diff --git a/Latex/Presentation/presentation.tex b/Latex/Presentation/presentation.tex index db4049c..3c14e17 100644 --- a/Latex/Presentation/presentation.tex +++ b/Latex/Presentation/presentation.tex @@ -28,8 +28,6 @@ \input{../assets/preambles/GeneralPreamble.tex} - - %---------------------------------------------------------------------------------------- % TITLE PAGE %---------------------------------------------------------------------------------------- @@ -67,25 +65,9 @@ Washington State University \\ % Your institution for the title page \vspace{12pt} - This research investigates the pathways by which market conditions + This research investigates the ways 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 @@ -107,17 +89,17 @@ Washington State University \\ % Your institution for the title page % - Background on drug process % - Literature on clinical trials % - My questions +% add info about trials +% - Requirements (pre registered design [2007], updated "regularly" on clinicaltrials.gov) +% - Phases (1,2,3,4, mixed) +% - Safety and Ethicas (oversight boards, restrictions on payments) +% - Approval processes (biologics vs small-molecule) +% add info about drugs %------------------------------------------------------------------------------------- %------------------------------- \begin{frame} \frametitle{Clinical Trials and Drug develoment} - % add info about trials - % - Requirements (pre registered design [2007], updated "regularly" on clinicaltrials.gov) - % - Phases (1,2,3,4, mixed) - % - Safety and Ethicas (oversight boards, restrictions on payments) - % - Approval processes (biologics vs small-molecule) - % add info about drugs The FDA requires clinical trials before approving new drug compounds \begin{itemize} @@ -160,68 +142,14 @@ Washington State University \\ % Your institution for the title page 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. +% \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 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} - -\end{frame} -%----------------------------- -\begin{frame} - \frametitle{Questions of Interest} - + Questions \begin{itemize} \item How do the competitors on the market affect clinical trial completion? \item How is this effect moderated by the enrollment of participants? @@ -233,59 +161,61 @@ Washington State University \\ % Your institution for the title page \center{What can I clarify?} \end{frame} -%------------------------------- -%------------------------------------------------------------------------------------- -%%%%%%%%%%%%%%%%%%%% Causality and Data %%%%%%%%%%%%%%%%%%%%%%%% -\section{Causal Story and Data} -% TOC -% - Causal Story (no subsection) -% - Clinical trials: targets specific drug/condition combination. -% - Enrollment process: patients counsel with providers -% - Trials terminate if unsafe, ineffective, unprofitable, or cannot enroll patients -% - Ethical concerns exist throughout. -% - This is complicated by the fact that the experiment reveals information over time. -% - Formalization -% - Data Sources -%------------------------------------------------------------------------------------- - +%%------------------------------------------------------------------------------------- +%%%%%%%%%%%%%%%%%%%%% Causality and Data %%%%%%%%%%%%%%%%%%%%%%%% +%\section{Causal Story and Data} +%% TOC +%% - Causal Story (no subsection) +%% - Clinical trials: targets specific drug/condition combination. +%% - Enrollment process: patients counsel with providers +%% - Trials terminate if unsafe, ineffective, unprofitable, or cannot enroll patients +%% - Ethical concerns exist throughout. +%% - This is complicated by the fact that the experiment reveals information over time. +%% - Formalization +%% - Data Sources +%% Data Generating process +%% - Agents and their decisions +%% - Factors that influence each decision +%%------------------------------------------------------------------------------------- +% %------------------------------- \begin{frame}[shrink=10] %evil option is helpful here. \frametitle{How do clinical trials proceed?