# Approaches for Dealing with Seasonality in Clinical Prediction Models for Infections
## 5 Discussion  
According to the obtained results, no one specific approach or combination clearly outperforms the rest when seasonality, high dimensionality, and class imbalance are all present. However, the results provide useful information with which to discuss the advantages and disadvantages of each combination. Despite the fact that all the experiments used LASSO or winnowing, in most cases the use of a feature selection technique reduced model complexity even more. In particular, FCBF drastically reduced the number of features; the effect of the filter based on the \(p\) value, while not as significant, was noticeable in most cases. Therefore, extra filtering techniques  
Figure 15: (a) Coefficients of the logistic regression models obtained in the monthly ensemble approach and (b) the weight matrix required to obtain the result of the ensemble. The intercept of the models is not displayed for clarity. appear to be advisable even in the presence of seasonality when reducing the complexity of the model is a critical requisite. The use of feature selection techniques to reduce model complexity had differing effects on model performance. In the synthetic _condensed_ dataset they clearly improved the AUC when combined with logistic regression, yet in most of the experiments they tended to slightly decrease model performance. It may be possible that when the underlying model is simple, as for the synthetic datasets, the reduction in complexity leads to the final models approximating the real ones. In the case of more complicated interactions and dependencies, as certainly occurs in clinical datasets, relevant features may be discarded, and the resulting models may lose accuracy. Therefore, the common trade-off between model simplicity and performance is present in these kinds of datasets. In certain experiments combining techniques that severely reduced the number of observations used to train the models, the \(p\)-value filter was unable to select any features at all. For example, the combination of the \(p\)-value filter, monthly ensemble, and undersampling was unable to create valid models for most of the training/validation sampled datasets. As is well known, the P value is affected by the number of observations; thus, if no strong correlation is clear in the dataset, no feature is able to reach the cut-off value. Therefore, these combinations should be used with caution when the available training data are scarce. In the _Acinetobacter_ dataset, the seven-month and five-month window approaches obtained the best results for logistic regression and the monthly ensemble obtained the best results for decision trees. The good results of month-based approaches rather than season-based ones with the MIMIC-III database may seem surprising, as the months in the timestamps of the MIMIC-III database are randomized to ensure patient confidentiality. However, because the season was maintained, the month of the randomized data was close to the real month; this may explain the good performance of these methods. Moreover, the drift in data might not occur precisely within an astronomical season, and may be delayed with respect to its boundaries or even occur multiple times throughout the year. Our proposed monthly window and monthly ensemble may be good options in these cases, provided that there is at least an approximate estimation of the month. The best sizes for the sliding window approach changed depending on the dataset. While the best results for the _Acinetobacter_ dataset were obtained with lengths of seven months, on the _condensed_ and _sinusoidal_ datasets a three-month window was the best option. Therefore, it is important to test with different windows sizes when using this approach for seasonality, as occurs with datastreams. The particularities of the base model may have an impact on the performance of different seasonality strategies.