%! Author = alex
%! Date = 3/6/25


\section{Discussion}\label{sec:discussion}

\subsection{Objective 1: Model Architecture Evaluation and Optimization}\label{subsec:discussion_rq1_model_evaluation}


The first research objective considered different model architectures and how they perform
under various hyperparameter configurations, with respect to the optimization goals of this study.

I found that non-convolutional models performed best with medium resolutions and longer input windows,
where they also outperformed their convolutional counterparts.
This suggests that including more historical context improves prediction accuracy.
However, there appears to be a trade-off:
while more information can improve predictions, it also introduces additional noise, which the models struggle to handle effectively.
The strong performance at medium resolutions indicates a possible sweet spot—balancing information richness with model capacity and generalization.

The convolutional variants performed best with medium-length input windows, which was somewhat surprising.
One would expect convolutional downsampling to enable more efficient data representation,
allowing the model to extract relevant patterns from high-resolution data and to perform better on longer sequences.
However, this was not observed in my experiments.
Instead, convolutional models performed worse than non-convolutional models on longer input windows,
suggesting that the benefits of downsampling may be offset by limitations in capturing long-range dependencies.
For medium and short input windows, however, convolutional models did outperform the non-convolutional
variants—indicating that the convolution itself provides an advantage when input length is limited.

To my knowledge, no prior studies have compared different deep learning architectures for real-time fertility prediction.
This highlights both the novelty and the exploratory nature of my approach.

All these results must be interpreted with caution, as they are based on single-shot experiments and are not statistically robust.
A more rigorous evaluation would involve training all models multiple times to minimize the
impact of random initialization and other stochastic processes in training.
For most metrics, differences in performance were small, often less than 1\%, and could easily be attributed to such variability.

I am also aware of potential losses in predictive quality due to class imbalance in the labels.
Especially in long cycles, the targets are mostly zero, except for a narrow window around ovulation
(for the fertility-probability target) or the area after ovulation (for the ov-over target).
Positive-to-negative target ratios can reach 10–20:1 in long cycles, meaning for each non-zero target day,
there are 10 to 20 days with all-zero targets.
This imbalance may introduce instability during training and reduce predictive performance.
Future iterations of this study could incorporate class-weighting or loss-balancing mechanisms to address this issue.

A central limitation of this study is that the training labels were generated
retrospectively from temperature curves, rather than being based on direct clinical
confirmation of ovulation (e.g., ultrasound or hormone assays).
Although the retrospective algorithm was validated against expert-labeled reference cycles,
it remains a proxy and can be biased by ambiguous patterns, illness, or sensor dropout.
The models therefore predict consistency with this retrospective labeling rather than
the absolute physiological ground truth.
Prospective validation against clinical reference standards will be essential to establish the reliability of
the approach in real-world use.

Future work should also include a more thorough parameter search and statistically more robust evaluation methodology.
A more sophisticated hyperparameter search may be necessary to identify globally optimal configurations for each model architecture.
Time and resource constraints could be alleviated using more efficient search algorithms such as Bayesian Optimization,
Genetic Algorithms, or Neural Architecture Search (NAS) to better explore the joint parameter space.

Additionally, I habe only focused on basic models—LSTMs and Transformers, with convolutional hybrids.
A closer look into alternative architectures, or tailoring architectures more specifically
to the characteristics of menstrual cycle data, could significantly improve predictions.
Recent Transformer variants for time series modeling, such as \emph{TimeXer}~\cite{wang_timexer_2024}
or \emph{MAMBA}~\cite{wang_is_2024}, may offer better performance.
Alternatively, a custom architecture could be developed to reflect the domain-specific structure of biological temperature data more closely.
This could be combined with a more sophisticated convolutional setup or preprocessing strategy
to handle high-resolution inputs more efficiently.
Such preprocessing might help overcome computational bottlenecks that raw LSTMs and Transformers encounter when dealing with large input sequences.

Moreover, a more statistically grounded approach to feature selection could further improve predictive performance.
Both raw and engineered features could be evaluated for their impact on model output.
Especially promising are intermediate features such as cycle-level aggregates,
temperature accumulation over time or space, and static user-level characteristics.
The database used in this study also contains an extensive set of user-logged marker events, such as intercourse,
intermediate bleeding, or illnesses, which could help the models learn correlations between these events and temperature fluctuations.

Finally, exploring alternative prediction targets may help address some of the core challenges of fertility prediction.
Beyond the fertility-probability and ov-over indicators used in this study,
targets such as the number of days to the next ovulation (or since the last), or the ovulation day
as a direct regression target, might prove more stable and informative.
As can be seen in the next section, the current targets are highly sensitive to anomalies,
which may not be the case for alternative formulations.

\subsection{Objective 2: Factors and Patterns that Influence Prediction}\label{susbsec:discussion_rq2_factors_and_patterns}

My second research objective focused on identifying potential factors and patterns in the data
that influence fertility prediction.

