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Abstract
Background
Findings from a VOI analysis are generally reported via several summary measures, described in detail below. The expected value of perfect information (EVPI) and the expected value of partial perfect information (EVPPI) are normally graphically presented over a range of willingness-to-pay (WTP) thresholds. In contrast, VOI analyses typically only report point estimates of measures of the expected value of sample information (EVSI), the expected net benefit of sampling (ENBS), and the optimal sample size (𝑛∗), which is the sample size that maximizes the ENBS of a data collection process (i.e., research study) that aims to reduce decision uncertainty (i.e., 𝑛∗ at a single WTP). However, as we illustrate below, 𝑛∗ can be sensitive to a decision maker’s WTP threshold. To increase the utility of VOI analyses, researchers should not only report point estimates for all VOI measures, but should report 𝑛∗ over a range of WTP thresholds and variation in 𝑛∗ in VOI parameters (e.g., cost of research).
Our objective is to help analysts report 𝑛∗ over a relevant set of sensitivity analyses on VOI-specific parameters that can help decision makers better understand findings from VOI analyses. We introduce the curve of optimal sample size (COSS), which is a graphical representation of 𝑛∗ over a range of WTP thresholds and can also be used to show how 𝑛∗ changes based on VOI-specific parameters. The COSS shows 𝑛∗ in a single figure for a range of decision maker operating characteristics, and it represents an additional graphical approach to summarize results from a VOI analysis.
Methods
We first identified values for the VOI parameters for the WTP threshold (input #1), discount rate (input #2), decision lifetime (input #3), number of prevalent gout cases that could benefit from the decision (input #4), and number of future incident gout cases that could benefit from the decision (input #5). We adopted a WTP range of $US0–$US150,000 per quality-adjusted life year (QALY) based on recommended decision thresholds (see the electronic supplementary material, eTable 2 assumptions of VOI analysis). Without an a priori decision threshold, we could also identify the range of WTP values for use in the VOI by identifying regions on the cost-effectiveness acceptability curve and frontier derived from the PSA where there is meaningful uncertainty regarding the optimal strategy (see eFigure 1 in the electronic supplementary material). We chose a discount rate of 3%, which corresponds with guidelines for discounting in cost-effectiveness analyses, and a decision lifetime of 5 years, which corresponds with the remaining lifetime of the patent for febuxostat. The numbers of prevalent and incident gout patients who could benefit from the decision regarding the cost-effectiveness of urate-lowering treatment strategies were obtained from epidemiological data
Results
From the COSS, a decision maker is able to determine the optimal sample size for a study design given their a priori WTP threshold. For example, given a decision maker’s WTP is $US50,000 per QALY, an observational study collecting data on health utilities should enroll 4300 subjects (rounded to nearest 25th) and a randomized trial on the effectiveness of allopurinol dose escalation should enroll 100 subjects, or 50 per arm. From a research prioritization perspective, the decision maker must also evaluate the ENBS of the proposed study designs to determine which study generates the largest benefit. While the optimal sample size of the randomized trial is less than that for the observational study, the ENBS of the randomized trial is greater, indicating it will generate a larger reduction in uncertainty.
Conclusions
VOI should be used beyond just informing the value of eliminating uncertainty and can and should inform future research funding and study design. Recent methodological developments allow researchers to quickly and efficiently calculate VOI measures. Similar to cost-effectiveness analyses, sensitivity analyses in VOI analysis should become the norm. To support the reporting of sensitivity analysis of parameters and assumptions, we propose the COSS as a standard for graphically representing 𝑛∗ over a range of WTP values and VOI parameters.