Confidence Intervals for Cost–Effectiveness Ratios: A Comparison of Four Methods

We evaluated four methods for computing confidence intervals for cost–effectiveness ratios developed from randomized controlled trials: the box method, the Taylor series method, the nonparametric bootstrap method and the Fieller theorem method. We performed a Monte Carlo experiment to compare these methods. We investigated the relative performance of each method and assessed whether or not it was affected by differing distributions of costs (normal and log normal) and effects (10% absolute difference in mortality resulting from mortality rates of 25% versus 15% in the two groups as well as from mortality rates of 55% versus 45%) or by differing levels of correlation between the costs and effects (correlations of −0.50, −0.25, 0.0, 0.25 and 0.50). The principal criterion used to evaluate the performance of the methods was the probability of miscoverage. Symmetrical miscoverage of the intervals was used as a secondary criterion for evaluating the four methods. Overall probabilities of miscoverage for the nonparametric bootstrap method and the Fieller theorem method were more accurate than those for the other the methods. The Taylor series method had confidence intervals that asymmetrically underestimated the upper limit of the interval. Confidence intervals for cost–effectiveness ratios resulting from the nonparametric bootstrap method and the Fieller theorem method were more dependably accurate than those estimated using the Taylor series or box methods. Routine reporting of these intervals will allow individuals using cost–effectiveness ratios to make clinical and policy judgments to better identify when an intervention is a good value for its cost. © 1997 by John Wiley & Sons, Ltd.     

Bayesian methods in cost–effectiveness studies: objectivity,computation and other relevant aspects

In a probabilistic sensitivity analysis (PSA) of a cost–effectiveness (CE) study, the unknown parameters are considered as random variables. A crucial question is what probabilistic distribution is suitable for synthesizing the available information (mainly data from clinical trials) about these parameters. In this context, the important role of Bayesian methodology has been recognized, where the parameters are of a random nature. We explore, in the context of CE analyses, how formal objective Bayesian methods can be implemented. We fully illustrate the methodology using two CE problems that frequently appear in the CE literature. The results are compared with those obtained with other popular approaches to PSA. We find that the discrepancies can be quite marked, specially when the number of patients enrolled in the simulated cohort under study is large. Finally, we describe in detail the numerical methods that need to be used to obtain the results. Copyright © 2009 John Wiley & Sons, Ltd.     

Nonparametric inference for time‐dependent incremental cost‐effectiveness ratios

As the costs of medical care increase, more studies are evaluating cost in addition to effectiveness of treatments. Cost‐effectiveness analyses in randomized clinical trials have typically been conducted only at the end of follow‐up. However, cost‐effectiveness may change over time. We therefore propose a nonparametric estimator to assess the incremental cost‐effectiveness ratio over time. We also derive the asymptotic variance of our estimator and present formulation of Fieller‐based simultaneous confidence bands. Simulation studies demonstrate the performance of our point estimators, variance estimators, and confidence bands. We also illustrate our methods using data from a randomized clinical trial, the second Multicenter Automatic Defibrillator Implantation Trial. This trial studied the effects of implantable cardioverter‐defibrillators on patients at high risk for cardiac arrhythmia. Results show that our estimator performs well in large samples, indicating promising future directions in the field of cost‐effectiveness. Copyright © 2015 John Wiley & Sons, Ltd.     

AXIOMATIC FOUNDATIONS FOR COST‐EFFECTIVENESS ANALYSIS

We show that individual utilities can be measured in units of healthy life years. Social preferences over these life metric utilities are assumed to satisfy the Pareto principle, anonymity, and invariance to a change in origin. These axioms generate a utilitarian social welfare function implying the use of cost‐effectiveness analysis in ordering health projects, based on maximizing the healthy years equivalents gained from a fixed health budget. For projects outside the health sector, our cost‐effectiveness axioms imply a form of cost–benefit analysis where both costs and benefits are measured in equivalent healthy life years. Copyright © 2013 John Wiley & Sons, Ltd.     