To my knowledge, no prior work has explicitly analyzed the relationship between temperature patterns
and ovulation—including the corresponding fertile window—in a way that could directly inform machine learning models.
This underscores the exploratory nature of this analysis.

I have identified a consistent pre-ovulatory temperature dip that aligned closely with the ground-truth fertility curve.
This drop was particularly pronounced in short and regular cycles.
In contrast, irregular cycles often exhibited too much variability and noise in the follicular phase
for the models to reliably detect this temperature drop, or to associate it meaningfully with increased fertility probability.
Interestingly, the magnitude of the temperature dip was strongly correlated with the predicted fertility probability:
larger dips tended to produce higher model confidence.

This observed correlation may be coincidental, or it may indicate a meaningful biological marker
for fertility and successful ovulation.
I hypothesize that there is a real association between the magnitude of the pre-ovulatory temperature dip and the likelihood of ovulation.

However, my method has a critical limitation: the ground-truth labels used were not based on clinically confirmed ovulation events.
This limitation may result not only in fertility-probability curves that are arbitrarily offset from their true value,
but also in the inclusion of cycles labeled as ovulatory that in fact were anovulatory.
As shown in Section~\ref{subsubsec:physiological_signs}, the only reliable indicator
of ovulation is daily transvaginal ultrasound, which was not feasible given the scale of my dataset.

Future studies could apply the current model to a smaller subset of cycles with clinically
confirmed ovulation and/or cycles exhibiting a clear temperature rise, to test the hypothesis
that a significant pre-ovulatory temperature drop is either necessary for ovulation or strongly correlated with fertility.

This approach may also help clarify the role of temperature anomalies in fertility prediction,
for example, the sharp spike shown in Figure~\ref{fig:results_rq2_anomaly_in_temperature_drop}.
Anomalies like this, which may be due to illness with fever symptoms, likely affect both
the menstrual cycle and the model's ability to detect pre-ovulatory fertility.
This case highlights that body temperature is highly sensitive to external physiological factors
that cannot be inferred from the temperature curve alone.

It is likely that many additional patterns or confounding factors in
the temperature data directly or indirectly affect model predictions.
Future research could explore this further, ideally in collaboration with experts in reproductive health.
This could lead to a more biologically grounded interpretation of the patterns uncovered by the models.

Moreover, improvements in label quality will naturally improve the interpretability and accuracy of predictions.
Better labels would also allow more reliable medical interpretation of the prediction outputs and the patterns driving them, as previously discussed.

\subsection{Objective 3: Performance Across Regular and Irregular Cycles}\label{subsec:discussion_rq3_regular_vs_irregular}

The third research objective of this study was to compare model performance across subsets of users
with regular and irregular menstrual cycles.

I have found that predictive performance is clearly sensitive to cycle irregularity.
Both overall accuracy and the improvement in performance over a growing user history
were substantially better for regular cycles compared to irregular ones.
This suggests that past cycles contain valuable information that helps the models
predict the current cycle more reliably, especially when those past cycles follow consistent patterns.

Some of this improvement can also be attributed to static features, several of which are
derived from aggregated past cycles, such as average cycle length or average ovulation day.
These features appear to be more informative and stable in the regular cycle group.

Based on the clear difference in performance, I hypothesize, that all models rely more on those static features
than on patterns identified in the temperature curves, since if that were the case, the difference would be smaller
or non-existent.
There might be additional factors that differentiate regular from irregular cycles, that might explain the results,
which have not been identified yet.
This could also point out, that it is hard or even impossible to reliably predict fertility based on temperature alone,
but this hypothesis needs to be investigated in further research.

\citeauthor{yu_tracking_2022} also report a significant drop in performance for irregular cycles
in their study~\cite{yu_tracking_2022}, particularly in terms of sensitivity.
While I cannot directly compare results due to methodological differences, especially since
my models do not perform explicit binary classification into fertile vs.\ non-fertile days, a similar trend is observable.
In my case, the models tend to overestimate fertility probability when faced with uncertainty, particularly in irregular cycles
(see Figure~\ref{fig:results_rq2_irregular_cycle_predictions_example}).
As a result, I do not report specificity or sensitivity values.
However, the use case scenarios in the next section offer a more binary evaluation framework.

A promising direction for future work would be to further investigate the causes of
performance degradation in irregular cycle groups.
One potential experiment could involve removing static features derived from past cycles to evaluate whether the models
are genuinely using the temperature patterns from previous cycles that fall within
the current input window, or relying mainly on those engineered features.

It may also be valuable to explore the effect of increasing the input window length further.
Ideally, the model would have access to the entire cycle history of a user for training and decision-making.
However, this would likely exceed the memory and capacity constraints of the architectures used in this study.
Overcoming this limitation may require more efficient or hierarchical time series architectures, as previously discussed.

