A framework for cost-effectiveness analysis from clinical trial data

Flexible Bayesian longitudinal models for cost-effectiveness analyses with informative missing data

Cost-effectiveness analyses (CEA) are recommended to include sensitivity analyses which make a range of contextually plausible assumptions about missing data. However, with longitudinal data on, for example, patients' health-related quality of life (HRQoL), the missingness patterns can be complicated because data are often missing both at specific timepoints (interim missingness) and following loss to follow-up. Methods to handle these complex missing data patterns have not been developed for CEA, and must recognize that data may be missing not at random, while accommodating both the correlation between costs and health outcomes and the non-normal distribution of these endpoints. We develop flexible Bayesian longitudinal models that allow the impact of interim missingness and loss to follow-up to be disentangled. This modeling framework enables studies to undertake sensitivity analyses according to various contextually plausible missing data mechanisms, jointly model costs and outcomes using appropriate distributions, and recognize the correlation among these endpoints over time. We exemplify these models in the REFLUX study in which 52% of participants had HRQoL data missing for at least one timepoint over the 5-year follow-up period. We provide guidance for sensitivity analyses and accompanying code to help future studies handle these complex forms of missing data.

A Bayesian Framework for Patient-Level Partitioned Survival Cost-Utility Analysis

Patient-level health economic data collected alongside clinical trials are an important component of the process of technology appraisal. For end-of-life treatments, the modeling of cost-effectiveness data may involve some form of partitioned survival analysis, in which measures of quality of life and survival for pre- and postprogression periods are combined to generate aggregate measures of clinical benefits (e.g., quality-adjusted survival). In addition, resource use data are often collected and costs are calculated for each type of health service (e.g., treatment, hospital, or adverse events costs). A critical problem in these analyses is that effectiveness and cost data present some complexities, such as nonnormality, spikes, and missingness, which should be addressed using appropriate methods to avoid biased results. This article proposes a general Bayesian framework that takes into account the complexities of trial-based partitioned survival cost-utility data to provide more adequate evidence for policy makers. Our approach is motivated by, and applied to, a working example based on data from a trial assessing the cost-effectiveness of a new treatment for patients with advanced non-small-cell lung cancer.[Box: see text].

Cost-effectiveness analysis of domiciliary topical sevoflurane for painful leg ulcers

Objectives

The general anesthetic sevoflurane is being repurposed as a topical analgesic for painful chronic wounds. We conducted a Bayesian cost-effectiveness analysis (CEA) comparing the addition of domiciliary topical sevoflurane to conventional analgesics (SEVOFLURANE, n = 38) versus conventional analgesics alone (CONVENTIONAL, n = 26) for the treatment of nonrevascularizable painful leg ulcers in an outpatient Pain Clinic of a Spanish tertiary hospital.

Methods

We used real-world data collected from charts to conduct this CEA from a public healthcare perspective and with a one-year time horizon. Costs of analgesics, visits and admissions were considered, expressed in €2016. Analgesic effectiveness was measured with SPID (Sum of Pain Intensity Difference). A Bayesian regression model was constructed, including “treatment” and baseline characteristics for patients (“arterial hypertension”) and ulcers (“duration”, “number”, “depth”, “pain”) as covariates. The findings were summarized as a cost-effectiveness plane and a cost-effectiveness acceptability curve. One-way sensitivity analyses, a re-analysis excluding those patients who died or suffered from leg amputation, and an extreme scenario analysis were conducted to reduce uncertainty.

Results

Compared to CONVENTIONAL, SEVOFLURANE was associated with a 46% reduction in costs, and the mean incremental effectiveness (28.15±3.70 effectiveness units) was favorable to SEVOFLURANE. The estimated probability for SEVOFLURANE being dominant was 99%. The regression model showed that costs were barely influenced by any covariate, whereas effectiveness was noticeably influenced by “treatment”. All sensitivity analyses showed the robustness of the model, even in the extreme scenario analysis against SEVOFLURANE.

Conclusions

SEVOFLURANE was dominant over CONVENTIONAL as it was less expensive and much more effective.

Joint Longitudinal Models for Dealing With Missing at Random Data in Trial-Based Economic Evaluations

OBJECTIVES

In trial-based economic evaluation, some individuals are typically associated with missing data at some time point, so that their corresponding aggregated outcomes (eg, quality-adjusted life-years) cannot be evaluated. Restricting the analysis to the complete cases is inefficient and can result in biased estimates, while imputation methods are often implemented under a missing at random (MAR) assumption. We propose the use of joint longitudinal models to extend standard approaches by taking into account the longitudinal structure to improve the estimation of the targeted quantities under MAR.

METHODS

We compare the results from methods that handle missingness at an aggregated (case deletion, baseline imputation, and joint aggregated models) and disaggregated (joint longitudinal models) level under MAR. The methods are compared using a simulation study and applied to data from 2 real case studies.

RESULTS

Simulations show that, according to which data affect the missingness process, aggregated methods may lead to biased results, while joint longitudinal models lead to valid inferences under MAR. The analysis of the 2 case studies support these results as both parameter estimates and cost-effectiveness results vary based on the amount of data incorporated into the model.

CONCLUSIONS

Our analyses suggest that methods implemented at the aggregated level are potentially biased under MAR as they ignore the information from the partially observed follow-up data. This limitation can be overcome by extending the analysis to a longitudinal framework using joint models, which can incorporate all the available evidence.

