Mathematical programming for the efficient allocation of health care resources

Rationing in an Era of Multiple Tight Constraints: Is Cost-Utility Analysis Still Fit for Purpose?

Cost-utility analysis may not be sufficient to support reimbursement decisions when the assessed health intervention requires a large proportion of the healthcare budget or when the monetary healthcare budget is not the only resource constraint. Such cases include joint replacement, coronavirus disease 2019 (COVID-19) interventions and settings where all resources are constrained (e.g. post-COVID-19 or in low/middle-income countries). Using literature on health technology assessment, rationing and reimbursement in healthcare, we identified seven alternative frameworks for simultaneous decisions about (dis)investment and proposed modifications to deal with multiple resource constraints. These frameworks comprised constrained optimisation; cost-effectiveness league table; 'step-in-the-right-direction' approach; heuristics based on effective gradients; weighted cost-effectiveness ratios; multicriteria decision analysis (MCDA); and programme budgeting and marginal analysis (PBMA). We used numerical examples to demonstrate how five of these alternative frameworks would operate. The modified frameworks we propose could be used in local commissioning and/or health technology assessment to supplement standard cost-utility analysis for interventions that have large budget impact and/or are subject to additional constraints.

Adapting Economic Evaluation Methods to Shifting Global Health Priorities: Assessing the Value of Health System Inputs

OBJECTIVES

We highlight the importance of undertaking value assessments for health system inputs if allocative efficiency is to be achieve with health sector resources, with a focus on low- and middle-income countries. However, methodological challenges complicated the application of current economic evaluation techniques to health system input investments.

METHODS

We undertake a review of the literature to examine how assessments of investments in health system inputs have been considered to date, highlighting several studies that have suggested ways to address the methodological issues. Additionally, we surveyed how empirical economic evaluations of health system inputs have approached these issues. Finally, we highlight the steps required to move toward a comprehensive standardized framework for undertaking economic evaluations to make value assessments for investments in health systems.

RESULTS

Although the methodological challenges have been illustrated, a comprehensive framework for value assessments of health system inputs, guiding the evidence required, does not exist. The applied literature of economic evaluations of health system inputs has largely ignored the issues, likely resulting in inaccurate assessments of cost-effectiveness.

CONCLUSIONS

A majority of health sector budgets are spent on health system inputs, facilitating the provision of healthcare interventions. Although economic evaluation methods are a key component in priority setting for healthcare interventions, such methods are less commonly applied to decision making for investments in health system inputs. Given the growing agenda for investments in health systems, a framework will be increasingly required to guide governments and development partners in prioritizing investments in scarce health sector budgets.

Constrained Optimization for Decision Making in Health Care Using Python: A Tutorial

HIGHLIGHTS

This tutorial provides a user-friendly guide to mathematically formulating constrained optimization problems and implementing them using Python.Two examples are presented to illustrate how constrained optimization is used in health applications, with accompanying Python code provided.

Considering equity in priority setting using transmission models: Recommendations and data needs

OBJECTIVES

Disease transmission models are used in impact assessment and economic evaluations of infectious disease prevention and treatment strategies, prominently so in the COVID-19 response. These models rarely consider dimensions of equity relating to the differential health burden between individuals and groups. We describe concepts and approaches which are useful when considering equity in the priority setting process, and outline the technical choices concerning model structure, outputs, and data requirements needed to use transmission models in analyses of health equity.

METHODS

We reviewed the literature on equity concepts and approaches to their application in economic evaluation and undertook a technical consultation on how equity can be incorporated in priority setting for infectious disease control. The technical consultation brought together health economists with an interest in equity-informative economic evaluation, ethicists specialising in public health, mathematical modellers from various disease backgrounds, and representatives of global health funding and technical assistance organisations, to formulate key areas of consensus and recommendations.

RESULTS

We provide a series of recommendations for applying the Reference Case for Economic Evaluation in Global Health to infectious disease interventions, comprising guidance on 1) the specification of equity concepts; 2) choice of evaluation framework; 3) model structure; and 4) data needs. We present available conceptual and analytical choices, for example how correlation between different equity- and disease-relevant strata should be considered dependent on available data, and outline how assumptions and data limitations can be reported transparently by noting key factors for consideration.

CONCLUSIONS

Current developments in economic evaluations in global health provide a wide range of methodologies to incorporate equity into economic evaluations. Those employing infectious disease models need to use these frameworks more in priority setting to accurately represent health inequities. We provide guidance on the technical approaches to support this goal and ultimately, to achieve more equitable health policies.

How to do (or not to do)… health resource allocations using constrained mathematical optimization

Despite the push towards evidence-based health policy, decisions about how to allocate health resources are all too often made on the basis of political forces or a continuation of the status quo. This results in wastage in health systems and loss of potential population health. However, if health systems are to serve people best, then they must operate efficiently and equitably, and appropriate valuation methods are needed to determine how to do this. With the advances in computing power over the past few decades, advanced mathematical optimization algorithms can now be run on personal computers and can be used to provide comprehensive, evidence-based recommendations for policymakers on how to prioritize health spending considering policy objectives, interactions of interventions, real-world system constraints and budget envelopes. Such methods provide an invaluable complement to traditional or extended cost-effectiveness analyses or league tables. In this paper, we describe how such methods work, how policymakers and programme managers can access them and implement their recommendations and how they have changed health spending in the world to date.

The diagonal approach: A theoretic framework for the economic evaluation of vertical and horizontal interventions in healthcare

The diagonal approach is a health system funding concept wherein vertical approaches targeting specific diseases are combined with horizontal approaches intended to strengthen health systems broadly. This taxonomy can also be used to classify health system interventions as either vertical or horizontal. Previous studies have used mathematical programming to evaluate horizontal interventions, but these models have not allowed concurrent evaluation of different types of horizontal interventions or captured spillovers and intertemporal effects. This paper aims to develop a theoretic framework for the diagonal approach. The framework is articulated through integer programming, maximizing health benefits given constraints by identifying the optimal set of both vertical and horizontal interventions to fund. The theoretic framework for the diagonal approach is developed by synthesizing and expanding three prior works. The decision problem is synthesised to allow concurrent evaluation of three different types of horizontal interventions, those: (i) improving health system efficiency, (ii) improving capacity, and (iii) investing in new platforms. Linear programs are converted to integer form, relaxing previous assumptions related to constant returns to scale and divisibility of interventions. The framework is expanded to evaluate multiple budget constraints and options for new platforms. A new form for the value function is used to estimate the benefits of intervention combinations, capturing spillovers between vertical and horizontal interventions and dynamic returns to scale. The decision problem is specified inferotemporally, explicitly capturing the impact of the time horizon on the optimal choice set. Dynamic examples are provided to demonstrate the advantages of the diagonal approach over prior frameworks. This framework extends existing works, enabling simultaneous comparison of various combinations of both vertical and horizontal interventions, capturing spillovers and intertemporal effects. The diagonal approach framework defines decision problems flexibly and realistically, forming the basis for future applied work. Implementation would improve resource allocation and patient health outcomes.

