Power and sample size in cost-effectiveness analysis

Power and sample size calculation for incremental net benefit in cost effectiveness analyses with applications to trials conducted by the Canadian Cancer Trials Group

BACKGROUND

Historically, a priori power and sample size calculations have not been routinely performed cost-effectiveness analyses (CEA), partly because the absence of published cost and effectiveness correlation and variance data, which are essential for power and sample size calculations. Importantly, the empirical correlation between cost and effectiveness has not been examined with respect to the estimation of value-for-money in clinical literature. Therefore, it is not well established if cost-effectiveness studies embedded within randomized-controlled-trials (RCTs) are under- or over-powered to detect changes in value-for-money. However, recently guidelines (such as those from ISPOR) and funding agencies have suggested sample size and power calculations should be considered in CEAs embedded in clinical trials.

METHODS

We examined all RCTs conducted by the Canadian Cancer Trials Group with an embedded cost-effectiveness analysis. Variance and correlation of effectiveness and costs were derived from original-trial data. The incremental net benefit method was used to calculate the power of the cost-effectiveness analysis, with exploration of alternative correlation and willingness-to-pay values.

RESULTS

We identified four trials for inclusion. We observed that a hypothetical scenario of correlation coefficient of zero between cost and effectiveness led to a conservative estimate of sample size. The cost-effectiveness analysis was under-powered to detect changes in value-for-money in two trials, at willingness-to-pay of $100,000. Based on our observations, we present six considerations for future economic evaluations, and an online program to help analysts include a priori sample size and power calculations in future clinical trials.

CONCLUSION

The correlation between cost and effectiveness had a potentially meaningful impact on the power and variance of value-for-money estimates in the examined cost-effectiveness analyses. Therefore, the six considerations and online program, may facilitate a priori power calculations in embedded cost-effectiveness analyses in future clinical trials.

Adding emollient bath additives to standard eczema management for children with eczema: the BATHE RCT

BACKGROUND

Childhood eczema is very common. Treatment often includes emollient bath additives, despite there being little evidence of their effectiveness.

OBJECTIVES

To determine the clinical effectiveness and cost-effectiveness of emollient bath additives in the management of childhood eczema.

DESIGN

Pragmatic, randomised, open-label, multicentre superiority trial with two parallel groups.

SETTING

Ninety-six general practices in Wales, the west of England and southern England. Invitation by personal letter or opportunistically.

PARTICIPANTS

Children aged between 12 months and 12 years fulfilling the UK Diagnostic Criteria for Atopic Eczema. Children with inactive or very mild eczema (a score of ≤ 5 on the Nottingham Eczema Severity Scale) were excluded, as were children who bathed less than once per week or whose parents/carers were not prepared to accept randomisation.

INTERVENTIONS

The intervention group were prescribed bath additives by their usual clinical team and were asked to use them regularly for 12 months. The control group were asked to use no bath additives for 12 months. Both groups continued standard eczema management, including regular leave-on emollients and topical corticosteroids (TCSs) when required.

MAIN OUTCOME MEASURES

The primary outcome was eczema control measured by Patient Oriented Eczema Measure [POEM, 0 (clear) to 28 (severe)] weekly for 16 weeks. The secondary outcomes were eczema severity over 1 year (4-weekly POEM), number of eczema exacerbations, disease-specific quality of life (QoL) (Dermatitis Family Impact Questionnaire), generic QoL (Child Health Utility-9 Dimensions) and type and quantity of topical steroid/calcineurin inhibitors prescribed. Children were randomised (1 : 1) using online software to either bath additives plus standard eczema care or standard eczema care alone, stratified by recruiting centre, and there was open-label blinding.

