Value of Information: We've Got Speed, What More Do We Need?

Value of Information for Clinical Trial Design: The Importance of Considering All Relevant Comparators

Value of Information (VOI) analyses calculate the economic value that could be generated by obtaining further information to reduce uncertainty in a health economic decision model. VOI has been suggested as a tool for research prioritisation and trial design as it can highlight economically valuable avenues for future research. Recent methodological advances have made it increasingly feasible to use VOI in practice for research; however, there are critical differences between the VOI approach and the standard methods used to design research studies such as clinical trials. We aimed to highlight key differences between the research design approach based on VOI and standard clinical trial design methods, in particular the importance of considering the full decision context. We present two hypothetical examples to demonstrate that VOI methods are only accurate when (1) all feasible comparators are included in the decision model when designing research, and (2) all comparators are retained in the decision model once the data have been collected and a final treatment recommendation is made. Omitting comparators from either the design or analysis phase of research when using VOI methods can lead to incorrect trial designs and/or treatment recommendations. Overall, we conclude that incorrectly specifying the health economic model by ignoring potential comparators can lead to misleading VOI results and potentially waste scarce research resources.

Simulating Study Data to Support Expected Value of Sample Information Calculations: A Tutorial

The expected value of sample information (EVSI) can be used to prioritize avenues for future research and design studies that support medical decision making and offer value for money spent. EVSI is calculated based on 3 key elements. Two of these, a probabilistic model-based economic evaluation and updating model uncertainty based on simulated data, have been frequently discussed in the literature. By contrast, the third element, simulating data from the proposed studies, has received little attention. This tutorial contributes to bridging this gap by providing a step-by-step guide to simulating study data for EVSI calculations. We discuss a general-purpose algorithm for simulating data and demonstrate its use to simulate 3 different outcome types. We then discuss how to induce correlations in the generated data, how to adjust for common issues in study implementation such as missingness and censoring, and how individual patient data from previous studies can be leveraged to undertake EVSI calculations. For all examples, we provide comprehensive code written in the R language and, where possible, Excel spreadsheets in the supplementary materials. This tutorial facilitates practical EVSI calculations and allows EVSI to be used to prioritize research and design studies.

Multilevel and Quasi Monte Carlo Methods for the Calculation of the Expected Value of Partial Perfect Information

The expected value of partial perfect information (EVPPI) provides an upper bound on the value of collecting further evidence on a set of inputs to a cost-effectiveness decision model. Standard Monte Carlo estimation of EVPPI is computationally expensive as it requires nested simulation. Alternatives based on regression approximations to the model have been developed but are not practicable when the number of uncertain parameters of interest is large and when parameter estimates are highly correlated. The error associated with the regression approximation is difficult to determine, while MC allows the bias and precision to be controlled. In this article, we explore the potential of quasi Monte Carlo (QMC) and multilevel Monte Carlo (MLMC) estimation to reduce the computational cost of estimating EVPPI by reducing the variance compared with MC while preserving accuracy. We also develop methods to apply QMC and MLMC to EVPPI, addressing particular challenges that arise where Markov chain Monte Carlo (MCMC) has been used to estimate input parameter distributions. We illustrate the methods using 2 examples: a simplified decision tree model for treatments for depression and a complex Markov model for treatments to prevent stroke in atrial fibrillation, both of which use MCMC inputs. We compare the performance of QMC and MLMC with MC and the approximation techniques of generalized additive model (GAM) regression, Gaussian process (GP) regression, and integrated nested Laplace approximations (INLA-GP). We found QMC and MLMC to offer substantial computational savings when parameter sets are large and correlated and when the EVPPI is large. We also found that GP and INLA-GP were biased in those situations, whereas GAM cannot estimate EVPPI for large parameter sets.

Calculating the Expected Value of Sample Information in Practice: Considerations from 3 Case Studies

Background. Investing efficiently in future research to improve policy decisions is an important goal. Expected value of sample information (EVSI) can be used to select the specific design and sample size of a proposed study by assessing the benefit of a range of different studies. Estimating EVSI with the standard nested Monte Carlo algorithm has a notoriously high computational burden, especially when using a complex decision model or when optimizing over study sample sizes and designs. Recently, several more efficient EVSI approximation methods have been developed. However, these approximation methods have not been compared, and therefore their comparative performance across different examples has not been explored. Methods. We compared 4 EVSI methods using 3 previously published health economic models. The examples were chosen to represent a range of real-world contexts, including situations with multiple study outcomes, missing data, and data from an observational rather than a randomized study. The computational speed and accuracy of each method were compared. Results. In each example, the approximation methods took minutes or hours to achieve reasonably accurate EVSI estimates, whereas the traditional Monte Carlo method took weeks. Specific methods are particularly suited to problems where we wish to compare multiple proposed sample sizes, when the proposed sample size is large, or when the health economic model is computationally expensive. Conclusions. As all the evaluated methods gave estimates similar to those given by traditional Monte Carlo, we suggest that EVSI can now be efficiently computed with confidence in realistic examples. No systematically superior EVSI computation method exists as the properties of the different methods depend on the underlying health economic model, data generation process, and user expertise.

