Health economic decision models often involve a wide-ranging and complicated synthesis of evidence from a number of sources, making design and implementation of such models resource-heavy. When new data become available and reassessment of treatment recommendations is warranted, it may be more efficient to perform a Bayesian update of an existing model than to construct a new model. If the existing model depends on many, possibly correlated, covariates, then an update may produce biased estimates of model parameters if some of these covariates are completely absent from the new data. Motivated by the need to update a cost-effectiveness analysis comparing diagnostic strategies for coronary heart disease, this study develops methods to overcome this obstacle by either introducing additional data or using results from previous studies. We outline a framework to handle unobserved covariates, and use our motivating example to illustrate both the flexibility of the proposed methods and some potential difficulties in applying them.