Mathematical models that integrate information on efficacy, effectiveness, cost of care, and patient-reported outcomes are useful for informing discussions about the comparative effectiveness and efficiency of medical interventions [1–3]. A number of countries require such information to be submitted with applications for licensure of new drugs [4,5], and the recent US focus on the funding of research on comparative effectiveness may be expected to increase the use of modeling in economic studies. However, economic models have inherent strengths and weaknesses that must be considered whenever the results of a model are presented , and standards for performing modeling studies have evolved greatly over the last decade . Thus, whereas there is no one ‘right’ way to model HIV, there are a set of generally accepted guidelines that economic models should meet , and well developed lists of conditions that should be checked  before the results of an economic study are used to inform care or policy choices.
Microeconomic models predict economic and health outcomes for cohorts of patients in the future, based on current data and knowledge. As such they have inherent limitations associated with both the data used and with our understanding of the epidemiology of the modeled condition. Models are simplifications of reality, and modeling results may be biased by the use of inadequate structures and assumptions of the model, and/or by invalid parameters for variables that are included in the model. Thus, it is of utmost importance that the simplifications used in a model not affect the overall study result. There are two main areas of simplification: the way the data are linked together in a mathematical structure; and the parameters used to populate this model structure. A model's structure should be based on a coherent theory about the health condition being modeled, and be consistent with the available evidence on the types of variables being included . The parameters used in a model should be inclusive of the substantive literature of the subject, and include a meta-analysis, if needed .
Three main types of structural approaches may be used in microeconomic modeling: a decision tree, a Markov model, or a discrete event model structure . Decision trees aggregate data according to treatment types and outcomes. Each treatment is assigned to a major branch, with all possible types of outcomes aggregated onto ‘twigs’ on this branch. This type of structure works best for conditions with only a few possible outcomes and are therefore rarely used for HIV models. Markov models organize data according to patients' health state occupation for a specific time. It allows patients to progress through sequentially worse health states as time passes, until they arrive at a permanent health state (often death). Nearly all HIV microeconomic models use this type of organizing framework. A discrete event model assigns specific characteristics to each entity (patient) that enters the model. The patients then pass through a set of treatment paths that reflect our current knowledge of a disease, its treatments and outcomes. The modeling software keeps track of what has happened to patients at specific times. This type of model can use many parameters with well described distributions and specific correlations between variables for prediction, something that is very difficult to accomplish with the other model structures.
The design of an economic model for HIV treatments is a ‘team sport’. It requires knowledge from a number of separate expert fields (medicine, virology, epidemiology, economics, decision science/engineering), and the experts involved must work closely together and come to a joint agreement on which part of each of their scientific areas may safely be simplified for the modeling, without the loss of either face validity or predictive validity . This simplification process was performed in rather similar ways for the early HIV-economic models when our understanding of HIV disease was limited, there were few effective treatments, and life expectancy was relatively low . Thus, most of the early models, although different, were based on a very similar structure with three to five health states defined by CD4 cell count, AIDS status and death [9–12].
As data and knowledge about HIV-treatment effects increased, it became clear that more complex approaches were needed , and a ‘second-generation’ group of models were developed [13–16]. A Markov model structure is used in all of these second-generation models, with 5–13 health states specified by CD4 cell count and viral load combinations and death. All the models assume that patients move through several antiretroviral (ARV) regimens using a lifetime cost horizon, which is the appropriate perspective if HIV/AIDS is considered a chronic condition . The assumptions and details included in the original models have, in later versions of the models, often been extended to incorporate evidence on drug resistance, effects of adherence to ARV regimens, development of short- and long-term adverse events, and/or different versions of HIV/AIDS treatment guidelines.