Handling Uncertainty in Cost-Effectiveness Analysis: Budget Impact and Risk Aversion

Methods to handle uncertainty in economic evaluation have gained much attention in the literature, and the cost-effectiveness acceptability curve (CEAC) is the most widely used method to summarise and present uncertainty associated with program costs and effects in cost-effectiveness analysis. Some researchers have emphasised the limitations of the CEAC for informing decision and policy makers, as the CEAC is insensitive to radial shifts of the joint distribution of incremental costs and effects in the North-East and South-West quadrants of the cost-effective plane (CEP). Furthermore, it has been pointed out that the CEAC does not incorporate risk-aversion in valuing uncertain costs and effects. In the present article, we show that the cost-effectiveness affordability curve (CEAFC) captures both dimensions of the joint distribution of incremental costs and effects on the CEP and is, therefore, sensitive to radial shifts of the joint distribution on the CEP. Furthermore, the CEAFC also informs about the budget impact of a new intervention, as it can be used to estimate the joint probability that an intervention is both affordable and cost-effective. Moreover, we show that the cost-effectiveness risk-aversion curve (CERAC) allows the analyst to incorporate different levels of risk-aversion into the analysis and can, therefore, be used to inform decision-makers who are risk-averse. We use data from a published cost-effectiveness model of palbociclib in addition to letrozole versus letrozole alone for the treatment of oestrogen-receptor positive, HER-2 negative, advanced breast cancer to demonstrate the differences between CEAC, CEAFC and CERAC, and show how these can jointly be used to inform decision and policy makers.

Selection of healthcare waste disposal firms using a multi-method approach

The aim of this study is to propose a hybrid multi criteria decision making model with a linear programming (LP) model to tackle the issue of safe disposal of hazardous and infectious healthcare waste. For this, ten criteria in this study have been identified from literature and field surveys which are modelled using Decision making trial and evaluation (DEMATEL) and Analytic network process (ANP) methods to select the best disposal firm i.e. single sourcing for a hospital. We found that Experience of the firm, Technology for disposal, and Waste collection infrastructure acts as the most vital criteria in selecting a healthcare waste disposal firm for single sourcing. Furthermore, to optimize the total value of disposal and mitigating the risk involved in disposing waste through single sourcing; the LP model considering constraints such as waste lose constraint and waste processing constraint etc. Is solved for multiple sourcing using Lingo 18.0. The solution to LP results into allocation of 500, 500, and 1000 (kg/day) disposables to healthcare waste disposal firms D1, D2 and D3, respectively. The multi-method approach proposed in this study helps the hospital management in selecting economically, socially, and environmentally sustainable healthcare waste disposal firm.

Economic evaluation and health systems strengthening: a review of the literature

Health systems strengthening (HSS) is firmly on the global health and development agenda. While a growing evidence base seeks to understand the effectiveness of HSS, there is limited evidence regarding cost and cost-effectiveness. Without such evidence, it is hard to argue that HSS represents value for money and the level of investment needed cannot be quantified. This paper seeks to review the literature regarding the economic evaluation of HSS from low- and middle-income country (LMIC) settings, and to contribute towards the development of methods for the economic evaluation of HSS. A systematic search for literature was conducted in PubMed, Scopus and the Health Systems Evidence database. MeSH terms related to economic evaluation were combined with key words related to the concept of HSS. Of the 204 records retrieved, 52 were retained for full text review and 33 were included. Of these, 67% were published between January 2015 and June 2019. While many HSS interventions have system wide impacts, most studies (71%) investigated these impacts using a disease-specific lens (e.g. the impact of quality of care improvements on uptake of facility deliveries). HSS investments were categorized, with the majority being investments in platform efficiency (e.g. quality of care), followed by simultaneous investment in platform efficiency and platform capacity (e.g. quality of care and task shifting). This review identified a growing body of work seeking to undertake and/or conceptualize the economic evaluation of HSS in low- and middle-income countries. The majority assess HSS interventions using a disease-specific or programmatic lens, treating HSS in a similar manner to the economic evaluation of medicines and diagnostics. While this approach misses potential economies of scope from HSS investments, it allows for a preliminary understanding of relative value for money. Future research is needed to complement the emerging evidence base.

Program Evaluation of Population- and System-Level Policies: Evidence for Decision Making

BACKGROUND

Policy evaluations often focus on ex post estimation of causal effects on short-term surrogate outcomes. The value of such information is limited for decision making, as the failure to reflect policy-relevant outcomes and disregard for opportunity costs prohibits the assessment of value for money. Further, these evaluations do not always consider all relevant evidence, other courses of action, or decision uncertainty.

METHODS

In this article, we explore how policy evaluation could better meet the needs of decision making. We begin by defining the evidence required to inform decision making. We then conduct a literature review of challenges in evaluating policies. Finally, we highlight potential methods available to help address these challenges.

RESULTS

The evidence required to inform decision making includes the impacts on the policy-relevant outcomes, the costs and associated opportunity costs, and the consequences of uncertainty. Challenges in evaluating health policies are described using 8 categories: 1) valuation space; 2) comparators; 3) time of evaluation; 4) mechanisms of action; 5) effects; 6) resources, constraints, and opportunity costs; 7) fidelity, adaptation, and level of implementation; and 8) generalizability and external validity. Methods from a broad set of disciplines are available to improve policy evaluation, relating to causal inference, decision-analytic modeling, theory of change, realist evaluation, and structured expert elicitation.

LIMITATIONS

The targeted review may not identify all possible challenges, and the methods covered are not exhaustive.

CONCLUSIONS

Evaluations should provide appropriate evidence to inform decision making. There are challenges in evaluating policies, but methods from multiple disciplines are available to address these challenges.

IMPLICATIONS

Evaluators need to carefully consider the decision being informed, the necessary evidence to inform it, and the appropriate methods.[Box: see text].

[Equity in the health economic evaluation of public health: An overview]

AIM

Starting from the claim that public health interventions should aim to improve health equity, the article examines which methodological approaches of health economic evaluation exist to support the analysis of equity-related outcomes of different interventions.

METHOD

Critical review of the relevant literature.

RESULTS

Against the background of the normative foundations of health economic evaluation, three methodological approaches and three practical methods are presented that allow for considering health equity concerns in health economic evaluations. Implications of the different approaches and references to the German context are discussed.

