# Are the sum values 'No' and 'Not informed' in the Odds Ratio analysis correct? See the example

In a hypothetical study I am trying to assess whether the presence of allergy is a risk factor for the presence of any virus. For this purpose, a questionnaire was applied on which many individuals marked "yes" or "no" for the presence of allergy. Those who did not complete the questionnaire were labeled as "not informed". The data was crossed with the “presence” or “absence” of the virus, and as a result table 1 was generated.

In order to analyze the Odds Ratio, the values that were labeled as “not allergic” were added to those that did not inform this condition on the questionnaire, and as a result table 2 was generated. Then, from table 2, Odds Ratio was calculated using the statistical software PAST3.

My question is whether am I on the right track for this type of analysis, which I don’t have experience. If I am doing something wrong I am gladly open to corrections and suggestions.

My interpretation of the results: the presence of allergy does not increase the chance of carrying the virus. In other words, allergy is not a risk factor for the presence of the virus.

With this approach, you are effectively treating everyone who did not complete the survey as though they had answered No Allergies. I can't see any reason you'd want to do that - it would be equally (in)valid to take the opposite approach, and treat them all as if they had answered Yes Allergies.

In this situation, there's no theoretical or empirical reason why the presence of allergies would affect whether or not someone completed the survey. You can confirm this by doing a test of Not informed vs. Informed, and seeing that there is no difference in non-response rates between allergy groups. When you have data that is missing completely at random (i.e. there is no link between missingness and your variables of interest), you can just drop the missing data. In the end, you can run your statistical test on the 2x2 table, dropping the third row entirely. Even though you surveyed 110 individuals, you only got usable data from 90 of them. The other 20 are simply unusable for assessing the association of allergies and virus, since you don't know whether or not they have allergies.

It is important to think about whether data is missing completely at random, however. In domains like political polling, for example, it's been noted that certain demographics tend to be under-represented among survey respondents. That is, the fact that someone did not answer a survey is indeed informative about that person's political beliefs, so simply throwing away missing data and expecting the rest to accurately reflect the population at large will not work. But if there is no meaningful difference between the population who responded and the population who did not respond, throwing away missing data is acceptable, since the remainder is still representative of the whole population.