In this thread there have lots of interesting and valuable explanations of how odds ratios (and other stats from 2x2 confusion tables) should be explained, but very little evidence has been cited.
Gerd Gigerenzer has done a fair amount of work in this area and it is worth googling his name to find his books and papers. A very recent paper by him (behind a £$€wall) in the BMJ gives his key finding: when using a statistic whose calculation requires a numerator to be divided by a denominator, be explicit about both.
Statements like “60% reduction in annual risk of stroke” has been shown in studies to be ambiguous. And if a statement can be misinterpreted, it will be. (That is someone’s law, but I have forgotten their name.)
Following GG’s maxim, odds would be stated as “for every 4 people who recover, 6 people do not”.
Risk would be stated as “6 people die out of every 10 who are exposed”
OR’s and RRs are rather hard to explain using this formula, which might explain why they are hard to explain.
GG’s paper is here: http://www.bmj.com/content/344/bmj.e245
Don’t be put off by its confusing title “Why do single event probabilities confuse patients?”
Michael
From: Evidence based health (EBH) [mailto:[log in to unmask]] On Behalf Of Stephanie Chan
Sent: 17 February 2012 17:47
To: [log in to unmask]
Subject: Re: Odds ratios explained
I wouldn't completely replace ARR with RRR, and here's the reason why: Relative risk reduction tends to remain relatively constant for an intervention, over different patient populations. Absolute risk reduction changes according to the baseline risk. One example is warfarin for stroke prevention in afib. The RRR is fairly constant - about 60% reduction in annual risk of stroke. However, the ARR is greater in patients who have already had a stroke or TIA (on average, around 7.5%) than in those who have never had a stroke (on average, around 2.7%). I can take a RRR, and apply it to my particular patient by estimating his or her baseline risk of an event. I do this using the CHADS2 score for afib. It's not perfect, but it gives me a general idea if a patient will benefit a lot or a little from an intervention.
On Fri, Feb 17, 2012 at 2:50 AM, Paul Elias <[log in to unmask]> wrote:
I think to explain OR, one has to suggest that it is explaining chance or risk by also taking the risk of the non event occurring...also, from an EBM perspective, is it not best to do away with RRR entirely in the language given it over inflates or over deflates risk anyway you try to cut it?
Best,
Paul E. Alexander
--- On Thu, 2/16/12, Stephanie Chan <[log in to unmask]> wrote:
From: Stephanie Chan <[log in to unmask]>
Subject: Re: Odds ratios explained
To: [log in to unmask]
Received: Thursday, February 16, 2012, 11:05 PM
Personally, I don't think patients (unless they happen to be researchers or math teachers) have the sophistication to understand ORs. Most doctors don't, and even though I teach med students and housestaff about the difference between RRs and ORs, I myself have a hard time grasping this non-intuitive concept. I would settle for simply telling patients that "studies show you have an increased risk of whatever." Since we don't necessarily counsel patients on risk factors they can't control (e.g., male vs. female), we could focus instead on the effectiveness of interventions (e.g., if we start you on this medication, it will decrease your chances of a heart attack by X amount -- I express it in terms of relative risk reduction if I really want the patient to take the med, while I use absolute risk reduction if I have any reservations about it!).
Just my two cents.
Stephanie
On Thu, Feb 16, 2012 at 1:26 PM, s alhabib <[log in to unmask] <http:[log in to unmask]> > 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] <http:[log in to unmask]> >
To: [log in to unmask] <http:[log in to unmask]>
Cc: s alhabib <[log in to unmask] <http:[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] <http:[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] <http:[log in to unmask]> >
> To: [log in to unmask] <http:[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] <http:[log in to unmask]> ] on behalf of k.hopayian [[log in to unmask] <http:[log in to unmask]> ]
> Sent: Monday, 6 February 2012 12:52 a.m.
> To: [log in to unmask] <http:[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
--
Stephanie Chan, M.D.
http://www.evidencebasedmommy.com/
--
Stephanie Chan, M.D.
http://www.evidencebasedmommy.com/
