Probabilistic sensitivity analysis in cost-effectiveness models: determining model convergence in cohort models

Probabilistic sensitivity analysis (PSA) demonstrates the parameter uncertainty in a decision problem. The technique involves sampling parameters from their respective distributions (rather than simply using mean/median parameter values). Guidance in the literature, and from health technology assessment bodies, on the number of simulations that should be performed suggests a 'sufficient number', or until 'convergence', which is seldom defined. The objective of this tutorial is to describe possible outcomes from PSA, discuss appropriate levels of accuracy, and present guidance by which an analyst can determine if a sufficient number of simulations have been conducted, such that results are considered to have converged. The proposed approach considers the variance of the outcomes of interest in cost-effectiveness analysis as a function of the number of simulations. A worked example of the technique is presented using results from a published model, with recommendations made on best practice. While the technique presented remains essentially arbitrary, it does give a mechanism for assessing the level of simulation error, and thus represents an advance over current practice of a round number of simulations with no assessment of model convergence.