Cost-effectiveness analysis for multinational clinical trials

Clinical trials of cost-effectiveness are often conducted in more than one country. The two most common ways of dealing with the multinational nature of the data are either to calculate a pooled estimate or to stratify results by country. Since the between-country heterogeneity in costs is potentially substantial, pooled estimates may be difficult to interpret for any one country. Policy decisions are often made at a national level, and so country-specific results are important. However, country-specific analyses will be based on fewer patients and will often fail to provide adequate precision for statistical analyses.Shrinkage estimation is a compromise between these two methods and has been used successfully in other fields. These estimates are country-specific yet less variable than those derived through a subgroup approach. Univariate and multivariate shrinkage estimators for costs and effects are proposed, then compared with one another and to the traditional methods in a simulation study. The methods are illustrated using data from a multinational trial evaluating the cost-effectiveness of three thrombolytic drug regimens in patients with acute myocardial infarction.     

Estimating country-specific cost-effectiveness from multinational clinical trials

Because costs and outcomes of medical treatments may vary from country to country in important ways, decision makers are increasingly interested in having data based on their own country's health care situations. This paper proposes methods for estimating country-specific cost-effectiveness ratios from data available from multinational clinical trials. It examines how clinical and economic outcomes interact when estimating treatment effects on cost and proposes empirical methods for capturing these interactions and incorporating them when making country-specific estimates. We use data from a multinational phase III trial of tirilazad mesylate for the treatment of subarachnoid haemorrhage to illustrate these methods. Our findings suggest that it is possible for meaningful country-by-country differences to be found in such trial data. These differences can be useful in informing reimbursement, utilization, and other decisions taken at the country level. © 1998 John Wiley & Sons, Ltd.     

Bayesian estimation of cost-effectiveness from censored data

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

Empirical estimation of life expectancy from large clinical trials: use of left-truncated, right-censored survival analysis methodology

In the current era of ever-increasing health care costs, economic analyses are an essential component in the comprehensive evaluation of new medical interventions. Cost-effectiveness analysis (CEA)--the most common form of economic analysis used in medicine--aids policy-makers in determining how to allocate finite health care dollars among possible alternative therapies. CEA relates the incremental benefits of a new technology to its incremental costs in a cost-effectiveness (CE) ratio. Although the generally agreed-upon standard of presentation for the CE ratio is the lifetime perspective (incremental lifetime cost to add one life year), this perspective presents an obvious challenge to the statistical analyst. Most large clinical trials collect limited follow-up data, and yet their findings form the basis of therapeutic recommendations that often extend far beyond the limits of the empirical data. Although clinical practice guidelines do not yet require explicit modeling to examine the long-term implications of their recommendations, health policy analyses routinely rely upon such extrapolations. This paper describes methods for using empirical patient-level data to extrapolate survival in large clinical trials and cohorts beyond a limited follow-up period in which most patients remain alive in order to estimate the entire survival distribution for a cohort of patients. We accomplish this task through a novel combination of models that estimate the hazard rate not only as a function of time but also as a function of patient age. Extrapolation of survival beyond a limited time frame is made possible by capitalizing on the extensive latitude of survival information available across the range of ages represented in the data. Variations in approach are presented, and issues arising in these analyses are discussed. The proposed methodology is developed, applied, and evaluated in both a large clinical trial cohort with 5-year follow-up on over 23,000 patients and a large observational database with long-term follow-up on over 4000 patients.     

Resource costing for multinational neurologic clinical trials: methods and results

We present the results of a multinational resource costing study for a prospective economic evaluation of a new medical technology for treatment of subarachnoid hemorrhage within a clinical trial. The study describes a framework for the collection and analysis of international resource cost data that can contribute to a consistent and accurate intercountry estimation of cost. Of the 15 countries that participated in the clinical trial, we collected cost information in the following seven: Australia, France, Germany, the UK, Italy, Spain, and Sweden. The collection of cost data in these countries was structured through the use of worksheets to provide accurate and efficient cost reporting. We converted total average costs to average variable costs and then aggregated the data to develop study unit costs. When unit costs were unavailable, we developed an index table, based on a market-basket approach, to estimate unit costs. To estimate the cost of a given procedure, the market-basket estimation process required that cost information be available for at least one country. When cost information was unavailable in all countries for a given procedure, we estimated costs using a method based on physician-work and practice-expense resource-based relative value units. Finally, we converted study unit costs to a common currency using purchasing power parity measures. Through this costing exercise we developed a set of unit costs for patient services and per diem hospital services. We conclude by discussing the implications of our costing exercise and suggest guidelines to facilitate more effective multinational costing exercises. © 1998 John Wiley & Sons, Ltd.     