RESULTS

From December 2014 to May 2016, 482 children were randomised: 51% were female, 84% were white and the mean age was 5 years (n = 264 in the intervention group, n = 218 in the control group). Reported adherence to randomised treatment allocation was > 92% in both groups, with 76.7% of participants completing at least 12 (80%) of the first 16 weekly questionnaires for the primary outcome. Baseline POEM score was 9.5 [standard deviation (SD) 5.7] in the bath additives group and 10.1 (SD 5.8) in the no bath additives group. Average POEM score over the first 16 weeks was 7.5 (SD 6.0) in the bath additives group and 8.4 (SD 6.0) in the no bath additives group, with no statistically significant difference between the groups. After controlling for baseline severity and confounders (ethnicity, TCS use, soap substitute use) and allowing for clustering of participants within centres and responses within participants over time, POEM scores in the no bath additive group were 0.41 points higher than in the bath additive group (95% confidence interval -0.27 to 1.10), which is well below the published minimal clinically important difference of 3 points. There was no difference between groups in secondary outcomes or in adverse effects such as redness, stinging or slipping.

LIMITATIONS

Simple randomisation resulted in an imbalance in baseline group size, although baseline characteristics were well balanced between groups.

CONCLUSION

This trial found no evidence of clinical benefit of including emollient bath additives in the standard management of childhood eczema.

FUTURE WORK

Further research is required on optimal regimens of leave-on emollients and the use of emollients as soap substitutes.

TRIAL REGISTRATION

Current Controlled Trials ISRCTN84102309.

FUNDING

This project was funded by the NIHR Health Technology Assessment Programme and will be published in full in Health Technology Assessment; Vol. 22, No. 57. See the NIHR Journals Library website for further project information.

Cost-effectiveness analysis alongside clinical trials II-An ISPOR Good Research Practices Task Force report

Clinical trials evaluating medicines, medical devices, and procedures now commonly assess the economic value of these interventions. The growing number of prospective clinical/economic trials reflects both widespread interest in economic information for new technologies and the regulatory and reimbursement requirements of many countries that now consider evidence of economic value along with clinical efficacy. As decision makers increasingly demand evidence of economic value for health care interventions, conducting high-quality economic analyses alongside clinical studies is desirable because they broaden the scope of information available on a particular intervention, and can efficiently provide timely information with high internal and, when designed and analyzed properly, reasonable external validity. In 2005, ISPOR published the Good Research Practices for Cost-Effectiveness Analysis Alongside Clinical Trials: The ISPOR RCT-CEA Task Force report. ISPOR initiated an update of the report in 2014 to include the methodological developments over the last 9 years. This report provides updated recommendations reflecting advances in several areas related to trial design, selecting data elements, database design and management, analysis, and reporting of results. Task force members note that trials should be designed to evaluate effectiveness (rather than efficacy) when possible, should include clinical outcome measures, and should obtain health resource use and health state utilities directly from study subjects. Collection of economic data should be fully integrated into the study. An incremental analysis should be conducted with an intention-to-treat approach, complemented by relevant subgroup analyses. Uncertainty should be characterized. Articles should adhere to established standards for reporting results of cost-effectiveness analyses. Economic studies alongside trials are complementary to other evaluations (e.g., modeling studies) as information for decision makers who consider evidence of economic value along with clinical efficacy when making resource allocation decisions.

Optimal and maximin sample sizes for multicentre cost-effectiveness trials

This paper deals with the optimal sample sizes for a multicentre trial in which the cost-effectiveness of two treatments in terms of net monetary benefit is studied. A bivariate random-effects model, with the treatment-by-centre interaction effect being random and the main effect of centres fixed or random, is assumed to describe both costs and effects. The optimal sample sizes concern the number of centres and the number of individuals per centre in each of the treatment conditions. These numbers maximize the efficiency or power for given research costs or minimize the research costs at a desired level of efficiency or power. Information on model parameters and sampling costs are required to calculate these optimal sample sizes. In case of limited information on relevant model parameters, sample size formulas are derived for so-called maximin sample sizes which guarantee a power level at the lowest study costs. Four different maximin sample sizes are derived based on the signs of the lower bounds of two model parameters, with one case being worst compared to others. We numerically evaluate the efficiency of the worst case instead of using others. Finally, an expression is derived for calculating optimal and maximin sample sizes that yield sufficient power to test the cost-effectiveness of two treatments.

