Something old,something new,something borrowed,something blue: a framework for the marriage of health econometrics and cost-effectiveness analysis

Economic evaluation is often seen as a branch of health economics divorced from mainstream econometric techniques. Instead, it is perceived as relying on statistical methods for clinical trials. Furthermore, the statistic of interest in cost-effectiveness analysis, the incremental cost-effectiveness ratio is not amenable to regression-based methods, hence the traditional reliance on comparing aggregate measures across the arms of a clinical trial. In this paper, we explore the potential for health economists undertaking cost-effectiveness analysis to exploit the plethora of established econometric techniques through the use of the net-benefit framework - a recently suggested reformulation of the cost-effectiveness problem that avoids the reliance on cost-effectiveness ratios and their associated statistical problems. This allows the formulation of the cost-effectiveness problem within a standard regression type framework. We provide an example with empirical data to illustrate how a regression type framework can enhance the net-benefit method. We go on to suggest that practical advantages of the net-benefit regression approach include being able to use established econometric techniques, adjust for imperfect randomisation, and identify important subgroups in order to estimate the marginal cost-effectiveness of an intervention.     

Bayesian estimation of cost-effectiveness from censored data

We describe a Bayesian methodology for estimating the cost-effectiveness of a new treatment compared to a standard in a clinical trial, when censoring of survival, the effectiveness variable, induces censoring of total cost. The statistical model assumes that survival follows a Weibull distribution and that total health care cost follows a gamma distribution whose mean has a linear regression on survival time. We summarize the posterior distributions of key parameters by importance sampling. We illustrate the method with an analysis of data from a randomized clinical trial of a treatment for cardiovascular disease.     

Regression methods for cost-effectiveness analysis with censored data

A system of seemingly unrelated regression equations is proposed for prognostic factor adjustment and subgroup analysis when comparing two groups in a cost-effectiveness analysis with censored data. Because of the induced dependent censoring on costs and quality-adjusted survival, inverse probability weighting is employed for parameter estimation. The method is illustrated with data from two recent examples using both survival time and quality-adjusted survival time as the measures of effectiveness.     

Estimating the cost-effectiveness of an intervention in a clinical trial when partial cost information is available: a Bayesian approach

There is an increasing need to establish whether health-care interventions are cost effective as well as clinically effective. It is becoming increasingly common for cost studies to be incorporated into clinical trials, either on all patients or more usually on a subset of patients. Establishing the total cost per patient is complex, as it requires information on resource use, which may come from a variety of different sources. This complexity may lead to considerable missing data, and can result in some patients only having partial cost information. In this paper we consider a clinical trial consisting of 351 patients with advanced non-small cell lung cancer comparing chemotherapy with standard palliative care. A subset of 115 patients was selected for the cost sub-study. Total cost was split into four components, for which resource use was collected. Complete resource data were available on 82 patients. For the remaining patients at least one of the cost components was missing. The objective of this paper is to develop a Bayesian approach which simultaneously models both the clinical effectiveness data and the cost data, by modelling the individual components. This also provides estimates of the cost-effectiveness in terms of the Incremental Net Monetary Benefit (INMB) and Cost-Effectiveness Acceptability Curves (CEAC). We compare a number of different models of increasing complexity. The models estimate the interrelationships between the four cost components and survival, and thus enable a predictive distribution for each missing cost item to be obtained.     

Bayesian cost-effectiveness analysis with two measures of effectiveness: the cost-effectiveness acceptability plane

Cost-effectiveness analysis (CEA) compares the costs and outcomes of two or more technologies. However, there is no consensus about which measure of effectiveness should be used in each analysis. Clinical researchers have to select an appropriate outcome for their purpose, and this choice can have dramatic consequences on the conclusions of their analysis. In this paper we present a Bayesian cost-effectiveness framework to carry out CEA when more than one measure is considered. In particular, we analyse the case in which two measures of effectiveness, one binary and the other continuous, are considered. Decision-making measures, such as the incremental cost-effectiveness ratio, incremental net-benefit and cost-effectiveness acceptability curves, are used to compare costs and one measure of outcome. We propose an extension of cost-acceptability curves, namely the cost-effectiveness acceptability plane, as a suitable measure for decision taking. The models were validated using data from two clinical trials. In the first one, we compared four highly active antiretroviral treatments applied to asymptomatic HIV patients. As measures of effectiveness, we considered the percentage of patients with undetectable levels of viral load, and changes in quality of life, measured according to EuroQol. In the second clinical trial we compared three methadone maintenance programmes for opioid-addicted patients. In this case, the measures of effectiveness considered were quality of life, according to the Nottingham Health Profile, and adherence to the treatment, measured as the percentage of patients who participated in the whole treatment programme.     

