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% Introduce clinicaltrials.gov
% - Describe different statuses 
% - status flowchart
% Introduce causal model
% - Diagram
% - List each node and what they influence (and why)
% Begin Discussing Data
% - Where did I get data for each node?

Because running randomized experiments on companies running clinical trials 
is unlikely to to happen anytime soon, 
causal identification will depend on observational methods. 
I use the do-calculus approach developed by Judea Pearl
\cite{pearl_CausalityModels_2009}
to describe what affects the success of a Phase III clinical trial. 
I then use that model to derive the econometric model capable of estimating
the effect of extending the recruiting period or of having an additional 
competing drug.



% In \cref{Fig:CausalModel} I diagram the directed acyclic graph that describes
% the data generating model.
The proposed data generating model consists of a decision maker
-- the study sponsor --
who must decide whether to let a trial run to completion or terminate
the trial early. 
While receiving updates regarding the status of the trial, they try to 
answer questions such as:
\begin{itemize}
    \item Do I need to terminate the trial due to safety incidents?
    \item Does it appear that the drug is effective?
    \item Are we recruiting enough participants to achive the statistical
        results we need?
    \item Does the current market conditions and expectations about 
        returns on 
        investment justify the expenditures we are making?
\end{itemize}
Althought I treat this as a single agent, in reality, there are multiple 
stakeholders involved in chosing whether the trial should continue, including
those running the trial (which may be a separate firm), 
the company developing the drug, additional rightsholders, 
or funding organizations.

% When appropriate, the study sponsor terminates the trial.
% If there are not enough issues to terminate the trial, it continues until it 
% is completed.

In the United States, clinical trials are required by law to be registered on 
\url{ClinicalTrials.gov}, where they are made available to the public. 
Trials must be registered 

% 


While conducting a trial, the safety and efficacy of a drug are driven by
fundamental pharmacokinetic properties of the compounds. 
These are only imperfectly measured both prior to and during any given trial.
Previously measured safety and efficacy inform the decision to start the trial
in the first place while currently observed safety and efficiency results
help the sponsor judge whether or not to continue the trial.
Of course, these decisions are both affected by the specific condition being
treated due to differences in the severity of the symptoms.

When a trial has been started, it comes time to recruit participancts.
The enrollment of participants in a trial depends on a few factors.
Participants usually depend on the advice of their physician when deciding 
to join a trial or not. 
As these physicians have a duty to seek their patients best interest; they, along
with their patients will evaluate if the previously observed safety and efficacy
results justify joining the trial in contrast to using the current standard 
of care. 
Thus enrollment rates are influenced by the treatments currently on the market. 
Recruitment can also be hindered if disease has a low impact 
-- in which participants might have little incentive to join -- 
or if there are few people who have the disease. 
The overall impact of the disease also influences whether or not there are 
already drugs on the market to treat that disease. 

The condition or disease of interest and how it progresses will determine how long
recruitiment will be held open versus just an observation of treatment arms.
Aditionally, a trial that has already reached a high enough enrollment will often
close recruitment. 
Both of these are reported as "Active, not recruting" to ClinicalTrials.gov. 
Finally, enrolling participants depends on how difficult it is to find people 
who suffer from the condition of interest.

The preceeding issue of population size also affects the number of alternatives available.
When there are less people affected by the disease, the smaller market reduces 
possible profitability, all else equal.
Thus the likelihood of companies paying the sunk costs to develop drugs for
these conditions may be lower.
Finally, the number of alternatives on the market may affect the return on
investment directly, causing a trial to terminate early if the return is
not high enough.

\begin{figure}[H] %use [H] to fix the figure here.
    \scalebox{0.6}{\tikzfig{../assets/tikzit/CausalGraph2}}
    \caption{Causal Model}
    \label{Fig:CausalModel}
\end{figure}
% 
By using Judea Pearl's do-calculus, I can show that by choosing an adjustment 
set of the decision to condut a phase III trial, the condition of interest, 
the current status of the trial, and the population size will casually
identify the direct effects of enrollment and market alternatives on the
probability of termination.
This is easily verified through the backdoor criterion, which states that
if every path between the exposure and outcome that starts with an arrow 
flowing into the exposure is blocked by one of the values in the adjustment
set, then the effect of the exposure on outcome is causally identified
(\cite{pearl_causality_2000}).
It can be easily visually verified by the DAG on the graph that this is the case.

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