The implications of parameter independence in probabilistic sensitivity analysis: An empirical test

Abstract: 

OBJECTIVES: In probabilistic sensitivity analysis (PSA), it is typical to see distributions assigned to all (relevant) parameters in a model. However, attention is only usually paid to estimating covariance or interactions between a small number of parameters, if any at all. This study explores the impact of interaction and non-interaction assumptions on the outcomes of PSA.

METHODS: A simple eight-state Markov model was developed, with corresponding input parameters for transition probabilities, costs and utilities for all health states. A range of alternative approaches to parameter correlation were taken, ranging from zero correlation to extreme cases such as ‘full dependent interaction’. These were applied to a range of different structural assumptions in the model (for example, rather than a single input parameter for 'monthly cost of health state X', individual parameters were created for 'cost of physician visits', 'cost of tests', 'cost of drugs', 'cost of hospital visits', etc). The impact of all permutations on the shapes of the PSA scatter plot and CEAC was recorded.

RESULTS: The analysis demonstrates that, if a specific input parameter is broken down into several components which are varied independently, then it is likely that the variation in each parameter will cancel out the effect of the changes in the other parameters, suggesting a false level of certainty in the PSA's results. The extent of this outcome depended on a number of factors, such as the complexity of the model structure, the proximity of the model’s base case results to the cost-effectiveness threshold and the level of artificial correlation applied to each parameter.

CONCLUSIONS: This analysis demonstrates the outcomes of a PSA can be influenced by the level of detail that the modellers choose to include and, counterintuitively, modellers can create 'false' confidence in PSA results by including more parameters. A number of recommendations are provided for the critical appraisal of probabilistic model outputs.