CONCLUSION

The use of the instruments presented offers good potential to improve transparency with respect to distributive effects of different allocation decisions. This appears to be necessary in order to meet demands for health equity improving public health interventions - especially in the context of the German Prevention Act.

Framework for Drug Formulary Decision Using Multiple-Criteria Decision Analysis

Background. Reviewing drugs to determine coverage or reimbursement level is a complex process that involves significant time and expertise. Review boards gather evidence from the submission provided, input from clinicians and patients, and results of clinical and economic reviews. This information consists of assessments on multiple criteria that often conflict with one another. Multiple-criteria decision analysis (MCDA) includes methods to address complex decision making problems with conflicting objectives and criteria. We propose an MCDA approach that infers a utility model based on reviews of previously submitted drugs. Methods. We use a recent extension of the UTilitiés Additives DIScriminantes approach, UTADIS^GMS. This disaggregation approach deconstructs a portfolio of elements such as a set of drugs that have been reviewed and for which a decision has been made. It derives global and marginal utility functions that are consistent with the preferences exhibited by the review boards in their recommendations. We apply the method to oncology drugs reviewed in Canada between 2011 and 2017. We also illustrate how to conduct scenario analyses and predict the coverage decisions for new drugs. Results. Applying the method yields a utility value for each submission along with a set of thresholds that partition the utility values based on the submission outcomes. Scenario analyses illustrate the predictive ability of the method. Conclusion. Preference disaggregation is an indirect way of eliciting an additive global utility value function. It requires less of a cognitive effort from the decision making bodies because it infers preferences from the data rather than relying on direct assessments of model parameters. We illustrate how it can be applied to validate existing decisions and to predict the recommendation of a new drug.

How should HIV resources be allocated? Lessons learnt from applying Optima HIV in 23 countries

Introduction

With limited funds available, meeting global health targets requires countries to both mobilize and prioritize their health spending. Within this context, countries have recognized the importance of allocating funds for HIV as efficiently as possible to maximize impact. Over the past six years, the governments of 23 countries in Africa, Asia, Eastern Europe and Latin America have used the Optima HIV tool to estimate the optimal allocation of HIV resources.

Methods

Each study commenced with a request by the national government for technical assistance in conducting an HIV allocative efficiency study using Optima HIV. Each study team validated the required data, calibrated the Optima HIV epidemic model to produce HIV epidemic projections, agreed on cost functions for interventions, and used the model to calculate the optimal allocation of available funds to best address national strategic plan targets. From a review and analysis of these 23 country studies, we extract common themes around the optimal allocation of HIV funding in different epidemiological contexts.

Results and discussion

The optimal distribution of HIV resources depends on the amount of funding available and the characteristics of each country's epidemic, response and targets. Universally, the modelling results indicated that scaling up treatment coverage is an efficient use of resources. There is scope for efficiency gains by targeting the HIV response towards the populations and geographical regions where HIV incidence is highest. Across a range of countries, the model results indicate that a more efficient allocation of HIV resources could reduce cumulative new HIV infections by an average of 18% over the years to 2020 and 25% over the years to 2030, along with an approximately 25% reduction in deaths for both timelines. However, in most countries this would still not be sufficient to meet the targets of the national strategic plan, with modelling results indicating that budget increases of up to 185% would be required.

Conclusions

Greater epidemiological impact would be possible through better targeting of existing resources, but additional resources would still be required to meet targets. Allocative efficiency models have proven valuable in improving the HIV planning and budgeting process.

Integrating a brief mental health intervention into primary care services for patients with HIV and diabetes in South Africa: study protocol for a trial-based economic evaluation

INTRODUCTION

Depression and alcohol use disorders are international public health priorities for which there is a substantial treatment gap. Brief mental health interventions delivered by lay health workers in primary care services may reduce this gap. There is limited economic evidence assessing the cost-effectiveness of such interventions in low-income and middle-income countries. This paper describes the proposed economic evaluation of a health systems intervention testing the effectiveness, cost-effectiveness and cost-utility of two task-sharing approaches to integrating services for common mental disorders with HIV and diabetes primary care services.

METHODS AND ANALYSIS

This evaluation will be conducted as part of a three-armed cluster randomised controlled trial of clinical effectiveness. Trial clinical outcome measures will include primary outcomes for risk of depression and alcohol use, and secondary outcomes for risk of chronic disease (HIV and diabetes) treatment failure. The cost-effectiveness analysis will evaluate cost per unit change in Alcohol Use Disorder Identification Test and Centre for Epidemiological Studies scale on Depression scores as well as cost per unit change in HIV RNA viral load and haemoglobin A1c, producing results of provider and patient cost per patient year for each study arm and chronic disease. The cost utility analyses will provide results of cost per quality-adjusted life year gained. Additional analyses relevant for implementation including budget impact analyses will be conducted to inform the development of a business case for scaling up the country's investment in mental health services.

ETHICS AND DISSEMINATION

The Western Cape Department of Health (WCDoH) (WC2016_RP6_9), the South African Medical Research Council (EC 004-2/2015), the University of Cape Town (089/2015) and Oxford University (OxTREC 2-17) provided ethical approval for this study. Results dissemination will include policy briefs, social media, peer-reviewed papers, a policy dialogue workshop and press briefings.

TRIAL REGISTRATION NUMBER

PACTR201610001825405.

Development of Advance Care Planning Research Priorities: A Call to Action

The objective of this study was to develop a national, prioritized research agenda for advance care planning (ACP). We first identified a list of comprehensive ACP research topics and determined priority criteria through focus groups. We next conducted a survey wherein importance weights were assigned to priority criteria and each ACP topic was rated. We combined weights and ratings into overall scores. A total of 17 ACP topics were developed and placed into four categories: patients and family members, the general public, professionals, and the healthcare system. Four main priority criteria were created: feasibility, consistency with ethical and societal values, economic considerations, and impact. Of the 100 individuals we invited to participate in the survey, 62 accepted. Prioritized topics centred largely on the impact of ACP on health resource utilization, communicating advance care planning across settings, and the preferred manner of engaging patients in ACP.

Application of Constrained Optimization Methods in Health Services Research: Report 2 of the ISPOR Optimization Methods Emerging Good Practices Task Force

BACKGROUND

Constrained optimization methods are already widely used in health care to solve problems that represent traditional applications of operations research methods, such as choosing the optimal location for new facilities or making the most efficient use of operating room capacity.