Each such model extension, however, adds complexity to these already complicated structures, and often results in a loss of model transparency. This situation reduces the usefulness of the model in two important ways. First, difficulty of getting the model information to decision makers increases exponentially with complexity. The model and its results become lengthy and difficult to explain in ways that reviewers and editors can follow, the complex mathematical structure and the parameters used require peer reviewers to have in-depth knowledge of both modeling and of HIV/AIDS, and thorough explanations require more space that most journals allow. Thus, it is becoming common for complex HIV models to have technical appendices that are publicly available [17,18••]. Secondly, decision-makers may not accept the findings of models if they can not intuitively grasp the essence of the model structure and explain it to others .
Recent findings: current economic models in HIV/AIDS
The review focuses, as the other reviews in this special issue, on the recently published literature of the last 12–24 months. Surprisingly, only a limited number of publications dealing with the issue of HIV economic modeling could be identified. Of these the widely published ‘Cost–Effectiveness of Preventing AIDS Complications’ (CEPAC) model was used to compare the impact of three methods of scaling up ARV therapy in South Africa [19•]; the cost–effectiveness of screening vs. not screening for HLA-B*5701 testing for patients initiating first-line therapy with an ARV regimen containing abacavir ; the cost–effectiveness of pre-exposure prophylaxis with in the USA [21•]; and the cost–effectiveness of early vs. late start of ARV in resource-limited settings [22•]. Our second-generation Markov model was used to compare the cost–effectiveness and budget impact of treating antiretroviral-experienced patients with tipranavir, based on the results of the RESIST 1 and 2 studies , and starting ARV-naïve patients on a lopinavir/ritonavir-based regimen vs. an atazanavir- and ritonavir-based regimen based on the CASTLE study results [24•].
A systematic review of economic and quality-of-life outcomes of ARV therapy for HIV/AIDS in developing countries  did not include any modeling studies. However, a recent trend in health economics literature towards use of short-term treatment comparisons using a cost–effectiveness frontier (CEF) [26–28] is reflected in several ARV studies. A CEF analysis uses a graphic approach to compare the cost to achieve a specific health outcome across multiple interventions. This type of comparison provides a very clear picture of the comparative economic advantage of treatments. However, it may be misleading if the health outcome that is used is not a comprehensive measure of health for the condition. A strikingly useful example of a CEF analysis is provided by Hill and Wood  in their analysis of numbers of individuals in Cambodia that can be treated by different drug combinations under a fixed budget assumption. However, a CEF approach was used less successfully to compare ARV regimens in developed countries. It used the cost by CD4 cell count category at 48 weeks for the UK  and the USA . Unfortunately, the use of short-term CD4 cell count improvement as the only measure of health does not capture the impacts of long-term effect differences of viral load, adverse events, and the risk of resistance. Thus, the value of such CEF studies for informing decisions is limited. Others  used a decision tree based on viral load suppression below 400 copies/ml to define effectiveness, and a time horizon of 24 months to compare the cost–effectiveness of ARV regimens in Spain. These findings are neither comprehensive by themselves, nor comparable with any benchmarks for cost–effectiveness. However, a recent study by Linas and colleagues [33••] provides an excellent example of a very useful application of the CEF approach. The authors use a discrete event model to assess outcomes for AIDS drug assistance programs. This study compares outcomes for programs when limited resources result in wait-listing, it defines outcome variables as death or first opportunistic infection occurring over a 5-year time horizon, and does so using a comprehensive modeling approach. However, it is unlikely that the use of CEF approaches will be able replace the information content of classical cost utility models until we agree on which combination of outcome variables captures ‘health’ for HIV patients, and also agree on the best time horizon for examining this aggregate health measure.
To ensure that this review captured all the most recent cost–effectiveness modeling studies for HIV treatments, a set of in-depth searches using known economic modeling authors' names and/or ARV drug names was undertaken. We specifically searched for economic modeling studies that examined newly marketed ARV drugs (raltegravir, maraviroc, darunavir or etravirine). However, we found no peer-reviewed economic modeling study published for any of these drugs in 2008 or 2009 (or in prior years), or any such studies listed as ‘published ahead of print’ in the journals AIDS, JAIDS, Antiviral Therapy, Value in Health or PharmacoEconomics. This was surprising because we found published abstracts and references to poster presentations for darunavir going back as far as 2007 , individual drug review papers with sections that reported on cost–effectiveness , published headlines in pharmacy news summary publications that one regimen ‘dominates’ most other combinations  and reports from the Pharmaceutical Benefits Advisory Committee (PBAC) in Australia , advice documents from the Scottish Medicines Consortium (SMC) , and appraisal reports from the New Medicines Group in Wales (NMGW)  that all summarized the results from economic modeling studies of these ARV drugs.
