this question makes me want to eat an e coli cookie and hope i bleed out
Did no one notice that the Odds ratio on the top left is wrong? Am I missing something? If you calculate it, it's 6 just like the top right one....
OR >1 indicates increased occurrence of event. The only OR greater than 1 was in the table that indicated that the subject ate cookies but didn't drink milk. Thus, that is the only one with a significant occurrence
For a more systematic approach. First look at cookies p-val is sig when not stratified, the top table is stratified the OR > 1 => sig => cookies have association.
Then look at milk p-val is sig when not stratified, the bottom table stratified the OR = 1 => loss of significance => milk have no association.
For people who generally had trouble reading the two charts:
First chart: We separated the entire population into two smaller populations to test for the cookies affect. In Population A (drank milk) there was an odds ratio of 6 (typo in the actual chart). In Population B (did not drink milk) there was an odds ratio of 6. Since the odds ratios are not 1, we can conclude that the cookies have an effect regardless of the population (ie drank milk people versus didn't drink milk people).
Second chart: New set of populations to test for the effect of milk. In Population C (ate cookies) there was an odds ratio of 1. In Population D (did not eat cookies) there was also an odds ratio of 1. This means that milk did not have an effect ever and didn't contribute to the disease.
"Only cookies are independently associated with E. coli cases" means that only the cookies cause the disease without the effects of something else.
The fact that the odds ratio in the top left is incorrect makes this question very difficult. It makes it appear as if the cookies are causative but the milk had some protective factor. So obnoxious.
Initially milk drinking was associated with E.coli outbreak with OR=3.9 and P<0.001 (Significant)... After stratification into ate cookies and did not eat cookies OR became 1 instead of 3.9 meaning the association disappeared. Therefore, eating cookies was a confounder and there is no real association between drinking milk and E.coli....instead, milk's (the confounder) contribution was responsible for the OR of 3.9 in the first place. This was furthered demonstrated with OR of 6 in the cookies alone group.
This one there were four odds ratios, one provided under each table. The only one that had an odds ratio greater than 1.0 was the table in the top right (
Odds Ratio = 6, I believe), which when you looked at the labels, led to the right answer.
"An odds ratio of 1 indicates that the condition or event under study is equally likely to occur in both groups. An odds ratio greater than 1 indicates that the condition or event is more likely to occur in the first group." (https://en.wikipedia.org/wiki/Odds_ratio)
The OR in the upper left 22 table is incorrect, which should be 6 (726/36*2 =6), not 1. This means the OR of "ate cookies" does not change after stratification by "drank milk", so "drank milk" is not a confounder, and "ate cookies" is independently asso w/ EHEC outbreak.
On the other hand, OR for "drank milk" changed a lot (from 3.9 to 1.0), which indicates "drank milk" might be a confounder and, therefore, is not independently asso w/ EHEc outbreak.
A question i more generally have is...
Is it possible that when you stratify the data, (i.e. comparing the effect that eating cookies has, in people who drink milk or people who do not drink milk) that the odds ratio will show significance for one but not the other?
Said differently, in the example above, could eating cookies in people who drink milk lead to a significant increase the risk of infection, but not in people who who didn't drink milk?
I've looked around in this comment thread, and have seen people mention the term "effect modification"; is that what my example above would show?
In other words, if eating cookies + drinking milk leads to a significant risk, but eating cookies + not drinking milk has no associated risk, would that mean that the milk has an "effect modification" on the risk of getting infection in people who eat cookies?
this is a bonus question.
when odds ratio is 1, meaning no association,
odds ratio> 1, whihc in this question is 6, means association
where is odds ratio ? a) at the ate cookie-didnot drink milk column. hence the answer, only cookie independently ass. with e coli
we can make things simple like this way: if we want to know whether X1,or X2 correlates Y, we just separately test X1 and Y, and X2 and Y accordingly. When test X1 with Y, we require no X2 exposure; When test X2 with Y, we require no X1 exposure;
We test cookie with diarrhea, when milk was not drunk (top right): positive We test milk with diarrhea, when no cookie was eaten (lower right): negative
conclusion: only cookie correlates to the diarrhea
The keyword is "INDEPENDENTLY"(associated). Which in human language means "NOT ASSOCIATED".