Date:         Sat, 31 Jan 2009 15:48:32 -0800
Reply-To:     Ryan <Ryan.Andrew.Black@GMAIL.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Ryan <Ryan.Andrew.Black@GMAIL.COM>
Organization: http://groups.google.com
Subject:      Rate Ratio Interpretation in a Zero Inflated Poisson Model
Comments: To: sas-l@uga.edu
Content-Type: text/plain; charset=ISO-8859-1

Dear SAS-L,

Dale recently helped me construct a Zero Inflated Poisson (ZIP) model
using the experimental MCMC procedure. My question does not relate to
this procedure, however. It is about Dale's suggestion of computing a
Rate Ratio (RR) using the formula below:

    /* Compute rate ratios of disease j to disease k as        */
    /* RRj_k = E(y|disease=j) / E(y|disease=k)                 */
    /* where E(y|disease=j) = (1 - P(ZI|disease=j)) *          */
    /*                        E(Y|Y is Poisson,disease=j)      */
    /* with                                                    */
    /*       P(ZI|disease=j) = probability of zero inflation   */
    /*                         given disease j                 */
    /*     E(Y|Y is Poisson,disease=j)                         */
    /*                       = expected value of the response  */
    /*                         given that the response is      */
    /*                         Poisson (not an excess 0) and   */
    /*                         given disease j                 */

RR2_1 = ((1 + exp(bl2)) / (1 + exp(bl1))) * exp(bp2 - bp1);

Note that the formula incorporates both the logistic and poisson part
of the model. I'm curious if anyone has ever seen both parts of a ZIP
model used to obtain an overall RR. In all the examples I've seen,
emphasis is usually placed on the poisson coefficients only.

Dependent Variable = number of days diagnosed with a particular
disease over the past 10 days. Most people do not have any disease,
while some have one or more for several days. Exposure level for each
disease over those ten days is part of the poisson part of the model.

The original post is here:

http://groups.google.com/group/comp.soft-sys.sas/browse_thread/thread/e38cd971a0f85c30/5675903605a8b0fd?hl=en&lnk=gst&q=zip+mcmc#5675903605a8b0fd

So, with all that said, *assuming the model is correct,* how would you
interpret the RR? Even if you're not sure how you'd interpret this
particular example, do you know of any example that has used this
formula?

Thanks,

Ryan