It can also be devided into a few different regimes.
% - spike at 0
% - the boxplot
% - 63% of mass below 0 : find better way to say that
% - For a random trial, there is a 63% chance that the impact is to reduce the probability of a termination.
% - 2 pctg-point wide band centered on 0 has ~13% of the masss
% - mean represents 9.x% increase in probability of termination. A quick simulation gives about the same pctg-point increase in terminated trials.
A few interesting interpretation bits come out of this.
% - there are 3 regimes: low impact (near zero), medium impact (concentrated in decreased probability of termination), and high impact (concentrated in increased probability of termination).
The first this that there appear to be three different regimes.
The first regime consists of the low impact results, i.e. those values of $\delta_p$
near zero.
About 13\% of trials lie within a single percentage point change of zero,
@ -146,63 +147,78 @@ The second regime consists of the moderate impact on clinical trials'
probabilities of termination, say values in the interval $[-0.5, 0.5]$
on the graph.
Most of this probability mass is represents a decrease in the probability of
a termination, some of it rather large decreases.
The third regime consists of the high impact region,
almost exclusively concentrated above increases in the probability of
termination $\delta_p > 0.75$.
a termination, some of it rather large.
Finally, there exists the high impact region, almost exclusively concentrated
around increases in the probability of termination at $\delta_p > 0.75$.
These represent cases where delaying the close of enrollemnt changes a trial
from a case where they were highly likely to complete their primary objectives to
a case where they were likely or almost certain to terminate the trial early.
% - the high impact regime is strange because it consists of trials that moved from unlikely (<20% chance) of termination to a high chance (>80% chance) of termination. Something like 5% of all trials have a greater than 98 percentage point increase in termination. Not sure what this is doing.
% Looking at the spike around zero, we find that 13.09% of the probability mass
% is contained within the band from [-1,1].
% Additionally, there was 33.4282738% of the probability above that
%– representing those with a general increase in the
% probability of termination – and 53.4817262% of the probability mass
% below the band – representing a decrease in the probability of termination.
% On average, if you keep the trial open instead of closing it, 0.6337363% of
% trials will see a decrease in the probability of termination, but, due to
% the high increase in probability of termination given termination was
% increased, the mean probability of termination increases by 0.0964726.
Figure \ref{fig:pred_dist_dif_delay2} shows how the different disease categories
tend to have a similar results:
% - Potential Explanations for high impact regime:
How could this intervention have such a wide range in the intensity
and direction of impacts?
A few explanations include that some trials are suceptable or that this is a
result of too little data.
% - Some trials are highly suceptable. This is the face value effect
One option is that some categories are more suceptable to
issues with participant enrollment.
If this is the case, we should be able to isolate categories that contribute
the most to this effect.
Another is that this might be a modelling artefact, due to the relatively
low number of trials in certain ICD-10 categories.
In short, there might be high levels of uncertanty in some parameter values,
which manifest as fat tails in the distributions of the $\beta$ parameters.
Because of the logistic format of the model, these fat tails lead to
extreme values of $p$, and potentally large changes $\delta_p$.
% - Could be uncertanty. If the model is highly uncertain, e.g. there isn't enough data, we could have a small percentage of large increases. This could be in general or just for a few categories with low amounts of data.
% -
% -
I believe that this second explanation -- a model artifact due to uncertanty --
is likely to be the cause.
Three points lead me to believe this:
\begin{itemize}
\item The low fractions of E-BFMI suggest that the sampler is struggling
to explore some regions of the posterior.
According to \cite{standevelopmentteam_RuntimeWarnings_2022} this is
often due to thick tails of posterior distributions.
\item When we examine the results across different ICD-10 groups,
\ref{fig:pred_dist_dif_delay2}
\todo{move figure from below}
we note this same issue.
\item In Figure \ref{fig:betas_delay}, we see that some some ICD-10 categories
\todo{add figure}
have \todo{note fat tails}.
\item There are few trials available, particularly among some specific
ICD-10 categories.
\end{itemize}
% - take a look at beta values and then discuss if that lines up with results from dist-diff by group.
% - My initial thought is that there is not enough data/too uncertain. I think this because it happens for most/all of the categories.
% -
% -
% -
Overally it is hard to escape the conclusion that more data is needed across
many -- if not all -- of the disease categories.
Figure \ref{fig:pred_dist_dif_delay2} shows how this overall
\caption{Distribution of Predicted differences by Disease Group}
\label{fig:pred_dist_dif_delay2}
\end{figure}
Again, note the high mass near zero, the general decrease in the probability
of termination, and then the strong upper tails.
Continuing to the $\beta$ parameters in figure
\ref{fig:parameters_ANR_by_group},
we can see the estimated distributions
the status: \textbf{Active, not recruiting}.
The prior distributions were centered on zero, but we can see that the
pooled learning has moved the mean
values negative, representing reductions in the probability of termination
across the board.
This decrease in the probability of termination is strongest in the categories of Neoplasms ($n=49$),
Musculoskeletal diseases ($n=17$), and Infections and Parasites ($n=20$), the three categories with the most data.
As this is a comparison against the trial status XXX, we note that YYY.
\todo{The natural comparison I want to make is against the Recruting status. Do I want to redo this so that I can read that directly?It shouldn't affect the $\delta_p$ analysis, but this could probably use it. YES, THIS UPDATE NEEDS TO HAPPEN. The base needs to be ``active not recruiting.''}
Overall, this is consistent with the result that extending a clinical trial's enrollment period will reduce the probability of termination.
