Investigating Input Correlation in Probabilistic Sensitivity Analysis

OBJECTIVES: Probabilistic sensitivity analysis (PSA) is used to characterize uncertainty in cost-effectiveness models. Inputs in PSA are often varied independently even when they may be correlated. This study investigated the effects of input correlation on PSA outputs.

METHODS: A Markov model was developed using R and Shiny to compare a hypothetical treatment and comparator. Three options were built into the model: no correlation (inputs varied independently); part correlation (correlation within but not between costs, utilities and transition matrices); and full correlation (correlation between all inputs). Inputs which improved the incremental cost-effectiveness ratio (ICER) were positively correlated with each other and negatively correlated with inputs which worsened the ICER, and vice versa. The treatment cost and the number of health states and health state costs were varied in scenario analyses to determine the circumstances in which correlation had the largest impact.

RESULTS: While the ICER was comparable across all correlation options, the likelihood of cost-effectiveness differed substantially from 61% to 93%. In all scenarios, the ‘no correlation’ option displayed the most certain likelihood (closest to either 0 or 1) of cost-effectiveness, while the least certain was produced by the full correlation option. The greater the complexity of the model (i.e. the greater the number of health states), the more pronounced the difference between correlating or not correlating inputs. Counterintuitively, correlating inputs increases uncertainty because it allows for a greater number of ‘extreme’ scenarios to be generated, whereas allowing independent generation of large numbers of inputs tends to lead to a ‘cancelling out’ effect. This effect is most pronounced when the ICER is moderately close to the willingness-to-pay threshold.

CONCLUSIONS: This analysis demonstrates that input correlation can have a substantial impact on the level of certainty in model outputs, and by ignoring this, the model may be over- or under-stating the true level of confidence.