Bayesian Regression Model for a Cost-Utility and Cost-Effectiveness Analysis Comparing Punch Grafting Versus Usual Care for the Treatment of Chronic Wounds

Punch grafting is a traditional technique used to promote epithelialization of hard-to-heal wounds. The main purpose of this observational study was to conduct a cost-utility analysis (CUA) and a cost-effectiveness analysis (CEA) comparing punch grafting (n = 46) with usual care (n = 34) for the treatment of chronic wounds in an outpatient specialized wound clinic from a public healthcare system perspective (Spanish National Health system) with a three-month time horizon. CUA outcome was quality-adjusted life years (QALYs) calculated from EuroQoL-5D, whereas CEA outcome was wound-free period. One-way sensitivity analyses, extreme scenario analysis, and re-analysis by subgroups were conducted to fight against uncertainty. Bayesian regression models were built to explore whether differences between groups in costs, wound-free period, and QALYs could be explained by other variables different to treatment. As main results, punch grafting was associated with a reduction of 37% in costs compared to usual care, whereas mean incremental utility (0.02 ± 0.03 QALYs) and mean incremental effectiveness (7.18 ± 5.30 days free of wound) were favorable to punch grafting. All sensitivity analyses proved the robustness of our models. To conclude, punch grafting is the dominant alternative over usual care because it is cheaper and its utility and effectiveness are greater.

The importance of accounting for the uncertainty around the preference-based health-related quality-of-life measures value sets: a systematic review

Preference-based measures of health-related quality-of-life including, but not limited to, the EQ-5D, HUI2 and the SF-6D have been increasingly used in calculations of quality-adjusted life years for cost effectiveness analyses. However, the uncertainty around the measures' value sets is commonly ignored in economic evaluation. There are several types of uncertainties, including methodological, structural, and parameter uncertainties, with the latter being the focus of this review paper. The objective is to highlight the gap in the literature regarding the existence of uncertainty in the value sets, focusing mainly on the EQ-5D and SF-6D. To the best of the authors' knowledge, this is the first systematic review revolving around uncertainty. After searching extensively for studies involving uncertainties in all preference-based measures, the results showed that uncertainty has been approached through different means, while parameter uncertainty has been ignored in most, if not all, cases. These findings suggest that uncertainty should be accounted for when using preference-based measures in economic evaluations. Ignoring this additional information could impact misleadingly on policy decisions.

A full Bayesian model to handle structural ones and missingness in economic evaluations from individual-level data

Economic evaluations from individual-level data are an important component of the process of technology appraisal, with a view to informing resource allocation decisions. A critical problem in these analyses is that both effectiveness and cost data typically present some complexity (eg, nonnormality, spikes, and missingness) that should be addressed using appropriate methods. However, in routine analyses, standardised approaches are typically used, possibly leading to biassed inferences. We present a general Bayesian framework that can handle the complexity. We show the benefits of using our approach with a motivating example, the MenSS trial, for which there are spikes at one in the effectiveness and missingness in both outcomes. We contrast a set of increasingly complex models and perform sensitivity analysis to assess the robustness of the conclusions to a range of plausible missingness assumptions. We demonstrate the flexibility of our approach with a second example, the PBS trial, and extend the framework to accommodate the characteristics of the data in this study. This paper highlights the importance of adopting a comprehensive modelling approach to economic evaluations and the strategic advantages of building these complex models within a Bayesian framework.

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.

Choice of statistical model for cost-effectiveness analysis and covariate adjustment: empirical application of prominent models and assessment of their results

CONTEXT

Statistical models employed in analysing patient-level cost and effectiveness data need to be flexible enough to adjust for any imbalanced covariates, account for correlations between key parameters, and accommodate potential skewed distributions of costs and/or effects. We compare prominent statistical models for cost-effectiveness analysis alongside randomised controlled trials (RCTs) and covariate adjustment to assess their performance and accuracy using data from a large RCT.

METHOD

Seemingly unrelated regressions, linear regression of net monetary benefits, and Bayesian generalized linear models with various distributional assumptions were used to analyse data from the TASMINH2 trial. Each model adjusted for covariates prognostic of costs and outcomes.

RESULTS

Cost-effectiveness results were notably sensitive to model choice. Models assuming normally distributed costs and effects provided a poor fit to the data, and potentially misleading inference. Allowing for a beta distribution captured the true incremental difference in effects and changed the decision as to which treatment is preferable.

CONCLUSIONS

Our findings suggest that Bayesian generalized linear models which allow for non-normality in estimation offer an attractive tool for researchers undertaking cost-effectiveness analyses. The flexibility provided by such methods allows the researcher to analyse patient-level data which are not necessarily normally distributed, while at the same time it enables assessing the effect of various baseline covariates on cost-effectiveness results.

Total ankle replacement versus arthrodesis (TARVA): protocol for a multicentre randomised controlled trial

INTRODUCTION

Total ankle replacement (TAR) or ankle arthrodesis (fusion) is the main surgical treatments for end-stage ankle osteoarthritis (OA). The popularity of ankle replacement is increasing while ankle fusion rates remain static. Both treatments have efficacy but to date all studies comparing the 2 have been observational without randomisation, and there are no published guidelines as to the most appropriate management. The TAR versus arthrodesis (TARVA) trial aims to compare the clinical and cost-effectiveness of TAR against ankle arthrodesis in the treatment of end-stage ankle OA in patients aged 50-85 years.

METHODS AND ANALYSIS

TARVA is a multicentre randomised controlled trial that will randomise 328 patients aged 50-85 years with end-stage ankle arthritis. The 2 arms of the study will be TAR or ankle arthrodesis with 164 patients in each group. Up to 16 UK centres will participate. Patients will have clinical assessments and complete questionnaires before their operation and at 6, 12, 26 and 52 weeks after surgery. The primary clinical outcome of the study is a validated patient-reported outcome measure, the Manchester Oxford foot questionnaire, captured preoperatively and 12 months after surgery. Secondary outcomes include quality-of-life scores, complications, revision, reoperation and a health economic analysis.

