Bayesian methods for design and analysis of cost-effectiveness trials in the evaluation of health care technologies

A scoping review of statistical methods for trial-based economic evaluations: The current state of play

The statistical quality of trial-based economic evaluations is often suboptimal, while a comprehensive overview of available statistical methods is lacking. Therefore, this review summarized and critically appraised available statistical methods for trial-based economic evaluations. A literature search was performed to identify studies on statistical methods for dealing with baseline imbalances, skewed costs and/or effects, correlated costs and effects, clustered data, longitudinal data, missing data and censoring in trial-based economic evaluations. Data was extracted on the statistical methods described, their advantages, disadvantages, relative performance and recommendations of the study. Sixty-eight studies were included. Of them, 27 (40%) assessed methods for baseline imbalances, 39 (57%) assessed methods for skewed costs and/or effects, 27 (40%) assessed methods for correlated costs and effects, 18 (26%) assessed methods for clustered data, 7 (10%) assessed methods for longitudinal data, 26 (38%) assessed methods for missing data and 10 (15%) assessed methods for censoring. All identified methods were narratively described. This review provides a comprehensive overview of available statistical methods for dealing with the most common statistical complexities in trial-based economic evaluations. Herewith, it can provide valuable input for researchers when deciding which statistical methods to use in a trial-based economic evaluation.

Using informative prior based on expert opinion in Bayesian estimation of the transition probability matrix in Markov modelling-an example from the cost-effectiveness analysis of the treatment of patients with predominantly negative symptoms of schizophrenia with cariprazine

Background

When patient health state transition evidence is missing from clinical literature, analysts are inclined to make simple assumptions to complete the transition matrices within a health economic model. Our aim was to provide a solution for estimating transition matrices by the Bayesian statistical method within a health economic model when empirical evidence is lacking.

Methods

We used a previously published cost-effectiveness analysis of the use of cariprazine compared to that of risperidone in patients with predominantly negative symptoms of schizophrenia. We generated the treatment-specific state transition probability matrices in three different ways: (1) based only on the observed clinical trial data; (2) based on Bayesian estimation where prior transition probabilities came from experts’ opinions; and (3) based on Bayesian estimation with vague prior transition probabilities (i.e., assigning equal prior probabilities to the missing transitions from one state to the others). For the second approach, we elicited Dirichlet prior distributions by three clinical experts. We compared the transition probability matrices and the incremental quality-adjusted life years (QALYs) across the three approaches.

Results

The estimates of the prior transition probabilities from the experts were feasible to obtain and showed considerable consistency with the clinical trial data. As expected, the estimated health benefit of the treatments was different when only the clinical trial data were considered (QALY difference 0.0260), its combination with the experts’ beliefs were used in the economic model (QALY difference 0.0253), and when vague prior distributions were used (QALY difference 0.0243).

Conclusions

Imputing zeros to missing transition probabilities in Markov models might be untenable from the clinical perspective and may result in inappropriate estimates. Bayesian statistics provides an appropriate framework for imputing missing values without making overly simple assumptions. Informative priors based on expert opinions might be more appropriate than vague priors.

Estimating the cost of caring for people with cancer at the end of life: A modelling study

BACKGROUND

People with advanced cancer require a range of health, social and informal care during the final phases of life. The cost of providing care to this group as they approach the end of their lives is unknown, but represents a significant cost to health and social care systems, charities patients and their families.

AIM

In this study, we estimate the direct and indirect costs for lung, breast, colorectal and prostate cancer patients at the end of life (from the start of strong opioids to death) in England and Wales.

METHODS

We use a modelling-based approach to estimate the costs of care. Data are estimated from the literature and publicly available data sets. Probabilistic sensitivity analysis is used to reflect uncertainty in model estimates.

RESULTS

Total estimated costs for treating people with these four cancers at the end of life are £ 641 million. Breast and prostate cancer patients have the highest expected cost per person at £ 12,663 (95% credible interval (CI): £ 1249-£ 38,712) and £ 14,859 (95% CI: £ 1391-£ 46,424), respectively. Lung cancer has the highest expected total cost (£ 226 m). The value of informal care giving accounts for approximately one-third of all costs.

