getting things up to date
will king
2 years ago
parent
ad0b0531fc
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6f6b5b20f0
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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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%
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% This template has been downloaded from:
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% http://www.LaTeXTemplates.com
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%
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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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%
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% Changed theme to WSU by William King
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%
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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{Clinical 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 management.
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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 ways 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}[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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%-------------------------------------------------------------------------------------
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%%%%%%%%%%%%%%%%%%%% Introduction and Background %%%%%%%%%%%%%%%%%%%%%%%%
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\section{Background}
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% TOC
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% - Background on drug process
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% - Literature on clinical trials
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% - My questions
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% add info about trials
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% - Requirements (pre registered design [2007], updated "regularly" on clinicaltrials.gov)
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% - Phases (1,2,3,4, mixed)
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% - Safety and Ethicas (oversight boards, restrictions on payments)
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% - Approval processes (biologics vs small-molecule)
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% add info about drugs
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%-------------------------------------------------------------------------------------
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%-------------------------------
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\begin{frame}
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\frametitle{Clinical Trials and Drug develoment}
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The FDA requires clinical trials before approving new drug compounds
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\begin{itemize}
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\item Pre-registered design
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\item Updated regularly on clinicaltrials.gov
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\item Often requires an oversight board.
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\item Goal is to prove efficacy and safety of a compound/dosage/route.
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\item A new drug candidate (NDC) must complete 3 phases of clinical trials before approval.
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\item Phases are reviewed with FDA.
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\item Not all clinical trials are for new drugs.
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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{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 correlations 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 life-cycle 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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%
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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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%
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\vspace{12pt}
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Questions
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\begin{itemize}
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\item How do the competitors on the market affect clinical trial completion?
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\item How is this effect moderated by the enrollment of participants?
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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{Audience Questions}
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\center{What can I clarify?}
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\end{frame}
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%-------------------------------------------------------------------------------------
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%%%%%%%%%%%%%%%%%%%% Causality and Data %%%%%%%%%%%%%%%%%%%%%%%%
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\section{Causal Story and Data}
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% TOC
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% - Causal Story (no subsection)
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% - Clinical trials: targets specific drug/condition combination.
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% - Enrollment process: patients counsel with providers
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% - Trials terminate if unsafe, ineffective, unprofitable, or cannot enroll patients
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% - Ethical concerns exist throughout.
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% - This is complicated by the fact that the experiment reveals information over time.
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% - Formalization
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% - Data Sources
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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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\begin{frame}[shrink=10] %evil option is helpful here.
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\frametitle{How do clinical trials proceed?}
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\begin{columns}[T]
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\begin{column}{0.5\textwidth}
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What does a \textif{Completed} trial look like?
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\begin{enumerate}
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\item Study sponsor comes up with design
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\item Apply for NCT ID from ClinicalTrials.gov
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\item Begin enrolling participants
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\item Update ClinicalTrials.gov to recruit
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\item Close Enrollment
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\item Update ClinicalTrials.gov as not recruiting*
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\item Reach primary objectives
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\item Update ClinicalTrials.gov as complete
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\item Reach secondary objectives
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\item Update ClinicalTrials.gov with more information
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\end{enumerate}
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\end{column}
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\begin{column}{0.5\textwidth}
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What does an \textif{Terminated} trial look like?
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\begin{enumerate}
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\item Study sponsor comes up with design
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\item Apply for NCT ID from ClinicalTrials.gov
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\item Begin enrolling participants
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\item Update ClinicalTrials.gov to advertise
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\item Run into issues:
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\begin{itemize}
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\item Safety
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\item Efficacy
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\item Profitability
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\item Feasiblity (enrollment, PI leaves, etc.)
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\end{itemize}
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\item Close Enrollment*
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\item Decide to terminate clinical trial.
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\item Update ClinicalTrials.gov as terminated.
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\end{enumerate}
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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{ClinicalTrials.gov}
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Thus ClinicalTrials.gov becomes an (append only) repository of
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the ``current'' status of clincal trials.
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As it is designed to help faciltate enrollment in clinical trials,
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the record includes important information such as
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\begin{itemize}
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\item drugs
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\item study arms
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\item conditions
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\item expected and final enrollment figures
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\item current status
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\end{itemize}
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ClinicalTrials.gov also reports the history from previous
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updates.