ETHICS AND DISSEMINATION

The protocol has been approved by the National Research Ethics Service Committee (London, Bloomsbury 14/LO/0807). This manuscript is based on V.5.0 of the protocol. The trial findings will be disseminated through peer-reviewed publications and conference presentations.

TRIAL REGISTRATION NUMBER

NCT02128555.

A Bayesian Approach to Net Health Benefits: An Illustration and Application to Modeling HIV Prevention

Purpose. To conduct a cost-effectiveness analysis of HIV prevention when costs and effects cannot be measured directly. To quantify the total estimation of uncertainty due to sampling variability as well as inexact knowledge of HIV transmission parameters. Methods. The authors focus on estimating the incremental net health benefit (INHB) in a randomized trial of HIV prevention with intervention and control conditions. Using a Bernoulli model of HIV transmission, changes in the participants’ risk behaviors are converted into the number of HIV infections averted. A sampling model is used to account for variation in the behavior measurements. Bayes’s theorem and Monte Carlo methods are used to attain the stated objectives. Results. The authors obtained a positive mean INHB of 0.0008, indicating that advocacy training is just slightly favored over the control condition for men, assuming a $50,000 per quality-adjusted life year (QALY) threshold. To be confident of a positive INHB, the decision maker would need to spend more than $100,000 per QALY.

Expected Value of Sample Information Calculations in Medical Decision Modeling

There has been an increasing interest in using expected value of information (EVI) theory in medical decision making, to identify the need for further research to reduce uncertainty in decision and as a tool for sensitivity analysis. Expected value of sample information (EVSI) has been proposed for determination of optimum sample size and allocation rates in randomized clinical trials. This article derives simple Monte Carlo, or nested Monte Carlo, methods that extend the use of EVSI calculations to medical decision applications with multiple sources of uncertainty, with particular attention to the form in which epidemiological data and research findings are structured. In particular, information on key decision parameters such as treatment efficacy are invariably available on measures of relative efficacy such as risk differences or odds ratios, but not on model parameters themselves. In addition, estimates of model parameters and of relative effect measures in the literature may be heterogeneous, reflecting additional sources of variation besides statistical sampling error. The authors describe Monte Carlo procedures for calculating EVSI for probability, rate, or continuous variable parameters in multi parameter decision models and approximate methods for relative measures such as risk differences, odds ratios, risk ratios, and hazard ratios. Where prior evidence is based on a random effects meta-analysis, the authors describe different ESVI calculations, one relevant for decisions concerning a specific patient group and the other for decisions concerning the entire population of patient groups. They also consider EVSI methods for new studies intended to update information on both baseline treatment efficacy and the relative efficacy of 2 treatments. Although there are restrictions regarding models with prior correlation between parameters, these methods can be applied to the majority of probabilistic decision models. Illustrative worked examples of EVSI calculations are given in an appendix.

Estimating the expected value of partial perfect information in health economic evaluations using integrated nested Laplace approximation

The Expected Value of Perfect Partial Information (EVPPI) is a decision‐theoretic measure of the ‘cost’ of parametric uncertainty in decision making used principally in health economic decision making. Despite this decision‐theoretic grounding, the uptake of EVPPI calculations in practice has been slow. This is in part due to the prohibitive computational time required to estimate the EVPPI via Monte Carlo simulations. However, recent developments have demonstrated that the EVPPI can be estimated by non‐parametric regression methods, which have significantly decreased the computation time required to approximate the EVPPI. Under certain circumstances, high‐dimensional Gaussian Process (GP) regression is suggested, but this can still be prohibitively expensive. Applying fast computation methods developed in spatial statistics using Integrated Nested Laplace Approximations (INLA) and projecting from a high‐dimensional into a low‐dimensional input space allows us to decrease the computation time for fitting these high‐dimensional GP, often substantially. We demonstrate that the EVPPI calculated using our method for GP regression is in line with the standard GP regression method and that despite the apparent methodological complexity of this new method, R functions are available in the package BCEA to implement it simply and efficiently. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Randomised, single-masked non-inferiority trial of femtosecond laser-assisted versus manual phacoemulsification cataract surgery for adults with visually significant cataract: the FACT trial protocol

INTRODUCTION

Cataract is one of the leading causes of low vision in the westernised world, and cataract surgery is one of the most commonly performed operations. Laser platforms for cataract surgery are now available, the anticipated advantages of which are broad and may include better visual outcomes through greater precision and reproducibility, and improved safety. FACT is a randomised single masked non-inferiority trial to establish whether laser-assisted cataract surgery is as good as or better than standard manual phacoemulsification.

METHODS AND ANALYSIS

808 patients aged 18 years and over with visually significant cataract will be randomised to manual phacoemulsification cataract surgery (standard care) or laser-assisted cataract surgery (intervention arm). Outcomes will be measured at 3 and 12 months after surgery. The primary clinical outcome is uncorrected distance visual acuity (UDVA, logMAR) at 3 months in the study eye recorded by an observer masked to the trial group. Secondary outcomes include UDVA at 12 months, corrected distance visual acuity at 3 and 12 months, complications, endothelial cell loss, patient-reported outcome measures and a health economic analysis conforming to National Institute for Health and Care Excellence standards.

ETHICS AND DISSEMINATION

Research Ethics Committee Approval was obtained on 6 February 2015, ref: 14/LO/1937. Current protocol: v2.0 (08/04/2015). Study findings will be published in peer-reviewed journals.

ISRCTN

77602616.

A cost-utility analysis of a rehabilitation service for people living with and beyond cancer

BACKGROUND

We conducted a wait-list control randomised trial of an outpatient rehabilitation service for people living with and beyond cancer, delivered in a hospice day care unit. We report the results of an economic evaluation undertaken using the trial data.

