OBJECTIVES: Probabilistic sensitivity analysis (PSA) in economic models involves sampling of model parameters from probability distributions and often assumes their independence. For parameters with known order, such as utilities or costs by disease severity, PSA may lead to inconsistent samples. In such cases, the recent ISPOR guidelines on health-state utilities recommend using the difference method. This method is cumbersome to implement as it requires additional sampling to obtain the required sampling parameters. We present an alternative method for sampling ordered bounded parameters that does not present such difficulty.

METHODS: Assuming two ordered and bounded random variables X₁ and X_2, with E(X₁) ≥ E(X₂), an ancillary random variable Y is introduced as the ratio of the lower (X₂) to the higher (X₁) variable. This variable is bounded in [0–1], with mean and variance calculated from the means and variances of X₁ and X₂. Samples of X₂ can then be generated by sampling X₁ and Y independently and setting X₂ = Y ∙ X₁. We tested this method under a range of scenarios, discussed its applicability, accuracy and limitations, and compared it both with independent sampling and with the difference method.

RESULTS: The method was able to match the mean and variance of the sampled parameters across all scenarios. No correlation between parameters other than that imposed by the ordering was detected in a visual inspection of their joint distributions. For certain combinations of means and variances (small differences in means but large differences in variances), a minor adjustment of the method was required.

CONCLUSIONS: The proposed method generates PSA samples in accordance to the bounds, order, and summary statistics of the sampled parameters. In comparison to the difference method, this method is easier to implement, as all distribution parameters can be calculated analytically, and no additional sampling is required.