Sample size calculation in cost-effectiveness cluster randomized trials: optimal and maximin approaches

In this paper, the optimal sample sizes at the cluster and person levels for each of two treatment arms are obtained for cluster randomized trials where the cost-effectiveness of treatments on a continuous scale is studied. The optimal sample sizes maximize the efficiency or power for a given budget or minimize the budget for a given efficiency or power. Optimal sample sizes require information on the intra-cluster correlations (ICCs) for effects and costs, the correlations between costs and effects at individual and cluster levels, the ratio of the variance of effects translated into costs to the variance of the costs (the variance ratio), sampling and measuring costs, and the budget. When planning, a study information on the model parameters usually is not available. To overcome this local optimality problem, the current paper also presents maximin sample sizes. The maximin sample sizes turn out to be rather robust against misspecifying the correlation between costs and effects at the cluster and individual levels but may lose much efficiency when misspecifying the variance ratio. The robustness of the maximin sample sizes against misspecifying the ICCs depends on the variance ratio. The maximin sample sizes are robust under misspecification of the ICC for costs for realistic values of the variance ratio greater than one but not robust under misspecification of the ICC for effects. Finally, we show how to calculate optimal or maximin sample sizes that yield sufficient power for a test on the cost-effectiveness of an intervention.

A C++ program to calculate sample sizes for cost-effectiveness trials in a Bayesian framework

Cost-Effectiveness Analysis (CEA) has become an increasingly important component of clinical trials. However, formal sample size calculations for such studies are not common. One of the reasons for this might be due to the absence of readily available computer software to perform complex calculations, particularly in a Bayesian setting. In this paper, a C++ program (using NAG library functions/subroutines) is presented to estimate the sample sizes for cost-effectiveness clinical trials in a Bayesian framework. The program can equally be used to calculate sample sizes for efficacy trials. The Bayesian approach to sample size calculation is based on that of O'Hagan and Stevens (A. O'Hagan, J.W. Stevens, Bayesian assessment of sample size for clinical trials of cost-effectiveness, Medical Decision Making 21 (2001) 219-230). With this program, the user can calculate sample sizes for various thresholds of willingness to pay and under various assumptions of the correlations between cost and effects. Under some prior, the program produces frequentist sample size as well. The program runs under windows environment and running time is very short.

Sample size determination for cost-effectiveness trials

Methods for determining sample size requirements for cost-effectiveness studies are reviewed and illustrated. Traditional methods based on tests of hypothesis and power arguments are given for the incremental cost-effectiveness ratio and incremental net benefit (INB). In addition, a full Bayesian approach using decision theory to determine optimal sample size is given for INB. The full Bayesian approach, based on the value of information, is proposed in reaction to concerns that traditional methods rely on arbitrarily chosen error probabilities and an ill-defined notion of the smallest clinically important difference. Furthermore, the results of cost-effectiveness studies are used for decision making (e.g. should a new intervention be adopted or the old one retained), and employing decision theory, which permits optimal use of current information and the optimal design of new studies, provides a more consistent approach.

Sample size and power for cost-effectiveness analysis (part 1)

Basic sample size and power formulae for cost-effectiveness analysis have been established in the literature. These formulae are reviewed and the similarities and differences between sample size and power for cost-effectiveness analysis and for the analysis of other continuous variables such as changes in blood pressure or weight are described. The types of sample size and power tables that are commonly calculated for cost-effectiveness analysis are also described and the impact of varying the assumed parameter values on the resulting sample size and power estimates is discussed. Finally, the way in which the data for these calculations may be derived are discussed.

