Using Entropy for Healthcare Analytics and Risk Management in Influenza Vaccination Programs

摘要

Annual influenza epidemics impose great losses in both human and financial terms. A key question arising in large-scale vaccination programs is to balance program costs and public benefits. For a vaccination supply chain (SC) consisting of one or several manufacturers, distribution centers, warehouses, pharmacies, clinics, and customers, we seek to decrease the total monetary expenses of all stakeholders while taking into account public benefits at a nation-wide level. Risks occur in the SC due to a stochastic nature of the vaccination process which fluctuates from year to year, depending on many factors that are difficult to predict and control: adverse events like the supply delay and mismatch between the vaccine stock and demand. It is impractical and unnecessary to construct the entire network of the vaccination supply chain which may have tens of thousands components. Instead, the entropy-based analytics permits to essentially reduce the SC model without discarding essential prognostic information about the possible risks. Entropy is a measure of the uncertainty in a random environment. Extending classical Shannon's entropy concept used in information theory, we use the term to quantify and evaluate the expected value of the information contained in a SC with uncertain but predictable data about the costs and benefits. Knowing the history of adverse events, we estimate the entropy and knowledge about the risks occurring in the vaccination SC, evaluate the loss, define most vulnerable components in the SC and reduce its size. An integer programming model is proposed in which the problem of minimizing the total loss is effectively solved on a reduced SC. This new analytics approach permits to balance the manufacturing, inventory and distribution costs with public benefits and to reduce the incurred losses. A case study is used to test the suggested methodology - we consider the nation-wide vaccination program carried out by the CLALIT Health Services (Israel), The entropy approach permits us to essentially decrease the model size in practice: whereas the initial supply chain in the CLALIT which is constructed for real-life data for year 2013 contains about 1,200 clinics located in different geographical places and serving about one million people grouped into 6,000 population clusters, the reduced supply chain contains only 24 clinic clusters and 120 population sub-groups. Then the mathematical programming problem for minimizing the total vaccination program costs has been formulated on the reduced SC and applied retroactively for the 2013 data. The problem has been solved by the GAMS software and permitted to decrease the annual total expenses by 12%.