OBJECTIVES

In this paper we illustrate the potential utility of these methods for finding optimal solutions to problems in health care delivery and policy. To do so, we selected three award-winning papers in health care delivery or policy development, reflecting a range of optimization algorithms. Two of the three papers are reviewed using the ISPOR Constrained Optimization Good Practice Checklist, adapted from the framework presented in the initial Optimization Task Force Report. The first case study illustrates application of linear programming to determine the optimal mix of screening and vaccination strategies for the prevention of cervical cancer. The second case illustrates application of the Markov Decision Process to find the optimal strategy for treating type 2 diabetes patients for hypercholesterolemia using statins. The third paper (described in Appendix 1) is used as an educational tool. The goal is to describe the characteristics of a radiation therapy optimization problem and then invite the reader to formulate the mathematical model for solving it. This example is particularly interesting because it lends itself to a range of possible models, including linear, nonlinear, and mixed-integer programming formulations. From the case studies presented, we hope the reader will develop an appreciation for the wide range of problem types that can be addressed with constrained optimization methods, as well as the variety of methods available.

CONCLUSIONS

Constrained optimization methods are informative in providing insights to decision makers about optimal target solutions and the magnitude of the loss of benefit or increased costs associated with the ultimate clinical decision or policy choice. Failing to identify a mathematically superior or optimal solution represents a missed opportunity to improve economic efficiency in the delivery of care and clinical outcomes for patients. The ISPOR Optimization Methods Emerging Good Practices Task Force's first report provided an introduction to constrained optimization methods to solve important clinical and health policy problems. This report also outlined the relationship of constrained optimization methods relative to traditional health economic modeling, graphically illustrated a simple formulation, and identified some of the major variants of constrained optimization models, such as linear programming, dynamic programming, integer programming, and stochastic programming. The second report illustrates the application of constrained optimization methods in health care decision making using three case studies. The studies focus on determining optimal screening and vaccination strategies for cervical cancer, optimal statin start times for diabetes, and an educational case to invite the reader to formulate radiation therapy optimization problems. These illustrate a wide range of problem types that can be addressed with constrained optimization methods.

Cost-Effectiveness Thresholds: the Past, the Present and the Future

Cost-effectiveness (CE) thresholds are being discussed more frequently and there have been many new developments in this area; however, there is a lack of understanding about what thresholds mean and their implications. This paper provides an overview of the CE threshold literature. First, the meaning of a CE threshold and the key assumptions involved (perfect divisibility, marginal increments in budget, etc.) are highlighted using a hypothetical example, and the use of historic/heuristic estimates of the threshold is noted along with their limitations. Recent endeavours to estimate the empirical value of the thresholds, both from the supply side and the demand side, are then presented. The impact on CE thresholds of future directions for the field, such as thresholds across sectors and the incorporation of multiple criteria beyond quality-adjusted life-years as a measure of 'value', are highlighted. Finally, a number of common issues and misconceptions associated with CE thresholds are addressed.

Health care input constraints and cost effectiveness analysis decision rules

Results of cost effectiveness analyses (CEA) studies are most useful for decision makers if they face only one constraint: the health care budget. However, in practice, decision makers wishing to use the results of CEA studies may face multiple resource constraints relating to, for instance, constraints in health care inputs such as a shortage of skilled labour. The presence of multiple resource constraints influences the decision rules of CEA and limits the usefulness of traditional CEA studies for decision makers. The goal of this paper is to illustrate how results of CEA can be interpreted and used in case a decision maker faces a health care input constraint. We set up a theoretical model describing the optimal allocation of the health care budget in the presence of a health care input constraint. Insights derived from that model were used to analyse a stylized example based on a decision about a surgical robot as well as a published cost effectiveness study on eye care services in Zambia. Our theoretical model shows that applying default decision rules in the presence of a health care input constraint leads to suboptimal decisions but that there are ways of preserving the traditional decision rules of CEA by reweighing different cost categories. The examples illustrate how such adjustments can be made, and makes clear that optimal decisions depend crucially on such adjustments. We conclude that it is possible to use the results of cost effectiveness studies in the presence of health care input constraints if results are properly adjusted.

Integrating social justice concerns into economic evaluation for healthcare and public health: A systematic review

Social justice is the moral imperative to avoid and remediate unfair distributions of societal disadvantage. In priority setting in healthcare and public health, social justice reaches beyond fairness in the distribution of health outcomes and economic impacts to encompass fairness in the distribution of policy impacts upon other dimensions of well-being. There is an emerging awareness of the need for economic evaluation to integrate all such concerns. We performed a systematic review (1) to describe methodological solutions suitable for integrating social justice concerns into economic evaluation, and (2) to describe the challenges that those solutions face. To be included, publications must have captured fairness considerations that (a) involve cross-dimensional subjective personal life experience and (b) can be manifested at the level of subpopulations. We identified relevant publications using an electronic search in EMBASE, PubMed, EconLit, PsycInfo, Philosopher's Index, and Scopus, including publications available in English in the past 20 years. Two reviewers independently appraised candidate publications, extracted data, and synthesized findings in narrative form. Out of 2388 publications reviewed, 26 were included. Solutions sought either to incorporate relevant fairness considerations directly into economic evaluation or to report them alongside cost-effectiveness measures. The majority of reviewed solutions, if adapted to integrate social justice concerns, would require their explicit quantification. Four broad challenges related to the implementation of these solutions were identified: clarifying the normative basis; measuring and determining the relative importance of criteria representing that basis; combining the criteria; and evaluating trade-offs. All included solutions must grapple with an inherent tension: they must either face the normative and operational challenges of quantifying social justice concerns or accede to offering incomplete policy guidance. Interdisciplinary research and broader collaborations are crucial to address these challenges and to support due attention to social justice in priority setting.

Population-level intervention and information collection in dynamic healthcare policy

We develop a general framework for optimal health policy design in a dynamic setting. We consider a hypothetical medical intervention for a cohort of patients where one parameter varies across cohorts with imperfectly observable linear dynamics. We seek to identify the optimal time to change the current health intervention policy and the optimal time to collect decision-relevant information. We formulate this problem as a discrete-time, infinite-horizon Markov decision process and we establish structural properties in terms of first and second-order monotonicity. We demonstrate that it is generally optimal to delay information acquisition until an effect on decisions is sufficiently likely. We apply this framework to the evaluation of hepatitis C virus (HCV) screening in the general population determining which birth cohorts to screen for HCV and when to collect information about HCV prevalence.

Constrained Optimization Methods in Health Services Research-An Introduction: Report 1 of the ISPOR Optimization Methods Emerging Good Practices Task Force

Providing health services with the greatest possible value to patients and society given the constraints imposed by patient characteristics, health care system characteristics, budgets, and so forth relies heavily on the design of structures and processes. Such problems are complex and require a rigorous and systematic approach to identify the best solution. Constrained optimization is a set of methods designed to identify efficiently and systematically the best solution (the optimal solution) to a problem characterized by a number of potential solutions in the presence of identified constraints. This report identifies 1) key concepts and the main steps in building an optimization model; 2) the types of problems for which optimal solutions can be determined in real-world health applications; and 3) the appropriate optimization methods for these problems. We first present a simple graphical model based on the treatment of "regular" and "severe" patients, which maximizes the overall health benefit subject to time and budget constraints. We then relate it back to how optimization is relevant in health services research for addressing present day challenges. We also explain how these mathematical optimization methods relate to simulation methods, to standard health economic analysis techniques, and to the emergent fields of analytics and machine learning.

