RE: st: Convert Odds Ratios to Risk Ratios after clogit?

["Knee, Alexander" <Alexander.Knee@baystatehealth.org>]

My concern with converting the OR to an RR is the use of an RR in the context of a case-control study.  If we take a simpler example of a logistic regression model, this is appropriate for both cohort and case-control studies.  However, in the presence of a common outcome (>10%), the OR no longer approximates the RR.  For the cohort study, we can use other models (preferably log-binomial or Poisson with robust SE) to generate estimates of the RR.  Based on the design of the case-control study, you are stuck with interpreting the OR.  So my first question would be: how common is your outcome? Based on your example below - even if we ignore the appropriateness of the RR, your "corrected" estimates are very similar (OR = .97 and the RR = .98.) so your outcome is likely rare and you can interpret as an RR.  As an alternative, I would investigate the use of  -margins - to generate predicted probabilities.  

For further explanation see:    Hailpern & Visintainer (2003) Odds ratios and logistic regression: further examples of their use and interpretation. The Stata Journal, 3(3) p213-25.



Alex Knee, MS
Research Assistant Professor, Tufts University School of Medicine
Biostatistician, Baystate Medical Center
Division of Academic Affairs
Epidemiology/Biostatistics Research Core
Springfield, MA
Alexander.Knee@baystatehealth.org 
 
-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Marcel Raab
Sent: Thursday, March 13, 2014 10:50 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Convert Odds Ratios to Risk Ratios after clogit?

Christian,
Being a social scientist I am not used to the terminology in 
epidemiology. After I checked the Stata Manual entry on -clogit- I would 
say that I have k1i:k2i matching with k1i >= 1 and i denoting that 
matching can change from group to group. My groups/strata are families 
consisting of a varying number of children (2-10). For most groups I 
have only one case but in roughly 25% of the groups I have multiple 
positive outcomes.

I was asking for risk ratios because our Information and Communication 
Department is struggling with the Odds Ratio interpretation. They (and 
also I) would prefer a more accessible interpretation of our 
multivariate results.

Therefore, I was first trying to work with some kind of predicted 
probabilities. But I had the impression that these are not correct in my 
case. The pc1-option of predict calculates the probability of a positive 
outcome conditional on one positive outcome within group but I have 
multiple positive outcomes in a lot of groups. And the pu0-option 
calculates the probability of a positive outcome, assuming that the 
fixed effect is zero which according to a Statalist-post of Maarten Buis 
is "a rather weird hybrid between average marginal effects and marginal 
effects at average values of explanatory variables" 
(http://www.stata.com/statalist/archive/2012-03/msg01167.html). Finally 
I turned to the OR to RR conversion which also seems to be problematic 
if I understand you correctly (unmatched matched case-control)..

Marcel



Am 13.03.2014 13:57, schrieb Christian Bautista:
> Marcel,
>
> The formula given by Zhang and Yu is for odds ratios from unmatched
> case-control studies but I see that you're using "clogit" which is the
> standard method for matched case-control studies. What kind of matching
> you have used? frequency-matching or incidence density-matching?
>
> /Christian
>
>  > Date: Thu, 13 Mar 2014 13:48:58 +0100
>  > From: marcel.raab@wzb.eu
>  > To: statalist@hsphsun2.harvard.edu
>  > Subject: st: Convert Odds Ratios to Risk Ratios after clogit?
>  >
>  > Dear Statalisters,
>  >
>  > although I am aware of the criticism that has been raised against
>  > converting Odds Ratios to Risk Ratios I was wondering if the formula
>  > proposed by Zhang and Yu (1998) can also be used in the context of a
>  > fixed effects model. As the -oddsrisk- module does not work for this
>  > purpose I was trying to apply the formula manually
>  >
>  > RR = OR / ((1 - pu) + (pu * OR))
>  > (pu = incidence rate of the unexposed group)
>  >
>  > Here is my example:
>  >
>  > . webuse union, clear
>  > . clogit union age grade not_smsa, group(idcode) or
>  > . sum union if not_smsa == 0 & e(sample) // mean is pu(?)
>  > . display exp(_b[not_smsa]) / ((1 - r(mean)) + (exp(_b[not_smsa]) *
>  > r(mean)))
>  >
>  > In the example the OR = .9673623 and the RR = .97958943.
>  >
>  > I read about the conversion of ORs to RRs only recently and I am
>  > definitely not an expert in the field of non linear models. Hence, I
>  > would be very glad if anyone could help me with this issue.
>  > Is it appropriate to convert ORs in RRs in a clogit context like
>  > suggested above?
>  > Is there an alternative/superior method to do it? And finally, if it is
>  > possible what would be the best way to obtain confidence intervals for
>  > the RRs?
>  >
>  > Thanks for your consideration,
>  > Marcel
>  >
>  > --
>  > Reference:
>  > J. Zhang and K. Yu, 1998. What's the Relative Risk, JAMA, Vol 280, No
>  > 19, pp 1690-1691.
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