Enhancing affordability and profit in a non-cooperative, coordinated, hypothetical pediatric vaccine market via sequential optimization.

This study considers a hypothetical global pediatric vaccine market where multiple coordinating entities make optimal procurement decisions on behalf of countries with different purchasing power. Each entity aims to improve affordability for its countries while maintaining a profitable market for vaccine producers. This study analyzes the effect of several factors on affordability and profitability, including the number of non-cooperative coordinating entities making procuring decisions, the number of market segments in which countries are grouped for tiered pricing purposes, how producers recover fixed production costs, and the procuring order of the coordinating entities. The study relies on a framework where entities negotiate sequentially with vaccine producers using a three-stage optimization process that solves a MIP and two LP problems to determine the optimal procurement plans and prices per dose that maximize savings for the entities' countries and profit for the vaccine producers. The study's results challenge current vaccine market dynamics and contribute novel alternative strategies to orchestrate the interaction of buyers, producers, and coordinating entities for enhancing affordability in a non-cooperative market. Key results show that the order in which the coordinating entities negotiate with vaccine producers and how the latter recuperate their fixed cost investments can significantly affect profitability and affordability. Furthermore, low-income countries can meet their demands more affordably by procuring vaccines through tiered pricing via entities coordinating many market segments. In contrast, upper-middle and high-income countries increase their affordability by procuring through entities with fewer and more extensive market segments. A procurement order that prioritizes entities based on the descending income level of their countries offers higher opportunities to increase affordability and profit when producers offer volume discounts.

Where Do the Salt and Water Go? A Case of Profound Hyponatremia.

Treatment of profound hyponatremia is challenging. Severe symptoms mandate correction by 4 to 6 mEq/L within hours, but with risk factors for osmotic demyelination, daily correction should be <8 mEq/L. With a therapeutic window this narrow, clinicians would like to know how serum sodium (SNa) concentration will respond to their therapy. Based on isotopic measurements, Edelman showed SNa level to be a function of exchangeable sodium and potassium divided by total-body water. Edelman defined this relationship with linear regression yielding an equation of the form y = mx + b, where y is SNa level, x is exchangeable sodium and potassium divided by total-body water, m is the slope, and b is the intercept. Edelman said that the intercept of his regression "probably is a measure of the quantity of osmotically inactive exchangeable sodium and potassium per unit of body water." Predictive formulas are derived from Edelman's original linear regression, some including and some omitting the regression's intercept. We illustrate the performance and limitations of these formulas using comprehensive data for electrolyte and fluid balance obtained during the treatment of a critically patient who presented with an SNa concentration of 101 mEq/L.

Scheduling internal medicine resident rotations to ensure fairness and facilitate continuity of care.

Completing a residency program is a requirement for medical students before they can practice medicine independently. Residency programs in internal medicine must undergo a series of supervised rotations in elective, inpatient, and ambulatory units. Typically, a team of chief residents is charged to develop a yearly rotational schedule. This process is complex, as it needs to consider academic, managerial, regulatory, and legal restrictions while also facilitating the provision of patient care, ensuring a diverse educational experience, balancing the workload, and improving resident satisfaction. This study proposes (1) a multi-stage multi-objective optimization approach for generating yearlong weekly resident rotation schedules and (2) the use of Analytical Hierarchy Process (AHP) to compare schedules across multiple criteria to select those that are more equitable and hence to facilitate their adoption and implementation. Furthermore, the proposed approach allows the scheduling of periodic clinic rotation schemes that are commonly used to facilitate continuity of care, such as "4+1" or the "8+2" policies. In the "4+1" policy residents rotate for four consecutive weeks in different units prior to return for a week to a predetermined clinical post. Similarly, in the "8+2" policy, residents rotate eight weeks across multiple units before doing a two week rotation at a predetermined clinic.

Determining the optimal vaccine vial size in developing countries: a Monte Carlo simulation approach.

Outreach immunization services, in which health workers immunize children in their own communities, are indispensable to improve vaccine coverage in rural areas of developing countries. One of the challenges faced by these services is how to reduce high levels of vaccine wastage. In particular, the open vial wastage (OVW) that result from the vaccine doses remaining in a vial after a time for safe use -since opening the vial- has elapsed. This wastage is highly dependent on the choice of vial size and the expected number of participants for which the outreach session is planned (i.e., session size). The use single-dose vials results in zero OVW, but it increases the vaccine purchase, transportation, and holding costs per dose as compared to those resulting from using larger vial sizes. The OVW also decreases when more people are immunized in a session. However, controlling the actual number of people that show to an outreach session in rural areas of developing countries highly depends on factors that are out of control of the immunization planners. This paper integrates a binary integer-programming model to a Monte Carlo simulation method to determine the choice of vial size and the optimal reordering point level to implement an (nQ, r, T) lot-sizing policy that provides the best tradeoff between procurement costs and wastage.

An analysis of the pediatric vaccine supply shortage problem.

In 2002, several factors resulted in pediatric vaccine manufacturers not being able to produce a sufficient number of vaccines to vaccinate all the children in the United States according to the Recommended Childhood Immunization Schedule. The resulting vaccine supply shortage resulted in thousands of children not being fully immunized according to this schedule, and hence, created an unnecessary risk for epidemic outbreaks of several childhood diseases. The Centers for Disease Control and Prevention responded to this crisis by using pediatric vaccine stockpiles to mitigate the impact of future shortages. This paper presents a stochastic model that captures the vaccine supply during production interruptions. This model is used to assess the impact of pediatric vaccine stockpile levels on vaccination coverage rates, by considering the probability that all children can be immunized according to the Recommended Childhood Immunization Schedule over a given time period and the expected minimum vaccine supply. The model is also used to assess the proposed pediatric vaccine stockpile levels recommended by the United States Department of Health and Human Services. The results of this analysis suggest that the proposed vaccine stockpile levels are adequate to meet future vaccine production interruptions, provided that such production interruptions do not last more than six months (which is not surprising, given that is the time period for which they were designed). However, given that recent vaccine production interruptions have lasted (on average) for over one year, the proposed vaccine stockpile levels are insufficient to meet the nation's pediatric immunization needs during such time periods, which in turn could lead to localized and/or widespread disease outbreaks. Moreover, a moderate investment in higher vaccine stockpile levels would lead to a significantly reduced risk of such events.

Stockpile levels for pediatric vaccines: how much is enough?

In recent years, several factors have led to pediatric vaccine manufacturers experiencing vaccine production interruptions that resulted in vaccine supply shortages. One unfortunate consequence of such events is that not all children in the United States could be vaccinated on time, as set forth by the Recommended Childhood Immunization Schedule, and hence, created the potential for epidemic outbreaks of several childhood diseases. The Centers for Disease Control and Prevention (CDC) have responded to such events by releasing vaccine supplies from the national pediatric vaccine stockpiles, which were designed to mitigate the impact of vaccine production interruptions. This paper analyzes the CDC-proposed vaccine stockpile levels using a stochastic inventory model. The results from this analysis examine the adequacy of the proposed pediatric vaccine stockpile levels, as well as provide insights into what the appropriate pediatric vaccine stockpile levels should be to achieve prespecified vaccination coverage rates. Given that the average pediatric vaccine production interruption has lasted more than 1 year, the model is used to compute appropriate pediatric vaccine stockpile levels sufficient to absorb the effect of such vaccine production interruptions. The level of funding needed to create such pediatric vaccine stockpile levels is also reported.