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