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odds ratio per standard deviation

6 messages · Greg Snow, (Ted Harding), David Winsemius +1 more

(Ted Harding)
# 
[Replies transposed so as to achieve bottom-posting ... ]
On 12-Jun-2013 14:53:02 Greg Snow wrote:
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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vinhnguyen04x
# 
L. Snow,
Ted,

Many thanks, I am sorry to made a question without context. I use three
parameters of facial temperature, heart rate, and respiratory rate to
distinguish infectious patients from healthy subjects. So I use logistic
regression to generate a classification model and calculate the odds ratio
for these three parameters. In my case, I would like to know what kinds of
odds ratio can be used, odds ratio per standard deviation or odds ratio. 

Thanks you in advance for your help




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David Winsemius
#
On Jun 12, 2013, at 4:58 PM, vinhnguyen04x wrote:

            

      
      
      
    

        
The answer will depend on the distribution of the covariates, about which you have offered no information. It may also depend on what would be considered a relevant distance along the covariate "axes" by your audience. Generally odds ratios comparing a single year of increased age are not very interesting, but a difference of a decade will be understood by most audiences. Frank Harrell's rms/Hmisc package displays differences comparing the interquartile range. For heart rate I would think comparing a value of 80 to a value of 81 would nnot be thought of as clinically relevant. Most people are not capable of transforming odds ratios presented for a single unit difference to ones comparing a ten unit contrast. Differences of a degree of facial temperature might be more sensible given the narrow range over which temeperatures are maintained.  It is your responsibility to make these decisions based on domain knowledge. Any knowledgeable practitioner of statistics can make transformation to another contrast if enough digits of accuracy are offered. (It is rather frustrating to see published comparisons for single units of difference presented with minimal accuracy.)