Modelling clustered survival data from multicentre clinical trials

In randomized clinical trials, subjects are recruited at multiple study centres. Factors that vary across centres may exert a powerful independent influence on study outcomes. A common problem is how to incorporate these centre effects into the analysis of censored time-to-event data. We survey various methods and find substantial advantages in the gamma frailty model. This approach compares favourably with competing methods and appears minimally affected by violation of the assumption of a gamma-distributed frailty. Recent computational advances make use of the gamma frailty model a practical and appealing tool for addressing centre effects in the analysis of multicentre trials.     

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.     

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

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

Semi-parametric and non-parametric methods for clinical trials with incomplete data

Last observation carried forward (LOCF) and analysis using only data from subjects who complete a trial (Completers) are commonly used techniques for analysing data in clinical trials with incomplete data when the endpoint is change from baseline at last scheduled visit. We propose two alternative methods. The semi-parametric method, which cumulates changes observed between consecutive time points, is conceptually similar to the familiar life-table method and corresponding Kaplan-Meier estimation when the primary endpoint is time to event. A non-parametric analogue of LOCF is obtained by carrying forward, not the observed value, but the rank of the change from baseline at the last observation for each subject. We refer to this method as the LRCF method. Both procedures retain the simplicity of LOCF and Completers analyses and, like these methods, do not require data imputation or modelling assumptions. In the absence of any incomplete data they reduce to the usual two-sample tests. In simulations intended to reflect chronic diseases that one might encounter in practice, LOCF was observed to produce markedly biased estimates and markedly inflated type I error rates when censoring was unequal in the two treatment arms. These problems did not arise with the Completers, Cumulative Change, or LRCF methods. Cumulative Change and LRCF were more powerful than Completers, and the Cumulative Change test provided more efficient estimates than the Completers analysis, in all simulations. We conclude that the Cumulative Change and LRCF methods are preferable to LOCF and Completers analyses. Mixed model repeated measures (MMRM) performed similarly to Cumulative Change and LRCF and makes somewhat less restrictive assumptions about missingness mechanisms, so that it is also a reasonable alternative to LOCF and Completers analyses.     

Country specific cost comparisons from multinational clinical trials using empirical Bayesian shrinkage estimation: the Canadian ASSENT-3 economic analysis

The growing number of multinational clinical trials in which patient-level health care resource data are collected have raised the issue of which is the best approach for making inference for individual countries with respect to the between-treatment difference in mean cost. We describe and discuss the relative merits of three approaches. The first uses the random effects pooled estimate from all countries to estimate the difference for any particular country. The second approach estimates the difference using only the data from the specific country in question. Using empirical Bayes estimation a third approach estimates the country-specific difference using a variance-weighted linear sum of the estimates provided by the other two approaches. The approaches are illustrated and compared using the data from the ASSENT-3 trial.     

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

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

Meta-analysis combining parallel and cross-over clinical trials. II: Binary outcomes

We examine different methods to pool binary outcomes used both in parallel and cross-over trials. Odds ratio (OR) estimators obtained from joint conditional probabilities in cross-over trials, such as the Mantel-Haenszel and Peto methods, are compared to an OR estimator using marginal results of cross-over trials. When there is correlation between the outcomes in the two cross-over periods, joint conditional ORs differ from marginal ORs and cannot be combined with OR estimates from parallel trials. The marginal OR estimate is independent of the between-period correlation and it includes a correction for cross-over correlation in the variance estimate. As its computation is similar in cross-over and parallel trials, it is the method of choice to pool results from parallel and cross-over trials in a combined design meta-analysis.     

Meta-analysis combining parallel and cross-over clinical trials. I: Continuous outcomes

Among clinical trials assessing a given treatment, often parallel and cross-over designs are used together. In the first paper of a series of three, we explore two methods to pool continuous outcomes in a meta-analysis combining parallel and cross-over trial designs: the weighted mean difference (WMD) and the standardized weighted mean difference (SWMD). The combined design meta-analytic formulae are based on a weighted average of the two design treatment estimates. A random effects model can be implemented. Both WMD and SWMD can be used, the choice of the method is determined by the type of outcomes obtained in the trials. Compared to the number of included subjects, the relative weight of the cross-over design is large in combined-design meta-analysis. Differences in the weight estimation between WMD and SWMD can also accentuate the relative weight of cross-over trials, which must be considered a case of design-specific bias.     

A framework for cost-effectiveness analysis from clinical trial data

We present a general Bayesian framework for cost-effectiveness analysis (CEA) from clinical trial data. This framework allows for very flexible modelling of both cost and efficacy related trial data. A common CEA technique is established for this wide class of models through linking mean efficacy and mean cost to the parameters of any given model. Examples are given in which efficacy may be measured as a continuous, binary, ordinal or time-to-event outcome, and in which costs are modelled as distributed normally, log-normally, as a mixture or non-parametrically. A case study is presented, illustrating the methodology and illuminating the role of prior information.     

