From f1fef9d5a622b3a01516afcaeae9f3641f38c99d Mon Sep 17 00:00:00 2001 From: will king Date: Wed, 12 Apr 2023 11:34:13 -0700 Subject: [PATCH] Created final draft for today's presentation --- Latex/Paper/Main.tex | 10 + Latex/Presentation/presentation.tex | 486 ++++++++++++++- Latex/Presentation/presentation.tex.bak | 573 ++++++++++++++++++ Latex/assets/img/2023-04-11_mu_dist.png | Bin 0 -> 31957 bytes Latex/assets/img/2023-04-11_mu_hist.png | Bin 0 -> 21476 bytes Latex/assets/img/2023-04-11_mu_points.png | Bin 0 -> 65492 bytes Latex/assets/img/2023-04-11_sigma_dist.png | Bin 0 -> 35611 bytes Latex/assets/img/2023-04-11_sigma_hist.png | Bin 0 -> 22780 bytes Latex/assets/img/2023-04-11_sigma_points.png | Bin 0 -> 66297 bytes .../assets/img/2023-04-12_durations_hist.png | Bin 0 -> 19302 bytes .../assets/img/2023-04-12_snapshots_hist.png | Bin 0 -> 17724 bytes ...04-12_status_duration_snapshots_points.png | Bin 0 -> 24510 bytes Latex/assets/img/methodology_trial.png | Bin 0 -> 28335 bytes 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mode 100644 Latex/assets/preambles/references/O.bib diff --git a/Latex/Paper/Main.tex b/Latex/Paper/Main.tex index f05e053..2e46390 100644 --- a/Latex/Paper/Main.tex +++ b/Latex/Paper/Main.tex @@ -13,6 +13,16 @@ \usepackage{float} + +%setup paragraph level indexing +\usepackage{titlesec} +\setcounter{secnumdepth}{4} + +\titleformat{\paragraph} +{\normalfont\normalsize\bfseries}{\theparagraph}{1em}{} +\titlespacing*{\paragraph} +{0pt}{3.25ex plus 1ex minus .2ex}{1.5ex plus .2ex} + \title{The effects of market conditions on enrollment and completion of clinical trials\\ \small{Preliminary Draft}} \author{William King} diff --git a/Latex/Presentation/presentation.tex b/Latex/Presentation/presentation.tex index cb6b45f..add128b 100644 --- a/Latex/Presentation/presentation.tex +++ b/Latex/Presentation/presentation.tex @@ -30,12 +30,11 @@ - %---------------------------------------------------------------------------------------- % TITLE PAGE %---------------------------------------------------------------------------------------- -\title[short title]{Long title} +\title[Clinical Trials]{The Effects of Market Conditions on Recruitment and Completion of Clinical Trials} \author{Will King} % Your name \institute[WSU] % Your institution as it will appear on the bottom of every slide, may be shorthand to save space @@ -54,68 +53,497 @@ Washington State University \\ % Your institution for the title page \begin{frame} \titlepage % Print the title page as the first slide \end{frame} +%---------------------------------- +\begin{frame} %Allow frame breaks +\frametitle{Clinical Trials} % Table of contents slide, comment this out to remove it + % - Intro and hook (Clinical Trials are key part of pharmacological pipeline) + Pharmaceuticals are a frequently discussed aspect of health care cost management. + Their development is dictated by scientific and regulatory hurdles + including passing clinical trials + (\cite{noauthor_fda_nodate}), + while their market is characterized by strategic competition and ambiguous + patent protection + (\cite{van_der_gronde_addressing_2017}). + \vspace{12pt} + This research investigates the pathways by which market conditions + affect clinical trial completion. +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{This research} + \textbf{Questions:} + \begin{enumerate} + \item Does the existence of alternative drugs on the market make it + harder for clinical trials to complete successfully? + \item How much of this is occurs due to increased recruitment difficulty? + \end{enumerate} + +\end{frame} +%-------------------------------- +\begin{frame} +\frametitle{Thanks} % Table of contents slide, comment this out to remove it + Thanks to Chris Adams and Rebecca Sachs of the Congressional Budget Office. +\end{frame} +%-------------------------------- \begin{frame}[allowframebreaks] %Allow frame breaks \frametitle{Overview} % Table of contents slide, comment this out to remove it \tableofcontents +% - Intro and hook +% - Literature review +% - Causal Identification +% - Data +% - Econometric model +% - Results +% - Improvements \end{frame} +%------------------------------------------------------------------------------------- +%%%%%%%%%%%%%%%%%%%% Lit Review %%%%%%%%%%%%%%%%%%%%%%%% +\section{Lit Review} +% First slide: +%------------------------------------------------------------------------------------- +%------------------------------- +\begin{frame} + \frametitle{Literature Highlights} + \begin{itemize} + \item \cite{van_der_gronde_addressing_2017}: + High level synthesis of overall discussion regarding drug costs. + Both academic and non-academic sources. + \item \cite{hwang_failure_2016}: + Answered the question "Why do late-stage (phase III) trials fail?" + Found that efficacy, safety, and competition reasons accounted for + 57\%, 17\%, and 22\% respectively. + \item \cite{abrantes-metz_pharmaceutical_2004}: + Described how drugs progress through the 3 phases of clinical trials + and correlations between various trial characteristics and the + clinical trial failures. + \item \cite{khmelnitskaya_competition_2021}: + Modeled clinical trial life-cycle of drugs, found method to separate + scientific from competitive reasons for failure to progress to the + next phase. +% \item \cite{}: + \end{itemize} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{This research, in context} + + In contrast to previous work looking at multiple phases of trials, + I seek to figure out what causes individual trials to fail. + + \vspace{12pt} + + Instead of focusing on the drug development pipeline, I attempt to + investigate the population of drug-based, phase III trials. +\end{frame} +%------------------------------- +\begin{frame} %Allow frame breaks +\frametitle{Why this approach?