Talk:Odds ratio

A correlation can certainly "imply" causality. However, it does not demonstrate causality. It does not have anything to do with etiological mechanisms. — Preceding unsigned comment added by Ugisb (talk • contribs) 20:21, 11 April 2020 (UTC)

Is the "motivating example" straight-up wrong?
It may have just been too long since I've done math, but the author wrote that OR = (Diseased-exposed/Healthy-exposed)/(Diseased-unexposed/Healthy-unexposed), which is in contrast with this pubmed article: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2938757/. This pubmed article defines OR = (Diseased-exposed/Diseased-unexposed)/(Healthy-exposed/Healthy-unexposed). I really, truly suck at statistics - anyone want to take a stab at this? 09/27/2018 — Preceding unsigned comment added by 137.53.245.138 (talk) 23:46, 27 September 2018 (UTC)
 * The two are mathematically equivalent, as explained later in the 'motivating example' section and also in the later section Odds ratio. Qwfp (talk) 19:59, 28 September 2018 (UTC)

Clarify calculating statistics
These sentences are opaque to me:

"An alternative approach to inference for odds ratios looks at the distribution of the data conditionally on the marginal frequencies of X and Y. An advantage of this approach is that the sampling distribution of the odds ratio can be expressed exactly."

Is the author talking about a chi-squared test? Please provide enough detail to actually perform the inference. dfrankow (talk) 17:15, 12 July 2018 (UTC)

Opening paragraph is a confusing jumble
(note: I am not a statistician): I like the opening paragraphs; but what is missing is the notation. I guess that you do not only state "OR = 1.1", because that does not denote if it is the odds that A has B or B has A. Or do I miss something? Postdeborinite (talk) 06:47, 7 November 2014 (UTC)

The opening paragraph is a verbose, hard to follow example without an appropriate framing of the actual odds ratio. The opening should be reworked to much in the same style as the Wikipedia entry on Relative Risk. Jleves61 (talk) 21:56, 24 September 2013 (UTC)

I've rewritten the opening paragraph, but haven't changed the second paragraph or later to fit, so it still needs a little work. Note that I'm not 100% sure that "greater than one means positive association" but I'm pretty sure it's accurate. Here's what I did: 174.29.54.119 (talk) 23:29, 5 January 2014 (UTC)

Much better opening, good edit. Jleves61 (talk) 17:52, 8 January 2014 (UTC)

In statistics, the odds ratio (OR) is a relation between the odds of an event $$A$$ occurring (for example, developing a disease, being injured) conditioned on whether another event $$B$$ occurs. An odds ratio greater than one indicates that the events are positively associated, while an odds ratio below one indicates a negative association.


 * $$RO= \frac {P(A|B) P(\neg A|\neg B)}{P(A|\neg B) P(\neg A|B)}$$

Consider an example where the probability where the probability of developing lung cancer among smokers was 20% and among non-smokers 1%. This situation is expressed in the 2x2 table on the right.

Here, a = 20, b = 80, c = 1, and d = 99. Then smoking is associated with the development of cancer with an odds ratio of


 * $$RO= \frac {a d}{b c}=\frac{20 \cdot 99}{80 \cdot 1} = 24.75$$

This indicates a strong positive association between smoking and cancer development.

Page name
Why the hyphen? Better call it Odds ratio. Any objections? -- Hugh2414 23:12, 16 Apr 2004 (UTC)

Link to LOD page
Seems like a natural connection should be made to connect this to genetic linkage and calculation of LOD scores. —The preceding unsigned comment was added by Piperb (talk • contribs) 22:37, 6 February 2007 (UTC).


 * If anything Genetic linkage should be linked with logit --Henrygb 00:17, 7 February 2007 (UTC)

Reference at the end of "Definition in terms of group-wise odds"?
At the end of the paragraph there's a [1] which looks like a reference but was not typeset entirely as one. I didn't feel like going and see whether the reference actually refers to the issue. I'll leave it up to whoever knows the reference to decide what to do. 212.126.224.100 (talk) 15:15, 19 July 2010 (UTC)

Worked example.
It is uncomprehensible. And should be in the beginning.

--Lucas Gallindo (talk) 14:44, 9 August 2010 (UTC)

Also the man/woman example is not only sexist but seems kinda offending to me as I am a recovering alcoholic.

