Two common outcomes of Monte Carlo studies in statistics are bias and Type I error rate. Several versions of bias statistics exist but all employ arbitrary cutoffs for deciding when bias is ignorable or non-ignorable. This article argues Type I error rates should be used when assessing bias.
Harwell, M. (2019). The importance of type I error rates when studying bias in Monte Carlo studies in statistics. Journal of Modern Applied Statistical Methods, 18(1), eP3295. doi: 10.22237/jmasm/1556670360