An omnibus test for several hazard alternatives in prevention randomized controlled clinical trials

The logrank test is optimal for testing the equality of survival distributions against a proportional hazards alternative. Under a late effects alternative, it is no longer appropriate, and one may turn to Fleming–Harrington's class of weighted logrank tests instead. In some settings, such as in preventive clinical trials where the statistical analysis has to be designed before the trial begins, it can be difficult to choose a priori between the logrank and Fleming–Harrington tests. A solution to this issue is provided. A decision rule is constructed for the problem of testing the equality of two survival distributions when the expected alternative may be one of the proportional hazards and late effects. A formula for computing the necessary sample size is obtained for this decision rule. A comprehensive simulation study is conducted to assess finite sample properties of the proposed test statistic. The proposed test improves both the logrank test and Fleming–Harrington's test for late effects. Finally, the methodology is illustrated on a data set in the field of prevention of Alzheimer's disease. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

The Use of Cost‐Effectiveness Analysis for Pediatric Immunization in Developing Countries

Context: Developing countries face critical choices for introducing needed, effective, but expensive new vaccines, especially given the accelerated need to decrease the mortality of children under age five and the increased immunization resources available from international donors. Cost‐effectiveness analysis (CEA) is a tool that decision makers can use for efficiently allocating expanding resources. Its use in developing countries, however, lags behind that in industrialized countries. Methods: We explored how CEA could be made more relevant to immunization policymaking in developing countries by identifying the limitations for using CEA in developing countries and the impact of donor funding on the CEA estimation. We conducted a comprehensive literature search using formal search protocols and hand searching indexed and gray literature sources. We then systematically summarized the application of CEA in industrialized and developing countries through thematic analysis, focusing on pediatric immunization and methodological and contextual issues relevant to developing countries. Findings: Industrialized and developing countries use CEA differently. The use of the Disability‐Adjusted Life Year (DALY) outcome measure and an alternative generalized cost‐effectiveness analysis approach is restricted to developing countries. In pediatric CEAs, the paucity of evaluations and the lack of attention to overcoming the methodological limitations pertinent to children's cognitive and development distinctiveness, such as discounting and preference characterization, means that pediatric interventions may be systematically understudied and undervalued. The ability to generate high‐quality CEA evidence in child health is further threatened by an inadequate consideration of the impact of donor funding (such as GAVI immunization funding) on measurement uncertainty and the determination of opportunity cost. Conclusions: Greater attention to pediatric interventions and donor funding in the conduct of CEA could lead to better policies and thus more worthwhile and good‐value programs to benefit children's health in developing countries.     

A small sample study of the STEPP approach to assessing treatment–covariate interactions in survival data

A new, intuitive method has recently been proposed to explore treatment–covariate interactions in survival data arising from two treatment arms of a clinical trial. The method is based on constructing overlapping subpopulations of patients with respect to one (or more) covariates of interest and in observing the pattern of the treatment effects estimated across the subpopulations. A plot of these treatment effects is called a subpopulation treatment effect pattern plot. Here, we explore the small sample characteristics of the asymptotic results associated with the method and develop an alternative permutation distribution‐based approach to inference that should be preferred for smaller sample sizes. We then describe an extension of the method to the case in which the pattern of estimated quantiles of survivor functions is of interest. Copyright © 2009 John Wiley & Sons, Ltd.     

Distributional Cost‐Effectiveness Analysis of Health Care Programmes – A Methodological Case Study of the UK Bowel Cancer Screening Programme

This paper presents an application of a new methodological framework for undertaking distributional cost‐effectiveness analysis to combine the objectives of maximising health and minimising unfair variation in health when evaluating population health interventions. The National Health Service bowel cancer screening programme introduced in 2006 is expected to improve population health on average and to worsen population health inequalities associated with deprivation and ethnicity – a classic case of ‘intervention‐generated inequality’. We demonstrate the distributional cost‐effectiveness analysis framework by examining two redesign options for the bowel cancer screening programme: (i) the introduction of an enhanced targeted reminder aimed at increasing screening uptake in deprived and ethnically diverse neighbourhoods and (ii) the introduction of a basic universal reminder aimed at increasing screening uptake across the whole population. Our analysis indicates that the universal reminder is the strategy that maximises population health, while the targeted reminder is the screening strategy that minimises unfair variation in health. The framework is used to demonstrate how these two objectives can be traded off against each other, and how alternative social value judgements influence the assessment of which strategy is best, including judgements about which dimensions of health variation are considered unfair and judgements about societal levels of inequality aversion. © 2014 The Authors. Health Economics published by John Wiley & Sons Ltd.     

