Clint, the calculations are straightforward:
(a / (a+c)) a/c
rr = ----------- or = -------
(b / (b+d)) b/d
given your numbers (as you have plugged them into -metan-):
num1=4, den1=5, num2=4, den2=51
rr= (4/(4+5)) / (4/(4+51)) = (4/9) / (4/55) = 6.111111
or = (4/5) / (4/51) = 10.2
The first question is whether you have plugged the data into -metan- in a
manner where either computation is correct. My interpretation of your study
leads me to say you have not done so.
Your 2x2 table is
diet successful
yes no total
---------------------------------------------
adhered 4 1 5
not adhered 4 47 51
---------------------------------------------
total 8 48 56
Thus OR is (4/1) / (4/47) = 47
and RR = (4/5) / (4/51) = 10.2
Those are the correct computations, but you must also ask yourself if either
statistic is appropriate for a study like yours.
OR's are usually computed for case-control studies. Case control studies are
studies in which patients who already have a certain condition (cases) are
compared with people who do not (controls). Your cases would be "successful
dieters" and your controls are "unsuccessful dieters". You start with the
two groups, then determine if they had an exposure of interest ("adherence
to the protocol" in your study). This does not appear to be how you ran
your study.
RR's are usually computed for cohort studies. A cohort study is a study in
which one group of subjects, who have a certain condition (adherers), and
another group of subjects, who do not have the condition (non-adherers), are
followed and, at some point in time, the subjects are observed to see if
they have the outcome of interest (successful diet). This is not exactly
how you ran your study either, but it is somewhat closer.
Your study started with one group that split into two groups over time
(creating your condition: adherence) and, later, you observed your outcome:
diet success (or not). The problem is that you don't know whether adhering
(or not) caused a successful diet (or not) or, contrastingly, whether an
apparently successful diet outcome (or not) encouraged continued adherence
(or not). Because the condition (adherence) was not predefined, you do not
know which caused what.
You can compute either statistic but interpretation remains difficult for
both.
Tom
----- Original Message -----
From: <[email protected]>
To: <[email protected]>
Sent: Tuesday, April 20, 2004 7:22 PM
Subject: st: metan command & binary variables
> Hello All --
> I'm using Stata version 8.2 and I hope someone can clarify a
> question I have regarding the -metan- command and it's
> estimation of odds ratios versus risk ratios. Suppose I have
> two rates that capture success on a diet where the first rate
> represents those who adhered to a certain protocol and the
> second rate represents those who dropped from the protocol
> after follow-up. Each rate is captured by the number
> successful divided by the number in the respective group
> (adhere vs follow-up). I created four variables: num1, den1,
> num2, & den2 where num1 is the # of successful dieters that
> adhered & den1 is the # of adherers; a similar interpretation
> follows for num2 & den2. When I run the following code
>
> -metan num1 den1 num2 den2, random or label(namevar=Trial)-
>
> I get an 'odds ratio' that works out to equal the ratio of the
> rate from the adherers over the rate for the droppers. If I
> specify -rr- instead of -or- the results differ and I am at a
> loss as to why. Consider the following values:
> num1=4, den1=5, num2=4, den2=51
> where the calculation of (4/5)/(4/51) = 10.2, which is
> consistent with -metan..., or- but if I specify -metan..., rr-
> I get a 'risk ratio' of 6.111. Am I not understanding the
> vernacular or can someone clue me into how the 6.111 was
> calculated?
>
> As always, your input is much appreciated!
> thank you -- Clint Thompson
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