  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 decision-relevant quantities. However, current uncertainty quantification
methodologies, including probabilistic sensitivity analysis (PSA), 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
unknown 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. We demonstrate the characteristics
and utility of PBA versus PSA using two case studies. In sum, this study
provides modelers with practical tools to conduct parameter uncertainty
quantification given the constraints of available data and with the fewest
assumptions.