} \begin{columns}[T] - \begin{column}{0.5\textwidth} - What does a complete trial look like. - \begin{enumerate} - \item Study sponsor comes up with design - \item Apply for NCT ID from ClinicalTrials.gov - \item Begin enrolling participants - \item Update ClinicalTrials.gov to recruit - \item Close Enrollment - \item Update ClinicalTrials.gov as not recruiting* - \item Reach primary objectives - \item Update ClinicalTrials.gov as complete - \item Reach secondary objectives - \item Update ClinicalTrials.gov with more information - \end{enumerate} - \end{column} - \begin{column}{0.5\textwidth} - What does an incomplete trial look like? - \begin{enumerate} - \item Study sponsor comes up with design - \item Apply for NCT ID from ClinicalTrials.gov - \item Begin enrolling participants - \item Update ClinicalTrials.gov to advertise - \item Run into issues: - \begin{itemize} - \item Safety - \item Efficacy - \item Profitability - \item Feasiblity (enrollment, PI leaves, etc.) - \end{itemize} - \item Close Enrollment* - \item Decide to terminate clinical trial. - \item Update ClinicalTrials.gov as terminated. - \end{enumerate} - \end{column} + \begin{column}{0.5\textwidth} + What does a \textbf{Completed} trial look like? + \begin{enumerate} + \item Study sponsor comes up with design + \item Apply for NCT ID from ClinicalTrials.gov + \item Begin enrolling participants + \item Update ClinicalTrials.gov to recruit + \item Close Enrollment + \item Update ClinicalTrials.gov as not recruiting* + \item Reach primary objectives + \item Update ClinicalTrials.gov as complete + \item Reach secondary objectives + \item Update ClinicalTrials.gov with more information + \end{enumerate} + \end{column} + \begin{column}{0.5\textwidth} + What does an \textbf{Terminated} trial look like? + \begin{enumerate} + \item Study sponsor comes up with design + \item Apply for NCT ID from ClinicalTrials.gov + \item Begin enrolling participants + \item Update ClinicalTrials.gov to advertise + \item Run into issues: + \begin{itemize} + \item Safety + \item Efficacy + \item Profitability + \item Feasiblity (enrollment, PI leaves, etc.) + \end{itemize} + \item Close Enrollment* + \item Decide to terminate clinical trial. + \item Update ClinicalTrials.gov as terminated. + \end{enumerate} + \end{column} \end{columns} \end{frame} %------------------------------- @@ -294,7 +224,6 @@ Washington State University \\ % Your institution for the title page Thus ClinicalTrials.gov becomes an (append only) repository of the ``current'' status of clincal trials. - As it is designed to help faciltate enrollment in clinical trials, the record includes important information such as @@ -312,10 +241,43 @@ Washington State University \\ % Your institution for the title page %------------------------------- \begin{frame} - \frametitle{Questions?} + \frametitle{Decision-Making 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} + + They plan their enrollment considering + \begin{itemize} + \item Total population affected + \item Likely participant response rates + \item Their network of clinicians + \end{itemize} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Decision-Making Process} + % participants + Participants decide to enroll (and dis-enroll) themselves in a trial based on + \begin{itemize} + \item Doctor Recommendations + \item Disease severity + \item Relative safety/efficacy compared to other treatments + \end{itemize} \end{frame} %------------------------------- +\begin{frame} + \frametitle{Questions?} + \center{What clarifying questions do you have?} +\end{frame} +%------------------------------- %-------------------------------- %%%%%%%%%%%%%%%%%%%% Causal Formalization \subsection{Formalization} @@ -325,45 +287,77 @@ Washington State University \\ % Your institution for the title page % - Add confounders and controls % - Introduce backdoor criterion %-------------------------------- - +%%------------------------------- +%%\begin{frame} %Allow frame breaks +%%\frametitle{Why this approach?} +%% \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} %------------------------------- \begin{frame} \frametitle{Framing my Questions} - Two potential causes of trial termination include - \begin{enumerate} - \item Alternative (competitor) treatments exist - \begin{itemize} - \item reduces future profitability. - \item reduces incentives to enroll as participants. - \end{itemize} - \item It can be difficult to recruit patients - \begin{itemize} - \item Are there few patients? - \item Are potential participants choosing other alternatives? - \end{itemize} - \end{enumerate} - Overall this can be described graphically as: - - INSERT IMAGE OF 4 NODES HERE - + \begin{columns}[T] + \begin{column}{0.5\textwidth} + Two potential causes of trial termination include + \begin{enumerate} + \item Alternative (competitor) treatments exist + \begin{itemize} + \item reduces future profitability. + \item reduces incentives to enroll as participants. + \end{itemize} + \item It can