O.R. Applications
Multi-level resource allocation for HIV prevention: A model for developing countries

https://doi.org/10.1016/j.ejor.2006.02.043Get rights and content

Abstract

Funds spent on HIV prevention commonly traverse several levels of distribution. For example, funds may be allocated to regions, and regional authorities may then allocate their funds to sub-regions or targeted risk groups. Decision makers at each level often make use of heuristics that may result in suboptimal allocation of resources. We examine the impact of equity-based heuristic allocation of HIV prevention funds versus optimal allocation of HIV prevention funds when there are two levels of decision making. Our results demonstrate that if optimization can only be applied to one level of the decision making process, there are more significant gains if it is applied at the lower level than at the upper level.

Introduction

In the last 20 years, over 60 million people have been infected with HIV, and of those cases, 95% are in developing countries [1]. In 2002, the average life expectancy in Sub-Saharan Africa was 47 years, while it would have been 62 years without AIDS [2]. Further, the vast majority of those affected by the disease are in their working years. Over 90% of the world’s HIV-infected children live in sub-Saharan African and mother-to-child transmission (MTCT) is responsible for almost all of those infections [3]. Without treatment, the probability of MTCT during pregnancy, labour and breastfeeding is approximately 30–45% [4].

Investment in HIV prevention prevents loss of life, human suffering, and negative social and developmental consequences. An estimated US$9.2 billion is required annually to implement an effective response to HIV in low- and middle-income countries [5]. This response includes a package of HIV prevention interventions which would avert 29 million infections by 2010 [6]. HIV funding falls short of estimated needs despite considerable recent increases in funding [2]. In 2003, actual spending on HIV/AIDS in resource poor countries totaled approximately $3.6 billion, while the estimated need for HIV/AIDS funding was $6.3 billion [7], [8]. Optimization techniques may help to more effectively use limited resources and narrow the gap between funding needs and availability.

The main sources of external funding for HIV/AIDS interventions in Africa are: donor governments, UN agencies (UNICEF, UNDP, UNESCO, WHO, etc.), the Global Fund to fight AIDS, Tuberculosis and Malaria, and the World Bank [9]. Funds targeted towards HIV interventions traverse several levels of decision making and resource allocation before being spent on the intended interventions. For example, as a centralized funding organization the Global Fund to Fight Aids, Tuberculosis and Malaria begins its financing process with a call for proposals. Proposals are submitted by public and private organizations that collaborate through a Country Coordinating Mechanism (CCM) at a local level. At the highest level of decision making, the Global Fund budget is allocated to countries, via the CCM, based primarily on the scientific merit of their proposal. In turn, the funded countries distribute their funds to local organizations and programs according to their own priorities [10]. Organizations that receive HIV prevention and treatment funds may make further resource allocation decisions before any money is spent on actual prevention and treatment efforts. However, they provide little information about the criteria used to make allocation decisions.

Health economics theory suggests that allocating resources to medical interventions in increasing order of their cost-effectiveness ratios until the available budget has been exhausted will result in the optimal allocation of funds [11]. However, this allocation process does not allow for several important factors such as, increasing or diminishing marginal returns to scale, mutual exclusivity of programs and interaction of program outcomes. Weinstein and Zeckhauser provide a binary integer program [12], and Stinnett and Paltiel develop a mixed integer programming formulation [13] to handle some of these issues. Basso and Peccatti propose a project selection approach which addresses minimum and maximum funding levels and fixed costs using a dynamic programming algorithm [14]. Heidenberger considers the problem of project selection under risk and presents a solution using a stochastic decision tree [15]. Zaric and Brandeau developed a multi-period resource allocation model for epidemic control programs [16].

More comprehensive resource allocation models for control of infectious disease epidemics have been studied. Sanders proposes a control theory approach where the objective is to find the control function which, over time, minimizes the cost of control plus the cost associated with the number of individuals who become infected [17]. Another common approach is to apply simulation in order to compare a set of resource allocation alternatives [18], [19], [20], [21], [22].

Dynamic compartmental models are commonly used to model the spread of HIV and population changes over time, and transitions to and from a compartment are typically defined by a system of dynamic equations [21], [22], [23], [24]. Brandeau et al. developed a compartmental HIV epidemic model to evaluate the costs and effects of a number of strategies for screening women of childbearing age [25]. Flessa proposes a compartmental systems dynamics model to project the spread of HIV, and then assesses the impact of health education, prevention of mother-to-child-transmission and hypothetical vaccination programs using simulation [26]. Similar approaches have also been suggested for malaria control [27].

A number of approaches have been developed in which the epidemic control problem is formulated as a nonlinear optimization problem. The problem is usually stated as one of choosing the amount to be invested in several interventions to optimize total health benefits subject to a budget constraint [28]. Linear programming models of resource allocations for health care in general have been developed; they suggest that the outcome measure used in the objective function has a strong influence on the resulting optimal allocation [29], [30]. Kaplan, and Kaplan and Pollack propose a nonlinear optimization formulation aimed at maximizing the number of averted HIV infections which uses a dynamic programming method for determining production functions [31], [32]. Zaric and Brandeau developed approximations for allocating epidemic control resources over short time horizons [33]. Nonlinear optimization approaches are summarized by Zaric [28].