CONCLUSION

The cost to society of providing care to people at the end of their lives is significant. Much of this cost is borne by informal care givers. The cost to formal care services of replacing this care with paid care giving would be significant and demand for care will increase as the demographic profile of the population ages.

Bayesian sample sizes for exploratory clinical trials comparing multiple experimental treatments with a control

In this paper, a Bayesian approach is developed for simultaneously comparing multiple experimental treatments with a common control treatment in an exploratory clinical trial. The sample size is set to ensure that, at the end of the study, there will be at least one treatment for which the investigators have a strong belief that it is better than control, or else they have a strong belief that none of the experimental treatments are substantially better than control. This criterion bears a direct relationship with conventional frequentist power requirements, while allowing prior opinion to feature in the analysis with a consequent reduction in sample size. If it is concluded that at least one of the experimental treatments shows promise, then it is envisaged that one or more of these promising treatments will be developed further in a definitive phase III trial. The approach is developed in the context of normally distributed responses sharing a common standard deviation regardless of treatment. To begin with, the standard deviation will be assumed known when the sample size is calculated. The final analysis will not rely upon this assumption, although the intended properties of the design may not be achieved if the anticipated standard deviation turns out to be inappropriate. Methods that formally allow for uncertainty about the standard deviation, expressed in the form of a Bayesian prior, are then explored. Illustrations of the sample sizes computed from the new method are presented, and comparisons are made with frequentist methods devised for the same situation.

Bayesian methods for setting sample sizes and choosing allocation ratios in phase II clinical trials with time-to-event endpoints

Conventional phase II trials using binary endpoints as early indicators of a time-to-event outcome are not always feasible. Uveal melanoma has no reliable intermediate marker of efficacy. In pancreatic cancer and viral clearance, the time to the event of interest is short, making an early indicator unnecessary. In the latter application, Weibull models have been used to analyse corresponding time-to-event data. Bayesian sample size calculations are presented for single-arm and randomised phase II trials assuming proportional hazards models for time-to-event endpoints. Special consideration is given to the case where survival times follow the Weibull distribution. The proposed methods are demonstrated through an illustrative trial based on uveal melanoma patient data. A procedure for prior specification based on knowledge or predictions of survival patterns is described. This enables investigation into the choice of allocation ratio in the randomised setting to assess whether a control arm is indeed required. The Bayesian framework enables sample sizes consistent with those used in practice to be obtained. When a confirmatory phase III trial will follow if suitable evidence of efficacy is identified, Bayesian approaches are less controversial than for definitive trials. In the randomised setting, a compromise for obtaining feasible sample sizes is a loss in certainty in the specified hypotheses: the Bayesian counterpart of power. However, this approach may still be preferable to running a single-arm trial where no data is collected on the control treatment. This dilemma is present in most phase II trials, where resources are not sufficient to conduct a definitive trial.

The impact of using informative priors in a Bayesian cost-effectiveness analysis: an application of endovascular versus open surgical repair for abdominal aortic aneurysms in high-risk patients

BACKGROUND

Bayesian methods have been proposed as a way of synthesizing all available evidence to inform decision making. However, few practical applications of the use of Bayesian methods for combining patient-level data (i.e., trial) with additional evidence (e.g., literature) exist in the cost-effectiveness literature. The objective of this study was to compare a Bayesian cost-effectiveness analysis using informative priors to a standard non-Bayesian nonparametric method to assess the impact of incorporating additional information into a cost-effectiveness analysis.

METHODS

Patient-level data from a previously published nonrandomized study were analyzed using traditional nonparametric bootstrap techniques and bivariate normal Bayesian models with vague and informative priors. Two different types of informative priors were considered to reflect different valuations of the additional evidence relative to the patient-level data (i.e., "face value" and "skeptical"). The impact of using different distributions and valuations was assessed in a sensitivity analysis. Models were compared in terms of incremental net monetary benefit (INMB) and cost-effectiveness acceptability frontiers (CEAFs).

