SOME HEALTH STATES ARE CERTAINLY BETTER THAN OTHERS: USING HEALTH STATE RANK ORDER TO IMPROVE PROBABILISTIC SENSITIVITY ANALYSES

Purpose: Standard probabilistic sensitivity analyses (PSA) may lead risk-averse policymakers to take non-optimal actions due to misestimates of decision uncertainty. This occurs because PSAs typically assume independent univariate uncertainty distributions, inducing bias when the true joint distribution contains correlation. We developed a method to extract correlations for joint uncertainty distributions of QALY weights that exploits the additional information contained in ordinal preferences over corresponding health states (i.e., perfect health is strictly preferred to cancer).

Method: Our method takes as inputs a health state preference ordering and univariate uncertainty distributions for each QALY weight. It samples and sorts values from each uncertainty distribution. Then, it establishes a correlation matrix roughly representing the Spearman correlation between QALY weights intended to preserve the preference ordering. Using the correlation matrix and a set of standard normal distributions, it samples a set of correlated values that it then transforms to correlated rank-orders. The rank-orders are used to index the sorted QALY weight samples, producing correlated QALY weight samples that preserve the preference ordering. It calculates the proportion of samples violating the preference ordering and iteratively adjusts the correlation matrix until the proportion of violations is below a user-defined tolerance, finally discarding these few samples. We illustrate our method using a 4 health state Markov model with a decision between Medical Therapy and Surgery, considering 3 scenarios in which the expected values of QALY weights remain fixed but uncertainty is varied. Finally, we compare our method to alternative approaches in terms of satisfying a set of ideal properties (e.g., preserving marginal uncertainty distributions).

Result: In scenarios with moderate-to-high uncertainty, standard PSA (correlation=0) resulted in preference ordering violations considerably in excess of our method (correlations >0.50) (Figure 1, Panel A). For example, with moderate uncertainty, standard PSA violations exceeded 30% vs. 5% with our method. Standard PSA also underestimated the likelihood of Medical Therapy being optimal and overestimated the Expected Value of Partial Perfect Information (EVPPI) (Figure 1, Panels B-C). While our method closely preserves marginal uncertainty distributions, using standard PSA but discarding violations does not.

Conclusion: We provide open-source implementations of the method in Matlab and Excel to support analysts in better characterizing the joint uncertainty of QALY weights and hence improving the accuracy of PSAs and Value-of-Information analyses.