Country-Level Cost-Effectiveness Thresholds: Initial Estimates and the Need for Further Research

BACKGROUND

Cost-effectiveness analysis can guide policymakers in resource allocation decisions. It assesses whether the health gains offered by an intervention are large enough relative to any additional costs to warrant adoption. When there are constraints on the health care system's budget or ability to increase expenditures, additional costs imposed by interventions have an "opportunity cost" in terms of the health foregone because other interventions cannot be provided. Cost-effectiveness thresholds (CETs) are typically used to assess whether an intervention is worthwhile and should reflect health opportunity cost. Nevertheless, CETs used by some decision makers-such as the World Health Organization that suggested CETs of 1 to 3 times the gross domestic product (GDP) per capita-do not.

OBJECTIVES

To estimate CETs based on opportunity cost for a wide range of countries.

METHODS

We estimated CETs based on recent empirical estimates of opportunity cost (from the English National Health Service), estimates of the relationship between country GDP per capita and the value of a statistical life, and a series of explicit assumptions.

RESULTS

CETs for Malawi (the country with the lowest income in the world), Cambodia (with borderline low/low-middle income), El Salvador (with borderline low-middle/upper-middle income), and Kazakhstan (with borderline high-middle/high income) were estimated to be $3 to $116 (1%-51% GDP per capita), $44 to $518 (4%-51%), $422 to $1967 (11%-51%), and $4485 to $8018 (32%-59%), respectively.

CONCLUSIONS

To date, opportunity-cost-based CETs for low-/middle-income countries have not been available. Although uncertainty exists in the underlying assumptions, these estimates can provide a useful input to inform resource allocation decisions and suggest that routinely used CETs have been too high.

Decision rules for allocation of finances to health systems strengthening

A key dilemma in global health is how to allocate funds between disease-specific "vertical projects" on the one hand and "horizontal programmes" which aim to strengthen the entire health system on the other. While economic evaluation provides a way of approaching the prioritisation of vertical projects, it provides less guidance on how to prioritise between horizontal and vertical spending. We approach this problem by formulating a mathematical program which captures the complementary benefits of funding both vertical projects and horizontal programmes. We show that our solution to this math program has an appealing intuitive structure. We illustrate our model by computationally solving two specialised versions of this problem, with illustrations based on the problem of allocating funding for infectious diseases in sub-Saharan Africa. We conclude by reflecting on how such a model may be developed in the future and used to guide empirical data collection and theory development.

Extended Cost-Effectiveness Analysis for Health Policy Assessment: A Tutorial

Health policy instruments such as the public financing of health technologies (e.g., new drugs, vaccines) entail consequences in multiple domains. Fundamentally, public health policies aim at increasing the uptake of effective and efficient interventions and at subsequently leading to better health benefits (e.g., premature mortality and morbidity averted). In addition, public health policies can provide non-health benefits in addition to the sole well-being of populations and beyond the health sector. For instance, public policies such as social and health insurance programs can prevent illness-related impoverishment and procure financial risk protection. Furthermore, public policies can improve the distribution of health in the population and promote the equalization of health among individuals. Extended cost-effectiveness analysis was developed to address health policy assessment, specifically to evaluate the health and financial consequences of public policies in four domains: (1) the health gains; (2) the financial risk protection benefits; (3) the total costs to the policy makers; and (4) the distributional benefits. Here, we present a tutorial that describes both the intent of extended cost-effectiveness analysis and its keys to allow easy implementation for health policy assessment.

Efficiency, Equity, and Budgetary Policies

The standard decision rules of cost-effectiveness analysis either require the decision maker to set a threshold willingness to pay for additional health care or to set an overall fixed budget. In practice, neither are generally taken, but instead an arbitrary decision rule is followed that may not be consistent with the overall budget, lead to an allocation of resources that is less than optimal, and is unable to identify the program that should be displaced at the margin. Recent work has shown how mathematical programming can be used as a generalization of the standard decision rules. The authors extend the use of mathematical programming, first to incorporate more complex budgetary rules about when expenditure can be incurred, and show the opportunity loss, in terms of health benefit forgone, of each budgetary policy. Second, the authors demonstrate that indivisibility in a patient population can be regarded as essentially a concern for horizontal equity and represent this and other equity concerns as constraints in the program. Third, the authors estimate the different opportunity costs of a range of equity concerns applied to particular patient populations, and when imposed on all patient populations. They apply this framework of analysis to a realistic and policy-relevant problem. Key words: cost-effectiveness analysis; cost-benefit analysis; mathematical programming; resource allocation. (Med Decis Making 2007;27:128—137)

Methods for the estimation of the National Institute for Health and Care Excellence cost-effectiveness threshold

BACKGROUND

Cost-effectiveness analysis involves the comparison of the incremental cost-effectiveness ratio of a new technology, which is more costly than existing alternatives, with the cost-effectiveness threshold. This indicates whether or not the health expected to be gained from its use exceeds the health expected to be lost elsewhere as other health-care activities are displaced. The threshold therefore represents the additional cost that has to be imposed on the system to forgo 1 quality-adjusted life-year (QALY) of health through displacement. There are no empirical estimates of the cost-effectiveness threshold used by the National Institute for Health and Care Excellence.

OBJECTIVES

(1) To provide a conceptual framework to define the cost-effectiveness threshold and to provide the basis for its empirical estimation. (2) Using programme budgeting data for the English NHS, to estimate the relationship between changes in overall NHS expenditure and changes in mortality. (3) To extend this mortality measure of the health effects of a change in expenditure to life-years and to QALYs by estimating the quality-of-life (QoL) associated with effects on years of life and the additional direct impact on QoL itself. (4) To present the best estimate of the cost-effectiveness threshold for policy purposes.

METHODS

Earlier econometric analysis estimated the relationship between differences in primary care trust (PCT) spending, across programme budget categories (PBCs), and associated disease-specific mortality. This research is extended in several ways including estimating the impact of marginal increases or decreases in overall NHS expenditure on spending in each of the 23 PBCs. Further stages of work link the econometrics to broader health effects in terms of QALYs.

