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Re: st: Additive interactions with Stata


From   Constantine Daskalakis <[email protected]>
To   [email protected]
Subject   Re: st: Additive interactions with Stata
Date   Fri, 23 Jan 2004 14:08:32 -0500

At 12:26 PM 1/23/2004, Andrea Baccarelli wrote:
My question is: Does anybody used Stata to test for additive interactions?

There are different ways to test for additive interactions:
1.
The simplier is to calculate the Sinergy Index (SI). SI is the ratio Observed/Expected, where Observed is the OR for the joint effect of A and B (OR_AB) and Expected is obtained from the main effects of A and B as follows: (OR_A+OR_B-1). If SI is significantly different from 1, then we have an additive interaction. I believe it could be possible to go this way with Stata, by using "lincom" after my usual logistic model (i.e., xi: logit depvar i.A*i.B, or). SI, in the end, is just a combination of ORs. Has anybody ever tried this?
SI, however, has been criticised and other methods are often prefered
Yes, under the logistic regression model, "no additive interaction" implies that

OR_A + OR_B - 1 = OR_AB (the sum of the main effects minus 1 equals the joint effect)

However, the synergy index you cite (one of many proposed) is actually a *non-linear* combination of odds ratios, because it is a *ratio* of odds ratios. But even if you used some other index that is indeed a linear combination of ORs, such as

RERI = OR_AB - OR_A - OR_B + 1

you would still not be able to use -lincom- or -test-, because these require a linear combination of beta coefficients, *not* odds ratios (logistic regression is linear on the logit, or log-odds scale).

There is a way to use the multivariate delta method to obtain the variance for such non-linear quantities (and hence conduct tests). You might look into -testnl- for that. But this approach performs very poorly in small to moderate samples. In your particular situation, the actual type-I error for a nominal .05-level test can be as high as .25, and the coverage of the confidence intervals is just awful.

A likelihood ratio test performs much better, but then you have to fit both
(i) the full logistic regression model -- the usual unconstrained model with main effects for A, B, as well as their A*B interaction term; *and*
(ii) the constrained model -- one that assumes no additive interaction, ie, one where exp(b_AB) is constrained to be equal to exp(b_A)+exp(b_B)-1.

The first is no problem. But the second one is a non-standard non-linear logistic regression model and cannot be easily fit with standard software. So, unless you write your own code (which I have done in SAS but not Stata), I think you're stuck.


2. Additive relative risk model (as implemented in Epicure)
Is there a way to do this in Stata?
You can do that with the -glm- command that is very flexible in Stata.
This is the *true* additive model and should be the preferred approach.

(1) and (2) are not one and the same. The broad difference is that

(1) considers additivity of A and B in the context of an otherwise multiplicative model (ie, the world is multiplicative, but maybe A and B are additive)

while

(2) assumes additivity of A and B within an overall additive model.

Greenland has a paper discussing the nuances of these issues.


I hope this was clear enough. Any suggestion/trick/experience on the issue would be most welcomed.

Thanks,

Andrea

Andrea Baccarelli, MD, MPH, PhD
Genetic Epidemiology Branch
Division of Cancer Epidemiology and Genetics
National Cancer Institute, NIH, DHHS
6120 Executive Blvd. - EPS 7110
Bethesda, MD 20892-7236
Tel. (301)-496-5786
Fax (301)-402-4489
[email protected]


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________________________________________________________________

Constantine Daskalakis, ScD
Assistant Professor,
Biostatistics Section, Thomas Jefferson University,
211 S. 9th St. #602, Philadelphia, PA 19107
Tel: 215-955-5695
Fax: 215-503-3804
Email: [email protected]
Webpage: http://www.jefferson.edu/medicine/pharmacology/bio/
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