METHODS

Forty-one participants were recruited into the study. A within-trial stochastic cost-utility analysis was undertaken using Monte-Carlo simulation. The outcome measure for the economic evaluation was quality adjusted life years (QALYs). Costs were measured from the perspective of the NHS and personal social services. Uncertainty in the observed data was captured through probabilistic sensitivity analysis. Scenario analysis was conducted to explore the effects of changing the way QALYs were estimated and adjusting for baseline difference in the population. We also explore assumptions about the length of treatment benefit being maintained.

RESULTS

The incremental cost-effectiveness ratio (ICER) for the base-case analysis was £14,231 per QALY. When QALYs were assumed to change linearly over time, this increased to £20,514 per QALY at three months. Adjusting the estimate of QALYs to account for differences in the population at baseline increased the ICER to £94,748 per QALY at three months. Increasing the assumed length of treatment benefit led to reduced ICERs in all scenarios.

CONCLUSIONS

Although the intervention is likely to be cost-effective in some circumstances, there is considerable uncertainty surrounding the decision to implement the service. Further research, informed by a formal value of information analysis, would reduce this uncertainty.

Value of information analysis optimizing future trial design from a pilot study on catheter securement devices

Background:

Value of information analysis has been proposed as an alternative to the standard hypothesis testing approach, which is based on type I and type II errors, in determining sample sizes for randomized clinical trials. However, in addition to sample size calculation, value of information analysis can optimize other aspects of research design such as possible comparator arms and alternative follow-up times, by considering trial designs that maximize the expected net benefit of research, which is the difference between the expected cost of the trial and the expected value of additional information.

Purpose:

To apply value of information methods to the results of a pilot study on catheter securement devices to determine the optimal design of a future larger clinical trial.

Methods:

An economic evaluation was performed using data from a multi-arm randomized controlled pilot study comparing the efficacy of four types of catheter securement devices: standard polyurethane, tissue adhesive, bordered polyurethane and sutureless securement device. Probabilistic Monte Carlo simulation was used to characterize uncertainty surrounding the study results and to calculate the expected value of additional information. To guide the optimal future trial design, the expected costs and benefits of the alternative trial designs were estimated and compared.

Results:

Analysis of the value of further information indicated that a randomized controlled trial on catheter securement devices is potentially worthwhile. Among the possible designs for the future trial, a four-arm study with 220 patients/arm would provide the highest expected net benefit corresponding to 130% return-on-investment. The initially considered design of 388 patients/arm, based on hypothesis testing calculations, would provide lower net benefit with return-on-investment of 79%.

Limitations:

Cost-effectiveness and value of information analyses were based on the data from a single pilot trial which might affect the accuracy of our uncertainty estimation. Another limitation was that different follow-up durations for the larger trial were not evaluated.

Conclusion:

The value of information approach allows efficient trial design by maximizing the expected net benefit of additional research. This approach should be considered early in the design of randomized clinical trials.

Bayesian models for cost-effectiveness analysis in the presence of structural zero costs

Bayesian modelling for cost-effectiveness data has received much attention in both the health economics and the statistical literature, in recent years. Cost-effectiveness data are characterised by a relatively complex structure of relationships linking a suitable measure of clinical benefit (e.g. quality-adjusted life years) and the associated costs. Simplifying assumptions, such as (bivariate) normality of the underlying distributions, are usually not granted, particularly for the cost variable, which is characterised by markedly skewed distributions. In addition, individual-level data sets are often characterised by the presence of structural zeros in the cost variable. Hurdle models can be used to account for the presence of excess zeros in a distribution and have been applied in the context of cost data. We extend their application to cost-effectiveness data, defining a full Bayesian specification, which consists of a model for the individual probability of null costs, a marginal model for the costs and a conditional model for the measure of effectiveness (given the observed costs). We presented the model using a working example to describe its main features. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.

The cost of generalized anxiety disorder in primary care settings: results of the ANCORA study

To assess the cost of illness of generalized anxiety disorder (GAD) in a primary healthcare setting in Spain. A cross-sectional, retrospective study was conducted. The sample comprised patients diagnosed with GAD according to ICD-10 criteria and a control group. Healthcare/non-healthcare resource utilization was recorded retrospectively for the 12 months prior to the study visit. Costs were estimated from a societal perspective. Two models have been produced to study the variables that influence the cost of the illness both, without and with controls. The study enrolled 456 patients [76.8 % women, 49.2 (17.0) years] with GAD and 74 controls without GAD [42.5 % women, 47.9 (16.7) years]. 67.8 % of subjects were on combination therapy (antidepressant + anxiolytic); 6 % were using 2 or more drugs to treat anxiety; and 23.4 % were on monotherapy. Total annual average costs were higher in the GAD group (€7,739 vs. €2,609), with mean costs attributable to GAD of €5,139 (healthcare costs: €1,329, indirect costs: 75 % of total cost, approximately). Age and health status measured by Hamilton Anxiety Rating Scale and clinical global impression were related to costs. The improvements in quality of life measured by EQ-5D index are associated to lower cost. GAD treated in Spanish primary healthcare settings generated considerable healthcare costs and, particularly, loss-of-productivity costs.

Multicriteria optimization model for the study of the efficacy of skin antiaging therapy

The evolution of the cutaneous structure after topical treatment with P63 antiaging complex, assessed with high frequency ultrasound, is studied by means of multicriteria optimization model. Due to the fact that the impact of the treatment may influence the quality of life, a medical index which measures, from this point of view, the efficacy of the treatment is given, also taking into account medical and economical aspects.

