Financial Impact of an Automated Oncology Dose-Rounding Initiative: One-Year Analysis

PURPOSE Infusion drugs are regarded as one of the high-cost health care expenditures. One approach to decrease drug expenditures is by dose-rounding biologics and cytotoxic agents. The Hematology/Oncology Pharmacy Association recommends that biologic and cytotoxic agents are rounded to the nearest vial size if they are within 10% of the ordered dose. The purpose of this initiative is to determine the impact of an automated dose-rounding algorithm on drug expenses. METHODS The dose-rounding algorithm was developed and integrated into the computerized physician order entry system for automated dose rounding to minimize impact on current workflow and to reduce medication errors. Twenty-four medications were preselected for dose rounding and included in the analysis. Ordered doses were automatically rounded to the nearest vial size if the dose was within 10% of the original dose. Prescribers then either reviewed and signed the rounded dose or manually entered the nonrounded dose. Cost savings were calculated as drug expense savings from doses rounded down. RESULTS From July 2018 to June 2019, 10,206 doses of the selected medications were administered. Dose rounding occurred in 5,069 doses (49.7%). All 24 medications within the initiative were administered within the time of analysis. Of the rounded doses administered, 2,516 (49.6%) were rounded down to a commercially available vial size. Using wholesale acquisition cost pricing, the drug expense savings was approximately $3.6 million US dollars (USD). The medications with the highest savings were trastuzumab and ipilimumab, with annual savings of $756,780 USD and $494,517 USD, respectively. CONCLUSION The automated dose-rounding algorithm at Michigan Medicine reduced drug expenditures substantially, and its integration within the computerized physician order entry system had minimal impact on current workflow.

Generalized Max-Cut and the Approximation Ratio

In this thesis, we formulate a new problem based on Max-Cut called Generalized Max-Cut. This problem requires a graph as input and two real numbers (a, b) where a > 0 and −a < b < a and outputs a number. The restriction on the pair (a, b) is to avoid trivializing the problem. We formulate a quadratic program for Generalized Max-Cut and relax it to a semi-definite program. Most algorithms in this thesis will require solving this semi-definite program. The main algorithm in this thesis is the 2-Dimensional Rounding algorithm, designed by Avidor and Zwick, with the restriction that the semi-definite program of the input graph must have 2-Dimensional solutions. This algorithm uses a factor of randomness, β ∈ [0, 1], that is dependent on the integer input to Generalized Max-Cut. We improve the performance of this algorithm by numerically finding better β.

Generalized Max-Cut and the Approximation Ratio

In this thesis, we formulate a new problem based on Max-Cut called Generalized Max-Cut. This problem requires a graph as input and two real numbers (a, b) where a > 0 and −a < b < a and outputs a number. The restriction on the pair (a, b) is to avoid trivializing the problem. We formulate a quadratic program for Generalized Max-Cut and relax it to a semi-definite program. Most algorithms in this thesis will require solving this semi-definite program. The main algorithm in this thesis is the 2-Dimensional Rounding algorithm, designed by Avidor and Zwick, with the restriction that the semi-definite program of the input graph must have 2-Dimensional solutions. This algorithm uses a factor of randomness, β ∈ [0, 1], that is dependent on the integer input to Generalized Max-Cut. We improve the performance of this algorithm by numerically finding better β.

A Primal-Dual Approach to Analyzing ATO Systems

We study assemble-to-order (ATO) problems from the literature. ATO problems with general structure and integrality constraints are well known to be difficult to solve, and we provide new insight into these issues by establishing worst-case approximation guarantees through primal-dual analyses and linear programming (LP) rounding. First, we relax the one-period ATO problem using a natural newsvendor decomposition and use the dual solution for the relaxation to derive a lower bound on optimal cost, providing a tight approximation guarantee that grows with the maximum product size in the system. Then, we present an LP rounding algorithm that achieves both asymptotic optimality as demand grows large, and a 1.8 approximation factor for any problem instance. In addition to theoretical guarantees, we perform comprehensive numerical simulations and find that our rounding algorithm outperforms existing techniques and is close to optimal. Finally, we demonstrate that our one-period LP rounding results can be used to develop an asymptotically optimal integral policy for dynamic ATO problems with backlogging and identical component lead-times. This paper was accepted by Yinyu Ye, optimization.

Approximation Algorithms for the Submodular Load Balancing with Submodular Penalties

In this paper, we study the submodular load balancing problem with submodular penalties. The objective of this problem is to balance the load among sets, while some elements can be rejected by paying some penalties. Officially, given an element set V, we want to find a subset R of rejected elements, and assign other elements to one of m sets A1,A2,⋯,Am. The objective is to minimize the sum of the maximum load among A1,A2,⋯,Am and the rejection penalty of R, where the load and rejection penalty are determined by different submodular functions. We study the submodular load balancing problem with submodular penalties under two settings: heterogenous setting (load functions are not identical) and homogenous setting (load functions are identical). Moreover, we design a Lovász rounding algorithm achieving a worst-case guarantee of m+1 under the heterogenous setting and a min{m,⌈nm⌉+1}=O(n)-approximation combinatorial algorithm under the homogenous setting.