RESULTS

The most relevant 'central' threshold is estimated to be £12,936 per QALY (2008 expenditure, 2008-10 mortality). Uncertainty analysis indicates that the probability that the threshold is < £20,000 per QALY is 0.89 and the probability that it is < £30,000 per QALY is 0.97. Additional 'structural' uncertainty suggests, on balance, that the central or best estimate is, if anything, likely to be an overestimate. The health effects of changes in expenditure are greater when PCTs are under more financial pressure and are more likely to be disinvesting than investing. This indicates that the central estimate of the threshold is likely to be an overestimate for all technologies which impose net costs on the NHS and the appropriate threshold to apply should be lower for technologies which have a greater impact on NHS costs.

LIMITATIONS

The central estimate is based on identifying a preferred analysis at each stage based on the analysis that made the best use of available information, whether or not the assumptions required appeared more reasonable than the other alternatives available, and which provided a more complete picture of the likely health effects of a change in expenditure. However, the limitation of currently available data means that there is substantial uncertainty associated with the estimate of the overall threshold.

CONCLUSIONS

The methods go some way to providing an empirical estimate of the scale of opportunity costs the NHS faces when considering whether or not the health benefits associated with new technologies are greater than the health that is likely to be lost elsewhere in the NHS. Priorities for future research include estimating the threshold for subsequent waves of expenditure and outcome data, for example by utilising expenditure and outcomes available at the level of Clinical Commissioning Groups as well as additional data collected on QoL and updated estimates of incidence (by age and gender) and duration of disease. Nonetheless, the study also starts to make the other NHS patients, who ultimately bear the opportunity costs of such decisions, less abstract and more 'known' in social decisions.

FUNDING

The National Institute for Health Research-Medical Research Council Methodology Research Programme.

A multi-criteria decision analysis perspective on the health economic evaluation of medical interventions

A standard practice in health economic evaluation is to monetize health effects by assuming a certain societal willingness-to-pay per unit of health gain. Although the resulting net monetary benefit (NMB) is easy to compute, the use of a single willingness-to-pay threshold assumes expressibility of the health effects on a single non-monetary scale. To relax this assumption, this article proves that the NMB framework is a special case of the more general stochastic multi-criteria acceptability analysis (SMAA) method. Specifically, as SMAA does not restrict the number of criteria to two and also does not require the marginal rates of substitution to be constant, there are problem instances for which the use of this more general method may result in a better understanding of the trade-offs underlying the reimbursement decision-making problem. This is illustrated by applying both methods in a case study related to infertility treatment.

Aversion to health inequalities in healthcare prioritisation: a multicriteria optimisation perspective

In this paper we discuss the prioritisation of healthcare projects where there is a concern about health inequalities, but the decision maker is reluctant to make explicit quantitative value judgements and the data systems only allow the measurement of health at an aggregate level. Our analysis begins with a standard welfare economic model of healthcare resource allocation. We show how - under the assumption that the healthcare projects under consideration have a small impact on individual health--the problem can be reformulated as one of finding a particular subset of the class of efficient solutions to an implied multicriteria optimisation problem. Algorithms for finding such solutions are readily available, and we demonstrate our approach through a worked example of treatment for clinical depression.

Modeling optimal cervical cancer prevention strategies in Nigeria

BACKGROUND

This study aims to assess the most efficient combinations of vaccination and screening coverage for the prevention of cervical cancer (CC) at different levels of expenditure in Nigeria.

METHODS

An optimization procedure, using a linear programming approach and requiring the use of two models (an evaluation and an optimization model), was developed. The evaluation model, a Markov model, estimated the annual number of CC cases at steady state in a population of 100,000 women for four alternative strategies: screening only; vaccination only; screening and vaccination; and no prevention. The results of the Markov model for each scenario were used as inputs to the optimization model determining the optimal proportion of the population to receive screening and/or vaccination under different scenarios. The scenarios varied by available budget, maximum screening and vaccination coverage, and overall reachable population.

RESULTS

In the base-case optimization model analyses, with a coverage constraint of 20% for one lifetime screening, 95% for vaccination and a budget constraint of $1 per woman per year to minimize CC incidence, the optimal mix of prevention strategies would result in a reduction of CC incidence of 31% (3-dose vaccination available) or 46% (2-dose vaccination available) compared with CC incidence pre-vaccination. With a 3-dose vaccination schedule, the optimal combination of the different strategies across the population would be 20% screening alone, 39% vaccination alone and 41% with no prevention, while with a 2-dose vaccination schedule the optimal combination would be 71% vaccination alone, and 29% with no prevention. Sensitivity analyses indicated that the results are sensitive to the constraints included in the optimization model as well as the cervical intraepithelial neoplasia (CIN) and CC treatment cost.

CONCLUSIONS

The results of the optimization model indicate that, in Nigeria, the most efficient allocation of a limited budget would be to invest in both vaccination and screening with a 3-dose vaccination schedule, and in vaccination alone before implementing a screening program with a 2-dose vaccination schedule.

Simulation models for socioeconomic inequalities in health: a systematic review

Background: The emergence and evolution of socioeconomic inequalities in health involves multiple factors interacting with each other at different levels. Simulation models are suitable for studying such complex and dynamic systems and have the ability to test the impact of policy interventions in silico. Objective: To explore how simulation models were used in the field of socioeconomic inequalities in health. Methods: An electronic search of studies assessing socioeconomic inequalities in health using a simulation model was conducted. Characteristics of the simulation models were extracted and distinct simulation approaches were identified. As an illustration, a simple agent-based model of the emergence of socioeconomic differences in alcohol abuse was developed. Results: We found 61 studies published between 1989 and 2013. Ten different simulation approaches were identified. The agent-based model illustration showed that multilevel, reciprocal and indirect effects of social determinants on health can be modeled flexibly. Discussion and Conclusions: Based on the review, we discuss the utility of using simulation models for studying health inequalities, and refer to good modeling practices for developing such models. The review and the simulation model example suggest that the use of simulation models may enhance the understanding and debate about existing and new socioeconomic inequalities of health frameworks.

Efficient and equitable HIV prevention: A case study of male circumcision in South Africa

Background

We determine efficient, equitable and mixed efficient-equitable allocations of a male circumcision (MC) intervention reducing female to male HIV transmission in South Africa (SA), as a case study of an efficiency-equity framework for resource allocation in HIV prevention.

Methods

We present a mathematical model developed with epidemiological and cost data from the nine provinces of SA. The hypothetical one-year-long MC intervention with a budget of US$ 10 million targeted adult men 15–49 years of age in SA. The intervention was evaluated according to two criteria: an efficiency criterion, which focused on maximizing the number of HIV infections averted by the intervention, and an equity criterion (defined geographically), which focused on maximizing the chance that each male adult individual had access to the intervention regardless of his province.

Results

A purely efficient intervention would prevent 4,008 HIV infections over a year. In the meantime, a purely equitable intervention would avert 3,198 infections, which represents a 20% reduction in infection outcome as compared to the purely efficient scenario. A half efficient-half equitable scenario would prevent 3,749 infections, that is, a 6% reduction in infection outcome as compared to the purely efficient scenario.

