As the country with the highest number of HIV-infected people, South Africa is home to 17% of the global HIV burden and shares borders with six of the seven countries with the world's highest HIV prevalence . In 2006 the United Nations General Assembly declared a goal of universal access to antiretroviral treatment (ART) by 2010 ; to reach this goal, it is urgent that countries set explicit priorities for scaling up their treatment programmes.
A number of publications have addressed the resource needs associated with HIV treatment [3,4] and the cost-effectiveness of various strategies [5–9]. Although the former help policy makers set the budgets required for treatment targets, they provide no guidance on whether the chosen strategies are technically efficient (i.e. cost-effective) when a technically efficient allocation is one that maximizes the health of HIV-positive people within the HIV treatment budget constraint . Meanwhile, technical efficiency within cost-effectiveness/utility analyses is normally assessed by comparing the cost per quality-adjusted life-year (QALY) to a threshold amount that society is willing to pay to gain one additional QALY. Even if a country has defined the threshold and so can judge whether the HIV treatment intervention is cost-effective, the costs of scaling up would still need to be considered to ensure that the programme could be scaled up to reach the country's treatment targets.
Because it is important to consider both technical efficiency and the costs of scaling up, this article proposes the use of linear programming [10,11] to allow the simultaneous assessment of both factors. We illustrate the approach through application to three mutually exclusive HIV treatment strategies: treatment and prophylaxis of opportunistic and HIV-related illnesses without antiretroviral drugs (hereafter referred to as ‘no-ART’); treatment and prophylaxis of opportunistic and HIV-related illnesses with first-line ART only; and treatment and prophylaxis of opportunistic and HIV-related illnesses with both first and second-line ART. Primary cost, utilization, health-related quality of life (HRQoL) and outcomes data have been derived from the long-term follow-up of a cohort of adult HIV-positive patients receiving care in a poor setting in South Africa.
In this study we assess technical efficiency in HIV treatment from the public health sector perspective at the population level. In the HIV treatment cost-effectiveness literature, technical efficiency is normally assessed through first computing lifetime costs and outcomes from interventions on a per-patient basis. Interventions are then ranked from the least to the most effective, and an incremental cost-effectiveness ratio (ICER) is calculated as the ratio of the difference in lifetime costs and outcomes between interventions. The value of the ICER is then compared with a threshold level that specifies the maximum willingness to pay per unit of outcome. The decision rule indicates that if the ICER is below this threshold, the intervention could be considered for implementation. We have previously presented data and methods for establishing patient-level cost-effectiveness . In this paper we build on this analysis to assess cost-effectiveness at the population level. Instead of per-patient lifetime costs and outcomes, this approach uses the costs of scaling up (i.e. the total resources required to deliver an HIV treatment intervention to a given number of patients over a particular planning period) and total health gains from alternative HIV treatment strategies. Linear programming is used to solve for the intervention or combination of interventions that maximizes the health of HIV-positive people within the HIV treatment budget. In the following sections, we briefly introduce methods for the patient-level analysis (see Cleary et al.  for additional details) before describing methods for assessing technical efficiency at the population level.
Patients in this study live in Khayelitsha, a largely informal settlement on the outskirts of Cape Town where unemployment is an estimated 46% . In April 2000, three HIV clinics were opened in public facilities to provide treatment and prophylaxis for HIV-related and opportunistic infections and events, counselling and support groups for HIV-positive people. Prophylactic medication included trimethoprim–sulphamethoxazole and fluconazole for eligible patients. Acute infections were managed at the clinics, whereas suspected tuberculosis cases were referred to tuberculosis facilities and severely ill patients were referred to secondary and tertiary hospitals.
In May 2001, the service was extended to include ART for patients with CD4 cell counts less than 200 cells/μl at any WHO stage, or at WHO stage IV with any CD4 cell level. Given that this was the first public sector ART programme in South Africa, the setting for this research has numerous advantages. Data are from one of the country's largest cohorts in terms of patient numbers and length of follow-up, and because experience from this initiative informed the development of local ART guidelines, the model of care is relatively representative of other ART services. After starting ART, patients continued to receive treatment and prophylaxis for acute infections as well as appropriate referrals.
