We present an approach for the analysis of clinical data from extremely preterm infants, in order to determine if they are ready to be removed from invasive endotracheal mechanical ventilation. The data includes over 100 clinical features, and the subject population is naturally quite small. To address this problem, we use feature selection, specifically mutual information, in order to choose a small subset of informative features. The other challenge we address is class imbalance, as there are many more babies that succeed extubation than those who fail. To handle this problem, we use SMOTE, an algorithm which creates synthetic examples of the minority class.