Handling Parameter Uncertainty in Cost-Effectiveness Models Simply and Responsibly

Cost-effectiveness models inevitably involve uncertainty. Among the different sources of uncertainty, parameter uncertainty, also known as second-order uncertainty, is defined as uncertainty about the true values of the parameters used as model inputs. Because the decisions informed by the model are affected by parameter uncertainty, it is important to represent parameter uncertainty well and completely. Traditionally, parameter uncertainty has been represented through a deterministic approach, which varies parameter values one at a time or several at a time over plausible ranges, to test how a model’s outcomes vary. Deterministic sensitivity analysis may take the form of threshold analysis, identifying the parameter value above or below which the decision changes, or scenario analysis, exploring scenarios defined by combinations of parameters, including best and worst cases. These analyses are straightforward for analysts and easily understood by decision makers, but they do not incorporate the probability of different parameter values, nor do they account for correlation among parameters. These limitations are addressed by probabilistic sensitivity analysis (PSA). In PSA, each parameter is assigned a distribution and all parameters are varied simultaneously through Monte Carlo simulation. The results of a PSA are typically summarized by showing the distributions of the main outcomes on the cost-effectiveness plane or in cost-effectiveness acceptability curves. A PSA that samples from the joint posterior distribution of parameters allows analysts to reflect correlation and thus correctly calculate expected values of model outcomes in nonlinear models, even when parameters are correlated. In addition, the outputs of a PSA enable analysts to conduct further analyses of parameter uncertainty, including analysis of covariance (ANCOVA) and value of information (VOI) analysis. ANCOVA calculates the sensitivity of the incremental costeffectiveness ratio or net monetary benefit to individual parameter values. VOI includes expected value of perfect information (EVPI), which provides an estimate of the upper limit on returns to future research on all model parameters, and expected value of partial perfect information (EVPPI), which identifies the value of future research for a specific parameter or set of parameters. The recent report on model parameter estimation and uncertainty analysis by the ISPOR-SMDM Modeling Good Research Practices Task Force recommends EVPI as the best measure of uncertainty surrounding a particular decision. EVPPI is considered the most advanced measure of parameter importance (influence), but estimation of EVPPI through 2-loop Monte Carlo simulation can be computationally burdensome, although there have been efforts to increase the efficiency of the process. There have been several guidelines for conducting sensitivity analysis, but there has not been clear guidance on how much more we learn from complex methods of modeling uncertainty (PSA and EVPI or Received 10 December 2014 from the Department of Management, Policy, and Community Health, University of Texas School of Public Health, San Antonio, TX, USA (SYK); Institute for Health and Department of Economics, Rutgers University, New Brunswick, NJ, USA (LBR); and Department of Preventive Medicine and Community Health, New Jersey Medical School, Rutgers University, Newark, NJ, USA (AS). Revision accepted for publication 15 December 2014.