A mixed integer programming model for vaccine pricing within a group purchasing organization.

BACKGROUND: Setting prices for life-saving medical or pharmaceutical products needs to consider multiple factors, e.g., affordability and health outcomes across different populations. When a group of buyers (e.g., countries) combine their purchasing power (e.g., via a group purchasing organization), the average procurement price decreases in the total volume. Decisions about what price to then charge to each member in a group are particularly challenging, considering the disparities in their respective ability and willingness to pay. Tiered pricing can be an effective way to set prices for a group of buyers, but its performance needs to be quantified and evaluated. METHODS: We modeled the decision of setting prices of a medical product (for example, a vaccine) for a group of buyers using a mixed integer programming model, considering the buyers' ability and willingness to pay. The objective is to minimize the unit price disparity adjusted by the buyers' willingness to pay, subject to the constraint that the prices decrease in the buyers' ability to pay. We also developed an analogous subsidy allocation model that applies if the group receives philanthropic donations to support procurement. The models were illustrated with two case studies based on the Bacillus Calmette-Guerin (BCG) vaccine procurement by Gavi, the Vaccine Alliance and Pan American Health Organization, and the performances of uniform, tiered, and differentiated pricing schemes were examined. RESULTS: The adjusted unit price disparity is non-increasing in the number of price tiers allowed. The biggest decrease in the adjusted price disparity occurs when switching to two-tier pricing from uniform pricing. Tiered pricing performs better in the Gavi group compared to the PAHO group, in part because the ability to pay and willingness to pay have a higher degree of rank correlation within the former group of countries. CONCLUSIONS: This work provides a model for price-setting (subsidy allocation) decisions for a group of buyers and provides a quantitative comparison of different pricing schemes. The results of the case studies suggest that the performance of tiered pricing depends on various factors, including the disparities in the ability and willingness to pay across the buyers. FUNDING: This research has been supported in part by the Center for Health and Humanitarian Systems, the William W. George endowment, and the following benefactors at Georgia Tech: Andrea Laliberte, Richard Rick E. and Charlene Zalesky, and Claudia and Paul Raines.

Split or whole liver transplantation? Utilization and posttransplant survival.

BACKGROUND: Split liver transplantation (SLT), where a single donor liver is divided for transplantation to 2 recipients, has the potential to increase the availability of size-matched livers for pediatric candidates and expand the supply of donor organs available for adult candidates. Although SLT is a well-established technique, the number of SLTs has remained flat during the past 2 decades, partly due to concerns about the posttransplant survival of SLT recipients compared with whole liver transplantation (WLT) recipients. Prior work on SLT versus WLT survival analysis had limitations because, for pediatric recipients, it did not consider the correlations between donor age/weight and the allograft type, and for adult recipients, it may have included records where the donor livers did not meet the split liver criteria (splittable). METHODS: Using the Organ Procurement and Transplantation Network's database (2003-2019), this study analyzes and compares (i) key characteristics of donors and recipients, (ii) donor-recipient match dynamics (organ offers and accept/decline decisions), and (iii) recipient posttransplant survival, for SLT and WLT. RESULTS AND CONCLUSIONS: The results in this study show that the posttransplant survival of SLT and WLT recipients is similar (controlling for other confounding factors that may impact posttransplant survival), highlighting the importance of SLT for increasing the liver supply and potential benefits for both pediatric and adult candidates.

Magnetic manipulation of Fe3O4@BaTiO3 nanochains to regulate extracellular topographical and electrical cues.

