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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. 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. 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. 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. 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. [ABSTRACT FROM AUTHOR]

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. 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. 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. 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. [ABSTRACT FROM AUTHOR]

[Display omitted] • Antibody testing as part of a COVID-19 vaccine distribution plan is effective. • Antibody testing should be used to prioritize vaccination when supply is limited. • Prioritization reduces infection attack rates and deaths. • The relative time between vaccination start and infection peak is important. To assess the value of using SARS-CoV-2 specific antibody testing to prioritize the vaccination of susceptible individuals as part of a COVID-19 vaccine distribution plan when vaccine supply is limited. An extended susceptible-infected-recovered (SIR) compartmental model was used to simulate COVID-19 spread when considering diagnosis, isolation, and vaccination of a cohort of 1 million individuals. The scenarios modeled represented 4 pandemic severity scenarios and various times when the vaccine becomes available during the pandemic. Eligible individuals have a probability p of receiving antibody testing prior to vaccination (p = 0, 0.25, 0.5, 0.75, and 1). The vaccine was modeled as a single dose vaccine with 90% and 70% efficacy. The value of serology testing was evaluated by comparing the infection attack rate, peak infections, peak day, and deaths. The use of antibody testing to prioritize the allocation of limited vaccines reduces infection attack rates and deaths. The size of the reduction depends on when the vaccine becomes available relative to the infection peak day. The largest percentage reduction in cases and deaths occurs when the vaccine is deployed before and close to the infection peak day. The reduction in the number of cases and deaths diminishes as vaccine deployment is delayed. Antibody testing as part of the vaccination plan is an effective method to maximize the benefit of a COVID-19 vaccine. Decision-makers need to consider relative timing between the infection peak day and when the vaccine becomes available. [ABSTRACT FROM AUTHOR]

Despite high vaccine coverage rates in children and efficacy of pneumococcal conjugate vaccines, invasive pneumococcal disease (IPD) episodes due to serotypes included in the vaccine following completion of the recommended course of immunisation (i.e. vaccine failure) have been reported. We used data gathered from a population-based enhanced passive surveillance for IPD in children under 18 years of age in Massachusetts and an ensemble model composed of three machine-learning algorithms to predict probability of 13-valent pneumococcal conjugated vaccine (PCV13) failure and to evaluate potential associated features including age, underlying comorbidity, clinical presentation, and vaccine schedule. Vaccine failure was defined as diagnosis of IPD due to vaccine serotype (VST), in a child who received age recommended doses recommended by Advisory Committee of Immunization Practices. During the 7-year study period, between April 01, 2010 and March 31, 2017, we identified 296 IPD cases. There were 107 (36%) IPD cases caused by VST, mostly serotype 19A (49, 17%), 7F (21, 7%), and 3 (18, 6%). Thirty-seven (34%) were in children who were completely vaccinated representing 13% of all IPD cases. Vaccine failure was more likely among children older than 60 months (predicted probability 0.40, observed prevalence 0.37, model prediction accuracy 79%), children presenting with pneumonia (predicted probability 0.27, observed prevalence 0.31, model accuracy 77%), and children with underlying comorbidity (predicted probability 0.24, observed prevalence 0.23, model accuracy 96%). Vaccine failure probability for those >60 months of age and had an underlying risk factor was 45% (observed prevalence 0.33, model accuracy 82%). The likelihood of vaccine failure was lowest among children who had completed 3 primary doses plus one booster dose PCV13 (predicted probability 0.14, observed prevalence 0.14, model prediction accuracy 100%). PCV13 vaccine failure is more frequent among older children with underlying comorbidity, and among those who present with pneumococcal pneumonia. Our study provides a preliminary framework to predict the patterns of vaccine failures and may contribute to decision-making processes to optimize PCV immunization schedules. [ABSTRACT FROM AUTHOR]

In addition to improved sanitation, hygiene, and better access to safe water, oral cholera vaccines can help to control the spread of cholera in the short term. However, there is currently no systematic method for determining the best allocation of oral cholera vaccines to minimize disease incidence in a population where the disease is endemic and resources are limited. We present a mathematical model for optimally allocating vaccines in a region under varying levels of demographic and incidence data availability. The model addresses the questions of where, when, and how many doses of vaccines to send. Considering vaccine efficacies (which may vary based on age and the number of years since vaccination), we analyze distribution strategies which allocate vaccines over multiple years. Results indicate that, given appropriate surveillance data, targeting age groups and regions with the highest disease incidence should be the first priority, followed by other groups primarily in order of disease incidence, as this approach is the most life-saving and cost-effective. A lack of detailed incidence data results in distribution strategies which are not cost-effective and can lead to thousands more deaths from the disease. The mathematical model allows for what-if analysis for various vaccine distribution strategies by providing the ability to easily vary parameters such as numbers and sizes of regions and age groups, risk levels, vaccine price, vaccine efficacy, production capacity and budget. [ABSTRACT FROM AUTHOR]