be difficult to recruit patients + \begin{itemize} + \item Are there few patients? + \item Are potential participants choosing other alternatives? + \end{itemize} + \end{enumerate} + \end{column} + \begin{column}{0.5\textwidth} + Overall this can be described graphically as: + \begin{figure} + \scalebox{0.8}{ + \tikzfig{../assets/tikzit/4Node} + } + \label{FIG:4Node} + \caption{Total Effect} + \end{figure} + \end{column} + \end{columns} \end{frame} %------------------------------- \begin{frame} - \frametitle{Causal Identification: Backdoor Criterion} + \frametitle{Causal Effects} %Discuss the two different effects: total effect, direct effects \begin{columns} - \begin{column}{0.5\textwidth} - Total Effect of Competitors - - INSERT TOTAL EFFECT GRAPH - \end{column} - \begin{column}{0.5\textwidth} - Direct Effects of Competitors and Enrollment - - INSERT DIRECT EFFECT GRAPH - \end{column} + \begin{column}{0.5\textwidth} + Total Effect of Competitors + + \begin{figure} + \scalebox{0.8}{ + \tikzfig{../assets/tikzit/4Node_total} + } + \label{FIG:4Node} + \caption{Total Effect} + \end{figure} + \end{column} + \begin{column}{0.5\textwidth} + Direct Effects of Competitors and Enrollment + + \begin{figure} + \scalebox{0.8}{ + \tikzfig{../assets/tikzit/4Node_direct} + } + \label{FIG:4Node} + \caption{Direct Effect} + \end{figure} + \end{column} \end{columns} \end{frame} @@ -372,8 +366,10 @@ Washington State University \\ % Your institution for the title page \frametitle{Rephrasing Questions} To rephrase my questions \begin{enumerate} - \item How large is the total effect of increasing the number of competing drugs on completing clinical trials? - \item How large is the direct effect of increasing the number of competing drugs on completing clincial trials? + \item How large is the total effect of increasing the number + of competing drugs on completing clinical trials? + \item How large is the direct effect of increasing the number + of competing drugs on completing clincial trials? \end{enumerate} \end{frame} %------------------------------- @@ -384,52 +380,97 @@ Washington State University \\ % Your institution for the title page \begin{enumerate} \item Population Effects \item Fundamental Safety and Efficacy of compound/dosage/route + \item How long the trial is taking + \item the total effects \end{enumerate} - \end{frame} %------------------------------- \begin{frame} \frametitle{Complete graph} %introduce backdoor criterion - INSERT COMPLETE GRAPH HERE + \begin{figure} + \scalebox{0.6}{ + \tikzfig{../assets/tikzit/CausalGraph} + } + \label{FIG:CausalGraph} + \caption{Full Causal Graph} + \end{figure} + Discuss concerns about Elapsed Duration and Enrollment \end{frame} -%------------------------------- +%%------------------------------- \begin{frame} - \frametitle{Causal Identification: Backdoor Criterion} - %introduce backdoor criterion - - \cite{PEARLYYYY} developed a method of verifying causal identification from DAGs like the one I presented. - - Of particular interest is the rule called the Backdoor criterion: - - INSERT DESCRIPTION OF THE BACK DOOR CRITERION - - + \frametitle{Causal Diagram: Backdoor Criterion} + \small + \begin{block}{$d$-separation} + A set $S$ of nodes blocks a path $p$ on a DAG 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{Sufficent Adjustment Set} %introduce backdoor criterion - INSERT COMPLETE GRAPH HERE with adjustment set highlighted + Thus the required adjustment set depends on the effects of interest. + + For the total effect these are controls for: + \begin{itemize} + \item Proceed with Phase III + \item Condition + \item Population + \end{itemize} + Discuss Regime Switching + + For the direct effect these are controls for: + \begin{itemize} + \item Proceed with Phase III + \item Condition + \item Population (optional) + \item Enrollment + \end{itemize} + Not causally identified due to Regime Switching + \end{frame} %------------------------------- \begin{frame} - \frametitle{Sufficent Adjustment Set} - %introduce backdoor criterion - - Thus the required adjustment set includes: - + \frametitle{Other testable hypotheses} + One advantage of this approach is that there are tools that can automatically \begin{itemize} - \item Population Measures - \item Safety and Efficacy Measures - \item INSERT MORE + \item verify causal identification + \item generate hypotheses to verify model \end{itemize} + In this case, the following are testable hyptheses + \begin{itemize} + \item Decision to continue Phase III $\perp$ Elapsed Duration + \item