Mathematical Modeling and Optimal Stopping Theory-Based Extra Layers for 30-Day Rate Risk Prediction of Readmission to Intensive Care Units

The importance of
$30$
-day patients’ readmissions (PRs) to intensive unit care stems from the significant cost and mortality risk when the patient's chosen class (i.e., readmitted or not to the hospital) is incorrect. The overall accuracy of the PRs classification obtained in the literature is still moderate, particularly for machine learning (ML) and deep artificial neural networks (ANNs), where the overall accuracy is around
$65\%$
, resulting in
$35\%$
of critical wrong decisions. The suggested technique for enhancing such an overall accuracy consists of three distinct phases. The first layer is an ML-assisted algorithm that uses support vector machines (SVMs) and ANNs techniques, while the second layer uses an arbitrary dataset's distribution and mathematical modeling of the problem to determine the optimal class probabilities interval that has the highest percentage of misclassified elements. Next, all items’ categories in that interval are altered, with the exception of those deemed by the generalized secretary problem (GSP) algorithm (the third layer) to be most likely correct. We provide a new theorem that applies to every distribution type and yields the GSP's optimum parameter. Starting with evidence that the Gilbrat and generalized logistic distributions suit the class probabilities produced by ANN and SVM, respectively, we demonstrate that our technique improves the overall accuracy by
$5\%$
and
$19\%$
, reaching
$85\%$
and
$87\%$
, respectively. It is important to point out that the suggested additional two layers may be utilized for any binary classification problem; this is independent of the dataset distribution and the stages that came before.