Value of Information Analytical Methods: Report 2 of the ISPOR Value of Information Analysis Emerging Good Practices Task Force

The allocation of healthcare resources among competing priorities requires an assessment of the expected costs and health effects of investing resources in the activities and of the opportunity cost of the expenditure. To date, much effort has been devoted to assessing the expected costs and health effects, but there remains an important need to also reflect the consequences of uncertainty in resource allocation decisions and the value of further research to reduce uncertainty. Decision making with uncertainty may turn out to be suboptimal, resulting in health loss. Consequently, there may be value in reducing uncertainty, through the collection of new evidence, to better inform resource decisions. This value can be quantified using value of information (VOI) analysis. This report from the ISPOR VOI Task Force describes methods for computing 4 VOI measures: the expected value of perfect information, expected value of partial perfect information (EVPPI), expected value of sample information (EVSI), and expected net benefit of sampling (ENBS). Several methods exist for computing EVPPI and EVSI, and this report provides guidance on selecting the most appropriate method based on the features of the decision problem. The report provides a number of recommendations for good practice when planning, undertaking, or reviewing VOI analyses. The software needed to compute VOI is discussed, and areas for future research are highlighted.

Directly Acting Oral Anticoagulants for the Prevention of Stroke in Atrial Fibrillation in England and Wales: Cost-Effectiveness Model and Value of Information Analysis

Objectives. Determine the optimal, licensed, first-line anticoagulant for prevention of ischemic stroke in patients with non-valvular atrial fibrillation (AF) in England and Wales from the UK National Health Service (NHS) perspective and estimate value to decision making of further research. Methods. We developed a cost-effectiveness model to compare warfarin (international normalized ratio target range 2-3) with directly acting (or non-vitamin K antagonist) oral anticoagulants (DOACs) apixaban 5 mg, dabigatran 150 mg, edoxaban 60 mg, and rivaroxaban 20 mg, over 30 years post treatment initiation. In addition to death, the 17-state Markov model included the events stroke, bleed, myocardial infarction, and intracranial hemorrhage. Input parameters were informed by systematic literature reviews and network meta-analysis. Expected value of perfect information (EVPI) and expected value of partial perfect information (EVPPI) were estimated to provide an upper bound on value of further research. Results. At willingness-to-pay threshold £20,000, all DOACs have positive expected incremental net benefit compared to warfarin, suggesting they are likely cost-effective. Apixaban has highest expected incremental net benefit (£7533), followed by dabigatran (£6365), rivaroxaban (£5279), and edoxaban (£5212). There was considerable uncertainty as to the optimal DOAC, with the probability apixaban has highest net benefit only 60%. Total estimated population EVPI was £17.94 million (17.85 million, 18.03 million), with relative effect between apixaban versus dabigatran making the largest contribution with EVPPI of £7.95 million (7.66 million, 8.24 million). Conclusions. At willingness-to-pay threshold £20,000, all DOACs have higher expected net benefit than warfarin but there is considerable uncertainty between the DOACs. Apixaban had the highest expected net benefit and greatest probability of having highest net benefit, but there is considerable uncertainty between DOACs. A head-to-head apixaban versus dabigatran trial may be of value.

Clinical and cost-effectiveness of the Ross procedure versus conventional aortic valve replacement in young adults

Objectives

In young and middle-aged adults, there are three current options for aortic valve replacement (AVR), namely mechanical AVR (mechAVR), tissue AVR (biological AVR) and the Ross operation, with no clear guidance on the best option. We aim to compare the clinical effectiveness and cost-effectiveness of the Ross procedure with conventional AVR in young and middle-aged adults.

Methods

This is a systematic literature review and meta-analysis of AVR options. Markov multistate model was adopted to compare cost-effectiveness. Lifetime costs, quality-adjusted life years (QALYs), net monetary benefit (NMB), population expected value of perfect information (EVPI) and expected value of partial perfect information were estimated.

Results

We identified 48 cohorts with a total number of 12 975 patients (mean age 44.5 years, mean follow-up 7.1 years). Mortality, bleeding and thromboembolic events over the follow-up period were lowest after the Ross operation, compared with mechAVR and biological AVR (p<0.001). Aortic reoperation rates were lower after Ross compared with biological AVR, but slightly higher when compared with mechAVR (p<0.001). At a willingness-to-pay threshold of £20effective. At a willingness-to-pay threshold of £20, 000 per QALY000 per QALY, the Ross procedure is more cost-effective compared the Ross procedure is more cost-effective compared withwith conventional AVR, with a lifetime incremental NMB of £60 conventional AVR, with a lifetime incremental NMB of £60 952 (952 (££3030 236236 to to ££7979 464). Incremental costs were £12464). Incremental costs were £12 323 (323 (££61086108 to to ££1515 972) and incremental QALYs 3.66 (1.81972) and incremental QALYs 3.66 (1.81 to to 4.76). The population EVPI indicates that a trial costing up to £2.03 million could be cost 4.76). The population EVPI indicates that a trial costing up to £2.03 million could be cost--effective.

