Constrained Optimization for the Selection of Influenza Vaccines to Maximize the Population Benefit: A Demonstration Project

Identification of an Optimal COVID-19 Booster Allocation Strategy to Minimize Hospital Bed-Days with a Fixed Healthcare Budget

Healthcare decision-makers face difficult decisions regarding COVID-19 booster selection given limited budgets and the need to maximize healthcare gain. A constrained optimization (CO) model was developed to identify booster allocation strategies that minimize bed-days by varying the proportion of the eligible population receiving different boosters, stratified by age, and given limited healthcare expenditure. Three booster options were included: B₁, costing US $1 per dose, B₂, costing US $2, and no booster (NB), costing US $0. B₁ and B₂ were assumed to be 55%/75% effective against mild/moderate COVID-19, respectively, and 90% effective against severe/critical COVID-19. Healthcare expenditure was limited to US$2.10 per person; the minimum expected expense using B_1, B_2, or NB for all. Brazil was the base-case country. The model demonstrated that B₁ for those aged <70 years and B₂ for those ≥70 years were optimal for minimizing bed-days. Compared with NB, bed-days were reduced by 75%, hospital admissions by 68%, and intensive care unit admissions by 90%. Total costs were reduced by 60% with medical resource use reduced by 81%. This illustrates that the CO model can be used by healthcare decision-makers to implement vaccine booster allocation strategies that provide the best healthcare outcomes in a broad range of contexts.

Economic Evaluation of Vaccination Programs: A Guide for Selecting Modeling Approaches

OBJECTIVES

Illustrate 3 economic evaluation methods whose value measures may be useful to decision makers considering vaccination programs.

METHODS

Keyword searches identified example publications of cost-effectiveness analysis (CEA), fiscal health modeling (FHM), and constrained optimization (CO) for economic evaluation of a vaccination program in countries where at least 2 of the methods had been used. We examined the extent to which different value measures may be useful for decision makers considering adoption of a new vaccination program. With these findings, we created a guide for selecting modeling approaches illustrating the decision-maker contexts and policy objectives for which each method may be useful.

RESULTS

We identified 8 countries with published evaluations for vaccination programs using >1 method for 4 infections: influenza, human papilloma virus, rotavirus, and malaria. CEA studies targeted health system decision makers using a threshold to determine the efficiency of a new vaccination program. FHM studies targeted public sector spending decision makers estimating lifetime changes in government tax revenue net of transfer payments. CO studies targeted decision makers selecting from a mix of options for preventing an infectious disease within budget and feasibility constraints. Cost and utility inputs, epidemiologic models, comparators, and constraints varied by modeling method.

CONCLUSIONS

Although CEAs measures of incremental cost-effectiveness ratios are critical for understanding vaccination program efficiency for all decision makers determining access and reimbursement, FHMs provide measures of the program's impact on public spending for government officials, and COs provide measures of the optimal mix of all prevention interventions for public health officials.

Optimization methods for large-scale vaccine supply chains: a rapid review

Global vaccine revenues are projected at $59.2 billion, yet large-scale vaccine distribution remains challenging for many diseases in countries around the world. Poor management of the vaccine supply chain can lead to a disease outbreak, or at worst, a pandemic. Fortunately, a large number of those challenges, such as decision-making for optimal allocation of resources, vaccination strategy, inventory management, among others, can be improved through optimization approaches. This work aims to understand how optimization has been applied to vaccine supply chain and logistics. To achieve this, we conducted a rapid review and searched for peer-reviewed journal articles, published between 2009 and March 2020, in four scientific databases. The search resulted in 345 articles, of which 25 unique studies met our inclusion criteria. Our analysis focused on the identification of article characteristics such as research objectives, vaccine supply chain stage addressed, the optimization method used, whether outbreak scenarios were considered, among others. Approximately 64% of the studies dealt with vaccination strategy, and the remainder dealt with logistics and inventory management. Only one addressed market competition (4%). There were 14 different types of optimization methods used, but control theory, linear programming, mathematical model and mixed integer programming were the most common (12% each). Uncertainties were considered in the models of 44% of the studies. One resulting observation was the lack of studies using optimization for vaccine inventory management and logistics. The results provide an understanding of how optimization models have been used to address challenges in large-scale vaccine supply chains.

Pneumococcal conjugate vaccines in Taiwan: optimizing health gains in children and older adults through constrained optimization modeling: Pneumococcal conjugate vaccines optimization in Taiwan

OBJECTIVES

Budgetary constraints force healthcare authorities to set priorities for optimal vaccine interventions. A comprehensive decision-making tool would help inform the best combination and sequence of introduction of vaccines within constrained budgets.

METHODS

Looking at available vaccines against pneumococcal infections in Taiwan (10/13-valent pneumococcal conjugate vaccines [PCV10, PCV13] and 23-valent pneumococcal polysaccharide vaccine [PPV23]), a constrained optimization (CO) model was used to assess the optimal combination of vaccines in children and older adults that would maximize the quality-adjusted life years under predefined budget constraints. Scenario analyses were carried out to evaluate the impact of vaccine efficacy (VE) on the optimized solution.

