further work on discussion

thesis/sections/discussion.tex

@@ -42,7 +42,7 @@ i.e., the LSTM model.
 
 Figure~\ref{fig:discussion_regular_cycle_fertility_prediction} shows the prediction curve for the fertility-probability target
 for a user with a regular cycle pattern.
-It is clearly visible, that the predictions improve with each cycle, until they almost exactly match the targets.
+For such a regular cycle pattern, the predictions almost exactly match the targets.
 Another noteworthy observation is the correlation between a clear temperature drop preceding ovulation and
 the fertility rising.
 This can be seen more prominently in Figure~\ref{fig:discussion_temperature_drop_fertility_prediction}.
@@ -63,6 +63,16 @@ but its intensity varies between users and also between cycles of the same user.
 Such a pattern can turn out to be a useful predictor for ovulation / fertility, but the models we trained don't seem
 to be able to differentiate between ovulation-related and unrelated temperature drops.
 
+This also points to a potential flaw in our workflow.
+We don't yet have clinically accurate labels for the cycles that were used for the training of our models.
+In fact, we cannot guarantee an ovulation, not even for the cycles with a clear temperature rise after the apparent ovulation.
+It is not uncommon for women to have a clear temperature rise without an ovulation and vice versa,
+to have an ovulation but no clear temperature rise.
+The identified temperature drop and the fertility that seems to come with it could be a base for further research
+with more accurate ovulation labeling.
+It might be an indicator for a successful upcoming ovulation.
+
+
 \begin{figure}[htbp]
     \centering
     \includegraphics[width=1.0\textwidth]{resources/figures/discussion/temperature_drop_fertility}
@@ -86,7 +96,7 @@ to be able to differentiate between ovulation-related and unrelated temperature
     \includegraphics[width=1.0\textwidth]{resources/figures/discussion/temperature_unclear_temperature_drop}
     \caption{
         Temperature rolling average and fertility-probability prediction with no clear temperature drop and a resulting
-        incorrect fertility-probability prediction. (Values are scaled features)
+        incorrect prediction. (Values are scaled features)
     }
     \label{fig:discussion_unclear_temperature_drop}
 \end{figure}
@@ -102,6 +112,25 @@ This is likely information indicating some form of regularity, which the models
 It would be interesting to take a close look at how and in what intensity the models use certain features,
 and whether the performance changes upon omitting certain features.
 
+\paragraph{Use-Case Study.}
+
+The threshold has a large effect on the overall effectiveness of the different use cases.
+For the contraception use case, changing the threshold doubles and even quadruples the pregnancy rate.
+It has to be noted, that the contraception use case is naive use-case, where the woman does not take any other
+measures next to the prediction of our models.
+In a real-world scenario, this is largely not the case, and thus the pregnancy rates should be even lower.
+A measure often taken is abstinence during the first cycle phase (luteal phase), which should significantly lower
+unwanted pregnancies.
+Even without additional measures, a threshold of 0.05 leads to an approximate \emph{Pearl-Index} (pregnancy rate over 1 year for 100 women)
+of 4--5, which is significantly better than methods such as the contraceptive pill (7) or the condom (13) for a typical use case.
+However, these numbers have to be taken with caution, as this is not an actual study, but a naive theoretical projection.
+Further research is necessary to find more reliable results.
+
+The pregnancy use case is harder to contextualize, as there are no comparable results for other methods,
+and the actual pregnancy probability is subject to many more factors, we could not take into consideration for this study.
+
+
+
 
 %
 %In general, we expect the transformer based model to outperform the LSTM basd models, as they have proven to be