Healthcare utilization including HIV clinic visits, tuberculosis treatment and inpatient care was established with a before-and-after study design, i.e. ART patients were used as their own control: the pre-ART period was used to calculate no-ART utilization whereas the post-baseline period informed ART estimates. HIV clinic utilization was calculated from 1729 patients, with 1146 no-ART patient years and 2229 ART patient years of follow-up over a median no-ART and ART follow-up of 0.63 years [interquartile range (IQR) 0.33–1.32, maximum 4.35] and 1.03 years (IQR 0.68–1.70, maximum 4.08), respectively. Data on the use of inpatient and tuberculosis care required extensive validation. This was undertaken on 670 patients, with 501 no-ART and 693 ART patient-years. In the ART interventions, relatively high mortality in the early months of ART and high rates of healthcare utilization decreased once immune recovery had been achieved. This variability was captured directly from primary data . On the other hand, healthcare utilization could be expected to increase for patients failing ART and dying. This was captured through specifying a ‘cost of dying’, based on a sample of 83 patients who had been using services in the HIV clinics but had died before starting ART as well as 81 patients on ART who died of HIV-related causes .
Unit costs of clinic visits, inpatient care and tuberculosis treatment
Costing takes a public healthcare perspective in the context of scaling up a large new healthcare programme over the long run. Scaling up requires medicines, laboratory investigations and other variable resources as well as long-run investments aimed at increasing the capacity of the healthcare system in order to provide care at the envisaged quantity whereas at the same time avoiding the crowding out of other priorities. The scope of costs therefore includes both variable and fixed direct healthcare costs given that both have an opportunity cost in this context; unit costs are therefore defined as the full economic cost per visit, per inpatient day and per tuberculosis case treated. To capture potential cost variations associated with economies or diseconomies of scale, unit costs were calculated by pooling primary and secondary data from full economic cost analyses of four inpatient [13–15], 15 clinic  and four tuberculosis  facilities.
The choice of antiretroviral drugs and laboratory investigation schedules in Khayelitsha was in line with South African ART guidelines . Patients received stavudine, lamivudine and nevirapine or efavirenz as the first-line regimen. If a patient failed this regimen (two consecutive viral loads above 5000 copies/ml) zidovudine, didanosine and lopinavir/ritonavir were offered as the second-line regimen. CD4 cell count and viral load monitoring was approximately twice annually.
Costs were expressed in 2003 prices, converted to US dollars using an average 2003 exchange rate (US$1 = 7.56 South African Rands) . Inflation adjustments were made using the consumer price index excluding mortgage bonds . Public sector antiretroviral drug costs (including delivery costs to provincial depots) were sourced from the South African national antiretroviral tender  and laboratory investigation costs were from the National Health Laboratory Services.
We used Markov modelling to extrapolate primary data at the patient and population levels. Markov models consist of mutually exclusive and collectively exhaustive health (Markov) states with transition probabilities describing movements between states. Transitions occur after discrete time periods called Markov cycles: defined to be 3 months in length. Markov states are defined such that ‘patients’ in the state have a similar risk of events such as death and similar costs of healthcare [21,22]. Patient-level models were run in TreeAge Pro 2005 until the cohort was dead. Additional details and a full validation of these models is available .
These patient-level models were replicated in Microsoft Office Excel 2003 to allow the calculation of total costs and outcomes at the population level, achieved by entering new patients who needed treatment into the models during each cycle of the planning period. The planning period started in 2004 given that most public sector ART provision began in South Africa. Because of the likelihood of future technological innovation in this field and the uncertain impact of ART on incidence , projections were limited to a 10-year duration. Therefore, although an unlimited time horizon was used to calculate lifetime costs and outcomes at the patient level, a 10-year planning period was used for population-level modelling. Need has been assumed to be equivalent to estimated new adult AIDS (WHO stage IV) cases between 2004 and 2014, as per the ASSA2003lite AIDS and Demographic Model of the Actuarial Society of South Africa, as downloaded in December 2005 from www.assa.org.za.
Transition probabilities are required to specify all relevant movements between Markov states. In the ART models, these were estimated from Kaplan–Meier product limit estimates of survival for 1729 patients receiving ART in the first 48 months of the Khayelitsha programme and extrapolated thereafter . Transition probabilities for the no-ART model were derived from the Cape Town AIDS Cohort, a local natural history cohort of 981 ART-naive patients [24,25]. The probabilities of dying from non-HIV-related causes were calculated from South African life tables .
Health gains (outcomes) are expressed as both unweighted life-years and QALY. The latter were calculated by weighting life expectancy by a HRQoL factor. Although HIV-positive people on ART have been shown to fare better in terms of both length and quality of life in comparison with those not receiving ART [27,28], life-years have been included to enhance comparability with other studies. HRQoL was measured on a subsample of the same patients , and data were converted to tariffs using time trade-off values from a general population survey in the United Kingdom , and see Cleary et al. .
