Representing both first- and second-order uncertainties by Monte Carlo simulation for groups of patients

Actual implementation of probabilistic sensitivity analysis may lead to misleading or improper conclusions when it is applied to groups of patients rather than individual patients. The practice of combining first- and second-order simulations when modeling the outcome for a group of more than one patient yields an erroneous marginal distribution whenever the parameter values are randomly sampled for each patient while the results are presented as simulated means for the group of patients. This practice results in underrepresenting the second-order uncertainty. It may also distort the shape (especially the symmetry or extent of the tails) in the simulated distribution. As a result, it may lead to premature or incorrect conclusions of superiority. It may also result in inappropriate estimates of the value of further research to inform parameter values.