} % Table of contents slide, comment this out to remove it + + \begin{figure} + \includegraphics[height=0.8\textheight]{../assets/img/methodology_trial.png} + \label{FIG:xkcd2726} + \caption{``If you think THAT'S unethical, you should see the stuff we approved via our Placebo IRB.'' + - \url{https://xkcd.com/2726} + } + \end{figure} +\end{frame} %------------------------------------------------------------------------------------- -%%%%%%%%%%%%%%%%%%%% Developing the Model%%%%%%%%%%%%%%%%%%%%%%%% -\section{Money: Supply and Demand} +%%%%%%%%%%%%%%%%%%%% Causal Identification / DGP%%%%%%%%%%%%%%%%%%%%%%%% +\section{Causal Model} +% Data Generating process +% - Agents and their decisions +% - Factors that influence each decision +% - +% - %------------------------------------------------------------------------------------- %------------------------------- \begin{frame} - \frametitle{What is Money?} - \begin{block}{Money} - A commodity that is: - \begin{itemize} - \item Medium of exchange: A generally accepted means of payment. - \item Store of value: A method to transfer value from now into the future. - \end{itemize} - \end{block} + \frametitle{Data Generating Process} + % study sponsors + Study Sponsors Decide to start a Phase 3 trial and whether to terminate it. + \\ + They ask themselves: + \begin{itemize} + \item Do safety incidents require terminating a trial? + \item Do efficacy results indicate the trial is worth continuing? + \item Is recruiting sufficient to achieve our results and contain costs? + \item Do expectations about future returns justify our expenditures? + \end{itemize} + +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Data Generating Process} + % participants + Participants decide to enroll (and dis-enroll) themselves in a trial based + \begin{itemize} + \item Disease severity + \item Relative safety/efficacy compared to other treatments + \end{itemize} + + Study sponsors plan their enrollment considering + \begin{itemize} + \item Total population affected + \item Likely participant response rates + \end{itemize} - What types of money exist? - \begin{itemize} - \item M0: Currency - \item \textbf{M1: M0 + Checking/bank deposits} - \end{itemize} \end{frame} %------------------------------- \begin{frame} - \frametitle{Money Demand} + \frametitle{Data Generating Process} + % Trial Snapshots and dependencies. + During a trial, the study sponsor reports snapshots of their trial. + This includes updates to: + + \begin{itemize} + \item enrollment (actual or anticipated) + \item current recruitment status (Recruiting, Active not recruiting, etc) + \item study sponsor + \item planned completion dates + \item elapsed duration + \end{itemize} - Nominal Money Demand + Note that final enrollment and the final status (Completed or Terminated) + of the trial are jointly determined. +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Causal Diagram: Key Pathways} + % Estimating Direct vs Total Effects + \begin{figure} + \resizebox{!}{0.5\textheight}{ + \tikzfig{../assets/tikzit/CausalGraph} + } + \label{FIG:CausalDiagram} + \caption{Causal Diagram highlighting direct and total pathways} + \end{figure} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Causal Diagram: Backdoor Criterion} + \small + \begin{block}{$d$-separation} + A set $S$ of nodes blocks a path $p$ if either + \begin{enumerate} + \item $p$ contains at least one arrow-emitting node in $S$ + \item $p$ contains at least one collision node $c$ that is outside $S$ + and has no descendants in $S$. + \end{enumerate} + If $S$ blocks all paths from X to Y, then it is said to ``$d$-separate'' + $X$ and $Y$, and then $X \perp Y | S$. + \end{block} + \begin{block}{Back-Door Criterion} + A set $S$ of covariates is admissible as controls on the + causal relationship $X \rightarrow Y$ if: + \begin{enumerate} + \item No element of $S$ is a descendant of $X$ + \item The elements of $S$ d-separate all paths from $X$ to $Y$ that include + parents of $X$. + \end{enumerate} + \end{block} + \cite{pearl_causality_2000} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Causal Diagram} + Key takeaways + \begin{itemize} + \item Measuring enrollment prior to trial completion is necessary for causal identification. + \item The backdoor criterion gives us the following adjustment sets: + \begin{itemize} + \item Total Effect for Market on Termination; Population, Condition, Phase III + \item Direct Effects for Enrollment, Market on Termination; Population, Condition Phase III, + Elapsed Duration, Planned Enrollment + \end{itemize} + \item Enrollment requires imputation + \end{itemize} +\end{frame} +%------------------------------------------------------------------------------------- +%%%%%%%%%%%%%%%%%%%% Data %%%%%%%%%%%%%%%%%%%%%%%% +\section{Data} +%------------------------------------------------------------------------------------- +%---------------------------------- +%%%%%%%%%%%%%%%%%%%% Sources +\subsection{Sources} +%---------------------------------- +%------------------------------- +\begin{frame} %Allow frame breaks + \frametitle{Data Sources} + \begin{itemize} + \item ClinicalTrials.gov - AACT \& custom scripts + \begin{itemize} + \item Select trials of interest + \item Trial details: + \begin{itemize} + \item conditions + \item final status + \item drugs/interventions + \end{itemize} + \item Trial snapshots: + \begin{itemize} + \item enrollment (anticipated, planned, or actual) + \item elapsed duration + \item current status + \end{itemize} + \end{itemize} + \item Medical Subject Headings (MeSH) Thesaurus + \begin{itemize} + \item A standardized nomenclature used to classify interventions + and conditions in the clinical trials database. + \end{itemize} + \end{itemize} +\end{frame} +%------------------------------- +\begin{frame} %Allow frame breaks + \frametitle{Data Sources} + \begin{itemize} + \item NSDE Files (New drug code Structured product labels Data Element) + \begin{itemize} + \item Contains information about when a given drug was on the market. + \end{itemize} + \item RxNorm + \begin{itemize} + \item Links pharmaceuticals between MeSH standardized terms and + NSDE files. + \end{itemize} + \item Global Disease Burden Survey (2019) + \begin{itemize} + \item Estimates of DALYs for categories of disease + \item Links of Categories to ICD-10 Codes + \end{itemize} + \item ICD-10 (2019) + \begin{itemize} + \item WHO version + \item CMS version (Clinical 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} +%---------------------------------- +%%%%%%%%%%%%%%%%%%%% Integration +\subsection{Integration} +%---------------------------------- +%------------------------------- +\begin{frame} + \frametitle{Data Summaries} + %put summaries now + \begin{itemize} + \item Number of Phase III, FDA monitored Drug Trials: 1,981 + \item Number of Trials matched to ICD-10: 186 + \item Number of Trials matched to ICD-10 with population measures: 67 + (51 completed, 16 terminated) + \item Number of Snapshots: 616 + \end{itemize} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Data used} + The following data points were used. + \begin{itemize} + \item elapsed duration + \item asinh(number of brands) + \item asinh(high sdi DALY estimate) + \item asinh(high-medium sdi DALY estimate) + \item asinh(medium sdi DALY estimate) + \item asinh(low-medium sdi DALY estimate) + \item asinh(low sdi DALY estimate) + \end{itemize} + The asinh operator was used because it parallels $\text{ln}(x)$ for + large values of $x$ but also handles $\text{asinh}(0)=0$. +\end{frame} +%---------------------------------- +\begin{frame} + \frametitle{Summaries: Trial Durations} + \begin{figure} + \includegraphics[height=0.8\textheight]{../assets/img/2023-04-12_durations_hist.png} + \label{FIG:durations} + \caption{Trial Durations (days)} + \end{figure} +\end{frame} +%---------------------------------- +\begin{frame} + \frametitle{Summaries: snapshots} + \begin{figure} + \includegraphics[height=0.8\textheight]{../assets/img/2023-04-12_snapshots_hist.png} + \label{FIG:snapshots} + \caption{Number of Snapshots per matched trial} + \end{figure} +\end{frame} +%---------------------------------- +\begin{frame} + \frametitle{Summaries: snapshots} + \begin{figure} + \includegraphics[height=0.8\textheight]{../assets/img/2023-04-12_status_duration_snapshots_points.png} + \label{FIG:snapshot_duration_scatter} + \caption{Scatterplot of snapshot count and durations} + \end{figure} +\end{frame} +%------------------------------------------------------------------------------------- +%%%%%%%%%%%%%%%%%%%% Econometric Model %%%%%%%%%%%%%%%%%%%%%%%% +\section{Econometric model} +%------------------------------------------------------------------------------------- +%------------------------------- +\begin{frame} + \frametitle{Econometric Model} + Estimating the total effect of brands on market \begin{align} - M^d = P \cdot L(R,Y) + y_n &\sim \text{Bernoulli}(p_n) \\ + p_n &= \text{logisticfn}(x_n * \beta(d_n)) \\ + \beta_k(d) &\sim \text{Normal}(\mu_k, \sigma_k) \\ + \mu_k &\sim \text{Normal}(0,1) \\ + \sigma_k &\sim \text{Gamma}(2,1) \end{align} - + $k$ indexes parameters and $d_n$ represents the ICD-10 group the trial corresponds to. +\end{frame} +%------------------------------------------------------------------------------------- +%%%%%%%%%%%%%%%%%%%% Results %%%%%%%%%%%%%%%%%%%%%%%% +\section{Results} +%------------------------------------------------------------------------------------- +%------------------------------- +\begin{frame} + \frametitle{Results} + Because Bayesian estimation is typically done numerically, we will first + validate convergence. + + Then we will take a look at preliminary results. + + Sampling details \begin{itemize} - \item $Y \uparrow \Rightarrow L(R,Y) \uparrow$ - \item $R \downarrow \Rightarrow L(R,Y) \uparrow$ + \item 6 chains + \item 2,500 warm-up, 2,500 sampling runs + \item seed = 11021585 \end{itemize} +\end{frame} +%---------------------------------- +%%%%%%%%%%%%%%%%%%%% Convergence Tests +\subsection{Convergence} +%---------------------------------- +%------------------------------- +\begin{frame} + \frametitle{Warnings} + \begin{itemize} + \item There were no diverging transitions. + \item There were 15,000 transitions that exceeded max treedepth. + Sampling efficiency is poor. + \item All chains had low Bayesian Fraction of Missing Information. + Some areas of the distribution were poorly explored. + \item R-hat = $1.23$, ideal is around 1, chains did not mix well. + \item Bulk and Tail Effective Sample sizes were low, + suggesting mean and variance/quantile estimates will be unreliable. + \end{itemize} + \cite{mc-stan} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Convergence: Mu} + \begin{figure} + \includegraphics[height=0.9\textheight]{../assets/img/2023-04-11_mu_points.png} + \label{FIG:caption} + \caption{Hyperparameter Points Plots: Mu} + \end{figure} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Convergence: Sigma} + \begin{figure} + \includegraphics[height=0.8\textheight]{../assets/img/2023-04-11_sigma_points.png} + \label{FIG:caption} + \caption{Hyperparameter Points Plots: Sigma} + \end{figure} \end{frame} +%---------------------------------- +%%%%%%%%%%%%%%%%%%%% Preliminary Results +\subsection{Preliminary Results} +%---------------------------------- %------------------------------- \begin{frame} - \frametitle{Equilibrium in the Money Market} - Interest rates are the price of money, so we need to compare - interest rates to the quantity of money demanded. + \frametitle{Preliminary Results: Mu} + \begin{columns} + \begin{column}{0.3\textwidth} + \begin{enumerate} + \item elapsed duration + \item asinh(n\_brands) + \item asinh(high sdi) + \item asinh(high-medium sdi) + \item asinh(medium sdi) + \item asinh(low-medium sdi) + \item asinh(low sdi) + \end{enumerate} + \end{column} + \begin{column}{0.7\textwidth} + \begin{figure} + \includegraphics[height=0.8\textheight]{../assets/img/2023-04-11_mu_dist.png} + \label{FIG:caption} + \caption{Hyperparameter Distribution: Mu} + \end{figure} + \end{column} + \end{columns} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Preliminary Results: Sigma} \begin{figure} -% \tikzfig{../Assets/tikzit/} - \label{FIG:costs} - \caption{Money Market Equilibrium} + \includegraphics[height=0.8\textheight]{../assets/img/2023-04-11_sigma_dist.png} + \label{FIG:caption} + \caption{Hyperparameter Distribution: Sigma} \end{figure} \end{frame} %------------------------------- +\begin{frame} + \frametitle{Interpretation} + All of the following interpretations are done in the context of insufficient data + + \begin{enumerate} + \item Elapsed Duration (Mu[1]): Trending Negative, reduced probability of termination. + \item Number of Brands(Mu[2]): Trending Positive, increased probability of termination. + \item Population Measures (Mu[3]-Mu[7]) + \begin{enumerate} + \item What is most surprising is that these are both positive and negative. + Probably need more data. + \end{enumerate} + \item It is surprising to see the wide distribution in sigma values. + \end{enumerate} +\end{frame} +%------------------------------------------------------------------------------------- +%%%%%%%%%%%%%%%%%%%% Improvements %%%%%%%%%%%%%%%%%%%%%%%% +\section{Improvements} +%------------------------------------------------------------------------------------- +%------------------------------- +\begin{frame} + \frametitle{Proposed improvements} + \begin{enumerate} + \item Match more trials to ICD-10 codes + \item Improve Measures of Market Conditions + \item Adjust Covariance Structure + \item Find Reasonable Priors + \item Remove disease categories that don't exist in the data from the priors + \item Imputing Enrollment + \item Improve Population Estimates + \end{enumerate} +\end{frame} +%------------------------------- \begin{frame} \frametitle{Questions?} + \center{\huge{Questions?}} \end{frame} %------------------------------- +\begin{frame}[allowframebreaks] + \frametitle{Bibliography} + \printbibliography +\end{frame} +%------------------------------- \end{document} %========================================= %\begin{frame} diff --git a/Latex/Presentation/presentation.tex.bak b/Latex/Presentation/presentation.tex.bak new file mode 100644 index 0000000..3003d08 --- /dev/null +++ b/Latex/Presentation/presentation.tex.bak @@ -0,0 +1,573 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Beamer Presentation +% LaTeX Template +% Version 1.0 (10/11/12) +% +% This template has been downloaded from: +% http://www.LaTeXTemplates.com +% +% License: +% CC BY-NC-SA 3.0 (http://creativecommons.org/licenses/by-nc-sa/3.0/) +% +% Changed theme to WSU by William King +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%---------------------------------------------------------------------------------------- +% PACKAGES AND THEMES +%---------------------------------------------------------------------------------------- + +\documentclass[xcolor=dvipsnames,aspectratio=169]{beamer} + + +%Import Preamble bits +\input{../assets/preambles/FormattingPreamble.tex} +\input{../assets/preambles/TikzitPreamble.tex} +\input{../assets/preambles/MathPreamble.tex} +\input{../assets/preambles/BibPreamble.tex} +\input{../assets/preambles/GeneralPreamble.tex} + + + + +%---------------------------------------------------------------------------------------- +% TITLE PAGE +%---------------------------------------------------------------------------------------- + +\title[Clinical Trials]{The Effects of Market Conditions on Recruitment and Completion of Clinical Trials} + +\author{Will King} % Your name +\institute[WSU] % Your institution as it will appear on the bottom of every slide, may be shorthand to save space +{ +Washington State University \\ % Your institution for the title page +\medskip +\textit{william.f.king@wsu.edu} % Your email address +} +\date{\today} % Date, can be changed to a custom date + + + + + +\begin{document} +\begin{frame} +\titlepage % Print the title page as the first slide +\end{frame} +%---------------------------------- +\begin{frame} %Allow frame breaks +\frametitle{Clincial Trials} % Table of contents slide, comment this out to remove it + % - Intro and hook (Clinical Trials are key part of pharmacological pipeline) + Pharmaceuticals are a frequently discussed aspect of health care cost managment. + Their development is dictated by scientific and regulatory hurdles + including passing clinical trials + (\cite{noauthor_fda_nodate}), + while their market is characterized by strategic competition and ambiguous + patent protection + (\cite{van_der_gronde_addressing_2017}). + + \vspace{12pt} + + This research investigates the pathways by which market conditions + affect clinical trial completion. +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{This