Uncertainty relating to data requirements has been assessed using probabilistic sensitivity analysis at the patient level. This technique propagates parameter and underlying modelling uncertainty through the model via first and second-order Monte Carlo simulation. First-order simulations track the different paths taken by ‘patients’ through the model in an attempt to capture the variability in the population being simulated. Second-order simulations capture parameter uncertainty; distributions were specified on all transition probabilities and utilization variables and a different value from each is chosen during each simulation. When a number of simulations are run, overall parameter uncertainty is captured as uncertainty intervals around lifetime costs, outcomes and cost-effectiveness ratios [31,32]. For this study, we ran 1000 second-order and 10 000 first-order simulations. Details of the full range of sensitivity analyses are provided elsewhere .
Technical efficiency at the population level
Following Stinnet and Paltiel , population-level efficiency has been assessed using the following objective function:
Equation (Uncited)Image Tools
Equation (Uncited)Image Tools
Where C is the present value of the HIV treatment budget over the planning period; i is an index describing the three interventions under consideration (i = 1,…,n); ci is the present value of the cost of providing intervention i over the planning period; Ei is the present value of the outcomes of intervention i over the planning period; and xi is the percentage implementation of intervention i.
This approach maximizes outcomes subject to a number of constraints. The first ensures that the implementation level of each intervention lies between 0% and 100%. The second ensures that total costs of scaling up lie within the budget. The final constraint ensures that the sum of the interventions implemented cannot exceed 100%. To implement this approach one therefore needs to estimate the total costs and outcomes of each intervention if it were offered to all patients in need.
Per-patient lifetime costs, outcomes, cost-effectiveness and probabilistic sensitivity analysis
Table 1 shows lifetime costs, outcomes and patient-level cost-effectiveness ratios. Undiscounted life-years were 2.9, 8.5 and 12.9 for no-ART, first-line ART and first and second-line ART, respectively, whereas discounted per-patient lifetime costs were US$2743, US$5779 and US$9435. The discounted cost per QALY ratio for first-line ART versus no-ART was US$795, whereas first and second-line ART costs US$1625 per QALY gained versus first-line ART only. These ratios are lower when costs and effects are discounted at a zero rate or when outcomes are life-years. The results of probabilistic sensitivity analysis, presented as 95% uncertainty intervals, reveal distinct differences in lifetime costs, outcomes and cost-effectiveness ratios for each intervention.
New AIDS cases and patients remaining in alternative treatment interventions
According to South African demographic modelling, 500 000 adults will develop AIDS annually over the projection period. Figure 1 shows the number of patients surviving and remaining in care if universal access is provided to each HIV treatment intervention. If all patients receive no-ART, 1.3 million patients would be in care by 2014; if all patients receive first-line ART, 2.8 million patients would be in care; and if all patients receive first and second-line ART, 3.3 million would be in care.
Total costs and quality-adjusted life-years for universal access
Figure 2 presents discounted cumulative costs and QALY for universal access to each HIV treatment intervention between 2004 and 2014. By the end of this period, the total cost of first and second-line ART would be US$12.5 billion for a gain of 12 million QALY. First-line ART only would have cumulative costs of US$11 billion for 10.5 million QALY, whereas no-ART would cost just over US$7.6 billion for 5 million QALY. Clinical personnel and patient-specific resources would be US$8.5 billion for first and second-line ART, US$7 billion for first-line ART only and US$2.6 billion for no-ART.
Technical efficiency at the population level
Table 2 compares the total QALY and proportion of patients who could be treated if the entire budget were devoted to each HIV treatment intervention on an exclusive basis. This contrasts with Table 3, in which the health-maximizing choice of intervention(s) is presented. As Table 2 shows, a high proportion of need is unmet in all strategies if the budget is low. Universal access to no-ART can be achieved at a budget of US$8 billion, whereas US$11–13 billion would be required for universal access to first-line only or first and second-line ART, respectively. Although more costly, first and second-line ART achieves the largest health gains.
Table 3 shows how a strategy's efficiency changes as the budget increases. No-ART is never efficient– it never maximizes health gains at any budget level. In contrast, first-line ART is the most efficient strategy if the budget is between US$1 and US$10 billion over the planning period. Whereas an individual patient would not receive more than one intervention, strategies can be mixed at the population level. Therefore for budgets greater than US$11 billion, sufficient resources are available to place a proportion of patients on first and second-line ART.
