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

Rowan Iskandar

doi:10.1002/sim.9195

Abstract

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 representing and 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 vs 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.

Highlights

Decision-analytic models (DAMs) have been used in numerous applications, from clinical decision-making to cost-effectiveness analysis (CEA)
The importance of explicitly accounting for incomplete knowledge about model parameters and propagating its effect through a decisional process is underscored in numerous guidance documents in health, including, but not limited to, the guidelines by the International Society for Pharmacoeconomics and Outcomes Research (ISPOR)-Society for Medical Decision Making (SMDM),[5] the Agency for Healthcare Research and Quality (AHRQ),[6] the 2nd panel for Cost-Effectiveness Analysis (CEA) in Health and Medicine,[7] and beyond.[8]
The goal of this paper is to introduce the probability bounds analysis (PBA) method for representing and propagating parameter uncertainty in situations where knowledge or data about the parameter is limited and a probability distribution can not be specified precisely or the practitioners are not willing to commit to a particular form

Summary

Introduction

Decision-analytic models (DAMs) have been used in numerous applications, from clinical decision-making to cost-effectiveness analysis (CEA). We only know the measures of central tendency (mean or median) from published papers, while, in more extreme cases, only the minimum and maximum values are known to the researchers. To handle such data sparsity situations, it is necessary to have an approach for quantifying parameter uncertainty using the fewest number of assumptions and without the need for assuming precise probability distributions

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