A comparison of economic modelling and clinical trials in the economic evaluation of cholesterol-modifying pharmacotherapy

There are various ways in which data for economic evaluations may be obtained, including via clinical trials and via economic modelling. There are numerous advantages and disadvantages associated with each method, although it is generally assumed that economic models lack the accuracy required for the calculation of meaningful cost-effectiveness data. In order to assess the predictive accuracy of economic modelling in the context of cholesterol-modifying pharmacotherapy it is possible to compare predicted coronary heart disease (CHD) incidence estimates obtained using CHD risk equations derived from the Framingham Heart Study (FHS) with actual CHD incidence rates achieved in a major clinical trial, the West of Scotland Coronary Prevention Study (WOSCOPS). FHS-derived CHD risk equations substantially underestimate the actual risks of nonfatal myocardial infarction obtained by WOSCOPS. However, in predicting risks of death from CHD, FHS-derived CHD risk equations estimate extremely accurately the incidence obtained by WOSCOPS. For example, from WOSCOPS the risk of an individual fulfilling the trial entry criteria incurring nonfatal myocardial infarction or CHD death in 4.9 years is 0.079 for placebo group and 0.055 for the intervention group. Therefore, the relative risk for the intervention group relative to placebo group is 0.696, implying a risk reduction of 30%. Comparable risks predicted using FHS-derived CHD risk equations are 0.116 for the placebo group and 0.088 for the intervention group. Consequent relative risks and risk reductions for the intervention relative to placebo are 0.757 and 24%, respectively. Using both model and trial estimates of CHD incidence in an economic evaluation of cholesterol-modifying pharmacotherapy, incremental costs per life year gained are £41 707 using WOSCOPS data and £36 480 using FHS-derived CHD risk equations. © 1997 John Wiley & Sons, Ltd.     

The assessment of the economic return from controlled clinical trials

Clinical trials can be considered health interventions as their primary aim is to impact on the health of a population. Given that resources are scarce for both health care and health related research, trials could be designed such that they can be demonstrated to be cost-effective, i.e., the costs of conducting the trial are justified given the forecasted long-term benefits.We demonstrate how a model can be used to predict the cost-effectiveness of undertaking a clinical trial comparing alternative regimens of colorectal cancer follow-up.The model forecasts costs and survival under two scenarios,with and without conducting a clinical trial, with the outcome assessed in terms of years to payback for the clinical trial.The methodology shown can be used both to provide information on appropriate trial design and/or in prioritizing between potential trials. Douglas Coyle Clinical Epidemiology Unit, Ottawa Health Research Institute, 1053 Carling Avenue,Ottawa Hospital,Ottawa, Ontario K1Y 4E9,Canada, e-mail: dcoyle@ohri.ca     

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

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

Assessing apparent treatment--covariate interactions in randomized clinical trials

In the context of clinical trials, a qualitative treatment--covariate interaction occurs when a patient's preferred treatment depends on his covariates. In this paper I review the nature and interpretation of various kinds of interactions, compare the use of overall tests for interaction to subset analysis, present some examples of apparent treatment-covariate interactions that have arisen in actual randomized clinical trials, and discuss some recent work by others related to significance testing, estimation and assessment of apparent treatment-covariate interactions.     

Beyond the cost‐effectiveness acceptability curve: The appropriateness of rank probabilities for presenting the results of economic evaluation in multiple technology appraisal

The cost‐effectiveness acceptability curve (CEAC) shows the probability that an option ranks first for net benefit. Where more than two options are under consideration, the CEAC offers only a partial picture of the decision uncertainty. This paper discusses the appropriateness of showing the full set of rank probabilities for reporting the results of economic evaluation in multiple technology appraisal (MTA). A case study is used to illustrate the calculation of rank probabilities and associated metrics, based on Monte Carlo simulations from a decision model. Rank probabilities are often used to show uncertainty in the results of network meta‐analysis, but until now have not been used for economic evaluation. They may be useful decision‐making tools to complement the CEAC in specific MTA contexts.     

Covariate adjustment in clinical trials with non-ignorable missing data and non-compliance

Estimating causal effects in psychiatric clinical trials is often complicated by treatment non-compliance and missing outcomes. While new estimators have recently been proposed to address these problems, they do not allow for inclusion of continuous covariates. We propose estimators that adjust for continuous covariates in addition to non-compliance and missing data. Using simulations, we compare mean squared errors for the new estimators with those of previously established estimators. We then illustrate our findings in a study examining the efficacy of clozapine versus haloperidol in the treatment of refractory schizophrenia. For data with continuous or binary outcomes in the presence of non-compliance, non-ignorable missing data, and a covariate effect, the new estimators generally performed better than the previously established estimators. In the clozapine trial, the new estimators gave point and interval estimates similar to established estimators. We recommend the new estimators as they are unbiased even when outcomes are not missing at random and they are more efficient than established estimators in the presence of covariate effects under the widest variety of circumstances.