Even if domestic budgets are supplemented by donor funding, HIV treatment programmes will be limited by the scarcity of resources such as clinical personnel and infrastructure. Over the planning period, if real South African healthcare budgets maintain their 2004 levels [33,34] and 20% of this budget (US$9 billion) is allocated to HIV treatment, then a health-maximizing strategy would provide first-line treatment to only 83% of patients in need. If one-third of the budget is allocated to HIV treatment, however, it would be feasible to place all patients on first and second-line ART.
A word of caution is, however, necessary. Annual HIV treatment costs increase rapidly. By 2014, the annual cost of universal access to no-ART would be US$0.9 billion, first-line only would be US$1.6 billion and first and second-line ART would be US$2.1 billion, or 20, 37 and 47%, respectively, of the 2004 healthcare budget. By comparison, in 2006 annual treatment costs consumed between 14 and 16% of this budget. The rapid annual increase in HIV treatment costs requires that governments and donors are aware of this dynamic and plan accordingly.
When assessing the efficiency of HIV treatment interventions in developing countries, the most common approach in the literature [5–8] has involved comparing the cost per QALY ratio to the gross domestic product per capita of the country in question . Most policy makers in developing countries are, however, most concerned about the costs of scaling up programmes. The implication is that critical decisions are frequently made without any consideration of the relative cost-effectiveness of alternative treatment strategies.
This paper recommends an alternative approach that considers both the total costs of scaling up and the health gains achieved by providing each of three interventions to a given number of patients. Armed with this information, policy makers can assess the intervention or combination of interventions that will maximize the health gains of people with HIV/AIDS, or expressed differently how much of currently unmet need can be addressed. As has been shown, if the HIV treatment budget is US$8 billion over the planning period, the most efficient strategy is to place three-quarters of eligible patients on first-line ART, for a gain of 7.8 million QALY. At the same budget, first and second-line ART treats only two-thirds of patients and gains 400 000 fewer QALY. Expressing the choices in this way is more accessible to policy makers. It makes the trade-off explicit between restricting treatment to a first-line regimen only, treating more people and achieving greater health outcomes overall, versus providing both first and second-line treatment to fewer people with more limited overall health gains. The latter option also raises difficult equity questions in terms of which patients would be prioritized for treatment. A population-level analysis can also help justify increasing HIV budgets, particularly if a government is committed to achieving universal access to the antiretroviral programmes it offers.
This approach has a number of strengths. First, it is more consistent with the theoretical roots of cost-effectiveness/utility analyses than the QALY threshold approach [10,11]. Second, because comparisons between interventions are made at the population level, the full costs of treatment over the planning period, the total health gains and the proportion of need that can be met is explicit. This also allows an assessment of the annual costs of treatment, which assists in HIV treatment budgeting and planning.
There are a number of limitations to this work. First, we have taken a public healthcare perspective; although this is debated [36–38] it is commonly argued that the societal perspective is most appropriate . There are also shortcomings in the costing approach. We have assumed that the unit cost (long-run average total cost) is a proxy for the marginal cost, which is the correct cost statistic to use in economic evaluation . Using the long-run average total cost means assuming that production takes place at the lowest point on this schedule where the marginal and average costs intersect, or that there are constant returns to scale. Whether or not this is the case is an empirical question that this article has not been able to assess, although we have reported the results of variations in the level of costs in an earlier publication . In addition, although our patient data are drawn from one of the largest cohorts available, we have not been able to assess whether these are generalizable to the general population of HIV-positive people in need. Similarly, facilities in which costing was undertaken were purposively sampled, which is a shortcoming.
Although we have focussed on technical efficiency, service providers often face a complex set of challenges of which resource allocation is only one. These challenges to providing universal access to ART often relate to the availability of staff, facilities and programme management, as well as patient-level considerations such as the tolerability of regimens and adherence. For clinicians who have accompanied their patients on the journey back to health, the notion of curtailing an individual's treatment in the interests of greater population-level gains is usually unpopular. Nevertheless, there are examples of national programmes that have opted for less effective protocols in the interests of greater population-level gains . Although service and patient-level factors should be important parts of programme design, we believe that technical efficiency at the population level is an essential consideration.
In conclusion, given the massive burden of providing HIV treatment, universal access will be impossible without considering the costs of scaling up. As increasing numbers of patients are successfully maintained in care, the annual costs of treatment will rise commensurately. Although assessing the costs of scaling up is valuable for informing budgets, it does not by itself gauge which treatment options are efficient. This paper has proposed a method for setting priorities that simultaneously takes account of both the relative efficiency of strategies and the budget required for their delivery.
Sponsorship: This research was supported by a grant from the Health Systems Trust (grant no. 302/02). There are no conflicts of interest.
Conflicts of interest: None.
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