# Approaches for Dealing with Seasonality in Clinical Prediction Models for Infections
## 4 Experiments and Results
### Analysis of the Impact of the Different Approaches on Interpretability
Figure 10: Coefficients of the logistic regression models obtained (**a**) without using any approach for dealing with seasonality and (**b**) when incorporating the season as a feature. The intercept of the models is not displayed for better clarity. Figure 12 illustrates the models generated when using the seasonal window strategy. Although the models appear similar to the model-per-season approach, the amount of data used to build each model is larger; therefore, the impact of seasonality on the models cannot be appreciated as clearly. However, the increased relevance of \(x_{2}\) in summer and \(x_{1}\) in winter can be observed, though not as clearly as in the previous approach. Despite this, it is important to consider how these models were generated when analyzing their structure; with this context, they are interpretable and the reasoning behind each prediction can be easily traced. The results when using models for each month with the monthly window approach is shown in Figure 13. The models were made using a three-month sliding window approach; therefore, the effects of seasonality are not as diluted as in the previous example. Despite the increase in complexity, the change in relevance of \(x_{1}\) and \(x_{2}\) in each model are noticeable, and the behavior of the approach as a whole can be easily analyzed. Figure 11: Coefficients of the logistic regression models obtained when creating a different model for each season. The intercept of the models is not displayed for clarity. Figure 12: Coefficients of the logistic regression models obtained when using the seasonal window approach. The intercept of the models is not displayed for better clarity. The use of ensembles has a noticeable impact on interpretability, as can be appreciated in Figure 14. In this approach, we have to combine the outputs of the different models using a weight matrix, such as the one in Figure 14b. Even though the models can be analyzed independently (indeed, they are the same as those frinom the model-per-season approach), the combination matrix can be easily understood. For example, the matrix in Figure 14b suggests that for predicting data in summer or winter the output mainly relies on the models generated using data from these seasons, while in spring and autumn the output is mainly a mixture of the models for the other seasons. Although the whole model is more complicated that the previous approaches, it can be understood and analyzed. The monthly ensemble, illustrated in Figure 15a,b, represents the most complex combination of all the studied approaches. Assessing the exact relevance of each feature on a specific output becomes challenging when using this approach. Nonetheless, the variations in the coefficients \(x_{1}\) and \(x_{2}\) can be observed across the monthly models. Additionally,  
Figure 14: (**a**) Coefficients of the logistic regression models obtained in the seasonal 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. Figure 13: Coefficients of the logistic regression models obtained when using the monthly window approach with a three-month sliding window. The intercept of the models is not displayed for clarity. from the model matrix we are able to discern that the models adjacent to the month of the observation to be predicted have a greater impact on the output of the ensemble.