There are a growing number of item response theory (IRT) studies that calibrate different patient-reported outcome (PRO) measures, such as anxiety, depression, physical function, and pain, on common, instrument-independent metrics. In the case of depression, it has been reported that there are considerable mean score differences when scoring on a common metric from different, previously linked instruments. Ideally, those estimates should be the same. We investigated to what extent those differences are influenced by different scoring methods that take into account several levels of uncertainty, such as measurement error (through plausible value imputation) and item parameter uncertainty (through full Bayesian IRT modeling). Depression estimates from different instruments were more similar, and their corresponding confidence/credible intervals were larger when plausible value imputation or Bayesian modeling was used, compared to the direct use of expected a posteriori (EAP) estimates. Furthermore, we explored the use of Bayesian IRT models to update item parameters based on newly collected data.