• A natural history model was introduced where probabilities were assigned to each health state based on patient characteristics such as age, gender, and history of depression. • Annual screening of all adults 18 years old or older for depression would be $11,134 and $34,065 cost per QALY gained for females and males, respectively. In comparison, screening every 5-years resulted in ICERs of $8627 for females and $26,892 for males. • The age-specific analysis showed that screening of old populations had higher ICERs than the young and middle age groups. • Our baseline model could be utilized to evaluate the potential consequences of medication strategies or alternative intervention scenarios. Depression is a treatable disease, and untreated depression can lead to serious health complications and decrease the quality of life. Therefore, prevention, early identification, and treatment efforts are essential. Screening has an essential role in preventive medicine in the general population. Ideally, screening tools detect patients early enough to manage the disease and reduce symptoms. We aimed to determine the cost-effectiveness of routine screening schedules. We used a discrete-time nonstationary Markov model to simulate the progression of depression. We used Monte Carlo techniques to simulate the stochastic model for 20 years or during the lifetime of individuals. Baseline and screening scenario models with screening frequencies of annual, 2-year, and 5-year strategies were compared based on incremental cost-effectiveness ratios (ICER). Monte Carlo (MC) simulation and one-way sensitivity analysis were conducted to manage uncertainties. In the general population, all screening strategies were cost-effective compared to the baseline. However, male and female populations differed based on cost over quality-adjusted life years (QALY). Females had lower ICERs, and annual screening had the highest ICER for females, with 11,134$/QALY gained. In contrast, males had around three times higher ICER, with annual screening costs of 34,065$/QALY gained. We assumed that the screening frequency was not changing at any time during the screening scenario. In our calculations, false-positive cases were not taking into account. Considering the high lifetime prevalence and recurrence rates of depression, detection and prevention efforts can be one critical cornerstone to support required care. Our analysis combined the expected benefits and costs of screening and assessed the effectiveness of screening scenarios. We conclude that routine screening is cost-effective for all age groups of females and young, middle-aged males. [ABSTRACT FROM AUTHOR]

Background: Depression is a treatable disease, and untreated depression can lead to serious health complications and decrease the quality of life. Therefore, prevention, early identification, and treatment efforts are essential. Screening has an essential role in preventive medicine in the general population. Ideally, screening tools detect patients early enough to manage the disease and reduce symptoms. We aimed to determine the cost-effectiveness of routine screening schedules.Methods: We used a discrete-time nonstationary Markov model to simulate the progression of depression. We used Monte Carlo techniques to simulate the stochastic model for 20 years or during the lifetime of individuals. Baseline and screening scenario models with screening frequencies of annual, 2-year, and 5-year strategies were compared based on incremental cost-effectiveness ratios (ICER). Monte Carlo (MC) simulation and one-way sensitivity analysis were conducted to manage uncertainties.Results: In the general population, all screening strategies were cost-effective compared to the baseline. However, male and female populations differed based on cost over quality-adjusted life years (QALY). Females had lower ICERs, and annual screening had the highest ICER for females, with 11,134$/QALY gained. In contrast, males had around three times higher ICER, with annual screening costs of 34,065$/QALY gained.Limitations: We assumed that the screening frequency was not changing at any time during the screening scenario. In our calculations, false-positive cases were not taking into account.Conclusions: Considering the high lifetime prevalence and recurrence rates of depression, detection and prevention efforts can be one critical cornerstone to support required care. Our analysis combined the expected benefits and costs of screening and assessed the effectiveness of screening scenarios. We conclude that routine screening is cost-effective for all age groups of females and young, middle-aged males. [ABSTRACT FROM AUTHOR]

Background: Major depression is a treatable disease, and untreated depression can lead to serious health complications. Therefore, prevention, early identification, and treatment efforts are essential. Natural history models can be utilized to make informed decisions about interventions and treatments of major depression.Methods: We propose a natural history model of major depression. We use steady-state analysis to study the discrete-time Markov chain model. For this purpose, we solved the system of linear equations and tested the parameter and transition probabilities empirically.Results: We showed that bias in parameters might collectively cause a significant mismatch in a model. If incidence is correct, then lifetime prevalence is 33.2% for females and 20.5% for males, which is higher than reported values. If prevalence is correct, then incidence is .0008 for females and .00065 for males, which is lower than reported values. The model can achieve feasibility if incidence is at low levels and recall bias of the lifetime prevalence is quantified to be 31.9% for females and 16.3% for males.Limitations: This model is limited to major depression, and patients who have other types of depression are assumed healthy. We assume that transition probabilities (except incidence rates) are correct.Conclusion: We constructed a preliminary model for the natural history of major depression. We determined the lifetime prevalences are underestimated and the average incidence rates may be underestimated for males. We conclude that recall bias needs to be accounted for in modeling or burden estimates, where the recall bias should increase with age. [ABSTRACT FROM AUTHOR]