research} + \textbf{Questions:} + \begin{enumerate} + \item Does the existence of alternative drugs on the market make it + harder for clinical trials to complete successfully? + \item How much of this is occurs due to increased recruitment difficulty? + \end{enumerate} + +\end{frame} +%-------------------------------- +\begin{frame} +\frametitle{Thanks} % Table of contents slide, comment this out to remove it + Thanks to Chris Adams and Rebecca Sachs of the Congressional Budget Office. +\end{frame} +%-------------------------------- +\begin{frame}[allowframebreaks] %Allow frame breaks +\frametitle{Overview} % Table of contents slide, comment this out to remove it +\tableofcontents +% - Intro and hook +% - Literature review +% - Causal Identification +% - Data +% - Econometric model +% - Results +% - Improvements +\end{frame} +%------------------------------------------------------------------------------------- +%%%%%%%%%%%%%%%%%%%% Lit Review %%%%%%%%%%%%%%%%%%%%%%%% +\section{Lit Review} +% First slide: +%------------------------------------------------------------------------------------- +%------------------------------- +\begin{frame} + \frametitle{Literature Highlights} + \begin{itemize} + \item \cite{van_der_gronde_addressing_2017}: + High level synthesis of overall discussion regarding drug costs. + Both academic and non-academic sources. + \item \cite{hwang_failure_2016}: + Answered the question "Why do late-stage (phase III) trials fail?" + Found that efficacy, safety, and competition reasons accounted for + 57\%, 17\%, and 22\% respectively. + \item \cite{abrantes-metz_pharmaceutical_2004}: + Described how drugs progress through the 3 phases of clinical trials + and correllations between various trial characteristics and the + clinical trial failures. + \item \cite{khmelnitskaya_competition_2021}: + Modeled clinical trial lifecycle of drugs, found method to separate + scientific from competitive reasons for failure to progress to the + next phase. +% \item \cite{}: + + \end{itemize} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{This research, in context} + + In contrast to previous work looking at multiple phases of trials, + I seek to figure out what causes individual trials to fail. + + \vspace{12pt} + + Instead of focusing on the drug development pipeline, I attempt to + investigate the population of drug-based, phase III trials. +\end{frame} +%------------------------------- +\begin{frame} %Allow frame breaks +\frametitle{Why this approach?} % Table of contents slide, comment this out to remove it + + \begin{figure} + \includegraphics[height=0.8\textheight]{../assets/img/methodology_trial.png} + \label{FIG:xkcd2726} + \caption{``If you think THAT'S unethical, you should see the stuff we approved via our Placebo IRB.'' + - \url{https://xkcd.com/2726} + } + \end{figure} +\end{frame} +%------------------------------------------------------------------------------------- +%%%%%%%%%%%%%%%%%%%% Causal Identification / DGP%%%%%%%%%%%%%%%%%%%%%%%% +\section{Causal Model} +% Data Generating process +% - Agents and their decisions +% - Factors that influence each decision +% - +% - +%------------------------------------------------------------------------------------- +%------------------------------- +\begin{frame} + \frametitle{Data Generating Process} + % study sponsors + Study Sponsors Decide to start a Phase 3 trial and whether to terminate it. + \\ + They ask themselves: + \begin{itemize} + \item Do safety incidents require terminating a trial? + \item Do efficacy results indicate the trial is worth continuing? + \item Is recruiting sufficient to achieve our results and contain costs? + \item Do expectations about future returns justify our expenditures? + \end{itemize} + +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Data Generating Process} + % participants + Participants decide to enroll (and disenroll) themselves in a trial based + \begin{itemize} + \item Disease severity + \item Relative safety/efficacy compared to other treatments + \end{itemize} + + Study sponsors plan their enrollment considering + \begin{itemize} + \item Total population affected + \item Likely participant response rates + \end{itemize} + +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Data Generating Process} + % Trial Snapshots and dependencies. + During a trial, the study sponsor reports snapshots of their trial. + This includes updates to: + + \begin{itemize} + \item enrollment (actual or anticipated) + \item current recruitment status (Recruiting, Active not recruiting, etc) + \item study sponsor + \item planned completion dates + \item elapsed duration + \end{itemize} + + Note that final enrollment and the final status (Completed or Terminated) + of the trial are jointly determined. +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Causal Diagram: Key Pathways} + % Estimating Direct vs Total Effects + \begin{figure} + \resizebox{!