RESULTS

The bootstrapping and Bayesian analyses using vague priors provided similar results. The most pronounced impact of incorporating the informative priors was the increase in estimated life years in the control arm relative to what was observed in the patient-level data alone. Consequently, the incremental difference in life years originally observed in the patient-level data was reduced, and the INMB and CEAF changed accordingly.

CONCLUSIONS

The results of this study demonstrate the potential impact and importance of incorporating additional information into an analysis of patient-level data, suggesting this could alter decisions as to whether a treatment should be adopted and whether more information should be acquired.

Bayesian cohort and cross-sectional analyses of the PINCER trial: a pharmacist-led intervention to reduce medication errors in primary care

Background

Medication errors are an important source of potentially preventable morbidity and mortality. The PINCER study, a cluster randomised controlled trial, is one of the world’s first experimental studies aiming to reduce the risk of such medication related potential for harm in general practice. Bayesian analyses can improve the clinical interpretability of trial findings.

Methods

Experts were asked to complete a questionnaire to elicit opinions of the likely effectiveness of the intervention for the key outcomes of interest - three important primary care medication errors. These were averaged to generate collective prior distributions, which were then combined with trial data to generate Bayesian posterior distributions. The trial data were analysed in two ways: firstly replicating the trial reported cohort analysis acknowledging pairing of observations, but excluding non-paired observations; and secondly as cross-sectional data, with no exclusions, but without acknowledgement of the pairing. Frequentist and Bayesian analyses were compared.

Findings

Bayesian evaluations suggest that the intervention is able to reduce the likelihood of one of the medication errors by about 50 (estimated to be between 20% and 70%). However, for the other two main outcomes considered, the evidence that the intervention is able to reduce the likelihood of prescription errors is less conclusive.

Conclusions

Clinicians are interested in what trial results mean to them, as opposed to what trial results suggest for future experiments. This analysis suggests that the PINCER intervention is strongly effective in reducing the likelihood of one of the important errors; not necessarily effective in reducing the other errors. Depending on the clinical importance of the respective errors, careful consideration should be given before implementation, and refinement targeted at the other errors may be something to consider.

Guidelines for conducting and reporting economic evaluation of fall prevention strategies

Falls in older people result in substantial health burden. Compelling evidence indicates that falls can be prevented. We developed comprehensive guidelines for economic evaluations of fall prevention interventions to facilitate publication of high-quality economic evaluations of the effective strategies and aid decision making.

INTRODUCTION

The importance of economics applied to falls and fall prevention in older people has largely been overlooked. The use of different methodologies to assess the costs and health benefits of the interventions and their comparators and the inconsistent reporting in the studies limits the usefulness of these economic evaluations for decision making. We developed guidelines to encourage and facilitate completion of high-quality economic evaluations of effective fall prevention strategies.

METHODS

We used a generic checklist for economic evaluations as a platform to develop comprehensive guidelines for conducting and reporting economic evaluations of fall prevention strategies. We considered the many challenges involved, particularly in identifying, measuring, and valuing the relevant cost items.

RESULTS

We recommend researchers include cost outcomes and report incremental cost-effectiveness ratios in terms of falls prevented and quality adjusted life years in all clinical trials of fall prevention interventions. Studies should include the following cost categories: (1) implementing the intervention, (2) delivering the comparator group intervention, (3) total health care costs, (4) costs of fall-related health care resource use, and (5) personal and informal carer opportunity costs.

CONCLUSIONS

This paper provides a timely benchmark to promote comparability and consistency for conducting and reporting economic evaluations of fall prevention strategies.

Methods to elicit experts' beliefs over uncertain quantities: application to a cost effectiveness transition model of negative pressure wound therapy for severe pressure ulceration

We can use decision models to estimate cost effectiveness, quantify uncertainty regarding the adoption decision and provide estimates of the value of further research. In many cases, the existence of only limited data with which to populate a decision model can mean that a cost-effectiveness analysis either does not proceed or may misrepresent the degree of uncertainty associated with model inputs. An example is the case of negative pressure wound therapy (NPWT) used to treat severe pressure ulceration, for which the evidence base is limited and sparse. There is, however, substantial practical experience of using this treatment and its comparators. We can capture this knowledge quantitatively to inform a cost-effectiveness model by eliciting beliefs from experts. This paper describes the design and conduct of an elicitation exercise to generate estimates of multiple uncertain model inputs and validate analytical assumptions for a decision model on the use of NPWT. In designing the exercise, the primary focus was the use of elicitation to inform decision models (multistate models), where representations of uncertain beliefs need to be probabilistically coherent. This paper demonstrates that it is feasible to collect formally elicited evidence to inform decision models.

