# when odds ratio is 0 or uncomputable

My apology for my rudimentary understanding of statistics. I did a lot of search on google but couldn't find anything, thus am posting the inquiry here hoping to get some feedback.

I am trying to do some association study between gene polymorphism and a disease. It's easy to understand when odds ratio for a gene polymorphism and the disease status is either between 0 and 1, 1 or above 1. However, I encounter a few gene polymorphism whose calculated odds ratios are either 0 or uncomputable. How do statisticians interpret it when there is no count for, in this case, a particular gene polymorphism in one or the other (normal v disease) category.

A very naive interpretation: as when the ratio is very close to 0, the interpretation is the association is very "negative" (in the case of disease, it means the polymorphism is likely protective (from having the disease), does this imply if the ratio is 0, the polymorphism is 100% protective ???

Any help (or direction for references) will be greatly appreciated !

• A similar question (semantically identical question title) has been asked, so I am a bit inclined to withdraw my question. But I am keeping this question for a bit longer as I would like to know if the interpretation of odds ratio = 0 or infinity would vary depending on the actual applied scenario ?? Thank you. Commented Jun 10, 2015 at 21:51

## 2 Answers

It is unlikely (an understatement) the polymorphism is 100% protective. Frequentist methods for contingency table analysis often fail under sparsity (very few observations in a given cell). Why not try some Bayesian analysis? This blog post explains the set up fairly well and includes example code.

I believe an odds ratio of zero is due to the fact that at bivariate level, the affected variable had categories which had 0% (or very small cases) and the other had 100% (or close to 100). Even when you use models which cater for perfect separation or skewness, this is likely to reappear. Given that an odds ration ranges from 0 to infinity, my simple interpretation is the there is a large difference between the reference category (whose odd ratio is 1) and the category under consideration (whose odds ratio is 0). This is also clear from the bivariate table where the reference category could be 100% and the study category 0% and vice versa for figures close to infinity.