Dealing with 0 in cell count for Fisher's exact test

Question

    Control Cases
  A     0       2
  B  1000     298

I am dealing with 0 in my 2x2 tables, and I was wondering what are some of my options when it comes to adjusting for these 0s. In class I did learn that it is not unheard of to just add 1 to the 0 counts, however, since the counts in category A are so low, I don't know how doing so would affect the analysis. I have read a similar post, and part of the answer involves thinking more about the experiment or obtaining more samples. If I cannot obtain more samples at this moment, what are some possible methods that I can use to adjust for the 0 counts?

Answer 1

Fisher's exact test does deal with zero cells without any problem.

Adding 0.5 to all cells is a commonly done to remove improve the small sample properties from the Chi-square test (and it asymptotically removes the first-order bias from the estimate of the log-odds ratio). This is (for a simple 2x2 table) equivalent to maximum-a-posteriori estimation using the Jefferys prior (=a Beta(0.5,0.5) prior for each proportion), as well as Firth's penalized likelihood logistic regression (for stratified tables these two approaches no longer match to adding 0.5 to each cell). Doing so penalizes the effect size (and test decision) towards no effect.

If you have prior information, a Bayesian approach with informative priors may be another option.