At a willingness-to-pay threshold of £20 000 per QALY, the Ross procedure is more cost-effective compared with conventional AVR, with a lifetime incremental NMB of £60 952 (£30 236 to £79 464). Incremental costs were £12 323 (£6108 to £15 972) and incremental QALYs 3.66 (1.81 to 4.76). The population EVPI indicates that a trial costing up to £2.03 million could be cost-effective.

Conclusions

In young and middle-aged adults with aortic valve disease, the Ross procedure may confer greater quality of life and be more cost-effective than conventional AVR. A high-quality randomised trial could be warranted and cost-effective.

A Gaussian Approximation Approach for Value of Information Analysis

Most decisions are associated with uncertainty. Value of information (VOI) analysis quantifies the opportunity loss associated with choosing a suboptimal intervention based on current imperfect information. VOI can inform the value of collecting additional information, resource allocation, research prioritization, and future research designs. However, in practice, VOI remains underused due to many conceptual and computational challenges associated with its application. Expected value of sample information (EVSI) is rooted in Bayesian statistical decision theory and measures the value of information from a finite sample. The past few years have witnessed a dramatic growth in computationally efficient methods to calculate EVSI, including metamodeling. However, little research has been done to simplify the experimental data collection step inherent to all EVSI computations, especially for correlated model parameters. This article proposes a general Gaussian approximation (GA) of the traditional Bayesian updating approach based on the original work by Raiffa and Schlaifer to compute EVSI. The proposed approach uses a single probabilistic sensitivity analysis (PSA) data set and involves 2 steps: 1) a linear metamodel step to compute the EVSI on the preposterior distributions and 2) a GA step to compute the preposterior distribution of the parameters of interest. The proposed approach is efficient and can be applied for a wide range of data collection designs involving multiple non-Gaussian parameters and unbalanced study designs. Our approach is particularly useful when the parameters of an economic evaluation are correlated or interact.

Implementing Generalized Additive Models to Estimate the Expected Value of Sample Information in a Microsimulation Model: Results of Three Case Studies

BACKGROUND

The expected value of sample information (EVSI) can help prioritize research but its application is hampered by computational infeasibility, especially for complex models. We investigated an approach by Strong and colleagues to estimate EVSI by applying generalized additive models (GAM) to results generated from a probabilistic sensitivity analysis (PSA).

METHODS

For 3 potential HIV prevention and treatment strategies, we estimated life expectancy and lifetime costs using the Cost-effectiveness of Preventing AIDS Complications (CEPAC) model, a complex patient-level microsimulation model of HIV progression. We fitted a GAM-a flexible regression model that estimates the functional form as part of the model fitting process-to the incremental net monetary benefits obtained from the CEPAC PSA. For each case study, we calculated the expected value of partial perfect information (EVPPI) using both the conventional nested Monte Carlo approach and the GAM approach. EVSI was calculated using the GAM approach.

RESULTS

For all 3 case studies, the GAM approach consistently gave similar estimates of EVPPI compared with the conventional approach. The EVSI behaved as expected: it increased and converged to EVPPI for larger sample sizes. For each case study, generating the PSA results for the GAM approach required 3 to 4 days on a shared cluster, after which EVPPI and EVSI across a range of sample sizes were evaluated in minutes. The conventional approach required approximately 5 weeks for the EVPPI calculation alone.

CONCLUSION

Estimating EVSI using the GAM approach with results from a PSA dramatically reduced the time required to conduct a computationally intense project, which would otherwise have been impractical. Using the GAM approach, we can efficiently provide policy makers with EVSI estimates, even for complex patient-level microsimulation models.

Efficient Value of Information Calculation Using a Nonparametric Regression Approach: An Applied Perspective

BACKGROUND

Value-of-information (VOI) analysis provides an analytical framework to assess whether obtaining additional evidence is worthwhile to reduce decision uncertainty. The reporting of VOI measures, particularly the expected value of perfect parameter information (EVPPI) and the expected value of sample information (EVSI), is limited because of the computational burden associated with typical two-level Monte-Carlo-based solution. Recently, a nonparametric regression approach was proposed that allows the estimation of multiparameter EVPPI and EVSI directly from a probabilistic sensitivity analysis sample.

OBJECTIVES

To demonstrate the value of the nonparametric regression approach in calculating VOI measures in real-world cases and to compare its performance with the standard approach of the Monte-Carlo simulation.

METHODS

We used the regression approach to calculate EVPPI and EVSI in two models, and compared the results with the estimates obtained via the standard Monte-Carlo simulation.

RESULTS

The VOI values from the two approaches were very close; computation using the regression method, however, was faster.

CONCLUSION

The nonparametric regression approach provides an efficient and easy-to-implement alternative for EVPPI and EVSI calculation in economic models.

Value of Information: A Tool to Improve Research Prioritization and Reduce Waste

In a Guest Editorial, Cosetta Minelli and Gianluca Baio explain how VOI analysis can prioritize research projects by identifying uncertainty in existing knowledge and then estimating expected benefits from reducing that uncertainty.