Unfortunately, it is nearly impossible to perform a thorough assessment of an economic modeling study of competing therapies based on the limited information presented in abstracts, posters, review papers, or summary of advice reports. In most cases, here is simply not enough information presented to make a valid judgment about a model's structural and parametric validity. In a few cases it is clear that a particular model contains assumption that most probably will negatively affect the validity of the modeling results. We found several examples of issues of model structure and choice of parameters in the ‘gray literature’ models that are of concern. One Markov model based the difference in the effects between the competing regimens on the differences observed in the hazard ratio for complete viral load suppression in the intention-to-treat (ITT) analysis from 24 to 96 weeks . This goes counter to the results from epidemiological studies that report failure rates after the first year to decline significantly . The authors of another model reported utility weights for the basic model health state to be 0.85, with the utility values for health state with adverse events assigned a decrement (based on cancer or chronic pain studies) equal to the multiplication of the original health state by the adverse event utility . This resulted in the model using decrements of 0.06 to 0.15 for diarrhea, comparable with the magnitude of the utility decrements reported for UK patients with asthma or stroke . The use of such a decrement is excessive. A recent study reports mean utility decrements of 0.009–0.021 for diarrhea in HIV patients [42,43]. Issues such as these are of great concern, because these types of results are included without comments in drug summaries published in peer-reviewed journals , as well as presented in pharmaceutical news headlines . Models with such problematic assumptions may reflect poorly on the science of economic modeling, and misinform evidence-based discussion about HIV care.
Need for improvement in HIV economic models
The need for modeling economic outcomes in HIV treatments will exist in the foreseeable future, because trials are too short to examine economic effects, and use combinations of surrogate marker endpoints as proxies to compare efficacy. Furthermore, the recent study by Granich and colleagues [44••] on modeling the effects of early diagnosis and treatment with ARV on the future of the epidemic makes a strong argument for the use of comprehensive microeconomic models in HIV for capturing all important economic effects. The current trend towards brief and simplified economic modeling studies (1-year outcomes and decision tree estimates for 2 years) may only partially answer the economic questions relevant for HIV/AIDS treatments. The use of short-term outcomes in cost–effectiveness studies is often driven by the limitations of the available data, and a desire to avoid the use of economic modeling, with its substantial analytical requirements, and attendant limitations. However, with a complex lifelong condition, such as HIV disease, we must consider the long-term combined health and economic effects in our decisions, and only well designed, comprehensive economic models will allow us to extrapolate long term from the available empirical data. Figs 1 and 2 below illustrate why short-term cost–effectiveness studies are not enough. In Fig. 1 we show the estimated cost differences observed in a modeling study for two ARV regimens over the first 10 years of treatment . Clearly, cost differences fluctuate greatly over time, and by 10 years the savings predicted from one regimen have disappeared. These fluctuations are due to the many regimen differences that may affect costs, including drug price, rate of switching to a second regimen, costs of adverse events, number who change to a more expensive regimen, need for viral resistance testing, and differences in combinations of drugs that can be used for salvage therapy. In Fig. 2 we show what happens to cumulative costs after 10 years, if the first ARV regimens have exactly the same cost, but one is 15% more effective in suppressing viral load at 48 weeks. Cumulative costs switch about half way through the expected survival time, and the more effective regimen becomes the most costly, because of the economic ‘penalty’ for survival that is common in costly chronic conditions. Thus, despite a desire for simple, short-term estimates, we need to continue to examine long-term cost–effectiveness of our interventions. However, the current second-generation set of Markov models may be close to the limit of the amount of complexity that they can capture. The economic models used in HIV/AIDS in the future must be able to encompass a tremendous amount of inter-related data. The new models should ideally reflect the effects of lipid changes and allow effects of treatments to manage lipid abnormalities, capture variations in adherence, include the short- and long-term effects of different adverse events on utility values, and easily reflect differences in treatment guidelines. To accomplish this we may have to use a discrete event structure instead of a Markov approach. Whereas such a change is possible , it may require that organizations, such as the National Institute for Health and Clinical Excellence in the United Kingdom (NICE), Pharmaceutical Benefits Advisory Committee of Australia (PBAC), the Scottish Medicines Consortium (SMC) and other regulatory agencies, change their policies to accept this type of model for economic evaluations.