The ISPOR Good Practices for Quality Improvement of Cost-Effectiveness Research Task Force Report

OBJECTIVES

The International Society for Pharmacoeconomics and Outcomes Research (ISPOR) Health Science Policy Council recommended and the ISPOR Board of Directors approved the formation of a Task Force to critically examine the major issues related to Quality Improvement in Cost-effectiveness Research (QICER). The Council's primary recommendation for this Task Force was that it should report on the quality of cost-effectiveness research and make recommendations to facilitate the improvement of pharmacoeconomics and health outcomes research and its use in stimulating better health care and policy. Task force members were knowledgeable and experienced in medicine, pharmacy, biostatistics, health policy and health-care decision-making, biomedical knowledge transfer, health economics, and pharmacoeconomics. They were drawn from industry, academia, consulting organizations, and advisors to governments and came from Japan, the Netherlands, Canada and the United States.

METHODS

Face-to-face meetings of the Task Force were held at ISPOR North American and European meetings and teleconferences occurred every few months. Literature reviews and surveys were conducted and the first preliminary findings presented at an open forum at the May 2008 ISPOR meeting in Toronto. The final draft report was circulated to the expert reviewer group and then to the entire membership for comment. The draft report was posted on the ISPOR Web site in April 2009. All formal comments received were posted to the association Web site and presented for discussion at the Task Force forum during the ISPOR 14th Annual International Meeting in May 2009. Comments and feedback from the forums, reviewers and membership were considered in the final report. Once Task Force consensus was reached, the article was submitted to Value in Health.

CONCLUSIONS

The QICER Task Force recommends that ISPOR implement the following: * With respect to CER guidelines, that ISPOR promote harmonization of guidelines, allowing for differences in application, regional needs and politics; evaluate available instruments or promote development of a new one that will allow standardized quantification of the impact of CER guidelines on the quality of CER studies; report periodically on those countries or regions that have developed guidelines; periodically evaluate the quality of published studies (those journals with CER guidances) or those submitted to decision-making bodies (as public transparency increases). * With respect to methodologies, that ISPOR promote publication of methodological guidelines in more applied journals in more easily understandable format to transfer knowledge to researchers who need to apply more rigorous methods; promote full availability of models in electronic format to combat space restrictions in hardcopy publications; promote consistency of methodological review for all CER studies; promote adoption of explicit best practices guidelines among regulatory and reimbursement authorities; periodically update all ISPOR Task Force reports; periodically review use of ISPOR Task Force guidelines; periodically report on statistical and methodological challenges in HE; evaluate periodically whether ISPOR's methodological guidelines lead to improved quality; and support training and knowledge transfer of rigorous CER methodologies to researchers and health care decision-makers. * With respect to publications, that ISPOR develop standard CER guidances to which journals will be able to refer their authors and their reviewers; lobby to establish these guidances within the International Committee for Medical Journal Editors (ICMJE) Requirements to which most journals refer in their Author Instructions; provide support in terms of additional reviewer expertise to those journals lacking appropriate reviewers; periodically report on journals publishing CER research; periodically report on the quality of CER publications; and support training and knowledge transfer of the use of these guidelines to researchers and reviewers. * With respect to evidence-based health-care decision-making, that ISPOR recognize at its annual meetings those countries/agencies/private companies/researchers using CER well, and those practitioners and researchers supporting good patient use of CER in decision-making; and promote public presentation of case studies of applied use of CER concepts or guidelines.

A behavioral Bayes method to determine the sample size of a clinical trial considering efficacy and safety

It is necessary for the calculation of sample size to achieve the best balance between the cost of a clinical trial and the possible benefits from a new treatment. Gittins and Pezeshk developed an innovative (behavioral Bayes) approach, which assumes that the number of users is an increasing function of the difference in performance between the new treatment and the standard treatment. The better a new treatment, the more the number of patients who want to switch to it. The optimal sample size is calculated in this framework. This BeBay approach takes account of three decision-makers, a pharmaceutical company, the health authority and medical advisers. Kikuchi, Pezeshk and Gittins generalized this approach by introducing a logistic benefit function, and by extending to the more usual unpaired case, and with unknown variance. The expected net benefit in this model is based on the efficacy of the new drug but does not take account of the incidence of adverse reactions. The present paper extends the model to include the costs of treating adverse reactions and focuses on societal cost-effectiveness as the criterion for determining sample size. The main application is likely to be to phase III clinical trials, for which the primary outcome is to compare the costs and benefits of a new drug with a standard drug in relation to national health-care.