Funds targeted towards HIV interventions are commonly allocated based on equity criteria, such as proportional to the number of HIV/AIDS cases in different subgroups [34], [35]. Zaric and Brandeau showed the impact of using equity heuristics [36], and Kaplan and Pollack showed what assumptions need to be made in order for equity based heuristics to be optimal [32]. HIV policy models have been suggested, but most relate to developed countries, and few models are specifically based on developing countries [37], [38], [39]. Conclusions drawn from studies in developed country settings are not generalizable to developing countries due to differences in the causes of epidemic proliferation, the cost-effectiveness of interventions and available resources.

In this paper, we evaluate the impact of simple resource allocation heuristics versus optimal allocation, given two levels of decision-making, in the context of Sub-Saharan Africa. If additional effort and rigour, such as that involved in optimization modelling, can only be applied to the decision making process at one level, we determine whether it should be at the higher or lower level of decision making. This research is innovative in its inclusion of both sexual contact and MTCT as modes of HIV transmission and in its evaluation of the impact of more than one level of allocation decision. Our results are intended to help policy makers in governments, public health agencies and non-government organizations make informed decisions regarding AIDS policy modelling and budget allocation. The remainder of this paper is organized as follows: we begin with a description of the mathematical models used; we then describe the results of our baseline and sensitivity analysis scenarios. Finally, we conclude with an interpretation of our results, some known limitations and suggestions for future work.

Section snippets

Methods

We model a two-level resource allocation process, as depicted in Fig. 1. We refer to the structure depicted in Fig. 1 as an “allocation network”. We assume a one-time allocation of funds to populations within this network over a fixed period. HIV prevalence rates tend to be higher among specific groups, such as commercial sex workers or young women attending antenatal clinics in urban areas. Thus, the allocation network is composed of two regions, Region 1 and Region 2, each of which is divided

Results

We compared the four methods for allocating resources at two levels of decision making. Our results are summarized in Table 3. In the absence of any investment in HIV prevention, there would be 7,577,097 new infections over 20 years. We found that Optimal–Optimal is the method that minimizes the total number of new infections with 2,377,079 new infections. This method calls for 91.4% of the budget to be allocated to Region 1 and the remaining 8.6% of the budget allocated to be allocated to

Discussion

In this paper we examined allocation of HIV prevention funds when there are two levels of decision making. In our baseline scenario, the number of new infections in the Equity–Optimal option represents an improvement of 7% over the number of new infections in the Optimal–Equity option. We conclude that if optimization can only be applied to one level of the decision making process, there are more significant gains if it is applied at the lower level than at the upper level. This conclusion has

Acknowledgements

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and by an Ontario Graduate Scholarship in Science and Technology (OGSST). GSZ also received support from the National Institute on Drug Abuse (DA-R01-15612).

References (65)

  • A. Vas

    AIDS now fourth biggest killer worldwide, report says

    British Medical Journal

    (2001)
  • UNAIDS, Report on the Global HIV/AIDS Epidemic 2002, UNAIDS, Geneva, Switzerland,...
  • UNAIDS, AIDS epidemic update, December 2000, UNAIDS, Geneva, Switzerland,...
  • K.M. De Cock et al.

    Prevention of mother-to-child HIV transmission in resource-poor countries – translating research into policy and practice

    JAMA

    (2000)
  • B. Schwartlander et al.

    Resource needs for HIV/AIDS

    Science

    (2001)
  • UNAIDS, Report on the State of HIV/AIDS Financing, Programme Coordinating Board 14th meeting, Geneva, 2003,...
  • T. Summers, J. Kates, Global Funding for HIV/AIDS in Resource Poor Settings, Kaiser Family Foundation, 2003,...
  • Global HIV Prevention Working Group, Access to HIV Prevention: Closing the Gap, Bill & Melinda Gates Foundation and the...
  • The Global Fund, The Global Fund Annual Report 2002/2003, The Global Fund to Fight AIDS, Tuberculosis and Malaria,...
  • G. Zaric et al.

    Dynamic resource allocation for epidemic control in multiple populations

    Mathematical Medicine and Biology

    (2003)
  • J.L. Sanders

    Quantitative guidelines for communicable disease control programs

    Biometrics

    (1971)
  • J.G. Kahn

    The cost-effectiveness of HIV prevention targeting: How much more bang for the buck?

    American Journal of Public Health

    (1996)
  • M.S. Rauner, S.C. Brailsford, S. Flessa, Using discrete event simulation to select affordable intervention programs for...
  • J.M. Stover

    Influence of mathematical modelling of HIV and AIDS on policies and programs in the developing world

    Sexually Transmitted Diseases

    (2000)
  • M.S. Rauner

    Resource allocation for HIV/AIDS control programs: A model-based policy analysis

    OR Spectrum

    (2002)
  • A.R. Wilson et al.

    Preventing HIV in injection drug users: Choosing the best mix of interventions for the population

    Journal of Urban Health

    (2003)
  • G.S. Zaric et al.

    Methadone maintenance treatment and HIV prevention: A cost effectiveness analysis

    Management Science

    (2000)
  • M.L. Brandeau et al.

    Screening women of childbearing age for human immunodeficiency virus: A model-based policy analysis

    Management Science

    (1993)
  • S. Flessa

    Decision support for AIDS control programmes in eastern Africa

    OR Spectrum

    (2003)
  • S. Flessa

    Decision support for malaria-control programmes – a system dynamics model

    Health Care Management Science

    (1999)
  • G.S. Zaric

    Resource allocation for control infectious disease epidemics

    Comments on Theoretical Biology

    (2003)
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