Bayesian cost-effectiveness analysis for censored data: an application to antiplatelet therapy

OBJECTIVE

Cost-effectiveness analysis (CEA) on trial-based data has played an important role in pharmacoeconomics. A regression model can be used to account for patient-level heterogeneity throughout covariates adjustment in CEA. However, the estimates from CEA could be biased if ignoring the censoring issue on effectiveness and costs. This study is to propose a regression model to account for both time-to-event effectiveness and cost.

METHODS

A bivariate regression model was proposed to analyze both effectiveness and cost simultaneously, while censored observations were also taken into account. The regression coefficients were estimated using a Bayesian approach by drawing a random sample from their posterior distribution derived from the Markov chain Monte Carlo (MCMC) method. The proposed method was illustrated using empirical data of anti-platelet therapies to the management of cardiovascular diseases for those patients with high risk of gastrointestinal (GI) bleeding, where cost-effectiveness between different therapies was analyzed under both censored and non-censored circumstances, where the effectiveness was defined as the time to re-hospitalization due to GI complications, and the cost was measured by the total drug expenditure.

RESULTS

Under censored circumstances, aspirin plus proton-pump inhibitors (PPIs) was considered more cost-effective than clopidogrel with/without PPIs, as shown in the cost-effectiveness acceptability curve, and clopidogrel was preferred to aspirin for a willingness-to-pay of 89 NTD for delaying 1 day to hospitalization due to GI complications.

CONCLUSIONS

Ignoring censoring problems could possibly bias the results in CEA. This study has provided an appropriate method to conduct regression-based CEA to improve the estimation which serves its purpose for CEA concerns.

LIMITATIONS

The normality assumption for the cost and effectiveness in the bivariate normal regression needs to be examined, and the conclusions may be biased if this assumption is violated. However, when sample size is sufficiently large, a slight deviation from normality would not be a serious problem.

Medicoeconomic index for photo-induced skin cancers

Like in every type of cancer, in skin cancer the efficiency of the medical treatment is very important. In the present paper, a Bayesian model for the management of this disease is given, and a medical index to measure the effectiveness of treatment from medical, economical, and quality of life point of view is presented, taking into account some of the patients characteristics.

Developing appropriate methods for cost-effectiveness analysis of cluster randomized trials

AIM

Cost-effectiveness analyses (CEAs) may use data from cluster randomized trials (CRTs), where the unit of randomization is the cluster, not the individual. However, most studies use analytical methods that ignore clustering. This article compares alternative statistical methods for accommodating clustering in CEAs of CRTs.

METHODS

Our simulation study compared the performance of statistical methods for CEAs of CRTs with 2 treatment arms. The study considered a method that ignored clustering--seemingly unrelated regression (SUR) without a robust standard error (SE)--and 4 methods that recognized clustering--SUR and generalized estimating equations (GEEs), both with robust SE, a "2-stage" nonparametric bootstrap (TSB) with shrinkage correction, and a multilevel model (MLM). The base case assumed CRTs with moderate numbers of balanced clusters (20 per arm) and normally distributed costs. Other scenarios included CRTs with few clusters, imbalanced cluster sizes, and skewed costs. Performance was reported as bias, root mean squared error (rMSE), and confidence interval (CI) coverage for estimating incremental net benefits (INBs). We also compared the methods in a case study.

RESULTS

Each method reported low levels of bias. Without the robust SE, SUR gave poor CI coverage (base case: 0.89 v. nominal level: 0.95). The MLM and TSB performed well in each scenario (CI coverage, 0.92-0.95). With few clusters, the GEE and SUR (with robust SE) had coverage below 0.90. In the case study, the mean INBs were similar across all methods, but ignoring clustering underestimated statistical uncertainty and the value of further research.

CONCLUSIONS

MLMs and the TSB are appropriate analytical methods for CEAs of CRTs with the characteristics described. SUR and GEE are not recommended for studies with few clusters.

Probabilistic sensitivity analysis in health economics

Health economic evaluations have recently become an important part of the clinical and medical research process and have built upon more advanced statistical decision-theoretic foundations. In some contexts, it is officially required that uncertainty about both parameters and observable variables be properly taken into account, increasingly often by means of Bayesian methods. Among these, probabilistic sensitivity analysis has assumed a predominant role. The objective of this article is to review the problem of health economic assessment from the standpoint of Bayesian statistical decision theory with particular attention to the philosophy underlying the procedures for sensitivity analysis.

Regression models for analyzing costs and their determinants in health care: an introductory review

OBJECTIVE

This article aims to describe the various approaches in multivariable modelling of healthcare costs data and to synthesize the respective criticisms as proposed in the literature.

METHODS

We present regression methods suitable for the analysis of healthcare costs and then apply them to an experimental setting in cardiovascular treatment (COSTAMI study) and an observational setting in diabetes hospital care.

RESULTS

We show how methods can produce different results depending on the degree of matching between the underlying assumptions of each method and the specific characteristics of the healthcare problem.

CONCLUSIONS

The matching of healthcare cost models to the analytic objectives and characteristics of the data available to a study requires caution. The study results and interpretation can be heavily dependent on the choice of model with a real risk of spurious results and conclusions.

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.

Handling uncertainty in economic evaluations of patient level data: A review of the use of Bayesian methods to inform health technology assessments

Objectives: Due to potential advantages (e.g., using all available evidence), Bayesian methods have been proposed to assist healthcare decision making. This review provides a detailed description of how Bayesian methods have been applied to economic evaluations of patient level data. The results serve both as a reference and as a means by which to examine the appropriate application of Bayesian methods to inform decision making.