Confidence bounds for nonlinear dose–response relationships

An important aim of drug trials is to characterize the dose–response relationship of a new compound. Such a relationship can often be described by a parametric (nonlinear) function that is monotone in dose. If such a model is fitted, it is useful to know the uncertainty of the fitted curve. It is well known that Wald confidence intervals are based on linear approximations and are often unsatisfactory in nonlinear models. Apart from incorrect coverage rates, they can be unreasonable in the sense that the lower confidence limit of the difference to placebo can be negative, even when an overall test shows a significant positive effect. Bootstrap confidence intervals solve many of the problems of the Wald confidence intervals but are computationally intensive and prone to undercoverage for small sample sizes. In this work, we propose a profile likelihood approach to compute confidence intervals for the dose–response curve. These confidence bounds have better coverage than Wald intervals and are more precise and generally faster than bootstrap methods. Moreover, if monotonicity is assumed, the profile likelihood approach takes this automatically into account. The approach is illustrated using a public dataset and simulations based on the Emax and sigmoid Emax models. Copyright © 2015 John Wiley & Sons, Ltd.     

Cost‐Effectiveness Analysis of a Capitated Patient Navigation Program for Medicare Beneficiaries with Lung Cancer

Objective

To assess the cost‐effectiveness of implementing a patient navigation (PN) program with capitated payment for Medicare beneficiaries diagnosed with lung cancer.

Data Sources/Study Setting

Cost‐effectiveness analysis.

Study Design

A Markov model to capture the disease progression of lung cancer and characterize clinical benefits of PN services as timeliness of treatment and care coordination. Taking a payer''s perspective, we estimated the lifetime costs, life years (LYs), and quality‐adjusted life years (QALYs) and addressed uncertainties in one‐way and probabilistic sensitivity analyses.

Data Collection/Extraction Methods

Model inputs were extracted from the literature, supplemented with data from a Centers for Medicare and Medicaid Services demonstration project.

Principal Findings

Compared to usual care, PN services incurred higher costs but also yielded better outcomes. The incremental cost and effectiveness was $9,145 and 0.47 QALYs, respectively, resulting in an incremental cost‐effectiveness ratio of $19,312/QALY. One‐way sensitivity analysis indicated that findings were most sensitive to a parameter capturing PN survival benefit for local‐stage patients. CE‐acceptability curve showed the probability that the PN program was cost‐effective was 0.80 and 0.91 at a societal willingness‐to‐pay of $50,000 and $100,000/QALY, respectively.

Conclusion

Instituting a capitated PN program is cost‐effective for lung cancer patients in Medicare. Future research should evaluate whether the same conclusion holds in other cancers.     

A social cost–benefit criterion for evaluating Voluntary Counseling and Testing with an application to Tanzania

Rationale: There are many interventions for HIV/AIDS that require that people know their status and hence require a HIV test. Testing that is driven by a desire to prevent the spread of the disease often has an indirect effect on others. These external effects need to be identified, quantified and included as part of the benefits and costs of testing. Pioneering analyses of HIV testing by Philipson and Posner have introduced the economic calculus of individual expected benefits and costs of activities into an understanding of the HIV epidemic. What is required for social evaluations is an extension of the analysis to ensure that external effects are included. Objectives: The objective of this paper is two‐fold. First we seek to formulate cost–benefit criteria that incorporate fully the external effects in the evaluation of Voluntary Counseling and Testing (VCT). We achieve this by recasting the individual calculus of benefits and costs to a couple setting. We can then compare an individual's cost–benefit analysis of being tested with social criteria that look at outcomes from a couple's perspective for both separate and dual/joint testing. Second we aim to apply our social criteria to VCT programs as they currently operate in Tanzania and how these programs might operate in the future when they are scaled up to relate to the general population. Methodology: We develop social criteria for evaluating separate and dual VCT using a couple's perspective with and without altruism. Therefore, the welfare function is based on two individual expected utility functions viewed as a couple, either married or regular partners. The benefits are the averted lives lost whenever discordant couples are revealed. The costs of VCT are the benefits of unprotected sex that the couple foregoes and the costs of the testing and counseling. The cost–benefit criteria are applied to VCT programs in Tanzania. The four main ingredients estimated are: the foregone benefit of unprotected sex (measured by the compensated wage differentials charged by commercial sex workers); the probability of infection; the cost of an infection (measured by both the value of a statistical life and the human capital approaches) and the cost of a single test (which includes behavior‐modifying counseling). Conclusions: We find separate testing in existing VCT programs to be only marginally worthwhile. However, in scaled‐up programs the benefit–cost ratio is over three. Dual testing is always more beneficial than separate testing. However, this advantage is reduced in scaled‐up programs. VCT should be greatly expanded throughout Tanzania as future returns would be even higher for both separate and joint counseling and HIV testing. Copyright © 2009 John Wiley & Sons, Ltd.     