Representing uncertainty: the role of cost-effectiveness acceptability curves.

Decision-making in health care is inevitably undertaken in a context of uncertainty concerning the effectiveness and costs of health care interventions and programmes. One method that has been suggested to represent this uncertainty is the cost-effectiveness acceptability curve. This technique, which directly addresses the decision-making problem, has advantages over confidence interval estimation for incremental cost-effectiveness ratios. However, despite these advantages, cost-effectiveness acceptability curves have yet to be widely adopted within the field of economic evaluation of health care technologies. In this paper we consider the relationship between cost-effectiveness acceptability curves and decision-making in health care, suggest the introduction of a new concept more relevant to decision-making, that of the cost-effectiveness frontier, and clarify the use of these techniques when considering decisions involving multiple interventions. We hope that as a result we can encourage the greater use of these techniques.     

Non‐parametric methods for cost‐effectiveness analysis: the central limit theorem and the bootstrap compared

Cost‐effectiveness analyses (CEA) alongside randomised controlled trials commonly estimate incremental net benefits (INB), with 95% confidence intervals, and compute cost‐effectiveness acceptability curves and confidence ellipses. Two alternative non‐parametric methods for estimating INB are to apply the central limit theorem (CLT) or to use the non‐parametric bootstrap method, although it is unclear which method is preferable. This paper describes the statistical rationale underlying each of these methods and illustrates their application with a trial‐based CEA. It compares the sampling uncertainty from using either technique in a Monte Carlo simulation. The experiments are repeated varying the sample size and the skewness of costs in the population. The results showed that, even when data were highly skewed, both methods accurately estimated the true standard errors (SEs) when sample sizes were moderate to large (n>50), and also gave good estimates for small data sets with low skewness. However, when sample sizes were relatively small and the data highly skewed, using the CLT rather than the bootstrap led to slightly more accurate SEs. We conclude that while in general using either method is appropriate, the CLT is easier to implement, and provides SEs that are at least as accurate as the bootstrap. Copyright © 2009 John Wiley & Sons, Ltd.     

Bayesian estimation of cost-effectiveness: an importance-sampling approach

We describe a method for estimating the cost-effectiveness of a new treatment compared to a standard, using data from a comparative clinical trial. We quantify the clinical effectiveness as a binary variable indicating success or failure. The underlying statistical model assumes that costs are uncensored and follow separate gamma distributions in each of the groups defined by the four possible combinations of treatment arm and effectiveness outcome. The method is subjectivist, in that it represents prior uncertainty about model parameters with a probability distribution, which we update via Bayes's theorem to produce a posterior distribution. We approximate the posterior by importance sampling, a straightforward simulation method. We illustrate the method with an analysis of cost (derived from resource usage data) and effectiveness (measured by one-year survival) in a clinical trial in heart disease. The example demonstrates that the method is practical and provides for a flexible data analysis.     

A framework for quantifying net benefits of alternative prognostic models

New prognostic models are traditionally evaluated using measures of discrimination and risk reclassification, but these do not take full account of the clinical and health economic context. We propose a framework for comparing prognostic models by quantifying the public health impact (net benefit) of the treatment decisions they support, assuming a set of predetermined clinical treatment guidelines. The change in net benefit is more clinically interpretable than changes in traditional measures and can be used in full health economic evaluations of prognostic models used for screening and allocating risk reduction interventions. We extend previous work in this area by quantifying net benefits in life years, thus linking prognostic performance to health economic measures; by taking full account of the occurrence of events over time; and by considering estimation and cross-validation in a multiple-study setting. The method is illustrated in the context of cardiovascular disease risk prediction using an individual participant data meta-analysis. We estimate the number of cardiovascular-disease-free life years gained when statin treatment is allocated based on a risk prediction model with five established risk factors instead of a model with just age, gender and region. We explore methodological issues associated with the multistudy design and show that cost-effectiveness comparisons based on the proposed methodology are robust against a range of modelling assumptions, including adjusting for competing risks.     

A Bayesian framework for health economic evaluation in studies with missing data

Health economics studies with missing data are increasingly using approaches such as multiple imputation that assume that the data are “missing at random.” This assumption is often questionable, as—even given the observed data—the probability that data are missing may reflect the true, unobserved outcomes, such as the patients' true health status. In these cases, methodological guidelines recommend sensitivity analyses to recognise data may be “missing not at random” (MNAR), and call for the development of practical, accessible approaches for exploring the robustness of conclusions to MNAR assumptions. Little attention has been paid to the problem that data may be MNAR in health economics in general and in cost‐effectiveness analyses (CEA) in particular. In this paper, we propose a Bayesian framework for CEA where outcome or cost data are missing. Our framework includes a practical, accessible approach to sensitivity analysis that allows the analyst to draw on expert opinion. We illustrate the framework in a CEA comparing an endovascular strategy with open repair for patients with ruptured abdominal aortic aneurysm, and provide software tools to implement this approach.     

