You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
83 lines
4.2 KiB
TeX
83 lines
4.2 KiB
TeX
\documentclass[../Main.tex]{subfiles}
|
|
\graphicspath{{\subfix{Assets/img/}}}
|
|
|
|
\begin{document}
|
|
|
|
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.
|
|
\includegraphics[width=\textwidth]{../assets/img/dagitty-model.jpg}
|
|
\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.
|
|
|
|
\end{document}
|