}{0.5\textheight}{ + \tikzfig{../assets/tikzit/CausalGraph} + } + \label{FIG:CausalDiagram} + \caption{Causal Diagram highlighting direct and total pathways} + \end{figure} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Causal Diagram: Backdoor Crieterion} + \small + \begin{block}{$d$-separation} + A set $S$ of nodes blocks a path $p$ if either + \begin{enumerate} + \item $p$ contains at least one arrow-emitting node in $S$ + \item $p$ contains at least one collision node $c$ that is outside $S$ + and has no descendants in $S$. + \end{enumerate} + If $S$ blocks all paths from X to Y, then it is said to ``$d$-separate'' + $X$ and $Y$, and then $X \perp Y | S$. + \end{block} + \begin{block}{Back-Door Criterion} + A set $S$ of covariates is admisible as controls on the + causal relationship $X \rightarrow Y$ if: + \begin{enumerate} + \item No element of $S$ is a decendant of $X$ + \item The elements of $S$ d-separate all paths from $X$ to $Y$ that include + parents of $X$. + \end{enumerate} + \end{block} + \cite{pearl_causality_2000} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Causal Diagram} + Key takeaways + \begin{itemize} + \item Measuring enrollment prior to trial completion is necessary for causal identification. + \item The backdoor criterion gives us the following adjustment sets: + \begin{itemize} + \item Total Effect for Market on Termination; Population, Condition, Phase III + \item Direct Effects for Enrollment, Market on Termination; Population, Condition Phase III, + Elapsed Duration, Planned Enrollment + \end{itemize} + \item Enrollment requires imputation + \end{itemize} +\end{frame} +%------------------------------------------------------------------------------------- +%%%%%%%%%%%%%%%%%%%% Data %%%%%%%%%%%%%%%%%%%%%%%% +\section{Data} +%------------------------------------------------------------------------------------- +%---------------------------------- +%%%%%%%%%%%%%%%%%%%% Sources +\subsection{Sources} +%---------------------------------- +%------------------------------- +\begin{frame} %Allow frame breaks + \frametitle{Data Sources} + \begin{itemize} + \item ClinicalTrials.gov - AACT \& custom scripts + \begin{itemize} + \item Select trials of interest + \item Trial details: + \begin{itemize} + \item conditions + \item final status + \item drugs/interventions + \end{itemize} + \item Trial snapshots: + \begin{itemize} + \item enrollment (anticipated, planned, or actual) + \item elapsed duration + \item current status + \end{itemize} + \end{itemize} + \item Medical Subject Headings (MeSH) Thesaurus + \begin{itemize} + \item A standardized nomenclature used to classify interventions + and conditions in the clinical trials database. + \end{itemize} + \end{itemize} +\end{frame} +%------------------------------- +\begin{frame} %Allow frame breaks + \frametitle{Data Sources} + \begin{itemize} + \item NSDE Files (New drug code Structured product labels Data Element) + \begin{itemize} + \item Contains information about when a given drug was on the market. + \end{itemize} + \item RxNorm + \begin{itemize} + \item Links pharmaceuticals between MeSH standardized terms and + NSDE files. + \end{itemize} + \item Global Disease Burden Survey (2019) + \begin{itemize} + \item Estimates of DALYs for categories of disease + \item Links of Categories to ICD-10 Codes + \end{itemize} + \item ICD-10 (2019) + \begin{itemize} + \item WHO version + \item CMS version (Clinical Managment) + \item Used to group disease conditions in hierarchal model + \end{itemize} + \item Unified Medical Language System Thesaurus + \begin{itemize} + \item Used to link MeSH standardized terms and ICD-10 conditions + \item Manual matching process + \end{itemize} + \end{itemize} +\end{frame} +%---------------------------------- +%%%%%%%%%%%%%%%%%%%% Integration +\subsection{Integration} +%---------------------------------- +%------------------------------- +\begin{frame} + \frametitle{Data Summaries} + %put summaries now + \begin{itemize} + \item Number of Phase III, FDA monitored Drug Trials: 1,981 + \item Number of Trials matched to ICD-10: 186 + \item Number of Trials matched to ICD-10 with population measures: 67 + (51 completed, 16 terminated) + \item Number of Snapshots: 616 + \end{itemize} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Data used} + The following data points were used. + \begin{itemize} + \item elapsed duration + \item asinh(number of brands) + \item asinh(high sdi DALY estimate) + \item asinh(high-medium sdi DALY estimate) + \item asinh(medium sdi DALY estimate) + \item asinh(low-medium sdi DALY estimate) + \item asinh(low sdi DALY estimate) + \end{itemize} + The asinh operator was used because it parallells $\text{ln}(x)$ for + large values of $x$ but also handles $\text{asinh}(0)=0$. +\end{frame} +%---------------------------------- +\begin{frame} + \frametitle{Summaries: Trial Durations} + \begin{figure} + \includegraphics[height=0.8\textheight]{../assets/img/2023-04-12_durations_hist.png} + \label{FIG:durations} + \caption{Trial Durations (days)} + \end{figure} +\end{frame} +%---------------------------------- +\begin{frame} + \frametitle{Summaries: snapshots} + \begin{figure} + \includegraphics[height=0.8\textheight]{../assets/img/2023-04-12_snapshots_hist.png} + \label{FIG:snapshots} + \caption{Number of Snapshots per matched trial} + \end{figure} +\end{frame} +%---------------------------------- +\begin{frame} + \frametitle{Summaries: snapshots} + \begin{figure} + \includegraphics[height=0.8\textheight]{../assets/img/2023-04-12_status_duration_snapshots_points.png} + \label{FIG:snapshot_duration_scatter} + \caption{Scatterplot of snapshot count and durations} + \end{figure} +\end{frame} +%------------------------------------------------------------------------------------- +%%%%%%%%%%%%%%%%%%%% Econometric Model %%%%%%%%%%%%%%%%%%%%%%%% +\section{Econometric model} +%------------------------------------------------------------------------------------- +%------------------------------- +\begin{frame} + \frametitle{Econometric Model} + Estimating the total effect of brands on market + \begin{align} + y_n &\sim \text{Bernoulli}(p_n) \\ + p_n &= \text{logisticfn}(x_n * \beta(d_n)) \\ + \beta_k(d) &\sim \text{Normal}(\mu_k, \sigma_k) \\ + \mu_k &\sim \text{Normal}(0,1) \\ + \sigma_k &\sim \text{Gamma}(2,1) + \end{align} + $k$ indexes parameters and $d_n$ represets the ICD-10 group the trial corresponds to. +\end{frame} +%------------------------------------------------------------------------------------- +%%%%%%%%%%%%%%%%%%%% Results %%%%%%%%%%%%%%%%%%%%%%%% +\section{Results} +%------------------------------------------------------------------------------------- +%------------------------------- +\begin{frame} + \frametitle{Results} + Because bayesian estimation is typically done numerically, we will first + validate convergence. + + Then we will take a look at preliminary results. + + Sampling details + \begin{itemize} + \item 6 chains + \item 2,500 warmup, 2,500 sampling runs + \item seed = 11021585 + \end{itemize} +\end{frame} +%---------------------------------- +%%%%%%%%%%%%%%%%%%%% Convergence Tests +\subsection{Convergence} +%---------------------------------- +%------------------------------- +\begin{frame} + \frametitle{Warnings} + + \begin{itemize} + \item There were no diverging transitions. + \item There were 15,000 transitions that exceeded max treedepth. + Sampling efficiency is poor. + \item All chains had low Bayesian Fraction of Missing Information. + Some areas of the distribution were poorly explored. + \item R-hat = $1.23$, ideal is around 1, chains did not mix well. + \item Bulk and Tail Effective Sample sizes were low, + suggesting mean and variance/quantile estimates will be unreliable. + \end{itemize} + \cite{mc-stan} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Convergence: Mu} + \begin{figure} + \includegraphics[height=0.9\textheight]{../assets/img/2023-04-11_mu_points.png} + \label{FIG:caption} + \caption{Hyperparameter Points Plots: Mu} + \end{figure} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Convergence: Sigma} + \begin{figure} + \includegraphics[height=0.8\textheight]{../assets/img/2023-04-11_sigma_points.png} + \label{FIG:caption} + \caption{Hyperparameter Points Plots: Sigma} + \end{figure} +\end{frame} +%---------------------------------- +%%%%%%%%%%%%%%%%%%%% Preliminary Results +\subsection{Preliminary Results} +%---------------------------------- +%------------------------------- +\begin{frame} + \frametitle{Preliminary Results: Mu} + + \begin{columns} + \begin{column}{0.3\textwidth} + \begin{enumerate} + \item elapsed duration + \item asinh(n\_brands) + \item asinh(high sdi) + \item asinh(high-medium sdi) + \item asinh(medium sdi) + \item asinh(low-medium sdi) + \item asinh(low sdi) + \end{enumerate} + \end{column} + \begin{column}{0.7\textwidth} + \begin{figure} + \includegraphics[height=0.8\textheight]{../assets/img/2023-04-11_mu_dist.png} + \label{FIG:caption} + \caption{Hyperparameter Distribution: Mu} + \end{figure} + \end{column} + \end{columns} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Preliminary Results: Sigma} + + \begin{figure} + \includegraphics[height=0.8\textheight]{../assets/img/2023-04-11_sigma_dist.png} + \label{FIG:caption} + \caption{Hyperparameter Distribution: Sigma} + \end{figure} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Interpretation} + All of the following interpretations are done in the context of insufficient data + + \begin{enumerate} + \item Elapsed Duration (Mu[1]): Trending Negative, reduced probability of termination. + \item Number of Brands(Mu[2]): Trending Positive, increased probability of termination. + \item Population Measures (Mu[3]-Mu[7]) + \begin{enumerate} + \item What is most surprising is that these are both positive and negative. + Probably need more data. + \end{enumerate} + \item It is surprising to see the wide distribution in sigma values. + \end{enumerate} +\end{frame} +%------------------------------------------------------------------------------------- +%%%%%%%%%%%%%%%%%%%% Improvements %%%%%%%%%%%%%%%%%%%%%%%% +\section{Improvements} +%------------------------------------------------------------------------------------- +%------------------------------- +\begin{frame} + \frametitle{Proposed improvements} + \begin{enumerate} + \item Match more trials to ICD-10 codes + \item Improve Measures of Market Conditions + \item Adjust Covariance Structure + \item Find Reasonable Priors + \item Remove disease categories that don't exist in the data from the priors + \item Imputing Enrollment + \item Improve Population Estimates + \end{enumerate} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Questions?} + \center{\huge{Questions?}} + +\end{frame} +%------------------------------- +\begin{frame}[allowframebreaks] + \frametitle{Bibliography} + \printbibliography +\end{frame} +%------------------------------- +\end{document} +%========================================= +%\begin{frame} +% \frametitle{MarginalRevenue} +% \begin{figure} +% \tikzfig{../Assets/owned/ch8_MarginalRevenue} +% \includegraphics[height=\textheight]{../Assets/copyrighted/KrugmanObsterfeldMeliz_fig8-7.jpg} +% \label{FIG:costs} +% \caption{Average Cost Curve as firms enter.} +% \end{figure} +%\end{frame} +%------------------------------- +%\begin{frame} +% \frametitle{Columns} +% \begin{columns} +% \begin{column}{0.5\textwidth} +% \end{column} +% \begin{column}{0.5\textwidth} +% \begin{figure} +% \tikzfig{../Assets/owned/ch7_EstablishedAdvantageExample2} +% \label{FIG:costs} +% \caption{Setting the Stage} +% \end{figure} +% \end{column} +% \end{columns} +%\end{frame} +% %--------------------------------------------------------------- diff --git a/Latex/assets/img/2023-04-11_mu_dist.png b/Latex/assets/img/2023-04-11_mu_dist.png new file mode 100644 index 0000000000000000000000000000000000000000..ab8ac06d3d35219f3ce9c16eb46124d2d5a33dde GIT binary patch literal 31957 zcmdSBWmJ}36fOGF9n#$bN=i!z0%A}G(hbrG(kUHEDoP572z-cicb7CsNlQpKNORYV z=bSOly<^}pCS;bH3$Ss0X8c9 zNy{$tF8si;f1u@vKoB+~|3hiF`_B}CU_v~UzpLiG+7e->wZm^4`>}!