Regression methods for covariate adjustment and subgroup analysis for non-censored cost-effectiveness data

The current interest in undertaking cost-effectiveness analyses alongside clinical trials has lead to the increasing availability of patient-level data on both the costs and effectiveness of intervention. In a recent paper, we show how cost-effectiveness analysis can be undertaken in a regression framework. In the current paper we develop a direct regression approach to cost-effectiveness analysis by proposing the use of a system of seemingly unrelated regression equations to provide a more general method for prognostic factor adjustment with emphasis on sub-group analysis. This more general method can be used in either an incremental cost-effectiveness or an incremental net-benefit approach, and does not require that the set of independent variables for costs and effectiveness be the same. Furthermore, the method can exhibit efficiency gains over unrelated ordinary least squares regression.     

Longevity bias in cost-effectiveness analysis

We use a simple lifetime utility maximization model to study the problem of medical resource allocation. This model leads to a welfare specification with a QALY (quality-adjusted life-year) component that captures an individual's preferences over both life expectancy and health status. The goal of medical cost-effectiveness analysis (CEA) is characterized as maximizing the QALY measure for a given total medical expenditure. We show that the CEA with such a goal has a longevity bias: the CEA-based division of a given total medical expenditure between extending life and improving health gives the former a larger share than is called for by welfare maximization.     

A propensity score approach to estimating the cost-effectiveness of medical therapies from observational data

Health summary measures are commonly used by policy makers to help make decisions on the allocation of societal resources for competing medical treatments. The net monetary benefit is a health summary measure that overcomes the statistical limitations of a popular measure namely, the cost-effectiveness ratio. We introduce a linear model framework to estimate propensity score adjusted net monetary benefit. This method provides less biased estimates in the presence of significant differences in baseline measures and demographic characteristics between treatment groups in quasi-randomized or observational studies. Simulation studies were conducted to better understand the utility of propensity score adjusted estimates of net monetary benefits when important covariates are unobserved. The results indicated that the propensity score adjusted net monetary benefit provides a robust measure of cost-effectiveness in the presence of hidden bias. The methods are illustrated using data from SEER-Medicare for the treatment of bladder cancer.     

Evidence synthesis from aggregate recurrent event data for clinical trial design and analysis

Information from historical trials is important for the design, interim monitoring, analysis, and interpretation of clinical trials. Meta‐analytic models can be used to synthesize the evidence from historical data, which are often only available in aggregate form. We consider evidence synthesis methods for trials with recurrent event endpoints, which are common in many therapeutic areas. Such endpoints are typically analyzed by negative binomial regression. However, the individual patient data necessary to fit such a model are usually unavailable for historical trials reported in the medical literature. We describe approaches for back‐calculating model parameter estimates and their standard errors from available summary statistics with various techniques, including approximate Bayesian computation. We propose to use a quadratic approximation to the log‐likelihood for each historical trial based on 2 independent terms for the log mean rate and the log of the dispersion parameter. A Bayesian hierarchical meta‐analysis model then provides the posterior predictive distribution for these parameters. Simulations show this approach with back‐calculated parameter estimates results in very similar inference as using parameter estimates from individual patient data as an input. We illustrate how to design and analyze a new randomized placebo‐controlled exacerbation trial in severe eosinophilic asthma using data from 11 historical trials.     

Why cost-effectiveness should trump (clinical) effectiveness: the ethical economics of the South West quadrant

In many health decision making situations there is a requirement that the effectiveness of interventions, usually their 'clinical' effectiveness, be established, as well as their cost-effectiveness. Often indeed this is effectively a prior requirement for their cost-effectiveness being investigated. If, however, one accepts the ethical argument for using a threshold incremental cost-effectiveness ratio (ICER) for interventions that are more effective but more costly (i.e. fall in the NE quadrant of the cost-effectiveness plane), one should apply the same decision rule in the SW quadrant, where the intervention is less effective but less costly. This implication is present in most standard treatments of cost-effectiveness analysis, including recent stochastic versions, and had gone relatively unquestioned within the discipline until the recent suggestion that the ICER threshold might be 'kinked'. A kinked threshold would, O'Brien et al. argue, better reflect the asymmetrical individual preferences found in empirical studies of consumer's willingness to pay and willingness to accept and justify different decision rules in the NE and SW quadrants. We reject the validity of such asymmetric preferences in the context of public health care decisions and consider and counter the two main 'ethical' objections that probably underlie the asymmetry in this case--the objection to 'taking away' and the objection to being required to undergo treatment that is less effective than no treatment at all.     

