  Purpose: Bayesian calibration is theoretically superior to standard
direct-search algorithm because it can reveal the full joint posterior
distribution of the calibrated parameters. However, to date, Bayesian
calibration has not been used often in health decision sciences due to
practical and computational burdens. In this paper we propose to use artificial
neural networks (ANN) as one solution to these limitations.
  Methods: Bayesian Calibration using Artificial Neural Networks (BayCANN)
involves (1) training an ANN metamodel on a sample of model inputs and outputs,
and (2) then calibrating the trained ANN metamodel instead of the full model in
a probabilistic programming language to obtain the posterior joint distribution
of the calibrated parameters. We demonstrate BayCANN by calibrating a natural
history model of colorectal cancer to adenoma prevalence and cancer incidence
data. In addition, we compare the efficiency and accuracy of BayCANN against
performing a Bayesian calibration directly on the simulation model using an
incremental mixture importance sampling (IMIS) algorithm.
  Results: BayCANN was generally more accurate than IMIS in recovering the
"true" parameter values. The ratio of the absolute ANN deviation from the truth
compared to IMIS for eight out of the nine calibrated parameters were less than
one indicating that BayCANN was more accurate than IMIS. In addition, BayCANN
took about 15 minutes total compared to the IMIS method which took 80 minutes.
  Conclusions: In our case study, BayCANN was more accurate than IMIS and was
five-folds faster. Because BayCANN does not depend on the structure of the
simulation model, it can be adapted to models of various levels of complexity
with minor changes to its structure. We provide BayCANN's open-source
implementation in R.