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Decision-Making 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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They 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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\item Their network of clinicians
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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{Decision-Making Process}
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% participants
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Participants decide to enroll (and dis-enroll) themselves in a trial based on
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\begin{itemize}
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\item Doctor Recommendations
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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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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Questions?}
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\center{What clarifying questions do you have?}
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\end{frame}
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%-------------------------------
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%--------------------------------
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%%%%%%%%%%%%%%%%%%%% Causal Formalization
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\subsection{Formalization}
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% - Introduce basic triangle
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% - discuss total vs direct effects
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% -
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% - Add confounders and controls
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% - Introduce backdoor criterion
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%--------------------------------
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%-------------------------------
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\begin{frame} %Allow frame breaks
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\frametitle{Why this approach?}
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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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\begin{frame}
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\frametitle{Framing my Questions}
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\begin{columns}[T]
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\begin{column}{0.5\textwidth}
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Two potential causes of trial termination include
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\begin{enumerate}
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\item Alternative (competitor) treatments exist
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\begin{itemize}
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\item reduces future profitability.
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\item reduces incentives to enroll as participants.
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\end{itemize}
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\item It can be difficult to recruit patients
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\begin{itemize}
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\item Are there few patients?
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\item Are potential participants choosing other alternatives?
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\end{itemize}
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\end{enumerate}
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\end{column}
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\begin{column}{0.5\textwidth}
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Overall this can be described graphically as:
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\begin{figure}
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\scalebox{0.8}{
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\tikzfig{../assets/tikzit/4Node}
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}
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\label{FIG:4Node}
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\caption{Total Effect}
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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{Causal Effects}
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%Discuss the two different effects: total effect, direct effects
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\begin{columns}
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\begin{column}{0.5\textwidth}
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Total Effect of Competitors
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\begin{figure}
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\scalebox{0.8}{
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\tikzfig{../assets/tikzit/4Node_total}
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}
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\label{FIG:4Node}
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\caption{Total Effect}
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\end{figure}
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\end{column}
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\begin{column}{0.5\textwidth}
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Direct Effects of Competitors and Enrollment
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\begin{figure}
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\scalebox{0.8}{
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\tikzfig{../assets/tikzit/4Node_direct}
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}
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\label{FIG:4Node}
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\caption{Direct Effect}
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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{Rephrasing Questions}
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To rephrase my questions
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\begin{enumerate}
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\item How large is the total effect of increasing the number
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of competing drugs on completing clinical trials?
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\item How large is the direct effect of increasing the number
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of competing drugs on completing clincial trials?
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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{Additional Concerns}
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%Confounders
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Of course, there are other confounding relationships
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\begin{enumerate}
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\item Population Effects
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\item Fundamental Safety and Efficacy of compound/dosage/route
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\item How long it is taking
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\item
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\end{enumerate}
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%TODO: Fill out with more details from graph
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Complete graph}
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%introduce backdoor criterion
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\begin{figure}
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\scalebox{0.6}{
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\tikzfig{../assets/tikzit/CausalGraph}
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}
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\label{FIG:CausalGraph}
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\caption{Full Causal Graph}
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\end{figure}
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Discuss concerns about Elapsed Duration and Enrollment
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Causal Diagram: Backdoor Criterion}
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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 $p$ on a DAG 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 admissible 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 descendant 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{Sufficent Adjustment Set}
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%introduce backdoor criterion
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Thus the required adjustment set depends on the effects of interest.