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.

Complementing the net benefit approach: a new framework for Bayesian cost-effectiveness analysis

OBJECTIVES

The aim of cost-effectiveness analysis is to maximize health benefits from a given budget, taking a societal perspective. Consequently, the comparison of alternative treatments or technologies is solely based on their expected effectiveness and cost. However, the expectation, or mean, poses important limitations as it might be a poor summary of the underlying distribution, for instance when the effectiveness is a categorical variable, or when the distributions of either effectiveness or cost present a high degree of asymmetry. Clinical variables often present these characteristics.

METHODS

In this study, we present a framework for cost-effectiveness analysis based on the whole posterior distribution of effectiveness and cost.

RESULTS

An application with real data is included to illustrate the analysis. Decision-making measures such as the incremental cost-effectiveness ratio, incremental net-benefit, and cost-effectiveness acceptability curves, can also be defined under the new framework.

CONCLUSIONS

This framework overcomes limitations of the mean and offers complementary information for the decision maker.

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.

Cost-effectiveness of palliation of unresectable esophageal cancer

INTRODUCTION

Different modalities of palliation for obstructive symptoms in patients with unresectable esophageal cancer (EC) exist. However, these therapeutic alternatives have significant differences in costs and effectiveness.

METHODS

A Markov model was designed to compare the cost-effectiveness (CE) of self-expandable stent (SES), brachytherapy and laser in the palliation of unresectable EC. Patients were assigned to one of the strategies, and the improvement in swallowing function was compared given the treatment efficacy, probability of survival, and risks of complications associated to each strategy. Probabilities and parameters for distribution were based on a 9-month time frame.

RESULTS

Under the base-case scenario, laser has the lowest CE ratio, followed by brachytherapy at an incremental cost-effectiveness ratio (ICER) of $4,400.00, and SES is a dominated strategy. In the probabilistic analysis, laser is the strategy with the highest probability of cost-effectiveness for willingness to pay (WTP) values lower than $3,201 and brachytherapy for all WTP yielding a positive net health benefit (NHB) (threshold $4,440). The highest probability of cost-effectiveness for brachytherapy is 96%, and consequently, selection of suboptimal strategies can lead to opportunity losses for the US health system, ranging from US$ 4.32 to US$ 38.09 million dollars over the next 5-20 years.

CONCLUSION

Conditional to the WTP and current US Medicare costs, palliation of unresectable esophageal cancers with brachytherapy provides the largest amount of NHB and is the strategy with the highest probability of CE. However, some level of uncertainly remains, and wrong decisions will be made until further knowledge is acquired.

Bayesian sample size for exploratory clinical trials incorporating historical data

This paper presents a simple Bayesian approach to sample size determination in clinical trials. It is required that the trial should be large enough to ensure that the data collected will provide convincing evidence either that an experimental treatment is better than a control or that it fails to improve upon control by some clinically relevant difference. The method resembles standard frequentist formulations of the problem, and indeed in certain circumstances involving 'non-informative' prior information it leads to identical answers. In particular, unlike many Bayesian approaches to sample size determination, use is made of an alternative hypothesis that an experimental treatment is better than a control treatment by some specified magnitude. The approach is introduced in the context of testing whether a single stream of binary observations are consistent with a given success rate p(0). Next the case of comparing two independent streams of normally distributed responses is considered, first under the assumption that their common variance is known and then for unknown variance. Finally, the more general situation in which a large sample is to be collected and analysed according to the asymptotic properties of the score statistic is explored.

