A New Approach for Sampling Ordered Parameters in Probabilistic Sensitivity Analysis

Probabilistic sensitivity analysis (PSA) in cost-effectiveness analysis involves sampling a large number of realisations of an economic model. For some parameters, we may be uncertain around the true mean values of the variables, but the ordering of the values is known. Typical sampling approaches lack either statistical or clinical validity. For example, sampling using a common number generator results in extreme dependence, and independent sampling can lead to realisations with incorrect ordering.

We propose a new sampling approach for ordered parameters, the difference method (DM) approach, which samples the parameters of interest via a difference parameter. If the parameters of interest are bounded, it involves transforming the variables so that they are unbounded and then sampling via the difference parameter. We have provided a Microsoft Excel workbook to implement the method. The proposed approach is illustrated with an example sampling ordered parameters for utility and cost.

The DM approach has a number of advantages when comparing with the typical approaches used in practice. It generates PSA samples that have similar summary statistics as the given values in our examples, while maintaining the constraint that one value was greater than another. The method also implies plausible positive correlation between the two ordered variables.

Both clinical and statistical validity should be checked when producing PSA samples. The DM approach should be considered as a solution to potential problems in generating PSA samples for ordered parameters.