Magnetic fields play an essential role in material science and biomedical engineering. Magnetic-responsive materials can be arranged orderly in matrix to realize the construction of an aligned scaffold under magnetic induction. However, a single topological cue is insufficient to activate neural tissue regeneration, demanding more cues to promote regeneration synergistically, such as electrical stimulation and a biomimetic matrix. Herein, we propose one-dimensional (1D) magnetoelectric Fe3O4@BaTiO3 nanochains with controllable lengths under the regulation of a magnetic field. These nanochains can be oriented in the biomimetic hydrogel under magnetic guidance and induce the hydrogel microfiber to align along the direction of the nanochains, which is beneficial for cell-oriented outgrowth. This aligned hydrogel enabled wireless electrical stimulation mediated by magnetoelectric nanochains under magnetic stimulation, thereby activating the voltage-gated ion channel. Consequently, topological and electrical cues in this multifunctional biomimetic hydrogel synergistically enhanced the expression of neural functional proteins, facilitating synapse remodeling and neural regeneration. Predictably, the construction of multifunctional hydrogels based on low-cost and facile synthesis of magnetoelectric nanochains is an emerging patient-friendly and effective therapeutic strategy for neural or other tissue regeneration. STATEMENT OF SIGNIFICANCE: A facile and controllable magnetic strategy is established to manipulate 1D nanomaterial growth, matrix topography, and wireless electrical stimulation of cells. First, the magnetic-assisted interface co-assembly was used to control the length of Fe3O4@BaTiO3 nanochains with enhanced magnetoelectric effect. Then, the motion of the magnetic-induced nanochains guided the orientation of nanofibers in a 3D biomimetic hydrogel matrix. Finally, wireless electrical signals and topological cues in the biomimetic matrix synergistically promoted orderly aligned cell outgrowth and membrane depolarization by Ca2+ influx, thus enhancing nerve cell synaptic plasticity and functional expression. Consequently, this work provides a conceptual strategy from material design to extracellular matrix signal manipulation and synergistic induction of tissue regeneration.

Flexible analytic model to inform multi-stakeholder pediatric vaccine scheduling decisions.

BACKGROUND: Pediatric immunization is important for preventing potentially life-threatening diseases in children. Over time, the number of recommended pediatric vaccines has increased and is likely to increase further as new vaccines are developed. Given the different number of doses for available vaccines and various constraints (e.g., the appropriate age for each dose of a vaccine or the time between doses), it is challenging to develop a recommended vaccination schedule or a catch-up schedule when a child falls behind on one or more vaccinations. METHODS: We developed an integer programming optimization model, enabled by Python programming and embedded into an Excel-based decision tool, to recommend childhood vaccination schedules or personalized catch-up schedules. The model recommends a vaccination schedule that balances the goal of being as close as possible to the clinically-indicated dosing schedules and the goal of minimizing clinic visits, and gives users the ability to trade off between these two goals. We illustrated the broad applicability of our proposed model with commonly-faced vaccine scheduling challenges in the United States. RESULTS: The illustrative computational case study confirms our model's ability to create personalized schedules based on each child's age and vaccination history, and to adjust appropriately when a new vaccine becomes available. CONCLUSIONS: The model presented in this paper fills the need for an easy-to-use tool to recommend vaccination schedules for de novo and catch-up purposes. It provides straightforward recommendations that can be easily used by physicians, is flexible to handle the requirements varying by region, and can be updated as new vaccines are approved for use.

The Impact of Testing Capacity and Compliance With Isolation on COVID-19: A Mathematical Modeling Study.

Introduction: Diagnostic tests can play an important role in reducing the transmission of infectious respiratory diseases, particularly during a pandemic. The potential benefit of diagnostic testing depends on at least 4 factors: (1) how soon testing becomes available after the beginning of the pandemic and (2) at what capacity; (3) compliance with isolation after testing positive; and (4) compliance with isolation when experiencing symptoms, even in the absence of testing. Methods: To understand the interplay between these factors and provide further insight into policy decisions for future pandemics, we developed a compartmental model and simulated numerous scenarios using the dynamics of COVID-19 as a case study. Results: Our results quantified the significant benefits of early start of testing and high compliance with isolation. Early start of testing, even with low testing capacity over time, could significantly slow down the disease spread if compliance with isolation is high. By contrast, when the start of testing was delayed, the benefit of testing on reducing infection spread was limited, even when testing capacity was high; the additional testing capacity required increased superlinearly for each day of delay to achieve a similar infection attack rate as in starting testing earlier. Conclusions: Our study highlighted the importance of the early start of testing and public health messaging to promote isolation compliance when needed for an ongoing effective response to COVID-19 and future pandemics.