# st: RE: ODDSRISK module to convert Logistic Odds Ratios to Risk Ratios

 From Jhilbe@aol.com To statalist@hsphsun2.harvard.edu Subject st: RE: ODDSRISK module to convert Logistic Odds Ratios to Risk Ratios Date Thu, 20 Dec 2007 12:00:23 EST

```'ODDSRISK': module to  convert Logistic Odds Ratios to Risk Ratios now on SSC

it seems that it  did
not make it. I take the Digest, so do not see what is posted until the  next
day. I apologize if the earlier one is posted today, as well as this one.

Zhang and Yu (1998, JAMA) proposed an algorithm to convert binary  logistic
regression odds ratios to estimated risk ratios. I have seen the method  used
in a number of medical research articles, and had written about the method  in
a book I am writing. I noticed a couple of Statalist communications during
the past couple of weeks related to the relationship of odds ratio to risk
to those interested in using this method to release a Stata implementation
now  rather than with the forthcoming book several months from now. I wrote the
program in such a manner that the logistic odds ratio, estimated risk ratio,
and  95% confidence intervals of the estimated risk ratios are displayed for
each  predictor in the model. The incidence rate of the unexposed risk factor,
or  primary predictor of interest (binary (1/0)), which is required for
calculation,  is also displayed.

The estimated risk ratios are particularly important  when we wish to use
terms such as "likely" in place of "odds of" when  interpreting the odds ratio of
a logistic model. This is primarily the case with  the odds ratio is under
0.5 or over 2.5 and the incidence rate is greater than  10%. To say something
like, "patients having an anterior infarct are 50% more  likely to die within 48
hours of hospital admission than are patients having  just sustained an
infarct at another primary site", is using risk language. Such  language may be
justified for many logistic models, but not all.  Using the  estimated risk
values and CI's calculated by -oddsrisk- presumably enhance the  justification for
using risk language with logistic models when the conditions  specified above
obtain.

Kit Baum has graciously posted the program,  called -oddsrisk- and the
associated help file to the SSC site.  You can  download it by typing
. ssc install oddsrisk
on the Stata  command line.

I have pasted the SSC site module description under my  name below.

Best,  Joseph  Hilbe

DESCRIPTION/AUTHOR(S)

oddsrisk converts logistic regression odds  ratios to relative
risk ratios. When the  incidence of an outcome is common in the
study  population; i.e. greater than 10%, the logistic  regression
odds ratio no longer approximates  the risk ratio. As the
incidence rate becomes  more frequent, the more the odds ratio
overestimates the risk  ratio when its value is greater than  1,
and the more it underestimates the risk  ratio  when under one. J.
Zhang and K. Yu  proposed a method of adjusting the logistic
regression odds ratio in a cohort study or clinical trial so  that
it approximates  the risk ratio.  This is particularly important
when the odds  ratio is greater than  2.5 or under 0.5. The  method
has also been shown to be applicable  for retrospective  and
observational  studies as well.

Author: Joseph M.  Hilbe
Arizona State  University
jhilbe@aol.com   or   hilbe@asu.edu

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