=F)0a_)tGFF5b)tKeW6NEbI2UTUHkHIx`+Bvq}xU zU6`I2bTs-7& z9ZfQ6e((p(L$d!5KZ_pAH8WlwwWDDXj#a(I=rk1|AR?N8-|P$x8%C~kWA0nmIL}{2 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blue,191}, draw=none, tikzit draw=blue, opacity=0.3] diff --git a/Latex/assets/preambles/references/O.bib b/Latex/assets/preambles/references/O.bib new file mode 100644 index 0000000..0ee121e --- /dev/null +++ b/Latex/assets/preambles/references/O.bib @@ -0,0 +1,10 @@ + +@online{noauthor_fda_nodate, + title = {{FDA} Drug Approval Process}, + url = {https://www.drugs.com/fda-approval-process.html}, + abstract = {It can take up to \$2 billion and 12 to 15 years to get a drug from the test tube to the market. What happens at the {FDA} to get this drug safely to you?}, + titleaddon = {Drugs.com}, + urldate = {2023-04-12}, + langid = {english}, + file = {Snapshot:/home/dad/Nextcloud/Zotero_data/storage/VTIGXXJB/fda-approval-process.html:text/html}, +} diff --git a/Latex/assets/tikzit/CausalGraph.tikz b/Latex/assets/tikzit/CausalGraph.tikz index 4c464be..2033196 100644 --- a/Latex/assets/tikzit/CausalGraph.tikz +++ b/Latex/assets/tikzit/CausalGraph.tikz @@ -1,34 +1,52 @@ \begin{tikzpicture} \begin{pgfonlayer}{nodelayer} - \node [style=emptyBox] (0) at (-18.5, 4) {Compound Safety}; - \node [style=emptyBox] (1) at (-18.5, -3.5) {Compound Effecacy}; - \node [style=Red Box] (3) at (-3.5, -4.25) {\begin{tabular}{l} Conclusion State \\ $\bullet$ Status\\ $\bullet$ Duration \\ $\bullet$ Enrollment \end{tabular}}; - \node [style=Red Box] (4) at (-2, 1) {\begin{tabular}{l} Snapshot State \\ $\bullet$ Status\\ $\bullet$ Duration \\ $\bullet$ Enrollment \end{tabular}}; - \node [style=Red Box] (5) at (3.25, -2) {Market Conditions}; - \node [style=Box] (6) at (-17.5, -5.5) {Sponsor Changes}; - \node [style=Box] (7) at (-15.25, 0.25) {\begin{tabular}{l}Prior \\ Trials \end{tabular}}; - \node [style=emptyBox] (8) at (-2.25, 4) {Beliefs about Compound}; - \node [style=emptyBox] (10) at (3.25, -5.25) {Unobserved}; - \node [style=Box] (11) at (3.25, -6.25) {Observed: Control}; - \node [style=Red Box] (12) at (3.25, -7.25) {Observed: Of interest}; - \node [style=emptyBox] (13) at (-11, 4) {Current Adverse Events}; - \node [style=emptyBox] (14) at (-10.5, -1.5) {Measured Effectiveness}; - \node [style=Box] (15) at (4.75, 1) {Disease Burden}; + \node [style=Red Box] (0) at (4, -1.5) {Will Terminate?}; + \node [style=Red Box] (1) at (-4.25, -1.5) {Market Measures}; + \node [style=emptyBox] (4) at (-6, -7.5) {Unobserved}; + \node [style=purple box] (5) at (0, 2) {Enrollment}; + \node [style=Red Box] (8) at (-5.75, -6) {Relationships of interest}; + \node [style=emptyBox] (9) at (12.25, 7.5) {Fundamental Efficacy/Safety}; + \node [style=emptyBox] (10) at (0, 9.25) {Previously Observed Efficacy/Safety}; + \node [style=emptyBox] (12) at (12.25, 0) {Currently Observed Efficacy/Safety}; + \node [style=Gray Box] (13) at (7, -6) {Observed, adjustment set 1}; + \node [style=GreyBoxDotted] (14) at (7, -7.25) {Observed, adjustment set 2}; + \node [style=GreyBoxDotted] (15) at (-4, 4.25) {Planned Enrollment}; + \node [style=GreyBoxDotted] (16) at (4.5, 4.5) {Anticipated Enrollment}; + \node [style=GreyBoxDotted] (17) at (7.5, 3) {Measured Enrollment}; + \node [style=Gray Box] (18) at (-6.5, 1.5) {Population}; + \node [style=GreyBoxDotted] (19) at (5.75, 1.5) {Current Status}; + \node [style=Gray Box] (20) at (0, 7.5) {Decision to procced with Phase III}; + \node [style=Gray Box] (21) at (0, -3.5) {Condition}; + \node [style=Gray Box] (22) at (14.5, -4.25) {Elapsed Duration}; + \node [style=purple box] (23) at (7, -8.5) {Partially observed}; \end{pgfonlayer} \begin{pgfonlayer}{edgelayer} - \draw [style=RightArrow] (4) to (3); - \draw [style=RightArrow] (5) to (3); - \draw [style=Light Arrow] (0) to (7); - \draw [style=Light Arrow] (1) to (7); - \draw [style=Light Arrow] (7) to (8); - \draw [style=Light Arrow] (8) to (4); - \draw [style=Light Arrow] (6) to (3); - \draw [style=Light Arrow] (0) to (13); - \draw [style=Light Arrow] (13) to (3); - \draw [style=Light Arrow] (1) to (14); - \draw [style=Light Arrow] (14) to (3); - \draw [style=Light Arrow] (15) to (5); - \draw [style=Light Arrow] (15) to (4); - \draw [style=RightArrow] (5) to (4); + \draw [style=lightredarrow] (1) to (0); + \draw [style=lightredarrow] (1) to (5); + \draw [style=lightredarrow] (5) to (0); + \draw [style=RightArrow] (15) to (5); + \draw [style=RightArrow] (5) to (16); + \draw [style=RightArrow] (5) to (17); + \draw [style=RightArrow] (5) to (19); + \draw [style=RightArrow] (18) to (5); + \draw [style=RightArrow] (18) to (1); + \draw [style=RightArrow] (9) to (10); + \draw [style=RightArrow] (10) to (20); + \draw [style=RightArrow] (9) to (12); + \draw [style=RightArrow] (12) to (0); + \draw [style=Light Arrow] (21) to (1); + \draw [style=Light Arrow, in=-75, out=105] (21) to (15); + \draw [style=Light Arrow] (21) to (0); + \draw [style=Light Arrow, in=-120, out=165, looseness=2.00] (21) to (18); + \draw [style=Light Arrow, in=180, out=180, looseness=2.75] (21) to (20); + \draw [style=Light Arrow, bend right=60, looseness=1.75] (21) to (9); + \draw [style=Light Arrow] (21) to (5); + \draw [style=lightredarrow, in=135, out=45, loop] (8) to (); + \draw [style=RightArrow, in=-180, out=165, looseness=2.00] (1) to (20); + \draw [style=RightArrow, in=120, out=180, looseness=1.25] (10) to (15); + \draw [style=RightArrow] (20) to (5); + \draw [style=RightArrow] (18) to (15); + \draw [style=RightArrow] (22) to (0); + \draw [style=RightArrow] (22) to (5); \end{pgfonlayer} \end{tikzpicture}