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For the total effect these are controls for:
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\begin{itemize}
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\item Proceed with Phase III
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\item Condition
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\item Population
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\end{itemize}
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Discuss Regime Switching
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For the direct effect these are controls for:
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\begin{itemize}
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\item Proceed with Phase III
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\item Condition
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\item Population (optional)
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\item Enrollment
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\end{itemize}
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Not causally identified due to Regime Switching
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Other testable hypotheses}
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One advantage of this approach tools can automatically
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\begin{itemize}
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\item verify causal identification
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\item generate hypotheses to verify model
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\end{itemize}
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Automatic hypotheses
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% \begin{itemize}
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% \item Condition $\perp$ Elapsed Duration
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% \item Decision to continue Phase III $\perp$ Elapsed Duration
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% \item Decision to continue Phase III $\perp$ Market Conditions | Condition
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% \item Decision to continue Phase III $\perp$ Population | Condition
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% \item Elapsed Duration $\perp$ Market Conditions
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% \item Elapsed Duration $\perp$ Population
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% \item Terminated $\perp$ Population | Condition, Decision to continue Phase III, Elapsed Duration, Enrollment Status, Market Conditions
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% \end{itemize}
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% \href{Dagitty.net model}{http://dagitty.net/mLyFuc5}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Questions?}
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\end{frame}
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%-------------------------------
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%--------------------------------
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%%%%%%%%%%%%%%%%%%%% Data sources
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\subsection{Data Sources}
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% TOC
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% - Main Data Sources
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% - ClinicalTrials.gov and AACT
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% - IHME Burden of Disease
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% - Marketing Data
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% - MeSH, RxNorm/RxNav
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% - How did I Link Data Sources
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% - Data Sizes
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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
|
||||
\end{itemize}
|
||||
\item Trial snapshots:
|
||||
\begin{itemize}
|
||||
\item elapsed duration
|
||||
\item enrollment status (NYE,EBI,R,ANR)
|
||||
\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 USP Drug Classification (2023)
|
||||
\begin{itemize}
|
||||
\item Used to measure which drugs
|
||||
\end{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.
|
||||
\item Used to find brand names that share active ingredients with those from trial.
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame} %Allow frame breaks
|
||||
\frametitle{Data Sources}
|
||||
\begin{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 Management)
|
||||
\item Used to group disease conditions in hierarchical 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}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Linking data}
|
||||
%
|
||||
The following linking process was used:
|
||||
\begin{enumerate}
|
||||
\item AACT trials to snapshots (internal ID)
|
||||
\item AACT trials to ICD-10 (hand match)
|
||||
\item ICD-10 to IHME (IHME)
|
||||
\item Snapshots to drug brands (RxNorm/RxNav/MeSh, SPL)
|
||||
\item AACT to USP DC alternates (RxNorm, USP DC, hand match)
|
||||
\end{enumerate}
|
||||
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Data used}
|
||||
The following data points were used.
|
||||
\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}
|
||||
The asinh operator was used because it parallels $\text{ln}(x)$ for
|
||||
large values of $x$ but also handles $\text{asinh}(0)=0$.
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Measures of Causes and Effects}
|
||||
|
||||
Here are the actual measures used for causes
|
||||
\begin{itemize}
|
||||
\item Final Status: Measured from AACT - status when trial is over.
|
||||
\item Competitors on Market: Measured by the number of drugs
|
||||
\begin{itemize}
|
||||
\item with same active ingredients (at the time of the snapshot)
|
||||
\item sharing the USP DC category and class (in 2023)
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
|
||||
Effects are measured in parameter values and changes in probability
|
||||
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Adjustment set}
|
||||
Here are the actual measures of the adjustment set
|
||||
\begin{itemize}
|
||||
\item Enrollment: Measured by enrollment status at the snapshot level.
|
||||
\item Elapsed Duration: Measured at snapshot level
|
||||
by $\frac{\text{Current Date} - \text{Start Date}}{\text{Planned Completion Date} - \text{Start Date}}$
|
||||
\item Population Measures
|
||||
\begin{itemize}
|
||||
\item IHME Global Disease Burden: DALYs, spread over 5 levels of the Social Development Index
|
||||
\end{itemize}
|
||||
\item Beliefs about safety \& efficacy: Restricted to Phase 3 trials.
|
||||
\item Disease Type: Hierarchal parameters in model
|
||||
\end{itemize}
|
||||
|
||||
Note the implicit conditioning on trials treating diseases with IHME data\footnote{
|
||||
IHME does not track data for W61.62XD: Struck by duck, subsequent encounter
|
||||
}.
