# [R] odds ratio per standard deviation

(Ted Harding) Ted.Harding at wlandres.net
Wed Jun 12 18:14:03 CEST 2013

```[Replies transposed so as to achieve bottom-posting ... ]

On 12-Jun-2013 14:53:02 Greg Snow wrote:
>
> On Tue, Jun 11, 2013 at 7:38 PM, vinhnguyen04x <imvinhs at yahoo.com.vn> wrote:
>
>> Hi all
>> i have a question:
>>
>> why and when do we use odds ratio per standard deviation instead of odds
>> ratio?
>> --
>> View this message in context:
>> http://r.789695.n4.nabble.com/odds-ratio-per-standard-deviation-tp4669315.htm
>> l
>> Sent from the R help mailing list archive at Nabble.com.
>> ______________________________________________
>
> Without context this is a shot in the dark, but my guess is this is
> referring to something like a logistic regression where the odds ratio
> (exponential of the coefficient) refers to the change in odds for the
> outcome for a 1 unit change in x.  Now often a 1 unit change in x is very
> meaningful, but other times it is not that meaningful, e.g. if x is
> measuring the size of diamonds in carats and the data does not span an
> entire carat, or x is measured in days and our x variable spans years.  In
> these cases it can make more sense to talk about the change in the odds
> relative to a different step size than just a 1 unit change in x, a
> reasonable thing to use is the change in odds for a one standard deviation
> change in x (much smaller than 1 for the diamonds, much larger for the
> days), this may be the odds ratio per standard deviation that you mention.
> --
> Gregory (Greg) L. Snow Ph.D.
> 538280 at gmail.com

I think there is one comment that needs to be made about this!

The odds ratio "per unit change in x" means exactly what it says,
and can be converted into the odds ratio per any other amount of
change in x very easily. With x originally in (say) days, and
with estimated logistic regression logodds = a + b*x, if you
change your unit of x to, say weeks, so that x' = x/7, then this
is equivalent to changing b to b' = 7*b. Now just take your sliderule;
no need for R (oops, now off-topic ... ).

Another comment: I do not favour blindly "standardising" a variable
relative to its standard deviation in the data. The SD may be what
it is for any number of reasons, ranging from x being randomly sampled
fron a population to x being assigned specific values in a designed
experiment.

Since, for exactly the same meanings of the variables in the regression,
the standard deviation may change from one set of data to another of
exactly the same kind, the "odds per standard deviation" could vary
from dataset to dataset of the same investigation, and even vary
dramatically. That looks like a situation to avoid, unless it is very
carefully discussed!

The one argument that might give some sense to "odds ratio per standard
deviation" could apply when x has been sampled from a population in
which the variation of x can be approximately described by a Normal
distribution. Then "odds ratio per standard deviation" refers to
a change from, say, the mean/median of the population to the 84th
percentile, or from the 31st percentile to the 69th percentile,
or from the 69th percentile to the 93rd percentile, etc.
But these steps cover somewhat different proportions of the populatipn:
50th to 85th = 35%; 31st to 69th = 38%; 69th to 93rd = 24%. So you are
still facing issues of what you mean, or what you want to mean.

Simpler to stick to the original "odds per unit of x" and then apply
it to whatever multiple of the unit you happen to be interested in
as a change (along with the reasons for that interest).

Ted.

-------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at wlandres.net>
Date: 12-Jun-2013  Time: 17:14:00
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