# Odds Ratio question

#### Bertta

##### New Member
Hi,

I'm very beginner in biostatistics. Now practicing odds ratio calculation for my project. I get different results than in practicular publication reported. Could you please help me to figure out where is mistake?

https://pubmed.ncbi.nlm.nih.gov/30039564/

Page 622, Table 2
Authors report for Collagenous colitis "Any PPI" use: a crude OR of 9.17 (95% CI: 8.52 - 9.88).

Numbers I calculated with Table 1 and used in Odds ratio calculator:
-Exposed cases (any PPI use in patients with collagenous colitis): 2470
-Unexposed cases (no PPI use in patients with collagenous colitis): 3780
-Exposed controls (any PPI use among control group): 6088
-Unxposed controls (no PPI use among control group): 53754

My result is OR 5.770 [95% CI: 5.449 - 6.109]

Crude ORs with other Table 2 variables are also significantly higher than my calculations.

Thank you if you could take a look and explain me where is the mistake.

#### fed2

##### Active Member
I got same as you, but I think mystery is in ' We used conditional logistic regression', so basically it is giving the 'matched odds ratio' associated with McNemar's test, https://horvath.genetics.ucla.edu/html/Class100B/Lecture2McNemarbasedonlc19.pdf.

But I think it may be a little more complicated than that because of the way the matching was done. Its probably a misnomre to call this 'crude', since it is inherently adjusted under the matching.

just a guess i did not read that close.

#### Bertta

##### New Member
I got same as you, but I think mystery is in ' We used conditional logistic regression', so basically it is giving the 'matched odds ratio' associated with McNemar's test, https://horvath.genetics.ucla.edu/html/Class100B/Lecture2McNemarbasedonlc19.pdf.

But I think it may be a little more complicated than that because of the way the matching was done. Its probably a misnomre to call this 'crude', since it is inherently adjusted under the matching.

just a guess i did not read that close.
That's good start for me that we got same results. Thank you!

This arises me a further question. Would it then be totally wrong to calculate any "crude" ORs from a case-control study, if the study has used any kind of matching of controls?

#### hlsmith

##### Less is more. Stay pure. Stay poor.
I am going to be pushing my knowledge here, but in a C-C study you are selecting based on outcome instead of exposure or group, making the use of rate or incidents inappropriate, so you end up using ORs. Now the next thing to take into consideration is that you have artificially changed the prevalence of the outcome in the target population. I don't believe this impacts the ORs (perhaps due to collapsibility), but if you decided to work with the predicted probabilities from the logistic regression they may need to be corrected for this issue, which is a monotonic transformation, meaning the ordering of the predicted probabilities are the same, but their values change. They also say you needed control for the matching variables in logistic reg if they impact the exposure, I am not as clear on this thought line. So for crudely calculating ORs based on matched data using a 2x2 contingency table, I can think of a reason you could not do that off hand. But I will stew on this some.

#### fed2

##### Active Member
So for crudely calculating ORs based on matched data using a 2x2 contingency table, I can think of a reason you could not do that off hand.
The answer is essentially no, barring some trickery. This study may have some trickery though, because of the way things were done its not strictly a case-control in the usual sense. By generally, the crude OR (by which I mean the population OR that would be obtained without matching) would not be estimable under such a study.

As lachin puts it: 'Therefore, the marginal retrospective odds ratio under matching does not equal the retrospective odds ratio in the general population of cases and controls'

So basically, the did conditional logistic regression rather than unconditional because thats what you got to do in this case.

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#### Bertta

##### New Member
Thanks your thoughts were helpful!

So in a summary: whenever a case-control study is matched, I should not calculate crude ORs in a 2x2 table. But when the case-control study is not matched, I could calculate the crude ORs.

#### fed2

##### Active Member
thats essentially right. For the analysis of matched data you would have to adjust for the matching variables in one fashion or another, these include:
1) Chochran mantel hantzel - adjust for the matched groups.
2) McNemars test, conditional logits (what was used in your paper), or related