INTRODUCING THE CURVE OF OPTIMAL SAMPLE SIZE (COSS): A GRAPHIC REPRESENTATION OF OPTIMAL SAMPLE SIZE BY WILLINGNESS-TO-PAY THRESHOLD

Purpose: The optimal sample size (n*) informs trial design and research prioritization and is one of the most powerful aspects of value of information analysis.  Using a metamodeling approach we computed n* over a range of willingness-to-pay thresholds (WTP) to inform study designs. We refer to this new representation as the curve of optimal sample size (COSS). 

Methods: We used output generated from a probabilistic sensitivity analysis of a cost-effectiveness analysis to: (1) Calculate the partial expected value of sample information for each parameter on a population level (popEVPSI), (2) Calculate the expected net benefit of sampling (ENBS) by comparing popEVPSI with the cost of conducting a research study to collect information on the parameter, (3) Obtain n* of future research studies where ENBS reaches a maximum, (4) Recalculate n* for various WTP. This approach can also be applied to sets of parameters. We assumed the same study design and cost per patient to collect information for all relevant parameters, though different costs for different parameters or sets of parameters can be used. The approach is illustrated with a published cost-effectiveness analysis of urate-lowering treatment strategies for the management of gout.

Results: The cost-effectiveness acceptability curve in Figure 1a shows that three strategies are optimal over a wide range of WTP. The thresholds at which the optimal strategy switches are $65,000 and $370,000 per quality-adjusted life year (QALY). COSS in Figure 1b shows n* for model parameters over a range of WTP. For the parameter evaluating allopurinol effectiveness n* ranges between 0-1,450 for WTP $135,000-$400,000 per QALY. Other parameters have positive n* but only within a smaller range of WTP, particularly where these parameters are part of strategies that compete at each threshold. For example, if WTP were $50,000-$70,000 per QALY then n* would be ~900 for utility studies and ~400 for efficacy studies. Information about treatments' effectiveness and differences in state utilities is valuable at defined WTP ranges in terms of its return on future research.

Conclusions: While CEAC displays which strategies are optimal over a certain range of WTP, COSS shows the parameters that are relevant to collect information and its corresponding n* at these WTP. This is an improvement over traditional implementations that only evaluate n* for a single WTP.