Decision to continue Phase III $\perp$ Market Conditions $\Vert$ Condition + \item Decision to continue Phase III $\perp$ Population $\Vert$ Condition + \item Elapsed Duration $\perp$ Market Conditions + \item Elapsed Duration $\perp$ Condition + \item Elapsed Duration $\perp$ Population + \item Population $\perp$ Terminated $\Vert$ Condition, Decision to continue Phase III, Elapsed Duration, Enrollment Status, Market Conditions + \end{itemize} + \href{http://dagitty.net/mLyFuc5}{Dagitty.net model} \end{frame} %------------------------------- \begin{frame} @@ -451,21 +492,71 @@ Washington State University \\ % Your institution for the title page %-------------------------------- %------------------------------- -\begin{frame} +\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 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} - %TODO: add citations - Data sources \begin{itemize} - \item ClinicalTrials.gov + \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 AACT-CTTI - \item Scraping historical snapshots + \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} - \item ICD-10 (CMS and WHO) - \item IHME Global Burden of Disease - \item Structured Product Labels - \item USP Drug Classification - \item Drugs@FDA: RxNav / RxNorm / MeSH \end{itemize} \end{frame} %------------------------------- @@ -483,9 +574,28 @@ Washington State University \\ % Your institution for the title page \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 @@ -493,17 +603,22 @@ Washington State University \\ % Your institution for the title page \item with same active ingredients (at the time of the snapshot) \item sharing the USP DC category and class (in 2023) \end{itemize} - \item Enrollment: Measured by enrollment status at the snapshot level. \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: QUALYs, spread over 5 levels of the Social Development Index + \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 @@ -528,40 +643,107 @@ Washington State University \\ % Your institution for the title page \end{itemize} \end{frame} -%------------------------------- -\begin{frame} - \frametitle{Questions?} - -\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: 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{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 %%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%% Analysis %%%%%%%%%%%%%%%%%%%%%%%% \section{Analysis} % TOC % - Review questions and datasets to use for each % - % - %------------------------------------------------------------------------------------- - %------------------------------- \begin{frame} - \frametitle{Questions?} + \frametitle{General Approach} + \begin{itemize} + \item Logistic model + \item Bayesian Hierarchal model + \begin{itemize} + \item Allows for transfer of probability between groups + \end{itemize} + \end{itemize} + \end{frame} -%-------------------------------- -%%%%%%%%%%%%%%%%%%%% Econometric Model -\subsection{Econometric Model} -% - Present model per effect -% - -% - -%-------------------------------- +%------------------------------- +\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} + %TODO: describe X\beta +\end{frame} + +%------------------------------- +\begin{frame} + \frametitle{Analysis} + + Review: + \begin{itemize} + \item Hyperparameters + \item Parameters of Interest + \item Distrbution of Predicted Differences (Hypothetical Causal Intervention) + \end{itemize} + +\end{frame} %------------------------------- \begin{frame} \frametitle{Questions?} \end{frame} %-------------------------------- +%-------------------------------- %%%%%%%%%%%%%%%%%%%% Results \subsection{Results} %-------------------------------- @@ -578,28 +760,55 @@ Washington State University \\ % Your institution for the title page %-------------------------------- %------------------------------- \begin{frame} - \frametitle{Questions?} + \frametitle{Results} + Because Bayesian estimation is typically done numerically, we will first + validate convergence. -\end{frame} -%------------------------------- -%-------------------------------- -\subsubsection{Direct Effects} -% - Review Parameter Values -% - hyperparameters -% - Table of MLE -% - Distributions -% - betas -% - Table of MLE -% - Distributions -% - Review Posterior Prediction for interventions -%-------------------------------- + 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} @@ -607,246 +816,28 @@ Washington State University \\ % Your institution for the title page %------------------------------- \begin{frame} - \frametitle{Final Questions} - - \center{\huge{Time is yours to ask any remaining questions.