An opportunity cost approach to sample size calculation in cost-effectiveness analysis

The inclusion of economic evaluations as part of clinical trials has led to concerns about the adequacy of trial sample size to support such analysis. The analytical tool of cost-effectiveness analysis is the incremental cost-effectiveness ratio (ICER), which is compared with a threshold value (lambda) as a method to determine the efficiency of a health-care intervention. Accordingly, many of the methods suggested to calculating the sample size requirements for the economic component of clinical trials are based on the properties of the ICER. However, use of the ICER and a threshold value as a basis for determining efficiency has been shown to be inconsistent with the economic concept of opportunity cost. As a result, the validity of the ICER-based approaches to sample size calculations can be challenged. Alternative methods for determining improvements in efficiency have been presented in the literature that does not depend upon ICER values. In this paper, we develop an opportunity cost approach to calculating sample size for economic evaluations alongside clinical trials, and illustrate the approach using a numerical example. We compare the sample size requirement of the opportunity cost method with the ICER threshold method. In general, either method may yield the larger required sample size. However, the opportunity cost approach, although simple to use, has additional data requirements. We believe that the additional data requirements represent a small price to pay for being able to perform an analysis consistent with both concept of opportunity cost and the problem faced by decision makers.

Estimation, power and sample size calculations for stochastic cost and effectiveness analysis

Various methods have been proposed to address uncertainty in economic evaluations of healthcare programmes. One approach suggested in the literature is to estimate separate confidence intervals for the incremental costs and effects of a new health programme in comparison with an existing programme. These intervals are then combined to generate a rectangular confidence region in the cost-effectiveness plane that implicitly defines a corresponding confidence interval for the incremental cost-effectiveness ratio (ICER). The same approach has been used to calculate sample sizes and study power. This application of the rectangle method is consistent with the adoption of ICERs and a threshold as a decision rule, this being the most commonly used approach in empirical applications of cost-effectiveness analysis, as well as the one recommended by agencies that assess medical technology around the world. In this paper, we first outline the rectangle method, and then propose a modification that recognises that separate inferences are being drawn on the cost and effectiveness domains, and that corrects for multiple statistical comparisons. The confidence rectangle is otherwise too small, the corresponding confidence interval for the ICER is too narrow and sample sizes are under-estimated. Our modification corrects these problems. A further difficulty is that the placement of the confidence rectangle around the null value is somewhat arbitrary, and does not correspond to a unique value of ICERs. As a result, different values of sample size and power for the estimation of ICERs can be obtained, depending on the null values of the cost and effectiveness. We conclude that it is important to clearly identify the analytic goal in terms of estimating differential costs, differential effects or a combination of the two using the ICER index. These ideas are illustrated using numerical examples.

Good research practices for cost-effectiveness analysis alongside clinical trials: the ISPOR RCT-CEA Task Force report

OBJECTIVES

A growing number of prospective clinical trials include economic end points. Recognizing the variation in methodology and reporting of these studies, the International Society for Pharmacoeconomics and Outcomes Research (ISPOR) chartered the Task Force on Good Research Practices: Randomized Clinical Trials-Cost-Effectiveness Analysis. Its goal was to develop a guidance document for designing, conducting, and reporting cost-effectiveness analyses conducted as a part of clinical trials.

METHODS

Task force cochairs were selected by the ISPOR Board of Directors. Cochairs invited panel members to participate. Panel members included representatives from academia, the pharmaceutical industry, and health insurance plans. An outline and a draft report developed by the panel were presented at the 2004 International and European ISPOR meetings, respectively. The manuscript was then submitted to a reference group for review and comment.