Conclusions

This paper provides a framework for resource allocation in the health sector which incorporates a simple equity metric in addition to efficiency. In the specific context of SA with a MC intervention for the prevention of HIV, incorporation of geographical equity only slightly reduces the overall efficiency of the intervention.

Whole disease modeling to inform resource allocation decisions in cancer: a methodological framework

OBJECTIVES

This article presents a methodological framework for developing health economic models of whole systems of disease and treatment pathways to inform decisions concerning resource allocation-an approach referred to as "Whole Disease Modeling." This system-level approach can provide a consistent mathematical infrastructure for the economic evaluation of virtually any intervention across a disease pathway.

METHODS

The framework has been developed for cancer but is broadly generalizable to other diseases. It has been informed by pilot work, a systematic review of economic analyses, a qualitative examination of model development processes, and other literature from the fields of operational research, statistics, and health economics.

RESULTS

The framework is built on three principles: 1) the model boundary and breadth should capture all relevant aspects of the disease and its treatment-from preclinical disease through to death, 2) the model should be developed such that the decision node is conceptually transferable across the model, and 3) the costs and consequences of service elements should be structurally related. A generalized process for developing Whole Disease Models is presented.

DISCUSSION

Although this approach involves a nontrivial investment of time and resource, its value may be realized when 1) multiple options for service change require economic analysis at a single time point, 2) a disease service changes rapidly and the model can be reused, 3) current services within a pathway have not been subjected to economic analysis, 4) upstream events are expected to have important downstream effects, or 5) simple cost-utility decision rules fail to reflect the complexity of the decision-makers' objectives.

What can economics add to health technology assessment? Please not just another cost-effectiveness analysis!

Evidence based medicine is not only important for clinical practice, but national governments have embraced it through health technology assessment (HTA). HTA combines data from randomized controlled trials (RCT) and observational studies with an economic component (among other issues). HTA, however, is not taking full advantage of economics. This paper presents five areas in which economics may improve not only HTA, but the RCT methods that underpin it. HTA needs to live up to its original agenda of being a interdisciplinary field and draw methods not just from biostatistics, but from a range of discipline, including economics. By focusing only on cost effectiveness analysis (CEA), however, we go nowhere close to fulfilling this potential.

Substance misuse prevention and economic analysis: challenges and opportunities regarding international utility

Economic analyses of substance misuse prevention assess the intervention cost necessary to achieve a particular outcome, and thereby provide an additional dimension for evaluating prevention programming. This article reviews several types of economic analysis, considers how they can be applied to substance misuse prevention, and discusses challenges to enhancing their international relevance, particularly their usefulness for informing policy decisions. Important first steps taken to address these challenges are presented, including the disease burden concept and the development of generalized cost-effectiveness, advances that facilitate international policy discussions by providing a common framework for evaluating health care needs and program effects.

Can cost-effectiveness analysis integrate concerns for equity? Systematic review

OBJECTIVES

The aim of this study was to promote approaches to health technology assessment (HTA) that are both evidence-based and values-based. We conducted a systematic review of published studies describing formal methods to consider equity in the context of cost-effectiveness analysis (CEA).

METHODS

Candidate studies were identified through an unrestricted search of the Pub Med and EMBASE databases. The search closed on January 20, 2011. We identified additional studies by consulting experts and checking article bibliographies. Two authors independently reviewed each candidate study to determine inclusion and extracted data from studies retained for review. In addition to documenting methods, data extraction identified implicit and explicit notions of fairness. Data were synthesized in narrative form. Study quality was not assessed.

RESULTS

Of the 695 candidate articles, 51 were retained for review. We identified three broad methods to facilitate quantitative consideration of equity concerns in economic evaluation: integration of distributional concerns through equity weights and social welfare functions, exploration of the opportunity costs of alternative policy options through mathematical programming, and multi-criteria decision analysis.

CONCLUSIONS

Several viable techniques to integrate equity concerns within CEA now exist, ranging from descriptive approaches to the quantitative methods studied in this review. Two obstacles at the normative level have impeded their use in decision making to date: the multiplicity of concepts and values discussed under the rubric of equity, and the lack of a widely accepted normative source on which to ground controversial value choices. Clarification of equity concepts and attention to procedural fairness may strengthen use of these techniques in HTA decision making.

Selecting a mix of prevention strategies against cervical cancer for maximum efficiency with an optimization program

BACKGROUND

Screening and vaccination against human papillomavirus (HPV) can protect against cervical cancer. Neither alone can provide 100% protection. Consequently it raises the important question about the most efficient combination of screening at specified time intervals and vaccination to prevent cervical cancer.

OBJECTIVE

Our objective was to identify the mix of cervical cancer prevention strategies (screening and/or vaccination against HPV) that achieves maximum reduction in cancer cases within a fixed budget.

METHODS

We assessed the optimal mix of strategies for the prevention of cervical cancer using an optimization program. The evaluation used two models. One was a Markov cohort model used as the evaluation model to estimate the costs and outcomes of 52 different prevention strategies. The other was an optimization model in which the results of each prevention strategy of the previous model were entered as input data. The latter model determined the combination of the different prevention options to minimize cervical cancer under budget, screening coverage and vaccination coverage constraints. We applied the model in two countries with different healthcare organizations, epidemiology, screening practices, resource settings and treatment costs: the UK and Brazil. 100,000 women aged 12 years and above across the whole population over a 1-year period at steady state were included. The intervention was papanicolaou (Pap) smear screening programmes and/or vaccination against HPV with the bivalent HPV 16/18 vaccine (Cervarix® [Cervarix is a registered trademark of the GlaxoSmithKline group of companies]). The main outcome measures were optimal distribution of the population between different interventions (screening, vaccination, screening plus vaccination and no screening or vaccination) with the resulting number of cervical cancer and associated costs.

RESULTS

In the base-case analysis (= same budget as today), the optimal prevention strategy would be, after introducing vaccination with a coverage rate of 80% in girls aged 12 years and retaining screening coverage at pre-vaccination levels (65% in the UK, 50% in Brazil), to increase the screening interval to 6 years (from 3) in the UK and to 5 years (from 3) in Brazil. This would result in a reduction of cervical cancer by 41% in the UK and by 54% in Brazil from pre-vaccination levels with no budget increase. Sensitivity analysis shows that vaccination alone at 80% coverage with no screening would achieve a cervical cancer reduction rate of 20% in the UK and 43% in Brazil compared with the pre-vaccination situation with a budget reduction of 30% and 14%, respectively. In both countries, the sharp reduction in cervical cancer is seen when the vaccine coverage rate exceeds the maximum screening coverage rate, or when screening coverage rate exceeds the maximum vaccine coverage rate, while maintaining the budget. As with any model, there are limitations to the value of predictions depending upon the assumptions made in each model.

