absolute bias and absolute relative bias

[ilovemane]

Hey, this is a fantastic package and really useful.
It is really popular to report absolute bias in simulation studies for epidemiology research. Would it be possible to implement it in this package?

thanks,

Mike

[ellessenne]

Hi Mike, thanks for your kind words and for your suggestion – could you please clarify what you mean by absolute bias, do you mean something like:

$$ \frac{1}{n_{\text{sim}}} \sum_{i=1}^{n_{\text{sim}}} | \hat{\theta}_i - \theta | $$

In my head, absolute bias corresponds to the currently implemented version of bias (see here) and not the other version I just included above.

Thank you!

[ilovemane]

yes, your formula above is what I meant.

[ilovemane]

For example, if the true treatment effect is 1 and the simulation results are 2 and 0, the bias will be 0, but the absolute bias will be 1. This shows that bias and absolute bias can sometimes lead to very different interpretations. Absolute bias focuses more on the magnitude of the error. I hope i am making sense.