Cost‐effectiveness of aftercare services for people with severe mental disorders: an analysis parallel to a randomised controlled clinical trial in Iran

Aftercare services are not part of the usual care for people with severe mental disorders in Iran. This study was performed to assess the cost‐effectiveness of aftercare services, including telephone follow‐up or home visit, in addition to caregivers’ education and training of social skills, for all subjects during the 20 months after hospital discharge. An economic evaluation was performed along with a registered randomised controlled trial (IRCT201009052557N2) on two groups of 60 persons recruited between 2010 and 2012. Intervention's effectiveness was measured by psychopathology and quality of life indicators. Cost‐effectiveness and cost‐utility were analysed from the societal and Ministry of Health (MoH) perspectives. All indicators of psychopathology, quality of life and satisfaction with services in the intervention group were significantly different from the control group. Mean intervention costs was US$674 (95% confidence interval [CI]: 572–776) per subject in the intervention group. Average total direct costs were US$1445 (95% CI: 1086–1804) and US$1640 (95% CI: 1087–2093) per subject in the intervention and control groups respectively. From the societal perspective, intervention had more effects with lower costs. The ratios for incremental cost‐effectiveness was US$8399.1 (95% CI: 8178.2–8620.0) per quality‐adjusted life year (QALY) gained from the MoH perspective for 20 months of follow‐up. This study showed that aftercare services can create opportunities to use hospital beds more efficiently for unmet needs of people with psychiatric disorders. Indirect and intangible costs were not considered in this study, if taken into account, they are likely to further increase the efficiency of intervention.     

Designs for dose–escalation trials with quantitative responses

In a dose–escalation trial for a new drug, each successive dose is tested on a new cohort of volunteer subjects, so that if any dose produces severe adverse reactions then higher doses are not tested. However, if there are other differences between the cohorts, such as differences in environmental health factors, type of person or experimental procedure, then these differences may obscure the differences between doses. Therefore, cohorts should be fitted in the analysis, as either fixed or random effects. I suggest that, if this is done, then there are three simple principles that reduce variance (i) allocating no more than half the subjects in any cohort to any single dose; (ii) subject to safety constraints, using as many different doses as possible in each cohort; (iii) using one more cohort than the number of doses, without increasing the total number of subjects. Using these principles, I propose some new designs that conform to the safety rules of traditional dose–escalation trials while reducing the variance of the estimators of differences between the doses by a factor of two or more, for the same number of subjects. Copyright © 2009 John Wiley & Sons, Ltd.     

Demand for self‐tests: Evidence from a Becker–DeGroot–Marschak mechanism field experiment

Self‐tests offer one approach for reducing frictions underlying low demand for preventive health inputs, yet there is little evidence on demand for self‐tests. We used the Becker–DeGroot–Marschak mechanism—an incentive‐compatible approach—to elicit exact willingness to pay (WTP) for HIV self‐tests in a field experiment with 822 participants at 66 health clinics/pharmacies in Kenya. Our analysis reveals substantial demand at low prices and highly elastic demand at a wide range of prices above this range. We find few participants with nonpositive WTP. We examine correlates of WTP and discuss policy and research implications of our findings.     

Bayesian adjustment for exposure misclassification in case–control studies

Poor measurement of explanatory variables occurs frequently in observational studies. Error‐prone observations may lead to biased estimation and loss of power in detecting the impact of explanatory variables on the response. We consider misclassified binary exposure in the context of case–control studies, assuming the availability of validation data to inform the magnitude of the misclassification. A Bayesian adjustment to correct the misclassification is investigated. Simulation studies show that the Bayesian method can have advantages over non‐Bayesian counterparts, particularly in the face of a rare exposure, small validation sample sizes, and uncertainty about whether exposure misclassification is differential or non‐differential. The method is illustrated via application to several real studies. Copyright © 2010 John Wiley & Sons, Ltd.     

Sample size for testing and estimating the difference between two paired and unpaired proportions: a 'two-step' procedure combining power and the probability of obtaining a precise estimate

Clinical trials and scientific research studies are currently planned calculating sample sizes to fulfill power requirements, but the simultaneous need to obtain a satisfactorily precise effect estimate is not widely recognized. I have devised a 'two-step' iterative procedure for comparing two binomial parameters for two paired and unpaired proportions (the most frequent situations in scientific research), which takes into account power and the probability of obtaining a predetermined precision of the effect estimate. The first step provides the sample size for the power of the statistical test, the expected width of its corresponding confidence interval, and the probability of obtaining, under the alternative hypothesis, confidence intervals whose width is less than that expected. The second step iteratively increases this sample size until the probability of obtaining such confidence intervals exceeds a required threshold.