It has to be stressed (to counteract any impression that an
"intuitive" explanation may create) that:
A: A Risk Ratio cannot be derived from an Odds Ratio
B: An Odds Ratio cannot be derived from a Risk Ratio
C: Absolute Risks cannot be derived from a Risk Ratio
D: Absolute Risks cannot be derived from an Odds Ratio
E: Risk Difference cannot be derived from an Odds Ratio
F: Risk Difference cannot be derived from a Risk Ratio
[and so on]
I think that when it comes to explaining things of this
kind, the inmportant issue is to somehow try to identify
what the other person best understands, and then use that.
Ted.
On 16-Feb-2012 Piersante Sestini wrote:
> ok, this is my low-level explanation for medical students (they don't
> properly qualify as "lay persons", but in mathematical matters they get
> very close)
>
> An Odds Ratio is a ratio between two Odds.
> Odds are just a different way of expressing proportions.
> Suppose that in the room there are 3 males and 7 females. How would you
> describe the proportion of males?
> The class would likely voice "30%"!
> Well, I would say, when expressed in percentage, it is indeed 30%. In
> odds, it would be reported as 3:7.
> Which one is simpler?
>
>
> Usually, the Odds Ratio is computed between the odds in a group
> presenting a certain risk factor and the odds in one without (control).
> So, if of 100 smokers 30 develop COPD at 60 years and 70 don't (odds
> 3:7), while in nonsmokers only 2 develop COPD and 98 don't (2:98, that
> is Odds= 1: 49), we will say that the odds ratio will be (3:7)/(1:49),
> that is =21.
>
> We could express the same data in percentage, and say that 30% of the
> smokers have developed COPD at 60 years versus 2% of nonsmokers. These
> percentages are called "Risks", and their ratio is called "Risk Ratio".
> In this case the Risk Ratio would be 30/2, or 15.
>
> Both the OR and the RR express the same data, though in different way.
> They both are "1" when there is no difference between two groups, they
> both increase above 1 towards infinity when the risk increase, and
> decrease between 1 and 0 when the risk decrease .
> Thus, a value of OR or RR above 1 indicates an increased risk (the
> greater the number, the greather the increase) and values below 1
> indicate a protection.
> Their value tend to be very similar when the proportion in controls is
> very low. As this increases, the value of the OR tend to be higher than
> the RR, for the same data.
>
> Therefore, one should *never* look (even less point to a patient) just
> to the RR or the OR, but rather look separately to the proportions in
> the two groups (either in Odds or in percentage).
>
> hope this helps
>
> Piersante Sestini
>
> On 16/02/2012 22.26, s alhabib wrote:
>> Dear John:
>> So what is your definition of OR if you have to explain to a patient?
>> Many in the list have explained the differences between OR and risk
>> ratio in statistical term, but no one came up with a simple "lay
>> person" explanation of OR? unless I missed some -emails? apologises if
>> I did...
>>
>> Dr. Samia Alhabib, MD, MSc PHC, PG-Dip EBHC
>> Research Associate
>> Academic Unit of Primary health Care
>> Faculty of Medicine
>> University of Bristol,
>> Barley House, Oakfield Grove
>> Bristol, BS8 2BN
>> UK
>>
>> ------------------------------------------------------------------------
>> *From:* John Carlisle <[log in to unmask]>
>> *To:* [log in to unmask]
>> *Cc:* s alhabib <[log in to unmask]>
>> *Sent:* Thursday, 16 February 2012, 11:59
>> *Subject:* Re: Odds ratios explained
>>
>> I've sent this once before but it got 'spammed' - so here is another
>> go as it may be of general interest.
>>
>> Ref to Samia Alhabib
>>
>> I'm afraid you've illustrated why it is difficult to explain what an
>> odds ratio is and that it's meaning is context-sensitive.
>>
>> Using your example, if we consider rates of diabetes in 200 males and
>> 200 females, and we keep the odds ratio at 4.5 (as close as I could
>> get to 4.5), you will see that as the odds of diabetes increase in
>> each group the ratio of males/females with diabetes becomes smaller,
>> making the explanation "male is 4.5 times more likely to have diabetes
>> than female" increasingly incorrect.
>>
>> Your explanation would be correct if you were talking about risk
>> ratios (which are context-insensitive), but not odds ratios.
>>
>> MALE FEMALE OR MALE/FEMALE
>> 17/183 4/196 4.55 4.25
>> 32/168 8/192 4.57 4
>> 56/144 16/184 4.47 3.5
>> 72/128 22/178 4.55 3.27
>> 90/110 30/170 4.51 2.9
>>
>>
>> On Sun, 5 Feb 2012 08:10:18 -0800
>> s alhabib <[log in to unmask] <mailto:[log in to unmask]>> wrote:
>> > Dear Simon:
>> >
>> > An Odd ratio of 4.5, for example, in explaining the risk of
>> developing diabetes in male than female is to say: male is 4.5 times
>> more likely to have diabetes than female if they did not
>> excercise...this is an a virtual example and does not imply any sort
>> of evidence,
>> >
>> > Samia
>> >
>> > Dr. Samia Alhabib, MD, MSc PHC, PG-Dip EBHC
>> > Research Associate
>> > Academic Unit of Primary health Care
>> > Faculty of Medicine
>> > University of Bristol,
>> > Barley House, Oakfield Grove
>> > Bristol, BS8 2BN
>> > UK
>> >
>> >
>> > ________________________________
>> > From: Simon Hatcher <[log in to unmask]
>> <mailto:[log in to unmask]>>
>> > To: [log in to unmask]
>> <mailto:[log in to unmask]> Sent: Sunday, 5 February
>> 2012, 15:35
>> > Subject: Re: Odds ratios explained
>> >
>> > In a previous post on this list someone asked the question "how do
>> you explain odds ratios to patients?" - which from memory no one ever
>> answered. I understand odds ratios and I can draw 2x2 tables with the
>> best of them however how do you include odds ratios in conversations
>> with patients - in simple language what do odds ratios mean for patients?
>> >
>> > Cheers
>> >
>> > Simon
>> >
>> > Associate Professor Simon Hatcher
>> > Department of Psychological Medicine
>> > Faculty of Medical and Health Sciences
>> > The University of Auckland
>> > New Zealand
>> >
>> >
>> > ________________________________________
>> > From: Evidence based health (EBH)
>> [[log in to unmask]
>> <mailto:[log in to unmask]>] on behalf of k.hopayian
>> [[log in to unmask] <mailto:[log in to unmask]>]
>> > Sent: Monday, 6 February 2012 12:52 a.m.
>> > To: [log in to unmask]
>> <mailto:[log in to unmask]>
>> > Subject: Re: Odds ratios explained
>> >
>> > 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
>>
>>
>
-------------------------------------------------
E-Mail: (Ted Harding) <[log in to unmask]>
Date: 16-Feb-2012 Time: 23:53:20
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