OBJECTIVES: To test under which circumstances the normal distribution would generate negative costs in probabilistic sensitivity analysis (PSA), and estimate the impact on PSA results between assuming a normal, gamma or lognormal distribution for costs in cohort models.
METHODS: In PSA, the normal distribution is more likely to generate negative costs if the SE is too high. Therefore, stepwise increasing SE values were tested with 1000 repeats of 1,000,000 samples each. This high number of samples was chosen because it is greater than the 10,000 samples typically generated in PSA and should therefore produce a conservative estimate of the critical SE, the point at which negative costs occur. These computations were performed in R and confirmed in Excel. Subsequently, PSA was run on 4 different real-life cohort models, whose indications included attention deficit hyperactivity disorder, nasal polyps, leukaemia and sarcoma. Each model underwent 2 runs where all costs were gamma distributed (to compare within-distribution vs between-distribution differences), 1 run where all were lognormal and 1 run where all were normal. PSA was run beyond convergence of the cost-effectiveness acceptability curves (i.e. Monte Carlo error < 5%). Each model had its specific set of SEs. No SE exceeded the critical SE.
RESULTS: The normal distribution did not generate negative costs in PSA so long as SE ≤ 16% of the mean cost. Assuming a normal, gamma or lognormal distribution for costs had a negligible impact on the PSA results in our models. The greatest ICER difference was found to be 9% and the resulting CEAC curves were essentially undistinguishable from each other.
CONCLUSIONS: The normal distribution can be used without generating negative costs in PSA so long as SE ≤ 16%. Using a normal, gamma or lognormal distribution for costs makes little difference to the probabilistic ICER or to the CEAC.
