An Integrated Framework for Reducing Hospital Readmissions using Risk Trajectories Characterization and Discharge Timing Optimization

Abstract

When patients leave the hospital for lower levels of care, they experience a risk of adverse events on a daily basis. The advent of value-based purchasing among other major initiatives has led to an increasing emphasis on reducing the occurrences of these post-discharge adverse events. This has spurred the development of new prediction technologies to identify which patients are at risk for an adverse event as well as actions to mitigate those risks. Those actions include pre-discharge and post-discharge interventions to reduce risk. However, traditional prediction models have been developed to support only post-discharge actions; predicting risk of adverse events at the time of discharge only. In this paper we develop an integrated framework of risk prediction and discharge optimization that supports both types of interventions: discharge timing and post-discharge monitoring. Our method combines a kernel approach for capturing the non-linear relationship between length of stay and risk of an adverse event, with a Principle Component Analysis method that makes the resulting estimation tractable. We then demonstrate how this prediction model could be used to support both types of interventions by developing a simple and easily implementable discharge timing optimization.

Keywords: Cox Mixture Model; Discharge Decision Optimization; Expectation-Maximization Algorithm; Kernel PCA; Readmission Prediction.

Fig. 1:

Prediction accuracy of Mixture KPCA COX model for various number of clusters.

Fig. 2:

Prediction accuracy of the comparing methods for estimating readmission 5, 10, 20, and 30 days after discharge.

Fig. 3:. Predicted 30-day cumulative readmission probability against length of stay (LOS).

In Figure 3(a), we compare the LOS for different patients according to the readmission event 30 days after discharge. In Figure 3(b), each curve represents the predicted readmission probability trajectory for each of 1032 randomly selected patients. In Figure 3(c), we group the 1032 randomly selected patients into three groups based on the three clusters of the proposed mixture KPCA Cox model; the three curves in this plot correspond to the average readmission probability of the each group.

Fig. 4:

Flow chart of the optimization framework.

Fig. 5:. Threshold discharge policy: expected queue length, the expected re-admissions, and the total cost.

We set N = 32, Λ = 6.25, R = 20, and C = 1. For the risk trajectory function s = f(l), we use the average one from group 2 and group 3 patients, respectively, in the left and right plots. The x-axis denotes the LOS l, while the y-axis denotes the corresponding value of the expected queue length, the expected re-admissions, and the total cost for the blue, red, and green curve, respectively.

Fig. 6:. Threshold discharge policy with multiple classes: expected queue length, expected number of re-admission events, and the total cost.

We set N = 52, Λ = 6.25, R = 20, and C = 1. The “LOS index” on the x-axis denotes an index of the combination of l₁, l₂, l₃, so that we can plot the cost against different choices of (l₁, l₂, l₃) on a two-dimensional figure. We impose a lower bound of 3 and an upper bound of 20 for each l_m, and the LOS index equals 17²·l₁ + 17 · l₂ + l₃. The y-axis denotes the corresponding value of the expected queue length, the expected re-admissions, and the total cost for the blue, red, and green curve, respectively.