At a minimum, the structure of HIV economic models must be improved to better reflect actual treatment paths instead of reflecting biostatistical efficacy assumptions. Serious work must be done to capture the effects of bias due to the limitations of clinical trial data for modeling; development of resistance to future regimens; short- and long-term adverse events; additive risks of exposure to ARV, such as lipodystrophy and lipoatrophy, and risks, such as cholesterol increases, that increase as patients age; effects of fixed dose combinations, including partial regimen adherence; and correlation between patient adherence, viral suppression, resistance development and study dropout. Ideally, models would also be able to capture economic effects external to the individual patient, such as effects of differences in viral transmissions to uninfected individuals. This development may require us to abandon the Markov model structure and switch to using a discrete event structure that uses parameters with well described distributions and specified correlations between variables for prediction.
It is important that the issue of bias due to the limitations of clinical trial data for modeling is dealt with in an appropriate manner. Most current models assume that patients who drop out of a study have failed therapy, and some assume that the failure rate recorded during the first 24–96 weeks of a trial is the appropriate rate to use for all subsequent time periods . This flawed structural assumption persists despite evidence that shows that failure rates decline over time . The structure of future models must allow no-penalty switching and early cross-over between regimens. It is tempting to define an economic model that compares ARV regimens as a ‘cost efficacy’ model to get around the issue, that the biostatistical approach to the analysis of trial data is not well suited for an economic analysis. The unquestioned use of ITT, ‘missing equals failure’, in HIV treatment models is problematic when patients in real practice may be switched to a new therapy if they do not do well on the original regimen. If there is no penalty, such as the risk of resistance associated with the switch, then it does not result in faster progression to failure of the second regimen, it only generates visit and testing costs. The use of early trial discontinuation rates for later years, as was the case for the model used for the approval of ATV in Scotland , is contradicted by published epidemiological data that indicates that switching rates decline markedly over time . However, this assumption persists in many ARV models because reviewers fail to recognize its great potential for induction of bias into the estimates.
Surrogate endpoints consisting of measures of viral load suppression and CD4 cell count improvement have been used in ARV clinical trials since the approval of saquinavir in 1995, and most economic models to date use them to define Markov model health states. However, nearly all published models assume that the trial randomization results in an unbiased baseline distribution of these two key measures. This situation is not always the case, and such an assumption may have a seriously biasing effect, which is especially important if a Markov model is used. In a recent modeling study based on the ACTG 5142 data we found an unbalanced randomization in favor of lopinavir/r that affected the baseline distribution of patients among the combined viral load and CD4 cell count-defined health states. When we controlled for this bias by stratified random sampling of observations within each baseline strata, the incremental cost–effectiveness ratio (ICER) for lopinavir/r worsened by 32% .