Methods: MEDLINE, EMBASE, and Cochrane Economic Evaluation databases were searched to identify studies, published up to November 2007, meeting three inclusion criteria: (i) the study conducted an economic evaluation, (ii) sampling uncertainty was incorporated using Bayesian methods, (iii) the likelihood function was informed by patient level data from a single source. Data were collected on key study characteristics (e.g., prior distribution, likelihood function, presentation of uncertainty).

Results: The search identified 366 potentially relevant studies, from which 103 studies underwent full-text review. Sixteen studies met the inclusion criteria. Half of the studies used uninformative priors; most studies incorporated the potential dependence between costs and effects, and presented cost-effectiveness acceptability curves. Results were sensitive to changes in the priors and likelihoods.

Conclusions: Limited use of informative priors, among the included studies, gives policy makers little guidance on one of the main benefits of Bayesian methods, the ability to integrate all available evidence to capture the uncertainty inherent in decision making.

A Bayesian model averaging approach for cost-effectiveness analyses

We consider the problem of assessing new and existing technologies for their cost-effectiveness in the case where data on both costs and effects are available from a clinical trial, and we address it by means of the cost-effectiveness acceptability curve. The main difficulty in these analyses is that cost data usually exhibit highly skew and heavy-tailed distributions so that it can be extremely difficult to produce realistic probabilistic models for the underlying population distribution, and in particular to model accurately the tail of the distribution, which is highly influential in estimating the population mean. Here, in order to integrate the uncertainty about the model into the analysis of cost data and into cost-effectiveness analyses, we consider an approach based on Bayesian model averaging: instead of choosing a single parametric model, we specify a set of plausible models for costs and estimate the mean cost with a weighted mean of its posterior expectations under each model, with weights given by the posterior model probabilities. The results are compared with those obtained with a semi-parametric approach that does not require any assumption about the distribution of costs.

A decision-theoretic framework for the application of cost-effectiveness analysis in regulatory processes

Cost-effectiveness analysis (CEA) represents the most important tool in the health economics literature to quantify and qualify the reasoning behind the optimal decision process in terms of the allocation of resources to a given health intervention. However, the practical application of CEA in the regulatory process is often limited by some critical barriers, and decisions in clinical practice are frequently influenced by factors that do not contribute to efficient resource allocation, leading to inappropriate drug prescription and utilization. Moreover, most of the time there is uncertainty about the real cost-effectiveness profile of an innovative intervention, with the consequence that it is usually impossible to obtain an immediate and perfect substitution of a product with another having a better cost-effectiveness ratio. The objective of this article is to propose a rational approach to CEA within regulatory processes, basing our analysis in a Bayesian decision-theoretic framework and proposing an extension of the application of well known tools (such as the expected value of information) to such cases. The regulator can use these tools to identify the economic value of reducing the uncertainty surrounding the cost-effectiveness profile of the several alternatives. This value can be compared with the one that is generated by the actual market share of the different treatment options: one that is the most cost effective and others in the same therapeutic category that, despite producing clinical benefits, are less cost effective.

Incorporating model uncertainty in cost-effectiveness analysis: a Bayesian model averaging approach

Recently, several authors have proposed the use of linear regression models in cost-effectiveness analysis. In this paper, by modelling costs and outcomes using patient and Health Centre covariates, we seek to identify the part of the cost or outcome difference that is not attributable to the treatment itself, but to the patients' condition or to characteristics of the Centres. Selection of the covariates to be included as predictors of effectiveness and cost is usually assumed by the researcher. This behaviour ignores the uncertainty associated with model selection and leads to underestimation of the uncertainty about quantities of interest. We propose the use of Bayesian model averaging as a mechanism to account for such uncertainty about the model. Data from a clinical trial are used to analyze the effect of incorporating model uncertainty, by comparing two highly active antiretroviral treatments applied to asymptomatic HIV patients. The joint posterior density of incremental effectiveness and cost and cost-effectiveness acceptability curves are proposed as decision-making measures.

A comparison of methods for combining quality and efficiency performance measures: profiling the value of hospital care following acute myocardial infarction

Health plans have begun to combine data on the quality and cost of medical providers in an attempt to identify and reward those that offer the greatest 'value.' The analytical methods used to combine these measures in the context of provider profiling have not been rigorously studied. We propose three methods to measure and compare the value of hospital care following acute myocardial infarction by combining a single measure of quality, in-hospital survival, and the cost of an episode of acute care. To illustrate these methods, we use administrative data for heart attack patients treated at 69 acute care hospitals in Massachusetts in fiscal year 2003. In the first method we reproduce a common approach to value profiling by modeling the two case mix-standardized outcomes independently. In the second approach, survival is regressed on patient risk factors and the average cost of care at each hospital. The third method models survival and cost for each hospital jointly and combines the outcomes on a common scale using a cost-effectiveness framework. For each method we use the resulting parameter estimates or functions of the estimates to compute posterior tail probabilities, representing the probability of being classified in the upper or lower quartile of the statewide distribution. Hospitals estimated to have the highest and lowest value according to each method are compared for consistency, and the advantages and disadvantages of each approach are discussed.

Measuring and illustrating statistical evidence in a cost-effectiveness analysis

Recently, there has been much interest in using the cost-effectiveness acceptability curve (CEAC) to measure the statistical evidence of cost-effectiveness. The CEAC has two well established but fundamentally different interpretations: one frequentist and one Bayesian. As an alternative, we suggest characterizing the statistical evidence about cost-effectiveness using the likelihood function (the key element of both approaches). Its interpretation is neither dependent on the sample space nor on the prior distribution. Moreover, the probability of observing misleading evidence is low and controllable, so this approach is justifiable in the traditional sense of frequentist long-run behaviour. We propose a new graphic for displaying the evidence about cost-effectiveness and explore the strengths of likelihood methods using data from an economic evaluation of a Program in Assertive Community Treatment (PACT).