\subsection{Objective 4: Use Case Evaluations}\label{subsec:discussion_rq4_use_case_evaluations}

The fourth research objective was to evaluate two practical use cases—natural contraception
and natural family planning (NFP), using predefined evaluation algorithms.
These algorithms approximate the effectiveness of different models across varying fertility thresholds.

I have found that for both use cases, all trained models outperformed the baselines.
There was notable variability between model types, with the Transformer model
performing best, especially for low fertility thresholds, followed closely by the convolutional variants.
The LSTM model consistently showed the weakest performance across all metrics.
Still, both trained and baseline models yielded significant
improvements over the control group, indicating that all model types offer meaningful predictive value.

To my knowledge, no previous work has explicitly evaluated use cases of natural
contraception or NFP with machine learning, or compared them to traditional contraceptive methods.
This highlights the exploratory nature of this analysis.

\paragraph{Contraception Use Case.}
For the natural contraception scenario, Transformer-based architectures produced competitive results,
achieving fewer than 5 pregnancies per 100 user-years for low thresholds.
For context, the expected pregnancy rates per 100 user-years are approximately 12 for male condoms
and around 7 for oral contraceptives (e.g., “the pill”).
Only implanted hormonal contraceptives and sterilization achieve lower rates (under 1)~\cite{noauthor_birth_nodate}.
In contrast, the control group, representing no contraception, resulted in 90 pregnancies per 100 user-years,
which closely aligns with literature values (85 pregnancies per 100 women per year)~\cite{trussell_contraceptive_2011}.

As expected, the number of denials, i.e.,
days on which a potential application would suggest abstinence, increases with the threshold.
Therefore, a trade-off exists between minimizing pregnancies and minimizing denials.
This trade-off is user-dependent: while some users prefer certainty and are comfortable with frequent denials,
others may accept higher risk or use additional protective measures to mitigate it.

This highlights a critical limitation: all results are based on a naive,
rigid denial strategy that did not incorporate any additional measures or contextual information
beyond the raw model predictions.
When combined with established behavioral protocols, such as abstinence during the early cycle phase,
as used in several commercial products~\cite{thigpen_oura_2025, bull_real-world_2019},
significantly lower pregnancy rates are likely achievable.

As shown in previous sections, irregular cycles require additional caution.
All trained models had difficulty accurately predicting fertile days in these cases.
Therefore, any real-world application must include mechanisms that warn users about
potential inaccuracies and recommend additional precautions when irregular patterns are detected.

Future work could explore models that combine predicted fertility probabilities
with contextual features—such as current follicular phase length—to generate
more nuanced contraceptive guidance.

\paragraph{Pregnancy Use Case.}
For the NFP use case (i.e., attempting to conceive), all trained models achieved
nearly double the pregnancy rate compared to the baselines.
However, at low fertility thresholds, the baseline models showed higher efficiency in terms
of pregnancies per 1000 intercourse events.
Despite this, trained models maintained the overall advantage in total pregnancies per 100 user-years.

At low thresholds, all models achieved approximately 90 pregnancies per 100 user-years,
decreasing to 70--80 at higher thresholds.
The number of correct deferrals, days correctly identified as non-fertile, rose with increasing thresholds,
again suggesting that users may benefit from personalized thresholds depending
on the intensity of their conception efforts.

Most related studies report pregnancy outcomes over 12 cycles, which I assume to represent roughly one year.
I will use the 100 user-years metric for consistency.
Since fertility status of couples in my dataset is unknown,  assume that all included users are generally fertile.

Among commercial fertility monitors, pregnancy rates over 12 cycles range
from 68\% to 72\% (with additional cervical mucus tracking)~\cite{bouchard_achieving_2018}.
My method reaches approximately 80\%, without requiring additional measures,
placing it at the upper end of current non-invasive fertility prediction tools.

Interestingly, control group results show that high pregnancy rates are achievable
even without targeted timing: random intercourse (approximately 6 times per month)
resulted in 90 out of 100 women becoming pregnant within one year, which aligns
with literature estimates that ~85\% of couples conceive within a year without
timing-based intervention~\cite{pfeifer_optimizing_2017}.

The benefit of model-based prediction becomes more evident when examining efficiency.
While most related work ignores intercourse frequency, my results show that
trained and baseline models significantly outperform the control group in pregnancies per 1000 intercourse events.
At mid-range threshold values, trained models demonstrated a four-fold increase in efficiency,
indicating that model guidance can substantially optimize the effort-to-outcome ratio for couples trying to conceive.

Another useful metric could be time-to-pregnancy across different models and the control group.
The same pregnancy rate over one year can represent conception in the first or twelfth month,
which has practical significance for users.
Including this temporal dimension would allow for a more detailed comparative analysis.

As in the contraception use case, all results are based on statistical assumptions
that may not fully hold in real-world scenarios.
Therefore, findings should be interpreted accordingly.
A more detailed investigation of these assumptions, along with further medical interpretation,
would improve the reliability and applicability of the predictions.