Using Parameter Constraints to Choose State Structures in Cost-Effectiveness Modelling

Howard Thom, Chris Jackson, Nicky Welton, Linda Sharples

This article addresses the choice of state structure in a cost-effectiveness multi-state model. Key model outputs, such as treatment recommendations and prioritisation of future research, may be sensitive to state structure choice. For example, it may be uncertain whether to consider similar disease severities or similar clinical events as the same state or as separate states. Standard statistical methods for comparing models require a common reference dataset but merging states in a model aggregates the data, rendering these methods invalid. We propose a method that involves re-expressing a model with merged states as a model on the larger state space in which particular transition probabilities, costs and utilities are constrained to be equal between states. This produces a model that gives identical estimates of cost effectiveness to the model with merged states, while leaving the data unchanged. The comparison of state structures can be achieved by comparing maximised likelihoods or information criteria between constrained and unconstrained models. We can thus test whether the costs and/or health consequences for a patient in two states are the same, and hence if the states can be merged. We note that different structures can be used for rates, costs and utilities, as appropriate. We illustrate our method with applications to two recent models evaluating the cost effectiveness of prescribing anti-depressant medications by depression severity and the cost effectiveness of diagnostic tests for coronary artery disease. State structures in cost-effectiveness models can be compared using standard methods to compare constrained and unconstrained models.