The choice of sample size: a mixed Bayesian / frequentist approach

Sample size computations are largely based on frequentist or classical methods. In the Bayesian approach the prior information on the unknown parameters is taken into account. In this work we consider a fully Bayesian approach to the sample size determination problem which was introduced by Grundy et al. and developed by Lindley. This approach treats the problem as a decision problem and employs a utility function to find the optimal sample size of a trial. Furthermore, we assume that a regulatory authority, which is deciding on whether or not to grant a licence to a new treatment, uses a frequentist approach. We then find the optimal sample size for the trial by maximising the expected net benefit, which is the expected benefit of subsequent use of the new treatment minus the cost of the trial.

Cost-effectiveness analysis using data from multinational trials: the use of bivariate hierarchical modeling

Health care cost-effectiveness analysis (CEA) often uses individual patient data (IPD) from multinational randomized controlled trials. Although designed to account for between-patient sampling variability in the clinical and economic data, standard analytical approaches to CEA ignore the presence of between-location variability in the study results. This is a restrictive limitation given that countries often differ in factors that could affect the results of CEAs, such as the availability of health care resources, their unit costs, clinical practice, and patient case mix. The authors advocate the use of Bayesian bivariate hierarchical modeling to analyze multinational cost-effectiveness data. This analytical framework explicitly recognizes that patient-level costs and outcomes are nested within countries. Using real-life data, the authors illustrate how the proposed methods can be applied to obtain (a) more appropriate estimates of overall cost-effectiveness and associated measure of sampling uncertainty compared to standard CEA and (b) country-specific cost-effectiveness estimates that can be used to assess the between-location variability of the study results while controlling for differences in country-specific and patient-specific characteristics. It is demonstrated that results from standard CEA using IPD from multinational trials display a large degree of variability across the 17 countries included in the analysis, producing potentially misleading results. In contrast, "shrinkage estimates'' obtained from the modeling approach proposed here facilitate the appropriate quantification of country-specific cost-effectiveness estimates while weighting the results based on the level of information available within each country. The authors suggest that the methods presented here represent a general framework for the analysis of economic data collected from different locations.

Bayesian statistics in medicine: a 25 year review

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.

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.

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.

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.

Estimating Incremental Cost-Effectiveness Ratios and Their Confidence Intervals with Differentially Censored Data

With medical costs escalating over recent years, cost analysis is being conducted more and more to assess economic impact of new treatment options. An incremental cost-effectiveness ratio (ICER) is a measure that assesses the additional cost for a new treatment for each additional unit of effectiveness, such as saving 1 year of life. In this article, we consider cost-effectiveness analysis for new treatments evaluated in a randomized clinical trial setting with staggered entries. In particular, the censoring times are different for cost and survival data. We propose a method for estimating the ICER and obtaining its confidence interval when differential censoring exists. Simulation experiments are conducted to evaluate our proposed method. We also apply our methods to a clinical trial example comparing the cost-effectiveness of implanted defibrillators with conventional therapy for individuals with reduced left ventricular function after myocardial infarction.

Bayesian evidence synthesis to extrapolate survival estimates in cost-effectiveness studies

This paper is concerned with survival extrapolation that represents an integral part of cost-effectiveness analysis. In the absence of long-term survival estimates from randomized clinical trials or meta-analysis we show how age-sex matched U.K. population data can additionally be used to estimate survival patterns. We adopt a Bayesian approach and we synthesize evidence from different sources such as patient registries, U.K. population statistics and meta-analyses. We also present methodology for Bayesian analysis of the additive hazards model and we show how to apply the techniques using freely available software. The methods are illustrated using data from a cohort of cardiac arrhythmia patients.

Collection of health-economic data alongside clinical trials: is there a future for piggyback evaluations?

OBJECTIVE

The objective of this article is to discuss issues surrounding the conduct of "piggyback evaluations," in which health-economic data are collected within an otherwise typical clinical trial.

METHODS

We review the methodologic literature on piggyback economic evaluations, as well as selected empiric studies. We summarize the challenges encountered in the conduct of these studies, alternative ways of addressing these challenges, and their future role in pharmacoeconomic research.