\subsection{Secondary Results}
% Examine beta parameters
% - Little movement except where data is strong, general negative movement. Still really wide
% - Note how they all learned (partial pooling) reduction in \beta from ANR?
% - Need to discuss the 5 different states. Can't remember which one is dropped for the life of me. May need to fix parameterization.
Values near 1 indicate a near perfect increase in the probability
of termination.
Values near 0 indicate little change in probability,
while values near -1, represent a decrease in the probability
of termination.
The scale is in probability points, thus a value near 1 is a change
from unlikely to terminate under control, to highly likely to
terminate.
}
\caption{Histogram of the Distribution of Predicted Differences}
\label{fig:pred_dist_diff_delay}
\end{figure}
There are a few interesting things to point out here.
Let's start by getting aquainted with the details of the distribution above.
% - spike at 0
% - the boxplot
% - 63% of mass below 0 : find better way to say that
% - For a random trial, there is a 63% chance that the impact is to reduce the probability of a termination.
% - 2 pctg-point wide band centered on 0 has ~13% of the masss
% - mean represents 9.x% increase in probability of termination. A quick simulation gives about the same pctg-point increase in terminated trials.
A few interesting interpretation bits come out of this.
% - there are 3 regimes: low impact (near zero), medium impact (concentrated in decreased probability of termination), and high impact (concentrated in increased probability of termination).
The first this that there appear to be three different regimes.
The first regime consists of the low impact results, i.e. those values of $\delta_p$
near zero.
About 13\% of trials lie within a single percentage point change of zero,
suggesting that there is a reasonable chance that delaying
a close of enrollment has no impact.
The second regime consists of the moderate impact on clinical trials'
probabilities of termination, say values in the interval $[-0.5, 0.5]$
on the graph.
Most of this probability mass is represents a decrease in the probability of
a termination, some of it rather large.
Finally, there exists the high impact region, almost exclusively concentrated
around increases in the probability of termination at $\delta_p > 0.75$.
These represent cases where delaying the close of enrollemnt changes a trial
from a case where they were highly likely to complete their primary objectives to
a case where they were likely or almost certain to terminate the trial early.
% - the high impact regime is strange because it consists of trials that moved from unlikely (<20% chance) of termination to a high chance (>80% chance) of termination. Something like 5% of all trials have a greater than 98 percentage point increase in termination. Not sure what this is doing.
% - Potential Explanations for high impact regime:
This leads to the question:
``How could this intervention have such a wide range in the intensity
and direction of impacts?''
The most likely explanations in my mind are that either
some trials are highly suceptable to enrollment struggles or that this is a
modelling artifact.
How could this intervention have such a wide range in the intensity
and direction of impacts?
A few explanations include that some trials are suceptable or that this is a
result of too little data.
% - Some trials are highly suceptable. This is the face value effect
The first option -- that some trials are more suceptable to
issues with participant enrollment -- should allow us to
isolate categories or trials that contribute the most to this effect.
This is not what we find when we inspect the categories
in figure
\ref{fig:pred_dist_dif_delay2}.
Instead it appears that most of the categories have this high
impact regime when $\delta_p > 0.75$, although the maximum value
of this regime varies considerably.
Another explanation is that this is a modelling artefact due to priors
with strong tails and the relatively low number of trials in
each ICD-10 categories.
One option is that some categories are more suceptable to
issues with participant enrollment.
If this is the case, we should be able to isolate categories that contribute
the most to this effect.
Another is that this might be a modelling artefact, due to the relatively
low number of trials in certain ICD-10 categories.
In short, there might be high levels of uncertanty in some parameter values,
which manifest as fat tails in the distributions of the $\beta$ parameters.
Because of the logistic format of the model, these fat tails lead to
extreme values of $p$, and potentally large changes $\delta_p$.
% - Could be uncertanty. If the model is highly uncertain, e.g. there isn't enough data, we could have a small percentage of large increases. This could be in general or just for a few categories with low amounts of data.
% -
% -
I believe that this second explanation -- a model artifact due to uncertanty --
is likely to be the cause.
A few things lead me to believe this:
Three points lead me to believe this:
\begin{itemize}
\item The low fractions of E-BFMI suggest that the sampler is struggling
\caption{Distribution of Predicted differences by Disease Group}
\label{fig:pred_dist_dif_delay2}
\end{figure}
% Examine beta parameters
% - Little movement except where data is strong, general negative movement. Still really wide
% - Note how they all learned (partial pooling) reduction in \beta from ANR?
% - Need to discuss the 5 different states. Can't remember which one is dropped for the life of me. May need to fix parameterization.
% -
Finally, in figure \ref{fig:parameters_ANR_by_group}, we can see the estimated distributions of the $\beta$ parameter for
the status: \textbf{Active, not recruiting}.
The prior distributions were centered on zero, but we can see that the pooled learning has moved the mean
values negative, representing reductions in the probability of termination across the board.
This decrease in the probability of termination is strongest in the categories of Neoplasms ($n=$),
Musculoskeletal diseases ($n=$), and Infections and Parasites ($n=$), the three categories with the most data.
As this is a comparison against the trial status XXX, we note that
\todo{The natural comparison I want to make is against the Recruting status. Do I want to redo this so that I can read that directly?It shouldn't affect the $\delta_p$ analysis, but this could probably use it.}
Overall, this suggests that extending a clinical trial's enrollment period will reduce the probability of termination.
Will King