}} -\end{frame} -%------------------------------------------------------------------------------------- -%%%%%%%%%%%%%%%%%%%% Appendicies %%%%%%%%%%%%%%%%%%%%%%%% -\section{Appendices} -%------------------------------------------------------------------------------------- - -%------------------------------- -\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 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} + \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} -%---------------------------------- -%%%%%%%%%%%%%%%%%%%% 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} + \frametitle{Summary} \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} - 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. + \frametitle{Final Questions} + + \center{\huge{Time is yours to ask any remaining questions.}} \end{frame} %------------------------------------------------------------------------------------- -%%%%%%%%%%%%%%%%%%%% Results %%%%%%%%%%%%%%%%%%%%%%%% -\section{Results} +%%%%%%%%%%%%%%%%%%%% Appendicies %%%%%%%%%%%%%%%%%%%%%%%% +\section{Appendices} %------------------------------------------------------------------------------------- -%------------------------------- -\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 warm-up, 2,500 sampling runs - \item seed = 11021585 - \end{itemize} -\end{frame} %---------------------------------- %%%%%%%%%%%%%%%%%%%% Convergence Tests \subsection{Convergence} @@ -854,6 +845,7 @@ Washington State University \\ % Your institution for the title page %------------------------------- \begin{frame} \frametitle{Warnings} + %TODO: UPDATE \begin{itemize} \item There were no diverging transitions. @@ -871,7 +863,8 @@ Washington State University \\ % Your institution for the title page \begin{frame} \frametitle{Convergence: Mu} \begin{figure} - \includegraphics[height=0.9\textheight]{../assets/img/2023-04-11_mu_points.png} + %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} @@ -880,89 +873,12 @@ Washington State University \\ % Your institution for the title page \begin{frame} \frametitle{Convergence: Sigma} \begin{figure} - \includegraphics[height=0.8\textheight]{../assets/img/2023-04-11_sigma_points.png} + %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} -%---------------------------------- -%%%%%%%%%%%%%%%%%%%% 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} diff --git a/Latex/assets/img/0000163.png b/Latex/assets/img/0000163.png deleted file mode 100644 index 80d98bd..0000000 Binary files a/Latex/assets/img/0000163.png and /dev/null differ diff --git a/Latex/assets/img/0000164.png b/Latex/assets/img/0000164.png deleted file mode 100644 index 5d49196..0000000 Binary files a/Latex/assets/img/0000164.png and /dev/null differ diff --git a/Latex/assets/img/000016a.png b/Latex/assets/img/000016a.png deleted file mode 100644 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diff --git a/Latex/assets/img/dagitty-model.jpg b/Latex/assets/img/dagitty-model.jpg deleted file mode 100644 index f7a7e56..0000000 Binary files a/Latex/assets/img/dagitty-model.jpg and /dev/null differ diff --git a/Latex/assets/img/dagitty-model.svg b/Latex/assets/img/dagitty-model.svg deleted file mode 100644 index 5c4b241..0000000 --- a/Latex/assets/img/dagitty-model.svg +++ /dev/null @@ -1 +0,0 @@ -Currently Observed EfficacyCurrently Observed SafetyFundamental EfficacyFundamental SafetyPreviously observed efficacyPreviously observed safetycurrent statusdecision to proceed w/ phase 3 trialexpected remaining durationmarket alternativespopulation sizesafety/efficacy concernswill terminate?conditionenrollment diff --git a/Latex/assets/img/mu_batman.png b/Latex/assets/img/mu_batman.png deleted file mode 100644 index 58dd207..0000000 Binary files a/Latex/assets/img/mu_batman.png and /dev/null differ diff --git a/Latex/assets/img/mu_mix.png b/Latex/assets/img/mu_mix.png deleted file 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index a1bdfea..0000000 Binary files a/Latex/assets/img/sigma_pairs_5-9.png and /dev/null differ diff --git a/Latex/assets/img/sigma_posterior.png b/Latex/assets/img/sigma_posterior.png deleted file mode 100644 index 6de606b..0000000 Binary files a/Latex/assets/img/sigma_posterior.png and /dev/null differ diff --git a/Latex/assets/img/sigma_trank.png b/Latex/assets/img/sigma_trank.png deleted file mode 100644 index 6c4447c..0000000 Binary files a/Latex/assets/img/sigma_trank.png and /dev/null differ diff --git