For 2x2 contingency tables I already know the RR (Relative Risk) and the OR (Odds Ratio). However none of these two is good dealing with empty cells in the table.

   |  A  | -A  |    
 B | n11 | n12 | n1.
-B | n21 | n22 | n2.
   | n.1 | n.2 |  N 

OR does not like n12 or n21 to be zero. RR won't handle n11+n21=0 and n12=0 if I am correct.

I am looking for some indicator, that does not take infinite values (e.g., when dividing by zero) like the very simple percentage. My idea is to take the relative difference from the expected value for n11.

Relative Difference: RD = ((n.1 * n1.) / N - n11) / (n.1)

(If n11+n21 = 0 => RD=0)

So the question is, if this is already used somewhere so I can quote something or if I have to "proof" that this is a useful indicator. Or can you come up with some other ideas? I will use this indicator for some visual representation, so it is quite useful if it has an upper and lower bound.


1 Answer 1


The risk difference would be the simplest option to handle this scenario (with zero counts of events/non-events) and is calculable in situations where the relative risk or odds ratio cannot be estimated due to divisions involving zeros.

The risk difference will of course have upper and lower bounds since the individual group risks are bounded by 0 and 1 [0% and 100%].

As a summary statistic, it is used quite regularly in epidemiology. You should be able to find references in most basic/intermediate biostatistics textbooks or epidemiology textbooks. Also implemented in most stats packages (SAS, Stata, R in the Epicalc library I believe although haven't used R for this calculation.)

Readings available freely available online:

Statistics at square one: In chapter two, "Summary statistics for quantitative and binary data" (starts p. 21 of text version) available in print or at http://www.bmj.com/about-bmj/resources-readers/publications/statistics-square-one

WHO Basic epidemiology (p. 34 of pdf, or search for Risk Difference) at http://whqlibdoc.who.int/publications/2006/9241547073_eng.pdf

Wikipedia has a few notes on this too under "Attributable_risk"

Two textbooks I had near my desk:

Kirkwood, B., & Sterne, J. (2003). Essential Medical Statistics. John Wiley & Sons. p 151-153

Rothman, T. L. L., Sander Greenland, Kenneth J., Greenland, S., & Lash, T. L. (2008). Modern Epidemiology. Lippincott Williams & Wilkins. p. 52-53


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