RESULTS

The report addresses issues related to trial design, selecting data elements, database design and management, analysis, and reporting of results. Task force members agreed that trials should be designed to evaluate effectiveness (rather than efficacy), should include clinical outcome measures, and should obtain health resource use and health state utilities directly from study subjects. Collection of economic data should be fully integrated into the study. Analyses should be guided by an analysis plan and hypotheses. An incremental analysis should be conducted with an intention-to-treat approach. Uncertainty should be characterized. Manuscripts should adhere to established standards for reporting results of cost-effectiveness analyses.

CONCLUSIONS

Trial-based cost-effectiveness studies have appeal because of their high internal validity and timeliness. Improving the quality and uniformity of these studies will increase their value to decision makers who consider evidence of economic value along with clinical efficacy when making resource allocation decisions.

Incremental net benefit in randomized clinical trials with quality-adjusted survival

Owing to induced dependent censoring, estimating mean costs and quality-adjusted survival in a cost-effectiveness comparison of two groups using standard life-table methods leads to biased results. In this paper we propose methods for estimating the difference in mean costs and the difference in mean effectiveness, together with their respective variances and covariance in the presence of dependent censoring. We consider the situation in which the measure of effectiveness is either the probability of surviving a duration of interest or mean quality-adjusted survival time over a duration of interest. The methods are illustrated in an example using an incremental net benefit analysis.

Advantages of using the net-benefit approach for analysing uncertainty in economic evaluation studies

No consensus has yet been reached on how to analyse uncertainty in economic evaluation studies where individual patient data are available for costs and health effects. This paper summarises the available results regarding the analysis of uncertainty on the cost-effectiveness plane and argues for using the net-benefit approach when analysing uncertainty in cost-effectiveness studies. The net-benefit approach avoids the interpretation and statistical problems related to the incremental cost effectiveness ratio and implies several advantages. First, traditional statistical methods can be used for confidence-interval estimation and hypothesis testing. Second, calculation of the optimal sample size and the power of the study are facilitated allowing the correlation between costs and effects to vary within and between patient groups. Third, the use of a Bayesian approach to cost-effectiveness analysis is facilitated. Fourth, a formal relation between cost-effectiveness acceptability curves and statistical inference is provided. Finally, the net-benefit approach gives the Fieller's limits of the confidence interval for the incremental cost-effectiveness ratio in the cost-effectiveness plane. Based on these advantages the net-benefit approach should strongly be considered when analysing uncertainty in cost-effectiveness analyses.

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

We review the development of Bayesian statistical methods for the design and analysis of randomized controlled trials in the assessment of the cost-effectiveness of health care technologies. We place particular emphasis on the benefits of the Bayesian approach; the implications of skew cost data; the need to model the data appropriately to generate efficient and robust inferences instead of relying on distribution-free methods; the importance of making full use of quantitative and structural prior information to produce realistic inferences; and issues in the determination of sample size. Several new examples are presented to illustrate the methods. We conclude with a discussion of the key areas for future research.

Using inverse-weighting in cost-effectiveness analysis with censored data

Due to induced dependent censoring, estimating mean costs and quality-adjusted survival in a cost-effectiveness analysis using standard life-table methods leads to biased results. In this paper we propose methods for estimating the difference in mean costs and the difference in effectiveness, together with their respective variances and covariance in the presence of dependent censoring. We consider the situation in which the measure of effectiveness is either the probability of patients surviving a duration of interest, mean survival time over a duration of interest or mean quality-adjusted survival time over a duration of interest. The method of inverse-weighting is used for censored cost and quality of life data. The methods are illustrated in an example using an incremental net benefit analysis.

Use of randomised controlled trials for producing cost-effectiveness evidence: potential impact of design choices on sample size and study duration

BACKGROUND

A number of approaches to conducting economic evaluations could be adopted. However, some decision makers have a preference for wholly stochastic cost-effectiveness analyses, particularly if the sampled data are derived from randomised controlled trials (RCTs). Formal requirements for cost-effectiveness evidence have heightened concerns in the pharmaceutical industry that development costs and times might be increased if formal requirements increase the number, duration or costs of RCTs. Whether this proves to be the case or not will depend upon the timing, nature and extent of the cost-effectiveness evidence required.

