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61 lines
2.3 KiB
TeX
61 lines
2.3 KiB
TeX
\documentclass[../Main.tex]{subfiles}
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\graphicspath{{\subfix{Assets/img/}}}
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\begin{document}
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%% Describe goal
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% Estimate probability distribution of normalized durations and conclusion statuses.
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% Explain why this answers questions well.
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% How do I propose estimating that?
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%%NOTATION
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First, some notation:
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\begin{itemize}
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\item $t,i$ index trial and snapshot of the trial respectively.
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\item $S_{it}$ : status (``Terminated'', ``Concluded'')
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at the conclusion of the trial
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\item $\tau_{it}$ : elapsed percentage of planned duration, i.e. the normalized elapsed duration.
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\item $s_{it}$: current status variable(s) describing current trial status as one of:
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``Recruiting'', ``Active, not recruiting'', or ``Suspended''
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\item $X_{it}$: data describing the trial at the snapshot level
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\begin{itemize}
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\item number of sponsor changes so far
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\item percentage currently enrolled of planned enrolled
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\end{itemize}
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\item $M_{t}$: data describing market conditions at the time of the snapshot.
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\begin{itemize}
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\item number of compounds approved for the same indication
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\item total number of marketers approved for the same indication
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\item number of marketers for this specific compound
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\end{itemize}
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\item $T_t$: Trial Level Data
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\begin{itemize}
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\item Indication or indication class
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\item Sponsor Type
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\end{itemize}
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\end{itemize}
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Other variables used when selecting trials to include as observations are:
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\begin{itemize}
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\item Trial Phase\footnote{
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Conditioning on previous trials can be as simple as selecting only
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phase 2 or phase 3 trials.
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}.
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\item Does the trial have a Data Monitoring Committee?
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\item Are the compounds an FDA regulated drug?
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\end{itemize}
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The goal is to estimate the probability distribution of conclusion status and duration conditional on the active snapshot status.
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\begin{align}
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\pr{ t, S | X,M,T} = \sum_{S\in\{\text{Terminated},\text{Concluded}\}} \pr{t|S,X,M,T} \pr{S|X,M,T}
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\end{align}
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Note how this has two component parts:
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\begin{itemize}
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\item The survival probability portion $\pr{t|S,X,M,T}$
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\item The conclusion status portion $\pr{S|X,M,T}$
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\end{itemize}
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\end{document}
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