A Cost-Effectiveness Framework for Profiling the Value of Hospital Care

Provider profiling and performance-based incentive programs have expanded in recent years but need a theoretical framework for measuring and comparing the ``value'' of clinical care across medical providers. Cost-effectiveness analysis provides such a framework but has rarely been used outside of the treatment choice context. The authors present a profiling framework based on cost-effectiveness methods and illustrate their approach using data on in-hospital survival and the cost of care for a heart attack from a sample of Massachusetts hospitals during fiscal year 2003. They model each outcome using hierarchical models that allow performance to vary across hospitals as a function of a latent quality effect and an effect of case mix. They also estimate incremental outcomes by conditioning on each hospital's pair of random effects, using indirect standardization to estimate ``expected'' outcomes, and then taking their difference. Incremental cost and effectiveness outcomes are combined using incremental net monetary benefits. Using cost-effectiveness methods to profile hospital ``value'' permits the comparison of the benefit of a service relative to the cost using existing societal weights.

The contrast and convergence of Bayesian and frequentist statistical approaches in pharmacoeconomic analysis

The application of Bayesian statistical analyses has been facilitated in recent years by methodological advances and an increasing complexity necessitated within research. Substantial debate has historically accompanied this analytic approach relative to the frequentist method, which is the predominant statistical ideology employed in clinical studies. While the essence of the debate between the two branches of statistics centres on differences in the use of prior information and the definition of probability, the ramifications involve the breadth of research design, analysis and interpretation. The purpose of this paper is to discuss the application of frequentist and Bayesian statistics in the pharmacoeconomic assessment of healthcare technology. A description of both paradigms is offered in the context of potential advantages and disadvantages, and applications within pharmacoeconomics are briefly addressed. Additional considerations are presented to stimulate further development and to direct appropriate applications of each method such that the integrity and robustness of scientific inference be strengthened.

Cost-effectiveness of surgery plus radiotherapy versus radiotherapy alone for metastatic epidural spinal cord compression

PURPOSE

A recent randomized clinical trial has demonstrated that direct decompressive surgery plus radiotherapy was superior to radiotherapy alone for the treatment of metastatic epidural spinal cord compression. The current study compared the cost-effectiveness of the two approaches.

METHODS AND MATERIALS

In the original clinical trial, clinical effectiveness was measured by ambulation and survival time until death. In this study, an incremental cost-effectiveness analysis was performed from a societal perspective. Costs related to treatment and posttreatment care were estimated and extended to the lifetime of the cohort. Weibull regression was applied to extrapolate outcomes in the presence of censored clinical effectiveness data.

RESULTS

From a societal perspective, the baseline incremental cost-effectiveness ratio (ICER) was found to be $60 per additional day of ambulation (all costs in 2003 Canadian dollars). Using probabilistic sensitivity analysis, 50% of all generated ICERs were lower than $57, and 95% were lower than $242 per additional day of ambulation. This analysis had a 95% CI of -$72.74 to 309.44, meaning that this intervention ranged from a financial savings of $72.74 to a cost of $309.44 per additional day of ambulation. Using survival as the measure of effectiveness resulted in an ICER of $30,940 per life-year gained.

CONCLUSIONS

We found strong evidence that treatment of metastatic epidural spinal cord compression with surgery in addition to radiotherapy is cost-effective both in terms of cost per additional day of ambulation, and cost per life-year gained.

Using the net benefit regression framework to construct cost-effectiveness acceptability curves: an example using data from a trial of external loop recorders versus Holter monitoring for ambulatory monitoring of "community acquired" syncope

Background

Cost-effectiveness acceptability curves (CEACs) describe the probability that a new treatment or intervention is cost-effective. The net benefit regression framework (NBRF) allows cost-effectiveness analysis to be done in a simple regression framework. The objective of the paper is to illustrate how net benefit regression can be used to construct a CEAC.

Methods

One hundred patients referred for ambulatory monitoring with syncope or presyncope were randomized to a one-month external loop recorder (n = 49) or 48-hour Holter monitor (n = 51). The primary endpoint was symptom-rhythm correlation during monitoring. Direct costs were calculated based on the 2003 Ontario Health Insurance Plan (OHIP) fee schedule combined with hospital case costing of labour, materials, service and overhead costs for diagnostic testing and related equipment.

Results

In the loop recorder group, 63.27% of patients (31/49) had symptom recurrence and successful activation, compared to 23.53% in the Holter group (12/51). The cost in US dollars for loop recording was $648.50 and $212.92 for Holter monitoring. The incremental cost-effectiveness ratio (ICER) of the loop recorder was $1,096 per extra successful diagnosis. The probability that the loop recorder was cost-effective compared to the Holter monitor was estimated using net benefit regression and plotted on a CEAC. In a sensitivity analysis, bootstrapping was used to examine the effect of distributional assumptions.

Conclusion

The NBRF is straightforward to use and interpret. The resulting uncertainty surrounding the regression coefficient relates to the CEAC. When the link from the regression's p-value to the probability of cost-effectiveness is tentative, bootstrapping may be used.

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.

How sensitive are cost-effectiveness analyses to choice of parametric distributions?

BACKGROUND

Cost-effectiveness analyses of clinical trial data are based on assumptions about the distributions of costs and effects. Cost data usually have very skewed distributions and can be difficult to model. The authors investigate whether choice of distribution can make a difference to the conclusions drawn.

METHODS

The authors compare 3 distributions for cost data-normal, gamma, and lognormal-using similar parametric models for the cost-effectiveness analyses. Inferences on the cost-effectiveness plane are derived, together with cost-effectiveness acceptability curves. These methods are applied to data from a trial of rapid magnetic resonance imaging (rMRI) investigation in patients with low back pain.

