sim \text{Normal}(\mu_k, \sigma_k) \\
-        \mu_k &\sim \text{Normal}(0,1) \\
-        \sigma_k &\sim \text{Gamma}(2,1)
-    \end{align}
-    $k$ indexes parameters and $d_n$ represets the ICD-10 group the trial corresponds to.
-\end{frame}
-%-------------------------------------------------------------------------------------
-%%%%%%%%%%%%%%%%%%%% Results %%%%%%%%%%%%%%%%%%%%%%%%
-\section{Results}
-%-------------------------------------------------------------------------------------
-%-------------------------------
-\begin{frame}
-    \frametitle{Results}
-    Because bayesian estimation is typically done numerically, we will first 
-    validate convergence.
-
-    Then we will take a look at preliminary results.
-
-    Sampling details
-    \begin{itemize}
-        \item 6 chains
-        \item 2,500 warmup, 2,500 sampling runs
-        \item seed = 11021585
-    \end{itemize}
-\end{frame}
-%----------------------------------
-%%%%%%%%%%%%%%%%%%%% Convergence Tests
-\subsection{Convergence}
-%----------------------------------
-%-------------------------------
-\begin{frame}
-    \frametitle{Warnings}
-
-    \begin{itemize}
-        \item There were no diverging transitions.
-        \item There were 15,000 transitions that exceeded max treedepth. 
-            Sampling efficiency is poor.
-        \item All chains had low Bayesian Fraction of Missing Information. 
-            Some areas of the distribution were poorly explored.
-        \item R-hat = $1.23$, ideal is around 1, chains did not mix well.
-        \item Bulk and Tail Effective Sample sizes were low, 
-            suggesting mean and variance/quantile estimates will be unreliable.
-    \end{itemize}
-    \cite{mc-stan}
-\end{frame}
-%-------------------------------
-\begin{frame}
-    \frametitle{Convergence: Mu}
-    \begin{figure}
-        \includegraphics[height=0.9\textheight]{../assets/img/2023-04-11_mu_points.png}
-        \label{FIG:caption}
-        \caption{Hyperparameter Points Plots: Mu}
-    \end{figure}
-\end{frame}
-%-------------------------------
-\begin{frame}
-    \frametitle{Convergence: Sigma}
-    \begin{figure}
-        \includegraphics[height=0.8\textheight]{../assets/img/2023-04-11_sigma_points.png}
-        \label{FIG:caption}
-        \caption{Hyperparameter Points Plots: Sigma}
-    \end{figure}
-\end{frame}
-%----------------------------------
-%%%%%%%%%%%%%%%%%%%% Preliminary Results
-\subsection{Preliminary Results}
-%----------------------------------
-%-------------------------------
-\begin{frame}
-    \frametitle{Preliminary Results: Mu}
-
-    \begin{columns}
-        \begin{column}{0.3\textwidth}
-            \begin{enumerate}
-                \item elapsed duration 
-                \item asinh(n\_brands)
-                \item asinh(high sdi)
-                \item asinh(high-medium sdi)
-                \item asinh(medium sdi)
-                \item asinh(low-medium sdi)
-                \item asinh(low sdi)
-            \end{enumerate}
-        \end{column}
-        \begin{column}{0.7\textwidth}
-            \begin{figure}
-                \includegraphics[height=0.8\textheight]{../assets/img/2023-04-11_mu_dist.png}
-                \label{FIG:caption}
-                \caption{Hyperparameter Distribution: Mu}
-            \end{figure}
-        \end{column}
-    \end{columns}
-\end{frame}
-%-------------------------------
-\begin{frame}
-    \frametitle{Preliminary Results: Sigma}
-
-    \begin{figure}
-        \includegraphics[height=0.8\textheight]{../assets/img/2023-04-11_sigma_dist.png}
-        \label{FIG:caption}
-        \caption{Hyperparameter Distribution: Sigma}
-    \end{figure}
-\end{frame}
-%-------------------------------
-\begin{frame}
-    \frametitle{Interpretation}
-    All of the following interpretations are done in the context of insufficient data
-
-    \begin{enumerate}
-        \item Elapsed Duration (Mu[1]): Trending Negative, reduced probability of termination.
-        \item Number of Brands(Mu[2]): Trending Positive, increased probability of termination.
-        \item Population Measures (Mu[3]-Mu[7])
-            \begin{enumerate}
-                \item What is most surprising is that these are both positive and negative.
-                    Probably need more data.
-            \end{enumerate}
-        \item It is surprising to see the wide distribution in sigma values.
-    \end{enumerate}
-\end{frame}
-%-------------------------------------------------------------------------------------
-%%%%%%%%%%%%%%%%%%%% Improvements %%%%%%%%%%%%%%%%%%%%%%%%
-\section{Improvements}
-%-------------------------------------------------------------------------------------
-%-------------------------------
-\begin{frame}
-    \frametitle{Proposed improvements}
-    \begin{enumerate}
-        \item Match more trials to ICD-10 codes
-        \item Improve Measures of Market Conditions
-        \item Adjust Covariance Structure
-        \item Find Reasonable Priors
-        \item Remove disease categories that don't exist in the data from the priors
-        \item Imputing Enrollment
-        \item Improve Population Estimates
-    \end{enumerate}
-\end{frame}
-%-------------------------------
-\begin{frame}
-    \frametitle{Questions?}
-    \center{\huge{Questions?}}
-
-\end{frame}
-%-------------------------------
-\begin{frame}[allowframebreaks]
-    \frametitle{Bibliography}
-    \printbibliography
-\end{frame}
-%-------------------------------
-\end{document} 
-%=========================================
-%\begin{frame}
-%    \frametitle{MarginalRevenue}
-%    \begin{figure}
-%        \tikzfig{../Assets/owned/ch8_MarginalRevenue}
-%        \includegraphics[height=\textheight]{../Assets/copyrighted/KrugmanObsterfeldMeliz_fig8-7.jpg}
-%        \label{FIG:costs}
-%        \caption{Average Cost Curve as firms enter.}
-%    \end{figure}
-%\end{frame}
-%-------------------------------
-%\begin{frame}
-%    \frametitle{Columns}
-%     \begin{columns}
-%        \begin{column}{0.5\textwidth}
-%        \end{column}
-%        \begin{column}{0.5\textwidth}
-%               \begin{figure}
-%                   \tikzfig{../Assets/owned/ch7_EstablishedAdvantageExample2}
-%                   \label{FIG:costs}
-%                   \caption{Setting the Stage}
-%               \end{figure}
-%        \end{column}
-%     \end{columns}
-%\end{frame}
-% %---------------------------------------------------------------

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