I am comparing two surgical approaches and the odds ratios favor A over B but when I calculate the percentage of incidence of complications the outcome favors B over A. Is this possible? under what conditions would this be possible and why?
Percentage of incidence = # of patients with outcome relative to total sample size
It sounds like you might have a 2x2 table. If so, please show it to us. Thanks.
Bruce Weaver Thank you for your interest helping me out. I have added a table to make things a bit clearer. Please let me know if you have any questions.
Using the following Stata code, I can duplicate the percentages at the bottom of your table and your crude ORs.
clear
input comp a ab c cd
1 9042 729884 1046 72911
2 8737 729884 1042 72911
3 26967 729884 3193 72911
end
generate b = ab-a
generate d = cd-c
generate Apct = 100*a/ab
generate Bpct = 100*c/cd
generate OR = (a*d)/(b*c)
format Apct Bpct %8.2f
format OR %8.3f
list comp a b c d Apct Bpct OR, clean noobs
OUTPUT from the list command (copy and paste into an editor that allows a fixed font to make things align better):
comp a b c d Apct Bpct OR
1 9042 720842 1046 71865 1.24 1.43 0.862
2 8737 721147 1042 71869 1.20 1.43 0.836
3 26967 702917 3193 69718 3.69 4.38 0.838
The italicized numbers are the 4 cell counts (a, b, c, & d). And the last number in each row (in boldface) is the crude OR.
Where do the adjusted ORs in your table come from? Did you estimate a logistic regression model? What other variable(s) are you adjusting for?
Meanwhile, I do not see anything about the percentage variables that contradicts what the crude odds ratios show.
Kelvyn Jones, the table was added to the original question. Now I see it twice. ;-)
Correct me if I am wrong but my understanding from the table is that Procedure B has a 23% lower complication 2 and a 12% lower complication 3 compared with Procedure A (adjusted model). However, considering the percentages I can see that the percentage of complication 2 and 3 are higher in Procedure B. Am I interpreting something wrong here? Are these differences caused because I am adjusting for covariates when calculating the odds ratios but not when calculating the percentages? Thank you so much for your help Bruce Weaver!
Where did that table come from? And why does it have Procedure A and Procedure B as headings in the top row? That makes no sense to me. I did my calculations (above) using the raw data shown in the bottom part of the table. And using those raw data, I got the same values your table shows in the Crude OR column. Each one of those ORs can be computed as:
(odds of complication | Method A) / (odds of complication | Method B)
where | means "given".
The adjusted ORs will also show (odds|A)/(odds|B), but with adjustment for some other variable(s) that were included in a logistic regression model. It would be crazy and very confusing to readers for a paper to show crude ORs for A relative to B, and then switch to showing B relative to A for the adjusted ORs. That is why the Procedure A and Procedure B headings in your table make no sense to me, and I wonder how they got there. HTH.
Bruce, I was not the person creating the tables but my understanding is that Procedure A is just the reference group. The rest of the values are from crude and adjusted models comparing the Procedure B against the procedure A.
Hi Elisa Morales Marroquín. As noted above, the crude ORs in your table are for Procedure A relative to Procedure B. That means Procedure B is the reference group. And the adjusted ORs must also be for A relative to B.
When I divide 1.24/1.43, I get 0.86; this means those receiving Procedure A are 16% less likely to suffer Complication 1 than Procedure B. It looks like your software is just using Procedure B as the referent for the odds.
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