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% Begin by talking about goal, what does it mean? This might need some work prior to give more background.
As I am trying to separate strategic concerns 
(the effect of a marginal treatment methodology) 
and an operational concern 
(the effect of a delay in closing enrollment), 
we need to look at what confounds these effects and how we might measure them.

There are a few fundamental issues.
The first is that the severity of the disease and the size of the population 
who has that disease affects the ease of enrolling participants. 
For example, a large population may make it easier to find enough participants
to achieve the required statistical discrimination between 
control and treatment.
Second, for some diseases there exists an endogenous dynamic 
between the treatments available for a disease and the 
market size/population with that disease. 
\authorcite{cerda_EndogenousInnovations_2007} proposes two mechanisms
that link drugs on the market and market size. 
The first is that a large market will tends to have more drugs to treat it. 
The inverse is that for many chronic diseases with high mortality rates, 
more drugs cause better survivability, increasing the size of those markets.


%%%%% \/\/\/\/\/ OLD STUFF \/\/\/\/\/

Because running experiments on companies running clinical trials is not going
to happen anytime soon, causal identification will depend on creating a 
structural causal model.
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 ask 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 enough to achieve our 
        goals, justifying continuing the trial?
    \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}
When appropriate, the study sponsor terminates the trial.
If there are not enough issues to terminate the trial, it continues until it 
is completed.

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.
Participants frequently 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 over using current standard treatments.
Thus the current market conditions may affect the rate at which participants 
enroll in the trial.

The enrollment of participants in a trial depends on a few other factors.
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 by switching to an "Active, not recruiting" stage to manage costs.
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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