I am interested to know if the explanation below is any better than Wikipedia, it is the one I use with students and trainees.

Dr Kev (Kevork) Hopayian, MD FRCGP
Hon Sen Lecturer
Norwich Medical School
University of East Anglia
Norwich 
NR4 7TJ
Making your practice evidence-based http://www.rcgp.org.uk/bookshop

The odds of something happening is the ratio of the probability of it happening to the probability of it not happening.

Let probability of an event = p                        (NB p is a proportion between 0 and 1)

Then the probability of an event not happening = 1–p

So odds = p/(1–p)

(In racing, odds are usually given as the odds against something happening but we are dealing here with more lofty matters than the 2.15 at Epsom).

The odds ratio for two groups is simply the ratio of their odds. 

 

Disorder present

Disorder absent

Exposed group

a

b

Comparison group

c

d

 

 Look at the 2X2 table and see if you can follow this:

p in exposed group = a/(a+b)

Probability of event not happening in exposed group

= 1–p             = 1– a/(a+b)            = b/(a+b)

Odds in exposed group

            = { a/(a+b)}/{ b/(a+b)}= a/b

Similarly, odds in control group

= c/d

So OR = {a/b}/{c/d}                         = ad/bc

If draw a line between the cells that multiply each other in the 2X2 table (a to d and b to c), you may see why some people call the OR the cross test.

Three important things you need to know about ORs to get by in life without learning the calculation:

  • An OR <1 means that fewer things happen in the exposed group than the comparison group (good when the thing is bad, e.g. a fall). An OR >1 means that more things happen in the exposed  group than the  comparison group (good when the thing is good, e.g. post-op pain relief, bad when the thing is bad, e.g. osteoporotic fracture). An OR =1 means no difference.
  • ORs are not intuitive, e.g., OR = 2 does not mean the risk is doubled, it is not the same as RR (relative risk) = 2 except…
  • …when the frequency of events (risk, event rate) is low, then OR is approximately the same as RR.




On 5 Feb 2012, at 10:51, Jane Hartley wrote:

Can anyone suggest an easy guide to odds ratios and other basic stats functions?

A clinical friend has asked for some help with a dissertation and understanding source papers, this is not her area of expertise and she has been frightened off by the scholarly texts she has been directed too - I suspect her supervisors are not in their area of comfort with this either.

I have moved professionally away from supporting EBH and so am not up to date with user friendly articles.  Dare I admit that I looked at the wikipedia which seemed comprehensive but impenetrable to the novice.

suggestions very welcome

Jane Hartley