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

[Steve Samuels <sjsamuels@gmail.com>]

This version fixes a couple of typos

S.

You'd get much more interpretable results from fitting a sufficiently rich
mixed-effects model with -melogit- or -meqrlogit-. By "sufficiently rich", I mean
one that considers interactions, including differential heterogeneity in
subgroups.

These commands produce predictions on the probability scale. You can
then use -margins- to plot the results, which might lead to simple
interpretations (i.e. of linear differences in probabilities). As a
bonus, you can have group-level variables as predictors.


Steve
sjsamuels@gmail.com


> On Mar 13, 2014, at 10:50 AM, Marcel Raab <marcel.raab@wzb.eu> wrote:
> 
> 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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