# Approaches for Dealing with Seasonality in Clinical Prediction Models for Infections
## 4 Experiments and Results
### Analysis of the Effects of Different Approaches in Combination
#### 4.4.1 Synthetic Dataset--Condensed  
The combinations that achieved the best AUC on the _condensed_ dataset are ranked in Table 1, which shows the combinations with logistic regression models, and in Table 2, which shows the best results obtained by combinations with decision trees. The approach that obtained the best mean AUC in logistic regression models was the use of one model per season, while including the season as a feature worked better for decision trees. The proposed sliding window approach using three-month windows showed promising results in both models. With regard to the filtering and balancing techniques, the combination of FCBF with 2:1 oversampling obtained the best mark with logistic regression, while oversampling with both ratios and no filter had the best results for decision trees. FCBF clearly led to simpler logistic regression models, with a mean of 1.08 features per model obtained in the best combination for logistic regression. However, FCBF did not achieve good AUC results in decision tree models. In those experiments, the simpler models were those based on a three-month window and one model per season. In all cases, the use of seasonal techniques obtained much better results than simply creating the model by ignoring seasonality. Figure 9: Values of (**a**) AUC and (**b**) number of features per model when using only a seasonal drift compensation approach in each dataset. The inclusion of the season as a feature led to the best results with the logistic regression models and to good results with decision trees. With regard to the latter, the seasonal window obtained the best results when combined with 1:1 undersampling and a \(p\)-value filter. The combination of these techniques did not drastically improve the results for logistic regression models in this dataset, to the point that the models trained with no more than LASSO and logistic regression are among the top ten results. In the case of decision trees, the use of any balancing strategy is again decisive with regard to obtaining a valid model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Filter** & **Balancing** & **Seasonal Drift Approach** & **Mean AUC** & **Mean Features per Model** \\ \hline \(p\)-Value & Oversample 2:1 & 3-month window & 0.976 (0.974, 0.978) & 6.862 (6.684, 7.041) \\ None & Oversample 2:1 & 3-month window & 0.976 (0.974, 0.978) & 6.947 (6.764, 7.131) \\ \(p\)-Value & Oversample 1:1 & 3-month window & 0.976 (0.974, 0.978) & 7.112 (6.905, 7.319) \\ None & Oversample 1:1 & 3-month window & 0.975 (0.973, 0.977) & 7.208 (6.993, 7.423) \\ FCBF & Oversample 2:1 & 3-month window & 0.975 (0.973, 0.977) & 2.859 (2.812, 2.906) \\ FCBF & Oversample 1:1 & 3-month window & 0.973 (0.970, 0.976) & 2.533 (2.492, 2.573) \\ \(p\)-Value & Oversample 1:1 & 5-month window & 0.968 (0.967, 0.969) & 14.316 (14.200, 14.431) \\ \(p\)-Value & Oversample 2:1 & 5-month window & 0.968 (0.967, 0.969) & 13.209 (13.110, 13.308) \\ None & Oversample 1:1 & 5-month window & 0.968 (0.967, 0.969) & 14.779 (14.647, 14.912) \\ None & Oversample 2:1 & 5-month window & 0.967 (0.966, 0.968) & 13.718 (13.138, 13.824) \\... &... &... &... \\ None & None & None & 0.852 (0.846, 0.859) & 14.270 (13.451, 15.089) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Top ten results obtained on the _sinusoidal_ synthetic dataset with decision tree models.