\todo{Replace this graphic with the histdiff with boxplot}
\small{
\small{
Values near 1 indicate a near perfect increase in the probability
Values near 1 indicate a near perfect increase in the probability
of termination.
of termination.
@ -52,26 +102,84 @@ keeping enrollment open.
\label{fig:pred_dist_diff_delay}
\label{fig:pred_dist_diff_delay}
\end{figure}
\end{figure}
We can see from figure
There are a few interesting things to point out here.
\ref{fig:pred_dist_diff_delay}
Let's start by getting aquainted with the details of the distribution above.
That there are roughly four regimes.
% - spike at 0
The first consists of trials that experiences nearly no effect,
% - the boxplot
i.e. have values near zero.
% - 63% of mass below 0 : find better way to say that
Trials in the second regime experience a mild to large reduction in
% - For a random trial, there is a 63% chance that the impact is to reduce the probability of a termination.
the probability of termination, with X percent of the probability mass
% - 2 pctg-point wide band centered on 0 has ~13% of the masss
between about 5 percentage points and 50 percentage point reductions.
% - mean represents 9.x% increase in probability of termination. A quick simulation gives about the same pctg-point increase in terminated trials.
The third regime is those trials that experience a mild to large
increase in the probability of termination,
A few interesting interpretation bits come out of this.
from an increase o 5 percentage points to about 75 percentage points.
% - 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 fourth and final regime is the X\% of trials that experience a significant
The first this that there appear to be three different regimes.
(greater than 75 percentage point) increase in the probability of
The first regime consists of the low impact results, i.e. those values of $\delta_p$
termination.
near zero.
%Notes on interpretation
About 13\% of trials lie within a single percentage point change of zero,
% - increase vs decrease on graph
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:
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 IDC-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}
% NOTE: maybe change order to be ebfmi, group hist-diff or distdiff, tail width, then data size.
% - 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 result that more data is needed, across
many, if not all, of the disease categories.
% The probability mass associated with a each 10 percentage point change are in table \ref{tab:regimes}
% The probability mass associated with a each 10 percentage point change are in table \ref{tab:regimes}
%\begin{table}[H]
%\begin{table}[H]
@ -100,15 +208,6 @@ result comes from different disease categories.
\label{fig:pred_dist_dif_delay2}
\label{fig:pred_dist_dif_delay2}
\end{figure}
\end{figure}
Overall, we can see that there appear to be some trials or situations
that are highly suceptable to enrollment difficulties, and this
appears to hold for all disease categories for which I have data.
This relative homogeneity of results may be due to the
partial pooling effect from the hierarchal model
and the fact that the sample size per disease is rather small.
An additional explanation is that the variance of the parameter distributions
might be high enough for each trial to have a few situation in which they have
will king
1 year ago