RESULTS

Piggyback evaluations have certain advantages over other types of pharmacoeconomic studies. An economic evaluation can benefit from the experimental design that maximizes the trial's internal validity, and it is often more practical to collect economic data alongside a trial rather than to fund a stand-alone economic study. However, piggyback evaluations are subject to problems deriving from the competing nature of clinical versus economic study objectives, which can give rise to tension in such fundamental aspects of study design as the selection of study subjects and sites; the extent of protocol-mandated health-care services; and the determination of sample size, length of follow-up, and the study comparator(s). Many solutions have been put forth in the literature to address these challenges.

CONCLUSIONS

Piggyback evaluations can be an appropriate means to measure the economic impact of medical interventions, provided that the methodologic challenges are acknowledged and addressed within the context of each individual study. As long as a desire for patient-level data from clinical trials exists, there will be a need for piggyback economic evaluations in the future.

Role of pharmacoeconomic analysis in R&D decision making: when, where, how?

Pharmacoeconomics is vitally important to drug manufacturers in terms of communicating to external decision-makers (payers, prescribers, patients) the value of their products, achieving regulatory and reimbursement approval and contributing to commercial success. Since development of new drugs is long, costly and risky, and decisions must be made how to allocate considerable research and development (R&D) resources, pharmacoeconomics also has an essential role informing internal decision-making (within a company) during drug development. The use of pharmacoeconomics in early development phases is likely to enhance the efficiency of R&D resource use and also provide a solid foundation for communicating product value to external decision-makers further downstream, increasing the likelihood of regulatory (reimbursement) approval and commercial success. This paper puts the case for use of pharmacoeconomic analyses earlier in the development process and outlines five techniques (clinical trial simulation [CTS], option pricing [OP], investment appraisal [IA], threshold analysis [TA] and value of information [VOI] analysis) that can provide useful input into the design of clinical development programmes, portfolio management and optimal pricing strategy. CTS can estimate efficacy and tolerability profiles before clinical data are available. OP can show the value of different clinical programme designs, sequencing of studies and stop decisions. IA can compare expected net present value (NPV) of different product profiles or study designs. TA can be used to understand development drug profile requirements given partial data. VOI can assist risk management by quantifying uncertainty and assessing the economic viability of gathering further information on the development drug. No amount of pharmacoeconomic data can make a bad drug good; what it can do is enhance the drug developers understanding of the characteristics of that drug. Decision-making, in light of this information, is likely to be better than that without it, whether it leads to faster termination of uneconomic projects or the allocation of more appropriate resources to attractive projects.

Economic endpoints in clinical trials

Healthcare decision makers are increasingly requesting information on the cost and cost-effectiveness of new medicines at the time of product launch. In order to provide this information, data on healthcare resource utilization and, in some cases, costs, may be collected in clinical trials. In this paper, we discuss some of the issues statisticians need to address when it is appropriate to include these economic endpoints in the trial. Several design issues are discussed, including the alternative types of and methods for collecting economic endpoint data, sample size and generalizability. Alternative approaches in the analysis of resource utilization, cost and cost-effectiveness are also presented. Finally, several of the analytic approaches are applied to actual data from a clinical trial.

Allowing for imprecision of the intracluster correlation coefficient in the design of cluster randomized trials

The sample size required for a cluster randomized trial depends on the magnitude of the intracluster correlation coefficient (ICC). The usual sample size calculation makes no allowance for the fact that the ICC is not known precisely in advance. We develop methods which allow for the uncertainty in a previously observed ICC, using a variety of distributional assumptions. Distributions for the power are derived, reflecting this uncertainty. Further, the observed ICC in a future study will not equal its true value, and we consider the impact of this on power. We implement calculations within a Bayesian simulation approach, and provide one simplification that can be performed using simple simulation within spreadsheet software. In our examples, recognizing the uncertainty in a previous ICC estimate decreases expected power, especially when the power calculated naively from the ICC estimate is high. To protect against the possibility of low power, sample sizes may need to be very substantially increased. Recognizing the variability in the future observed ICC has little effect if prior uncertainty has already been taken into account. We show how our method can be extended to the case in which multiple prior ICC estimates are available. The methods presented in this paper can be used by applied researchers to protect against loss of power, or to choose a design which reduces the impact of uncertainty in the ICC.