CONCLUSIONS

Spending the same budget that was used for screening and treatment of cervical cancer in the pre-vaccination era, results of the optimization program show that it would be possible to substantially reduce the number of cases by implementing an optimal combination of HPV vaccination (80% coverage) and screening at pre-vaccination coverage (65% UK, 50% Brazil) while extending the screening interval to every 6 years in the UK and 5 years in Brazil.

Communicating uncertainty in economic evaluations: verifying optimal strategies

BACKGROUND

In cost-effectiveness analysis (CEA), it is common to compare a single, new intervention with 1 or more existing interventions representing current practice ignoring other, unrelated interventions. Sectoral CEAs, in contrast, take a perspective in which the costs and effectiveness of all possible interventions within a certain disease area or health care sector are compared to maximize health in a society given resource constraints. Stochastic league tables (SLT) have been developed to represent uncertainty in sectoral CEAs but have 2 shortcomings: 1) the probabilities reflect inclusion of individual interventions and not strategies and 2) data on robustness are lacking. The authors developed an extension of SLT that addresses these shortcomings.

METHODS

Analogous to nonprobabilistic MAXIMIN decision rules, the uncertainty of the performance of strategies in sectoral CEAs may be judged with respect to worst possible outcomes, in terms of health effects obtainable within a given budget. Therefore, the authors assessed robustness of strategies likely to be optimal by performing optimization separately on all samples and on samples yielding worse than expected health benefits. The approach was tested on 2 examples, 1 with independent and 1 with correlated cost and effect data.

RESULTS

The method was applicable to the original SLT example and to a new example and provided clear and easily interpretable results. Identification of interventions with robust performance as well as the best performing strategies was straightforward. Furthermore, the robustness of strategies was assessed with a MAXIMIN decision rule.

CONCLUSION

The SLT extension improves the comprehensibility and extends the usefulness of outcomes of SLT for decision makers. Its use is recommended whenever an SLT approach is considered.

Incentives for Optimal Multi-level Allocation of HIV Prevention Resources

HIV/AIDS prevention funds are often allocated at multiple levels of decision-making. Optimal allocation of HIV prevention funds maximizes the number of HIV infections averted. However, decision makers often allocate using simple heuristics such as proportional allocation. We evaluate the impact of using incentives to encourage optimal allocation in a two-level decision-making process. We model an incentive based decision-making process consisting of an upper-level decision maker allocating funds to a single lower-level decision maker who then distributes funds to local programs. We assume that the lower-level utility function is linear in the amount of the budget received from the upper-level, the fraction of funds reserved for proportional allocation, and the number of infections averted. We assume that the upper level objective is to maximize the number of infections averted. We illustrate with an example using data from California, U.S.

Outcome based state budget allocation for diabetes prevention programs using multi-criteria optimization with robust weights

We consider the problem of outcomes based budget allocations to chronic disease prevention programs across the United States (US) to achieve greater geographical healthcare equity. We use Diabetes Prevention and Control Programs (DPCP) by the Center for Disease Control and Prevention (CDC) as an example. We present a multi-criteria robust weighted sum model for such multi-criteria decision making in a group decision setting. The principal component analysis and an inverse linear programming techniques are presented and used to study the actual 2009 budget allocation by CDC. Our results show that the CDC budget allocation process for the DPCPs is not likely model based. In our empirical study, the relative weights for different prevalence and comorbidity factors and the corresponding budgets obtained under different weight regions are discussed. Parametric analysis suggests that money should be allocated to states to promote diabetes education and to increase patient-healthcare provider interactions to reduce disparity across the US.

Discounting and decision making in the economic evaluation of health-care technologies

Discounting costs and health benefits in cost-effectiveness analysis has been the subject of recent debate - some authors suggesting a common rate for both and others suggesting a lower rate for health. We show how these views turn on key judgments of fact and value: on whether the social objective is to maximise discounted health outcomes or the present consumption value of health; on whether the budget for health care is fixed; on the expected growth in the cost-effectiveness threshold; and on the expected growth in the consumption value of health. We demonstrate that if the budget for health care is fixed and decisions are based on incremental cost effectiveness ratios (ICERs), discounting costs and health gains at the same rate is correct only if the threshold remains constant. Expecting growth in the consumption value of health does not itself justify differential rates but implies a lower rate for both. However, whether one believes that the objective should be the maximisation of the present value of health or the present consumption value of health, adopting the social time preference rate for consumption as the discount rate for costs and health gains is valid only under strong and implausible assumptions about values and facts.

Equity and efficiency in HIV-treatment in South Africa: the contribution of mathematical programming to priority setting

The HIV-epidemic is one of the greatest public health crises to face South Africa. A health care response to the treatment needs of HIV-positive people is a prime example of the desirability of an economic, rational approach to resource allocation in the face of scarcity. Despite this, almost no input based on economic analysis is currently used in national strategic planning. While cost-utility analysis is theoretically able to establish technical efficiency, in practice this is accomplished by comparing an intervention's ICER to a threshold level representing society's maximum willingness to pay to avoid death and improve health-related quality of life. Such an approach has been criticised for a number of reasons, including that it is inconsistent with a fixed budget for health care and that equity is not taken into account. It is also impractical if no national policy on the threshold exists. As an alternative, this paper proposes a mathematical programming approach that is capable of highlighting technical efficiency, equity, the equity/efficiency trade-off and the affordability of alternative HIV-treatment interventions. Government could use this information to plan an HIV-treatment strategy that best meets equity and efficiency objectives within budget constraints.

Optimal vaccine stockpile design for an eradicated disease: application to polio

Eradication of a disease promises significant health and financial benefits. Preserving those benefits, hopefully in perpetuity, requires preparing for the possibility that the causal agent could re-emerge (unintentionally or intentionally). In the case of a vaccine-preventable disease, creation and planning for the use of a vaccine stockpile becomes a primary concern. Doing so requires consideration of the dynamics at different levels, including the stockpile supply chain and transmission of the causal agent. This paper develops a mathematical framework for determining the optimal management of a vaccine stockpile over time. We apply the framework to the polio vaccine stockpile for the post-eradication era and present examples of solutions to one possible framing of the optimization problem. We use the framework to discuss issues relevant to the development and use of the polio vaccine stockpile, including capacity constraints, production and filling delays, risks associated with the stockpile, dynamics and uncertainty of vaccine needs, issues of funding, location, and serotype dependent behavior, and the implications of likely changes over time that might occur. This framework serves as a helpful context for discussions and analyses related to the process of designing and maintaining a stockpile for an eradicated disease.