RESULTS

The gamma and lognormal distributions fitted the cost data much better than the normal distribution. However, in terms of inferences about cost-effectiveness, it was the normal and gamma distributions that gave similar results. Using the lognormal distribution led to the conclusion that rMRI was cost-effective for a range of willingness-to-pay values where assuming a gamma or normal distribution did not.

CONCLUSIONS

Conclusions from cost-effectiveness analyses are sensitive to choice of distribution and, in particular, to how the upper tail of the cost distribution beyond the observed data is modeled. How well a distribution fits the data is an insufficient guide to model choice. A sensitivity analysis is therefore necessary to address uncertainty about choice of distribution.

Semi-parametric modelling for costs of health care technologies

Cost data that arise in the evaluation of health care technologies usually exhibit highly skew, heavy-tailed and, possibly, multi-modal distributions. Distribution-free methods for analysing these data, such as the bootstrap, or those based on the asymptotic normality of sample means, may often lead to inefficient or misleading inferences. On the other hand, parametric models that fit the data (or a transformation of the data) equally well can produce very different answers. We consider a Bayesian approach, and model cost data with a distribution composed of a piecewise constant density up to an unknown endpoint, and a generalized Pareto distribution for the remaining tail.

Methods for incorporating covariate adjustment, subgroup analysis and between-centre differences into cost-effectiveness evaluations

BACKGROUND

Overall assessments of cost-effectiveness are now commonplace in informing medical policy decision making. It is often important, however, also to investigate how cost-effectiveness varies between patient subgroups. Yet such analyses are rarely undertaken, because appropriate methods have not been sufficiently developed.

METHODS

We propose a coherent set of Bayesian methods to extend cost-effectiveness analyses to adjust for baseline covariates, to investigate differences between subgroups, and to allow for differences between centres in a multicentre study using a hierarchical model. These methods consider costs and effects jointly, and allow for the typically skewed distribution of cost data. The results are presented as inferences on the cost-effectiveness plane, and as cost-effectiveness acceptability curves.

RESULTS

In applying these methods to a randomised trial of case management of psychotic patients, we show that overall cost-effectiveness can be affected by ignoring the skewness of cost data, but that it may be difficult to gain substantial precision by adjusting for baseline covariates. While analyses of overall cost-effectiveness can mask important subgroup differences, crude differences between centres may provide an unrealistic indication of the true differences between them.

CONCLUSIONS

The methods developed allow a flexible choice for the distributions used for cost data, and have a wide range of applicability--to both randomised trials and observational studies. Experience needs to be gained in applying these methods in practice, and using their results in decision making.

Using covariates to reduce uncertainty in the economic evaluation of clinical trial data

As part of their practice, policymakers have to make economic evaluations using clinical trial data. Recent interest has been expressed in determining how cost-effectiveness analysis can be undertaken in a regression framework. In this respect, published research basically provides a general method for prognostic factor adjustment in the presence of imbalance, emphasizing sub-group analysis. In this paper, we present an alternative method from a Bayesian approach. We propose the use of covariates in Bayesian health technology assessment in order to reduce uncertainty about the effect of treatments. We show its advantages by comparison with another published method that do not adjust for covariates using simulated data.

Bayesian regression models for cost-effectiveness analysis

Recent studies have shown how cost-effectiveness analysis can be undertaken in a regression framework. This contribution explores the use of practical regression models for estimating cost-effectiveness from a Bayesian perspective. Two different Bayesian models are described. The first considers the outcome measure to be a quantitative variable. In the second model the individual outcome measure is a binary variable with value 1 if any objective has been achieved. We describe the implementation of the model using data from a trial that compares two highly active antiretroviral therapies in HIV asymptomatic patients. Data on direct cost and data effectiveness (percentage of patients with undetectable viral load and quality of life) were recorded. If we consider the quality of life as an effectiveness measure, the new treatment is preferred for a willingness to pay more than Euro 142.3 for an increase in the quality of life. For illustrative purposes, if we compare the results with an analogous model that does not include covariates, the critical value becomes Euro 247.4. For the binary measure of effectiveness the control treatment dominates the new treatment.

Bayesian techniques for sample size determination in clinical trials: a short review

The aim of this paper is to review some key techniques of Bayesian methods of sample size determination. The approach is to cover a small number of simple problems, such as estimating the mean of a normal distribution. The methods considered are in two groups: inferential and decision theoretic. In the inferential Bayesian methods of sample size determination, we are solely concerned with the inference about the parameter(s) of interest. The fully Bayesian or decision theoretic approach treats the problem as a decision problem and employs a loss or utility function.

Bayesian approaches to multiple sources of evidence and uncertainty in complex cost-effectiveness modelling

Increasingly complex models are being used to evaluate the cost-effectiveness of medical interventions. We describe the multiple sources of uncertainty that are relevant to such models, and their relation to either probabilistic or deterministic sensitivity analysis. A Bayesian approach appears natural in this context. We explore how sensitivity analysis to patient heterogeneity and parameter uncertainty can be simultaneously investigated, and illustrate the necessary computation when expected costs and benefits can be calculated in closed form, such as in discrete-time discrete-state Markov models. Information about parameters can either be expressed as a prior distribution, or derived as a posterior distribution given a generalized synthesis of available data in which multiple sources of evidence can be differentially weighted according to their assumed quality. The resulting joint posterior distributions on costs and benefits can then provide inferences on incremental cost-effectiveness, best presented as posterior distributions over net-benefit and cost-effectiveness acceptability curves. These ideas are illustrated with a detailed running example concerning the cost-effectiveness of hip prostheses in different age-sex subgroups. All computations are carried out using freely available software for conducting Markov chain Monte Carlo analysis.