RESULTS

The CO model demonstrated that the optimal sequence of vaccine introduction was PPV23 in older adults and PCV10 in children. The optimal solution was mostly driven by the potential to reduce disease burden in the older adult population. The VE of PPV23 in older adults and the VE of PCV vaccines against serotype 19A invasive pneumococcal disease had little impact on the optimal solution.

CONCLUSIONS

The CO approach can be used to set priorities for introducing new vaccines while maximizing health gains per age group within the constrained National Vaccine Fund for the prevention of pneumococcal disease in Taiwan.

Informing decision makers seeking to improve vaccination programs: case-study Serbia

Background:The optimisation of vaccine policies before their implementation is beholden upon public health decision makers, seeking to maximise population health. In this case study in Serbia, the childhood vaccines under consideration included pneumococcal conjugate vaccination (PCV), rotavirus (RV) vaccination and varicella zoster virus (VZV) vaccination. Objective: The objective of this study is to define the optimal order of introduction of vaccines to minimise deaths, quality adjusted life years (QALYs) lost, or hospitalisation days, under budget and vaccine coverage constraints. Methods: A constrained optimisation model was developed including a static multi-cohort decision-tree model for the three infectious diseases. Budget and vaccine coverage were constrained, and to rank the vaccines, the optimal solution to the linear programming problem was based upon the ratio of the outcome (deaths, QALYs or hospitalisation days) per unit of budget. A probabilistic decision analysis Monte Carlo simulation technique was used to test the robustness of the rankings. Results: PCV was the vaccine ranked first to minimise deaths, VZV vaccination for QALY loss minimisation and RV vaccination for hospitalisation day reduction. Sensitivity analysis demonstrated the most robust ranking was that for PCV minimizing deaths. Conclusion: Constrained optimisation modelling, whilst considering all potential interventions currently, provided a comprehensive and rational approach to decision making.

Constrained Optimization for Pneumococcal Vaccination in Brazil

OBJECTIVES

To identify the most cost-efficient combination of pneumococcal vaccines in infants and aging adults for a 10-year period in Brazil.

METHODS

Constrained optimization (CO) prioritized 9 pneumococcal vaccine regimens according to their gain in quality-adjusted life-years (QALYs) and their related costs over a prespecified time horizon with defined constraints for 2 age groups, infants and aging adults. The analysis starts from the current universal infant vaccination of pneumococcal non-typeable Haemophilus influenzae protein D conjugate vaccine (PHiD-CV), 2 primary and 1 booster dose at 2, 4, and 12 months, respectively. Key constraints are the fixed annual vaccine budget increase and the relative return on investment (ROI_R) per regimen, which must be > 1, the reference intervention being the current vaccination strategy in infants and the most cost-efficient one in aging adults.

RESULTS

The CO analysis including all the constraints indicates that over 10 years the maximum extra health gain is 126 194 QALYs for an extra budget of $974 million Brazilian reals (ROI_R = 1.15). Results could be improved with a higher proportion of the at-risk population in aging adults, less herd effect, and better QALY scores.

CONCLUSION

The study shows that with 4 constraints on budget, time horizon, vaccine coverage, and cost efficiency, a CO analysis could identify the most cost-efficient overall pneumococcal vaccination strategy for Brazil, allowing for limited vaccine budget increase while obtaining appropriate health gain.

How to assess for the full economic value of vaccines? From past to present, drawing lessons for the future

Background:Cost-effectiveness analysis (CEA) is the economic analysis method most commonly applied today in the context of replacing one treatment with a new one in a developed healthcare system to improve efficiency. CEA is often requested by local healthcare decision-makers to grant reimbursement. New preventative interventions, such as new vaccines, may however have much wider benefits inside and outside healthcare, when compared with treatment. These additional benefits include externalities on indirect clinical impact, reallocation of specific healthcare resources, improved quality of care, better productivity, better disease control, better fiscal revenues, and others. But these effects are sometimes difficult to integrate into a meaningful CEA result. They may appear as specific benefits for specific stakeholders, other than the stakeholders in healthcare. Objective: Based on a historical view about the application of economic assessments for vaccines our objective has been to make the inventory of who was/is interested in knowing the economic value of vaccines, in what those different stakeholders are likely to see the benefit from their perspective and how  were/are we able to measure those benefits and to report them well. Results: The historical view disclosed a limited interest in the economic assessment of vaccines at start, more than 50 years ago, that was comparable to the assessment of looking for more efficiency in new industries through optimization exercises. Today, we are exposed to a very rich panoply of different stakeholders (n= 16). They have their specific interest in many different facets of the vaccine benefit of which some are well known in the conventional economic analysis (n=9), but most outcomes are hidden and not enough evaluated and reported (n=26). Meanwhile we discovered that many different methods of evaluation have been explored to facilitate the measurement and reporting of the benefits (n=18). Conclusion: Our recommendation for future economic evaluations of new vaccines is therefore to find the right combination among the three entities of stakeholder type selection, outcome measure of interest for each stakeholder, and the right method to apply. We present at the end examples that illustrate how successful this approach can be.