OBJECTIVE

To illustrate how different requirements for wholly stochastic cost-effectiveness evidence could have a significant impact on two of the major determinants of new drug development costs and times, namely RCT sample size and study duration.

DESIGN

Using data collected prospectively in a clinical evaluation, sample sizes were calculated for a number of hypothetical cost-effectiveness study design scenarios. The results were compared with a baseline clinical trial design.

RESULTS

The sample sizes required for the cost-effectiveness study scenarios were mostly larger than those for the baseline clinical trial design. Circumstances can be such that a wholly stochastic cost-effectiveness analysis might not be a practical proposition even though its clinical counterpart is. In such situations, alternative research methodologies would be required. For wholly stochastic cost-effectiveness analyses, the importance of prior specification of the different components of study design is emphasised. However, it is doubtful whether all the information necessary for doing this will typically be available when product registration trials are being designed.

CONCLUSIONS

Formal requirements for wholly stochastic cost-effectiveness evidence based on the standard frequentist paradigm have the potential to increase the size, duration and number of RCTs significantly and hence the costs and timelines associated with new product development. Moreover, it is possible to envisage situations where such an approach would be impossible to adopt. Clearly, further research is required into the issue of how to appraise the economic consequences of alternative economic evaluation research strategies.

Incremental net benefit in randomized clinical trials

There are three approaches to health economic evaluation for comparing two therapies. These are (i) cost minimization, in which one assumes or observes no difference in effectiveness, (ii) incremental cost-effectiveness, and (iii) incremental net benefit. The latter can be expressed either in units of effectiveness or costs. When analysing data from a clinical trial, expressing incremental net benefit in units of cost allows the investigator to examine all three approaches in a single graph, complete with the corresponding statistical inferences. Furthermore, if costs and effectiveness are not censored, this can be achieved using common two-sample statistical procedures. The above will be illustrated using two examples, one with censoring and one without.

Statistical cost-effectiveness analysis of two treatments based on net health benefits

Statistical methods for cost-effectiveness analysis (CEA) for two treatments that mimic the deterministic optimal rules of CEA are presented. In these rules the objective is to determine the treatment with the maximal effectiveness whose unit cost is less than an amount, lambda, that a decision-maker is willing to pay (WTP). This is accomplished by identifying the treatment with the largest positive net health benefit (NHB), which is a function of lambda, while controlling the familywise error rate both when the WTP value is given and when it is unspecified. Fieller's theorem is used to determine a region of WTP values where the NHBs of the treatments are not distinguishable. For each lambda outside of the confidence region, the larger treatment is identified. A newly developed one-tailed analogue of Fieller's theorem is used to determine the WTP values where a treatment's NHB is positive. The situation in which both treatments are experimental is distinguished from the case where one of the treatments is usual care. The one-tailed confidence region is used in the latter case to obtain the lambda values where the NHBs are not different, and determining the region of positivity of the NHBs may be unnecessary. An example is presented in which the cost-effectiveness of two antipsychotic treatments is evaluated.

Power and sample assessments for tests of hypotheses on cost-effectiveness ratios

We address the issue of statistical power and sample size for cost-effectiveness studies. Tests of hypotheses on the cost-effectiveness ratio (CER) are constructed from the net cost and incremental effectiveness measures. When the difference in effectiveness is known, we derive formulae for statistical power and sample size assessments for one- and two-sided tests of hypotheses of the CER. We also construct a test of the joint hypothesis of cost-effectiveness and effectiveness and derive an expression connecting power and sample size. Our methods account for the correlation between cost and effectiveness and lead to smaller sample size requirements than comparative methods that ignore the correlation. The implications of our formulae for cost-effectiveness studies are illustrated through numerical examples. When compared with trials designed to demonstrate effectiveness alone, our results indicate that a trial appropriately powered to demonstrate cost-effectiveness might require sample sizes many times greater.