Probability bound analysis: A novel approach for quantifying parameter uncertainty in decision-analytic modeling and cost-effectiveness analysis

Decisions about health interventions are often made using limited evidence. Mathematical models used to inform such decisions often include uncertainty analysis to account for the effect of uncertainty in the current evidence-base on decisional-relevant quantities. However, current uncertainty quantification methodologies require modelers to specify a precise probability distribution to represent the uncertainty of a model parameter. This study introduces a novel approach for propagating parameter uncertainty, probability bounds analysis (PBA), where the uncertainty about the unknown probability distribution of a model parameter is expressed in terms of an interval bounded by lower and upper bounds on the cumulative distribution function (p-box) and without assuming a particular form of the distribution function. We give the formulas of the p-boxes for common situations (given combinations of data on minimum, maximum, median, mean, or standard deviation), describe an approach to propagate p-boxes into a black-box mathematical model, and introduce an approach for decision-making based on the results of PBA. Then, we demonstrate an application of PBA using a case study. In sum, this study will provide modelers with tools to conduct parameter uncertainty quantification given constraints of available data with the fewest number of assumptions.