-- anonymous — Preceding unsigned comment added by 89.69.82.55 (talk) 17:13, 1 July 2013 (UTC)

Table of odds ratios
I have added a table of odds ratios, one that I find helpful. Another editor finds the table unhelpful. Judge for yourself in this revision. --Dan Polansky (talk) 15:56, 13 September 2010 (UTC)
 * The table is not that intuitive as a display. Probably a graph would do better?


 * Can anyone explain to me what the point is of having the joint distribution tables of X and Y in the article at all? Odds ratio doesn't care about joint distributions at all, it only compares one marginal to another marginal. Am I missing something here?


 * I disagree, take a look at the logistic regression - it's all about joint distributions, or in other words, odds ratios = 1st odd ratio by 2nd odd ratio. Table was good, and chart is hundred times better.

Graph showing how the log odds ratio relates to the underlying probabilities

 * I think that there is a serious error in this graph: Odds_ratio_map.svg
 * I believe, that the odds ratios reported by for example Stata span from 0 to infinity, hence negative odds ratios are impossible. I believe that lines and gradient might be OK, but lines are subtitled wrong - straight line in the middle should be "1" (equal odds ratios = 1:1 = 1), curves above should be grater than one, and curves below should be smaller than one, but always greater than zero. — Preceding unsigned comment added by Iamunique3 (talk • contribs) 10:00, 30 May 2012 (UTC)
 * The legend describes the graph as presenting log odds ratio which can of course be negative, all the way to minus infinity. However, I find this graph difficult to comprehend and tautologous when comprehended. Personally, I'd !vote for removing it. Richard Keatinge (talk) 10:48, 30 May 2012 (UTC)

WikiProject Medicine
For some reason, this edit deletes WikiProject Medicine without a real explanation. It seems obvious to me that this is a core tool in medical research, particularly in epidemiology. LeadSongDog come howl!  14:37, 25 November 2010 (UTC)
 * I won't revert if you want to add it again, but it's one of many statistical methods frequently misused used in medical research. I wouldn't say it's a "core tool".  — Arthur Rubin  (talk) 16:09, 25 November 2010 (UTC)
 * It certainly crops up very consistently in epidemiology papers. Selvin's Statistical analysis of epidemiological data (ISBN 9780195172805) dedicates an entire appendix to "THE ODDS RATIO AND ITS PROPERTIES", sandwiched between "BINOMIAL AND POISSON PROBABILITY" and "PARTITIONING THE CHISQUARE STATISTIC". Still, would you'd prefer to raise the question at Wikipedia talk:WikiProject Medicine to see what the crowd there thinks? I'd be happy to go with their decision.LeadSongDog come howl!  21:52, 25 November 2010 (UTC)
 * I'd be willing to defer to a WPMED concensus. Coming at this from a mathematical statistics viewpoint, I see misuse of statistical methods as more common than proper use, even in medical papers.  — Arthur Rubin  (talk) 16:37, 26 November 2010 (UTC)
 * I saw LeadSongDog's note about this at WT:MED. I agree with LeadSD that the odds ratio is very frequently used in epidemiology papers and textbooks, though obviously this isn't the only usage.  It seems to me that whether it is used correctly is an entirely different question, and one that I'm not sure we should even try to address: is a type of valve irrelevant to plumbing because it is often installed backwards?  I also can't understand what harm is done by including WikiProject Medicine. Jakew (talk) 22:22, 26 November 2010 (UTC)
 * I'd agree with Arthur that the misuse of statistical methods is a concern when examining the conclusions of studies, but would disagree that it's an important factor in deciding whether this article would benefit from being within the scope of WPMED. My consistent experience when reading medical sources is that OR is a much-used tool in evidence-based medicine, and properly fits within the project's scope. --RexxS (talk) 23:30, 26 November 2010 (UTC)
 * (coming over from WPMED) The odds ratio is used often by medical experts; however, it is not created or modified by them without input from experts in math & statistics. As such, isn't this a tool, rather than a subject, of medicine?  Of course medicine has an interest in the tools it uses, but that's true of many disciplines.  -- Scray (talk) 04:34, 27 November 2010 (UTC)
 * I read "WikiProject_Medicine". "Odds ratio" is not part of these goals and should not be in WikiProject Medicine. Axl  ¤  [Talk]  10:24, 27 November 2010 (UTC)
 * Those goals as currently stated would appear to exclude all articles on the methodology of etiological epidemiology. Just an observation; whether the goals should be changed, or this particular article should be included or not, I'll leave to those active in WikiProject Medicine. Qwfp (talk) 11:35, 27 November 2010 (UTC)
 * I will not touch the edit or the goals, but I would like to share my perspective. I am currently doing my second degree in BioStatistics.  This degree consists of two thirds statistics courses and a third of the courses are from epidemiology.  In the statistics courses I remember encountering OR maybe twice.  In the epidemiology courses, every single course (except for the biochemistry and pathology courses I took), have mentioned OR. Talgalili (talk) 14:17, 27 November 2010 (UTC)


