Correlations in uncertainty analysis for medical decision making: an application to heart-valve replacement

A Monte Carlo uncertainty analysis with correlations between parameters is applied to a Markov-chain model that is used to support the choice of a replacement heart-valve. The objective is to quantify the effects of uncertainty in and of correlations between probabilities of valve-related events on the life expectancies of four valve types. The uncertainty in the logit- and log-transformed parameters-mostly representing probabilities and durations-is modeled as a multivariate normal distribution. The univariate distributions are obtained through values for the median and the 0.975 quantile of each parameter. Correlations between parameters are difficult to quantify. A sensitivity analysis is suggested to study their influences on the uncertainty in valve preference prior to further elicitation efforts. The results of the uncertainty analysis strengthen the conclusions from a preceding study, which did not include uncertainty in the model parameters, where the homograft turned out to be the best choice. It is concluded that the influence of correlations is limited in most cases. Preference statements become more certain when the correlation between valve types increases.