Estimating mean QALYs in trial-based cost-effectiveness analysis: the importance of controlling for baseline utility

In trial-based cost-effectiveness analysis baseline mean utility values are invariably imbalanced between treatment arms. A patient's baseline utility is likely to be highly correlated with their quality-adjusted life-years (QALYs) over the follow-up period, not least because it typically contributes to the QALY calculation. Therefore, imbalance in baseline utility needs to be accounted for in the estimation of mean differential QALYs, and failure to control for this imbalance can result in a misleading incremental cost-effectiveness ratio. This paper discusses the approaches that have been used in the cost-effectiveness literature to estimate absolute and differential mean QALYs alongside randomised trials, and illustrates the implications of baseline mean utility imbalance for QALY calculation. Using data from a recently conducted trial-based cost-effectiveness study and a micro-simulation exercise, the relative performance of alternative estimators is compared, showing that widely used methods to calculate differential QALYs provide incorrect results in the presence of baseline mean utility imbalance regardless of whether these differences are formally statistically significant. It is demonstrated that multiple regression methods can be usefully applied to generate appropriate estimates of differential mean QALYs and an associated measure of sampling variability, while controlling for differences in baseline mean utility between treatment arms in the trial.     

Bayesian cost-effectiveness analysis from clinical trial data

A key tool for assessing the relative cost-effectiveness of two treatments in health economics is the incremental C/E acceptability curve. We present Bayesian computations for this curve in the case where data on both costs and efficacy are available from a clinical trial. Analysis is given under various formulations of prior information. A case study is analysed in which reasonable prior information is shown to strengthen substantially the posterior inference, leading to a more conclusive assessment of cost-effectiveness. Calculations can be performed using readily available Bayesian software.     

Using propensity scores to estimate the cost-effectiveness of medical therapies

The cost-effectiveness ratio is a popular statistic that is used by policy makers to decide which programs are cost-effective in the public health sector. Recently, the net monetary benefit has been proposed as an alternative statistical summary measure to overcome the limitations associated with the cost-effectiveness ratio. Research on using the net monetary benefit to assess the cost-effectiveness of therapies in non-randomized studies has yet to be done. Propensity scores are useful in estimating adjusted effectiveness of programs that have non-randomized or quasi-experimental designs. This article introduces the use of propensity score adjustment in cost-effectiveness analyses to estimate net monetary benefits for non-randomized studies. The uncertainty associated with the net monetary benefit estimate is evaluated using cost-effectiveness acceptability curves. Our method is illustrated by applying it to SEER-Medicare data for muscle invasive bladder cancer to determine the most cost-effective treatment protocol.     

Discounting health and cost-effectiveness analysis: a response to Nord

Nord (2011) criticizes standard arguments which assert that consistency requires that future health benefits must be discounted at the same rate as future costs in cost-effectiveness analysis (CEA). He suggests these arguments are misguided because they require transitivity of preferences across decision contexts and that it can be appropriate to discount health at different rates depending on the programs to be compared. I claim that rejecting transitivity is unwarranted and would sharply diminish the utility of CEA. Factors that tempt Nord to reject consistency can be accommodated by recognizing that CEA does not perfectly mimic normative social preferences because it omits factors (like distribution of health in a population) that can be normatively significant. A better approach is to maintain consistency in application of CEA but authorize decision makers to depart from rankings implied by CEA when justified and to explain which specific factors justify the decision. Finally, the assertion that health must be discounted at the same rate as costs requires the additional assumption that the dollar value of health does not change over time, a point that is not always recognized in standard arguments.     

Bayesian estimation,simulation and uncertainty analysis: the cost-effectiveness of ganciclovir prophylaxis in liver transplantation

This paper demonstrates the usefulness of combining simulation with Bayesian estimation methods in analysis of cost-effectiveness data collected alongside a clinical trial. Specifically, we use Markov Chain Monte Carlo (MCMC) to estimate a system of generalized linear models relating costs and outcomes to a disease process affected by treatment under alternative therapies. The MCMC draws are used as parameters in simulations which yield inference about the relative cost-effectiveness of the novel therapy under a variety of scenarios. Total parametric uncertainty is assessed directly by examining the joint distribution of simulated average incremental cost and effectiveness. The approach allows flexibility in assessing treatment in various counterfactual premises and quantifies the global effect of parametric uncertainty on a decision-maker's confidence in adopting one therapy over the other.