|
||||
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Other Details}
|
||||
|
||||
Other Trial Selection Criteria
|
||||
\begin{itemize}
|
||||
\item Interventional Study
|
||||
\item Involved an FDA Regulated Drug
|
||||
\item Phase 3 trial
|
||||
\item Started after 2010-01-01
|
||||
\item Ended before 2022-01-01
|
||||
\end{itemize}
|
||||
|
||||
\end{frame}
|
||||
%----------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Summary
|
||||
\subsection{Data Summary}
|
||||
%----------------------------------
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Data Summaries}
|
||||
%TODO: Update
|
||||
\begin{itemize}
|
||||
\item Number of Phase III, FDA monitored Drug Trials: 1,981
|
||||
\item Number of Trials matched to ICD-10:
|
||||
\item Number of Trials matched to ICD-10 with population measures:
|
||||
( completed, terminated)
|
||||
\item Number of Snapshots:
|
||||
\end{itemize}
|
||||
\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}
|
||||
%%-------------------------------
|
||||
%\begin{frame}
|
||||
% \frametitle{Questions?}
|
||||
%
|
||||
%\end{frame}
|
||||
%-------------------------------
|
||||
%-------------------------------------------------------------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Analysis %%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Analysis}
|
||||
% TOC
|
||||
% - Review questions and datasets to use for each
|
||||
% -
|
||||
% -
|
||||
%-------------------------------------------------------------------------------------
|
||||
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{General Approach}
|
||||
|
||||
\begin{itemize}
|
||||
\item Logistic model
|
||||
\item Bayesian Hierarchal model
|
||||
\begin{itemize}
|
||||
\item Allows for transfer learning between groups
|
||||
\end{itemize}
|
||||
\item Distribution of Predicted Differences
|
||||
\begin{itemize}
|
||||
|
||||
\end{frame}
|
||||
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Total Effects Model}
|
||||
\begin{align}
|
||||
y_i \sim \text{Bernoulli}(p_i) \\
|
||||
p_i = \text{logistic}(X_i \vec\beta_{c(i)}) \\
|
||||
\vec\beta_{c(i)} \sim \text{MvNormal}(\vec\mu,\vec\sigma I)
|
||||
\end{align}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Questions?}
|
||||
|
||||
\end{frame}
|
||||
%--------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Results
|
||||
\subsection{Results}
|
||||
%--------------------------------
|
||||
%--------------------------------
|
||||
\subsubsection{Total Effect}
|
||||
% - Review Parameter Values
|
||||
% - hyperparameters
|
||||
% - Table of MLE
|
||||
% - Distributions
|
||||
% - betas
|
||||
% - Table of MLE
|
||||
% - Distributions
|
||||
% - Review Posterior Prediction for interventions
|
||||
%--------------------------------
|
||||
%-------------------------------
|
||||
\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
|
||||
|
||||
%TODO: Update
|
||||
\begin{itemize}
|
||||
\item 6 chains
|
||||
\item 2,500 warm-up, 2,500 sampling runs
|
||||
\item seed = 11021585
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Questions?}
|
||||
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
%--------------------------------
|
||||
\subsubsection{Direct Effects}
|
||||
% - Review Parameter Values
|
||||
% - hyperparameters
|
||||
% - Table of MLE
|
||||
% - Distributions
|
||||
% - betas
|
||||
% - Table of MLE
|
||||
% - Distributions
|
||||
% - Review Posterior Prediction for interventions
|
||||
%--------------------------------
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Convergence}
|
||||
Sampling details
|
||||
%TODO: UPDATE
|
||||
\begin{itemize}
|
||||
\item 6 chains
|
||||
\item 2,500 warm-up, 2,500 sampling runs
|
||||
\item seed = 11021585
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Questions?}
|
||||
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
%-------------------------------------------------------------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Conclusion %%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Conclusion}
|
||||
%-------------------------------------------------------------------------------------
|
||||
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Proposed improvements}
|
||||
\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 Imputing Enrollment
|
||||
\end{enumerate}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Summary}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Final Questions}
|
||||
|
||||
\center{\huge{Time is yours to ask any remaining questions.}}
|
||||
\end{frame}
|
||||
%-------------------------------------------------------------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Appendicies %%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Appendices}
|
||||
%-------------------------------------------------------------------------------------
|
||||
%----------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Convergence Tests
|
||||
\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}
|
||||
% \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}
|
||||
% %---------------------------------------------------------------
|
||||
Loading…
Reference in New Issue