diff --git a/Latex/Paper/sections/02_data.tex b/Latex/Paper/sections/02_data.tex index e248c24..5b419c9 100644 --- a/Latex/Paper/sections/02_data.tex +++ b/Latex/Paper/sections/02_data.tex @@ -2,19 +2,21 @@ \graphicspath{{\subfix{Assets/img/}}} \begin{document} -%Classes of data -% Trial Dynamics/snapshots -% Drugs on Market -% Market/Population Size -% Compounds, interactions \subsection{Data Sources} +The following are the data source I plan on using. \subsubsection{Clinical Trials Data} %ClinicalTrials.gov % Key features - brief description +% Snapshots % Why is it being included % What specific data is used +% Enrollment, status, duration, indication, compound % Data Manipulations for each +% Normalized: Enrollment, duration +% Categorical-to dummies: status +% Linked: indication, compound +% counts: number of sponsor changes since start. % Links to data \subsubsection{Drugs on Market} @@ -22,7 +24,10 @@ % Key features % Why is it being included % What specific data is used +% compound, spl, marketing dates % Data Manipulations for each +% Linked: compound, spl -> indication +% standardize start/end dates by getting a view: compound, dates, manufacturer. % Links to data \subsubsection{Global Disease Burden Survey} @@ -49,6 +54,6 @@ % Link Global disease burden to a generic indication registry % Link trial compounds a generic registry (MPT or whatever that was)? % Link SPL compounds to a generic registry -% +% Link Market data to SPLs \end{document} diff --git a/Latex/Paper/sections/04_EconometricModel.tex b/Latex/Paper/sections/04_EconometricModel.tex index 1825d25..e52cd58 100644 --- a/Latex/Paper/sections/04_EconometricModel.tex +++ b/Latex/Paper/sections/04_EconometricModel.tex @@ -2,11 +2,59 @@ \graphicspath{{\subfix{Assets/img/}}} \begin{document} -In September of 2019, the European Space Agency (ESA) released a tweet -explaining that they had performed an appendicotomy in space using -nothing more than radiation from the sun. -They are sad to announce that the patient died due to complications from -exposure to the cold vaccum of space. +%% Describe goal +% Estimate probability distribution of normalized durations and conclusion statuses. +% Explain why this answers questions well. +% How do I propose estimating that? +%%NOTATION + +First, some notation: +\begin{itemize} + \item $t,i$ index trial and snapshot of the trial respectively. + \item $S_{it}$ : status (``Terminated'', ``Concluded'') + at the conclusion of the trial + \item $\tau_{it}$ : elapsed percentage of planned duration, i.e. the normalized elapsed duration. + \item $s_{it}$: current status variable(s) describing current trial status as one of: + ``Recruiting'', ``Active, not recruiting'', or ``Suspended'' + \item $X_{it}$: data describing the trial at the snapshot level + \begin{itemize} + \item number of sponsor changes so far + \item percentage currently enrolled of planned enrolled + \end{itemize} + \item $M_{t}$: data describing market conditions at the time of the snapshot. + \begin{itemize} + \item number of compounds approved for the same indication + \item total number of marketers approved for the same indication + \item number of marketers for this specific compound + \end{itemize} + \item $T_t$: Trial Level Data + \begin{itemize} + \item Indication or indication class + \item Sponsor Type + \end{itemize} +\end{itemize} + +Other variables used when selecting trials to include as observations are: +\begin{itemize} + \item Trial Phase\footnote{ + Conditioning on previous trials can be as simple as selecting only + phase 2 or phase 3 trials. + }. + \item Does the trial have a Data Monitoring Committee? + \item Are the compounds an FDA regulated drug? +\end{itemize} + + +The goal is to estimate the probability distribution of conclusion status and duration conditional on the active snapshot status. + +\begin{align} + \pr{ t, S | X,M,T} = \sum_{S\in\{\text{Terminated},\text{Concluded}\}} \pr{t|S,X,M,T} \pr{S|X,M,T} +\end{align} +Note how this has two component parts: +\begin{itemize} + \item The survival probability portion $\pr{t|S,X,M,T}$ + \item The conclusion status portion $\pr{S|X,M,T}$ +\end{itemize} \end{document} diff --git a/Latex/assets/preambles/MathPreamble.tex b/Latex/assets/preambles/MathPreamble.tex index c81874f..0b39634 100644 --- a/Latex/assets/preambles/MathPreamble.tex +++ b/Latex/assets/preambles/MathPreamble.tex @@ -18,3 +18,4 @@ %Math Operators \DeclareMathOperator{\argmax}{argmax} \DeclareMathOperator{\argmin}{argmin} +\newcommand{\pr}[1]{\ensuremath{\text{Pr}\left( #1 \right)}} diff --git a/Latex/assets/tikzit/CausalGraph.tikz b/Latex/assets/tikzit/CausalGraph.tikz index e85bddc..4c464be 100644 --- a/Latex/assets/tikzit/CausalGraph.tikz +++ b/Latex/assets/tikzit/CausalGraph.tikz @@ -1,9 +1,9 @@ \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 Effectiveness}; - \node [style=Red Box] (3) at (-3.75, -3.5) {\begin{tabular}{l} Conclusion \\ $\bullet$ Status\\ $\bullet$ Duration \\ $\bullet$ Enrollment \end{tabular}}; - \node [style=Red Box] (4) at (-2.75, 1) {\begin{tabular}{l} Snapshot \\ $\bullet$ Status\\ $\bullet$ Duration \\ $\bullet$ Enrollment \end{tabular}}; + \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}}; @@ -11,9 +11,9 @@ \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) {Adverse Events}; + \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 (3.75, 1) {Disease Burden}; + \node [style=Box] (15) at (4.75, 1) {Disease Burden}; \end{pgfonlayer} \begin{pgfonlayer}{edgelayer} \draw [style=RightArrow] (4) to (3);