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106 lines
5.3 KiB
TeX
106 lines
5.3 KiB
TeX
\documentclass[../Main.tex]{subfiles}
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\graphicspath{{\subfix{Assets/img/}}}
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\begin{document}
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The identification strategy centers on the fact that, in the U.S., clinical trials
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update the publically available information on \url{ClinicalTrials.gov}, which are then made
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available as historical snapshots.
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These updates typically include information such as additional sites conducting the study,
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the study status, and expected or current enrollment figures.
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By measuring enrollment and other factors prior to the conclusion of a trial, we
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can measure the effect of enrollment on trial conclusion
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(specifically whether it is registered as completed or terminated).
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In particular, this avoids measuring the joint determination of enrollment and conclusion
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status arising from trials terminated early.
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Figure \ref{Fig:CausalModel} describes the structural causal model (SCM) used to justify
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the causal identification
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\begin{figure}[H] %use [H] to fix the figure here.
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\tikzfig{../assets/tikzit/CausalGraph}
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\caption{Causal Model}
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\label{Fig:CausalModel}
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\end{figure}
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The identification strategy is based on the backdoor criterion due to \cite{PEARL1995}.
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As the backdoor criteron depends on the SCM being a Directed Acyclic Graph (DAG, the first
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step is to justify the DAG in \cref{FIG:CausalModel}.
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% The data consists of individual snapshots
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% Describe "states"
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% Also, snapshot states are dependent across time
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% Define conclusion state vs snapshot state.
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The key feature of the data is that it consists of sequences of trial snapshots for each trial.
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Snapshots prior to the start of the trial capture expected enrollment and time to completion,
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while snapshots during the trial record actual enrollement figures, current status,
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and the date the snapshot was recorded.
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Finally, after a trial concludes, snapshots list final enrollment and the date at which the
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last participant was examined\cite{CLINICALTRIALS-data_spec}.
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In the discussion below, I refer to a snapshot's ``state'' as the enrollment, duration, and status
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recorded at the time of the snapshot.
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%TODO: make sure data section discusses the normalization of enrollment and duration.
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Additionally, I distinguish between the state at trial conclusion and state from a snapshot during the running trial as
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``conclusion state'' and ''active snapshot state''.
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% Describe market conditions.
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Associated with each trial snapshot are the market conditions existing at that point in time.
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%Describe the observed and unobserved events and their supposed relationships.
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%%%%% Relationships of interest
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% Snapshot State -> Conclusion state
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% Discuss how the data captures this - time dependence
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%TODO
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% Market -> Snapshot state
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% Market -> Conclusion state
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%%%%% Confounding relationships and controls
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% Disease Burden -> Market Conditions, Snapshot State
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In addition to the relationships of interest between teh active snapshot states and
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the conclusion states, there are various biasing effects that need to be accounted for.
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The first of these is the fact that enrollment and the drugs currently on the market are
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both affected by the number of people who are affected by the disease under examination.
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This biases not only the estimate of the total causal effect of market conditions
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on conclusion state but also the direct effects of both
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market conditions and active snapshot enrollment on conclusion state.
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Additionally, it biases the estimation of the effect of market conditions on
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active snapshot enrollment.
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I plan on using the WHO's Global Disease Burden Survey
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to control for population size. %CITE - ekaterina
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% Biasing Pathways
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% Compound Safety -> Current Adverse Events -> Conclusion State.
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% Note: Compound Safety -> Current Adverse Events -/> Snapshot State.
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% Even if it were an issue, the direct events should still be identified?
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A second biasing effect is related to the fact that a compounds safety drives both beliefs about
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the compound -- affecting active snapshot enrollment -- and the current adverse effects
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which directly influcences the conclusion state by leading to terminations.
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The backdoor criterion implies that controlling for whether or not prior trials have
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occurred will eliminate bias.
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%TODO: discuss how you will be conditioning on prior trials, i.e. per compound or just phase 3 etc.
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% Compound Efficacy -> Measured Effectiveness -> Conclusion State
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Similarly, the last confounding factor is that of measured effectiveness.
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When running a trial, the sponsor will get periodic updates as to the measured effectiveness.
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If this is lower than expected, the trial may conclude early.
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Although this is a direct effect, the issue comes through the backdoor path through prior trials
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and beliefs about the compound.
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Thus controlling for prior trials eliminates this path as well.
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% Control
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% Compound Safety, Compound Efficacy -> Prior Trials -> Beliefs about Compound
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%
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%%%% Variance controls
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% Sponsor Changes -> Conclusion Status
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Finally, the last control variable is that of sponsor changes.
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As sponsors are captured at each snapshot, it is possible to measure when a sponsor has changed.
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Changing sponsors is a potentially disruptive event, and so it is likely to affect the probability
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that the trial is canceled early.
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The purpose of including this control is to reduce the variance of our estimates.
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%Describe what causal effects are identified by the backdoor criterion.
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\end{document}
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