a/Latex/assets/preambles/WSU_Econ.tikzstyles b/Latex/assets/preambles/WSU_Econ.tikzstyles index d9ac56f..ce61b82 100644 --- a/Latex/assets/preambles/WSU_Econ.tikzstyles +++ b/Latex/assets/preambles/WSU_Econ.tikzstyles @@ -32,3 +32,4 @@ \tikzstyle{filled1}=[-, fill={rgb,255: red,191; green,191; blue,191}, draw=black, tikzit draw=black, opacity=0.5, tikzit fill={rgb,255: red,191; green,191; blue,191}] \tikzstyle{emptyFill1}=[-, fill={rgb,255: red,255; green,191; blue,191}, draw=none, tikzit draw=blue, opacity=0.3] \tikzstyle{new edge style 0}=[-, draw=none, fill={rgb,255: red,191; green,191; blue,191}, tikzit draw=green, opacity=0.3, tikzit fill={rgb,255: red,191; green,191; blue,191}] +\tikzstyle{PurpleArrow}=[->, draw={rgb,255: red,128; green,0; blue,128}, tikzit draw={rgb,255: red,128; green,0; blue,128}, line width=0.5mm] diff --git a/Latex/assets/tikzit/4Node.tikz b/Latex/assets/tikzit/4Node.tikz new file mode 100644 index 0000000..41c8460 --- /dev/null +++ b/Latex/assets/tikzit/4Node.tikz @@ -0,0 +1,15 @@ +\begin{tikzpicture} + \begin{pgfonlayer}{nodelayer} + \node [style=Red Box] (0) at (4, -1.5) {Will Terminate?}; + \node [style=Red Box] (1) at (-4.25, -1.5) {Alternate Drugs}; + \node [style=purple box] (5) at (0, 2) {Enrollment}; + \node [style=Gray Box] (18) at (-6.5, 1.5) {Population}; + \end{pgfonlayer} + \begin{pgfonlayer}{edgelayer} + \draw [style=lightredarrow] (1) to (0); + \draw [style=lightredarrow] (1) to (5); + \draw [style=lightredarrow] (5) to (0); + \draw [style=RightArrow] (18) to (5); + \draw [style=RightArrow] (18) to (1); + \end{pgfonlayer} +\end{tikzpicture} diff --git a/Latex/assets/tikzit/4Node_direct.tikz b/Latex/assets/tikzit/4Node_direct.tikz new file mode 100644 index 0000000..6619c65 --- /dev/null +++ b/Latex/assets/tikzit/4Node_direct.tikz @@ -0,0 +1,15 @@ +\begin{tikzpicture} + \begin{pgfonlayer}{nodelayer} + \node [style=Red Box] (0) at (4, -1.5) {Will Terminate?}; + \node [style=Red Box] (1) at (-4.25, -1.5) {Alternate Drugs}; + \node [style=purple box] (5) at (0, 2) {Enrollment}; + \node [style=Gray Box] (18) at (-6.5, 1.5) {Population}; + \end{pgfonlayer} + \begin{pgfonlayer}{edgelayer} + \draw [style=lightredarrow] (1) to (5); + \draw [style=lightredarrow] (5) to (0); + \draw [style=RightArrow] (18) to (5); + \draw [style=RightArrow] (18) to (1); + \draw [style=PurpleArrow] (1) to (0); + \end{pgfonlayer} +\end{tikzpicture} diff --git a/Latex/assets/tikzit/4Node_total.tikz b/Latex/assets/tikzit/4Node_total.tikz new file mode 100644 index 0000000..80d2325 --- /dev/null +++ b/Latex/assets/tikzit/4Node_total.tikz @@ -0,0 +1,15 @@ +\begin{tikzpicture} + \begin{pgfonlayer}{nodelayer} + \node [style=Red Box] (0) at (4, -1.5) {Will Terminate?}; + \node [style=Red Box] (1) at (-4.25, -1.5) {Alternate Drugs}; + \node [style=purple box] (5) at (0, 2) {Enrollment}; + \node [style=Gray Box] (18) at (-6.5, 1.5) {Population}; + \end{pgfonlayer} + \begin{pgfonlayer}{edgelayer} + \draw [style=RightArrow] (18) to (5); + \draw [style=RightArrow] (18) to (1); + \draw [style=PurpleArrow] (1) to (5); + \draw [style=PurpleArrow] (5) to (0); + \draw [style=PurpleArrow] (1) to (0); + \end{pgfonlayer} +\end{tikzpicture} diff --git a/Latex/assets/tikzit/CausalGraph.tikz b/Latex/assets/tikzit/CausalGraph.tikz index 2033196..10eddf6 100644 --- a/Latex/assets/tikzit/CausalGraph.tikz +++ b/Latex/assets/tikzit/CausalGraph.tikz @@ -3,31 +3,18 @@ \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] (5) at (-0.25, 2) {Enrollment Status}; \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=emptyBox] (9) at (12.25, 6.25) {Fundamental Efficacy/Safety}; + \node [style=emptyBox] (10) at (-0.25, 8) {Previously Observed Efficacy/Safety}; + \node [style=emptyBox] (12) at (14, 0.25) {Currently Observed Efficacy/Safety}; + \node [style=Gray Box] (13) at (7, -6) {Observed}; \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] (20) at (-0.25, 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}; + \node [style=Gray Box] (22) at (7.25, 2.75) {Elapsed Duration}; \end{pgfonlayer} \begin{pgfonlayer}{edgelayer} - \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); @@ -35,18 +22,20 @@ \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); + \draw [style=RightArrow, bend left] (20) to (0); + \draw [style=PurpleArrow] (1) to (0); + \draw [style=PurpleArrow] (1) to (5); + \draw [style=PurpleArrow] (5) to (0); + \draw [style=PurpleArrow, in=135, out=45, loop] (8) to (); + \draw [style=lightredarrow] (22) to (5); + \draw [style=lightredarrow] (5) to (22); \end{pgfonlayer} \end{tikzpicture}