The inclusion of adverse events is also an issue because long-term adverse event effects are becoming much more important. Improved models should attempt to implement the effects of adverse events as they are actually experienced, which means linking them to dropouts or switching patients, separating adverse events into acute or chronic events that are manageable or refractory to treatment. No double counting, such as including both costs of treatment to alleviate adverse events, and utility penalties for the condition. This area is one in which modeling can do much to inform practice. The statistical reporting of adverse event effects in HIV clinical trials is minimal, and focused on reporting of safety issues mainly associate with severe and life-threatening events, as well as on events that have very different rates for the regimens that are compared in the study. The problem with the adverse event analysis for new regimens is that it has to be performed against an enormous amount of background ‘noise’ related to the plethora of signs, symptoms and clinical events that patients with HIV disease experience. We recently performed a detailed analysis of adverse event data from one 96-week long clinical trial of about 700 ARV-naïve patients (Simpson, unpublished data). The data set had more than 15 000 individual observations of events, and even though standard coding was used, all the detailed descriptions of adverse events were recorded as free text. Thus we saw hundreds of different ways that events were described. In addition, there were a substantial number of events with no start date or with no end date, which made it difficult to estimate the duration of the event accurately. However, it was clear that very few ARs lasted the full length of the study, and most had a less than 90 days mean duration. Thus, economic modeling studies that apply a marginal disutility of different adverse event rates for competing regimens to a fixed proportion of patients in an economic model are likely to overestimate the effect of most of the adverse evens. This may seem like a minor issue, but it can have major implications in economic models of regimens used in ARV-naïve patients. This is because today's excellent initial ARV regimens may be expected to last a median time between 5 and 7 years. Thus, a utility decrement of 0.05 that is applied to 10–20% of the population in one arm of the model may have a large impact in models in which the predicted differences between regimens may be on the order of 0.2 QALYs.
The recent results of the modeling study by Granich and colleagues [44••] require us to reconsider our approach to limit HIV-treatment models to the treated individuals. Indeed, the use of a discrete event modeling framework would make it possible to estimate the effect of viral suppression on the size of the infected population over time. We would not need a detailed transmission model to incorporate this variable into a current model. The inclusion of a specific transmission variable based on reasonable parameters, and a summary output of total new HIV infections, and a global ‘new cases’ cost estimate for each therapy, would go far to illustrate the potential effects, if any, that competing therapies may have on this important outcome.
Few new economic modeling studies have been published in the peer-reviewed literature during the last 12–24 months, and most of those use validated second-generation Markov models to assess the economic effects of different treatment policy or drug choices. This fact is despite a large number of abstracts, posters presented at international HIV meetings, and many modeling results submitted to drug-approval authorities. The quality of modeling studies in the ‘gray’ literature varies greatly, and is difficult to assess due to the complexity require by second-generation modeling in HIV/AIDS. There is a great need to move on to a set of third-generation models in order to capture the many effects of new knowledge that is emerging about treatments. However, the new models must be carefully designed and transparent, or they may be of little value for informing decisions. The recent trend towards using simple decision trees or cost and consequences models, including cost–effectiveness frontier analyses, does not appear to be a good solution to the increasingly complex economic modeling required in HIV disease. These abbreviated types of studies could contribute valuable information if they were used together with classical cost utility models, and, if we can begin to agree on how effectiveness should be defined, and at which time point it should be measured. Until that time, these simplistic modeling approaches are likely to obscure the need for the consideration of both short-term budget impacts and long-term cost–effectiveness that should be weighted when decisions are made. Thus, economic models in HIV/AIDS are likely to become more complex if we adhere to good modeling standards, use the appropriate structures, and test the uncertainty of both the models' structure and parameters in a probabilistic manner. However, we have the tools available to make the new generation of economic models in HIV/AIDS both valid and transparent to decision makers.
I have received speaker fees or consultation payments for work related to the economics of antiretroviral drugs from Abbott, Pfizer, Bohringer Ingleheim, Glaxo Welcome, Tibotec, and Roche.
References and recommended reading
Papers of particular interest, published within the annual period of review, have been highlighted as:
• of special interest
•• of outstanding interest
Additional references related to this topic can also be found in the Current World Literature section in this issue (p. 263).
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Keywords:© 2010 Lippincott Williams & Wilkins, Inc.
cost–effectiveness; economics; HIV; modeling