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

Identifying cost-effective dynamic policies to control epidemics

We describe a mathematical decision model for identifying dynamic health policies for controlling epidemics. These dynamic policies aim to select the best current intervention based on accumulating epidemic data and the availability of resources at each decision point. We propose an algorithm to approximate dynamic policies that optimize the population's net health benefit, a performance measure which accounts for both health and monetary outcomes. We further illustrate how dynamic policies can be defined and optimized for the control of a novel viral pathogen, where a policy maker must decide (i) when to employ or lift a transmission-reducing intervention (e.g. school closure) and (ii) how to prioritize population members for vaccination when a limited quantity of vaccines first become available. Within the context of this application, we demonstrate that dynamic policies can produce higher net health benefit than more commonly described static policies that specify a pre-determined sequence of interventions to employ throughout epidemics. Copyright © 2016 John Wiley & Sons, Ltd.

Expected Value of Sample Information Calculations in Medical Decision Modeling

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

Computing Expected Value of Partial Sample Information from Probabilistic Sensitivity Analysis Using Linear Regression Metamodeling

Decision makers often desire both guidance on the most cost-effective interventions given current knowledge and also the value of collecting additional information to improve the decisions made (i.e., from value of information [VOI] analysis). Unfortunately, VOI analysis remains underused due to the conceptual, mathematical, and computational challenges of implementing Bayesian decision-theoretic approaches in models of sufficient complexity for real-world decision making. In this study, we propose a novel practical approach for conducting VOI analysis using a combination of probabilistic sensitivity analysis, linear regression metamodeling, and unit normal loss integral function--a parametric approach to VOI analysis. We adopt a linear approximation and leverage a fundamental assumption of VOI analysis, which requires that all sources of prior uncertainties be accurately specified. We provide examples of the approach and show that the assumptions we make do not induce substantial bias but greatly reduce the computational time needed to perform VOI analysis. Our approach avoids the need to analytically solve or approximate joint Bayesian updating, requires only one set of probabilistic sensitivity analysis simulations, and can be applied in models with correlated input parameters.

Incremental cost-effectiveness ratio and incremental net-health benefit: two sides of the same coin

In recent years, an alternative framework for cost-effectiveness analyses has been growing in popularity. Instead of the incremental cost-effectiveness ratio for which statistical inference is often difficult, the incremental net-health benefit (INHB), a linear transformation of incremental costs and effectiveness, has been utilized. The linear structure of this statistic allows easy computation and interpretation of confidence intervals, hypothesis tests and acceptability curves. It is often difficult, however, to switch decision-making procedures without first verifying the appropriateness of the new methods. In this paper, we demonstrate the decision-making similarities between the INHB and the incremental cost-effectiveness ratio and describe how the INHB can be used to clarify inference of the incremental cost-effectiveness ratio. We also describe the two statistics in terms of the DeltaE-DeltaC plane, thus allowing both a mathematical and graphical comparison of these similarities. We conclude with a general discussion of cost-effectiveness analyses and advocate Bayesian, rather than frequentist inference as the more intuitive and powerful decision-making framework.

Non-parametric methods for cost-effectiveness analysis: the central limit theorem and the bootstrap compared

Cost-effectiveness analyses (CEA) alongside randomised controlled trials commonly estimate incremental net benefits (INB), with 95% confidence intervals, and compute cost-effectiveness acceptability curves and confidence ellipses. Two alternative non-parametric methods for estimating INB are to apply the central limit theorem (CLT) or to use the non-parametric bootstrap method, although it is unclear which method is preferable. This paper describes the statistical rationale underlying each of these methods and illustrates their application with a trial-based CEA. It compares the sampling uncertainty from using either technique in a Monte Carlo simulation. The experiments are repeated varying the sample size and the skewness of costs in the population. The results showed that, even when data were highly skewed, both methods accurately estimated the true standard errors (SEs) when sample sizes were moderate to large (n>50), and also gave good estimates for small data sets with low skewness. However, when sample sizes were relatively small and the data highly skewed, using the CLT rather than the bootstrap led to slightly more accurate SEs. We conclude that while in general using either method is appropriate, the CLT is easier to implement, and provides SEs that are at least as accurate as the bootstrap.

SIMULTANEOUS CONFIDENCE BOUNDS FOR LOW-DOSE RISK ASSESSMENT WITH NONQUANTAL DATA

We study the use of simultaneous confidence bounds for making low-dose inferences in quantitative risk analysis. Confidence limits are constructed for outcomes measured on a continuous scale, assuming a simple linear model for the observed response. From the simultaneous confidence bounds, simultaneous lower limits on the benchmark dose associated with a particular risk are also constructed.

Statistical determination of cost-effectiveness frontier based on net health benefits

Statistical methods are given for producing a cost-effectiveness frontier for an arbitrary number of programs. In the deterministic case, the net health benefit (NHB) decision rule is optimal; the rule funds the program with the largest positive NHB at each lambda, the amount a decision-maker is willing to pay for an additional unit of effectiveness. For bivariate normally distributed cost and effectiveness variables and a specified lambda, a statistical procedure is presented, based on the method of constrained multiple comparisons with the best (CMCB), for determining the program with the largest NHB. A one-tailed t test is used to determine if the NHB is positive. To obtain a statistical frontier in the lambda-NHB plane, we develop a method to produce the region in which each program has the largest NHB, by pivoting a CMCB confidence interval. A one-sided version of Fieller's theorem is used to determine the region where the NHB of each program is positive. At each lambda, the pointwise error rate is bounded by a prespecified alpha. Upper bounds on the familywise error rate, the probability of an error at any value of lambda, are given. The methods are applied to a hypothetical clinical trial of antipsychotic agents.

The familywise error rate of a simultaneous confidence band for the incremental net health benefit

Interest in the use of net health benefit in cost-effectiveness analysis derives from its optimality property for decision-making. A description of the results of an economic evaluation of health care interventions is incomplete if it does not include point and interval estimates of this outcome measure. A simultaneous confidence band for the incremental net health benefit, INHB(lambda), for all lambda may be obtained by forming a confidence interval based on student's t statistic, and letting the willingness-to-pay value, lambda, run over all values. The familywise error rate (FWER) of the simultaneous confidence band is the probability that the confidence interval does not cover the true INHB(lambda) for some value of lambda. We show that the FWER equals P(T(2)>t(2)), where T(2) follows Hotelling's central distribution and that the simultaneous confidence band does not cover the true INHB(lambda) if and only if a T(2) based confidence ellipsoid does not cover the true mean c-e vector.