 * I am responding to the message at WT:MED. I have two general rules for WikiProject tagging:  Have the project's members helped with the article?  Would they respond usefully if someone asked a question about the article at the project's page?
 * The answer to both questions is "yes", and consequently I think this page should be tagged with WPMED. WhatamIdoing (talk) 23:22, 29 November 2010 (UTC)
 * I'm no expert on wikiproject tagging, but I like those criteria and would agree with WhatamIdoing's assessment on that basis. -- Scray (talk) 00:07, 30 November 2010 (UTC)
 * Those are good criteria and I'd endorse them. An additional consideration is whether it would be helpful if a WikiProject were notified when a particular article is nominated for renaming, merger, or deletion. In those cases, a WikiProject tag can guide a nominator to other editors who may help in discussion. --RexxS (talk) 00:52, 30 November 2010 (UTC)

""Have the project's members helped with the article? Would they respond usefully if someone asked a question about the article at the project's page?""

- WhatamIdoing


 * I disagree with this. The project's members contribute to the entire spectrum of articles in Wikipedia, not just "medical" articles. Are you sure that every "medical" article has received a contribution from a WikiProject Medicine member? Your second question is a circular argument. People who are interested in contributing to WikiProject Medicine will respond to the questions, whether they are relevant to medicine or not. Someone asked about "Odds Ratio" and several members responded in a useful way. Does this define "Odds Ratio" as part of WikiProject Medicine? Axl  ¤  [Talk]  10:37, 30 November 2010 (UTC)


 * I acknowledge your point, but we're talking about a WikiProject, not the content category system. At some level, "what the members work on" is the "scope of the project".  I differentiate here between what we work on, and what each of us works on:  JFW sometimes edits articles related to Judaism, and I sometimes edit articles related to education, but "we"—taken as a group—don't edit in either of those areas.
 * The response matters: If someone turns up with a question about snake lemma at WT:MED, the response is going to look a lot more like "Maths folks are that way" than "I can help".  If someone turns up with a question about Odds ratio, the response is likely to be "I can help", not "Try the stats folks".
 * Purely as a procedural matter, if members of WPMED say that this article is (or is not) within their scope, then their word is final. It is the "exclusive right" of the project to define its scope.  WPMED could (if we all lost our collective marbles) declare that "Heart disease" is outside its scope, and that "Banana" was inside it.  WhatamIdoing (talk) 18:41, 6 December 2010 (UTC)
 * Well, we disagree on the best way to define articles within the scope of our WikiProject. On the other hand, I agree with your last paragraph. Best wishes. Axl  ¤  [Talk]  11:22, 7 December 2010 (UTC)


 * Since we are all agreed that it's WP:MED's call, and since most members who commented think this within the scope of the project because of its use in medical research and public health, I am restoring the project's banner (but without the tag for the non-existent epidemiology task force). WhatamIdoing (talk) 19:11, 15 January 2011 (UTC)

Bayes' theorem
It seems extraordinary that this article doesn't mention the very simple form that Bayes' theorem takes in terms of odds ratio, viz:
 * Posterior odds ratio = (Prior odds ratio) x (Marginalised likelihood ratio)

It is the simplicity of this form which makes odds-ratio so valuable. It is the basic Bayes factor equation.

It would seem appropriate, per WP:TECHNICAL to treat this at the top of the article, before getting into some of the much less intuitive and less direct material currently presented. Jheald (talk) 17:00, 7 November 2011 (UTC)


 * Bayes' theorem in terms of odds, not odds ratios, is treated in the article on Bayes' rule. I don't think odds ratios come into it. Qwfp (talk) 17:36, 7 November 2011 (UTC)


 * Ah, okay. Then maybe it is worth noting that an awful lot of Bayesian papers and books use "odds ratio" when they really just mean "odds" (google search, example), presumably because the odds themseves are a ratio, P(X+)/P(X-)).  That is indeed not what this is about, but perhaps that needs to be rammed home more strongly with a dab or a note at the top.
 * Alternatively, this article could be re-titled ratio of odds, with odds ratio going to a dab page for people to consciously choose what they mean. Jheald (talk) 18:16, 7 November 2011 (UTC)
 * The usual usage in epidemiology is "odds ratio" abbreviated as "OR". LeadSongDog come howl!  19:15, 7 November 2011 (UTC)
 * Just to complicate things, there is an important odds ratio connected with Bayes Rule. If we consider the odds formulation of Bayes rule, then the Bayes factor (in simple cases the likelihood ratio) is the odds ratio between the posterior odds and the prior odds.  And that was the specific domain in which many of the Bayesian Gbooks hits were using the term.
 * On the other hand I'm not yet clear whether it is interesting that the Bayes factor is an odds ratio -- do any of the properties of odds ratios currently noted in the article shed any interesting sidelight on Bayes factors? Or, do Bayes factors give in any way interesting examples of the properties of odds factors we are noting?  Will need to look into, think and read more about this (particularly in relation to the medical context).
 * But it may be worth remarking at the top of the article that the Bayes factor is a particularly notable example of an odds ratio. Jheald (talk) 20:31, 7 November 2011 (UTC)

Section "recovering the cell probabilities from the odds ratio and . . ." needs reference or explanation
At the end, it is not clear why the root with - S (instead of that with + S) is selected as the valid solution for p11. Either a reference or an explanation is needed. I have not been able to find a reference or to work out a proof — Preceding unsigned comment added by 171.64.39.211 (talk) 02:29, 24 May 2014 (UTC)

Standard Error in the log(Odds Ratio)
For a Bernoulli process with $$N$$ trials and $$M$$ successes and $$\mu =\frac{M}{N}$$, the variance in the number of successes is $$var(M) = N\cdot \mu\cdot(1-\mu) = M\cdot(1-\mu)$$ Right? This is symmetric in $$M$$ and $$(N-M)$$, i.e. for counting successes or failures. So the variance of the log of the Odds ratio should be $$var(log(Odds Ratio)) = \frac{1-\hat{p}_{00}}{n_{00}} + \frac{1-\hat{p}_{01}}{n_{01}} + \frac{1-\hat{p}_{10}}{n_{10}} + \frac{1-\hat{p}_{11}}{n_{11}} <  \frac{1}{n_{00}} + \frac{1}{n_{01}}  + \frac{1}{n_{10}} + \frac{1}{n_{11}}$$ What am I missing here? RSTate (talk) 18:26, 29 March 2017 (UTC)

Add a real example, perhaps on Influenza vaccine effectiveness
It will b helpful to feature a real-life example, perhaps illustrating Influenza vaccine effectiveness. Real data is available at: https://www.cdc.gov/vaccines/acip/meetings/downloads/slides-2017-06/flu-03-ferdinands.pdf and more at: https://www.cdc.gov/flu/professionals/vaccination/effectiveness-studies.htm Please work through an example in detail using this real data. Explain why Odds Ratio is used in these calculations. Use natural frequencies to illustrate the calculation and its real-world interpretation. Describe the differences in Odds Ratio and Vaccine Effectiveness.Why and how is the adjustment (shown in the vaccine data displays) made. Thanks! --Lbeaumont (talk) 13:35, 21 December 2017 (UTC)
 * Be bold! Qwfp (talk) 07:47, 22 December 2017 (UTC)

The Titanic passenger numbers are incorrect
Stephen Simon's 2001 article "Understanding the Odds Ratio and the Relative Risk" is used heavily in the section "Relation to relative risk". In Simon's article, he gives an example based on "data on survival of passengers on the Titanic" claiming 154 female passenger deaths and 709 male passenger deaths.

Wikipedia's own figures give 106 female passenger deaths and 659 male passenger deaths. While Simon's figures are a good illustrative example, I think we should avoid attributing them to the Titanic disaster in case they become a source of downstream misinformation. Tim Bennett (talk) 00:26, 10 January 2024 (UTC)