Perhaps I am not understanding this correctly, but I get an error that I don't expect after adjust.
. xi:xtgee zoster1 ra age65 sex,i(pat) robust eform fam(poisson) nolog exposure(exposure)
GEE population-averaged model                   Number of obs      =     92494
Group variable:                     patkey      Number of groups   =     20238
Link:                                  log      Obs per group: min =         1
Family:                            Poisson                     avg =       4.6
Correlation:                  exchangeable                     max =        11
                                                Wald chi2(3)       =     36.92
Scale parameter:                         1      Prob > chi2        =    0.0000
                           (standard errors adjusted for clustering on patkey)
------------------------------------------------------------------------------
             |             Semi-robust
  zoster1now |        IRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          ra |    1.22771   .0940327     2.68   0.007     1.056576    1.426563
       age65 |   1.368359   .0760525     5.64   0.000      1.22713    1.525841
         sex |   .9154671   .0617301    -1.31   0.190     .8021324    1.044815
    exposure | (exposure)
------------------------------------------------------------------------------
. adjust age65 sex,by(ra) exp ci
offset (ln(exposure)) not constant within by()
However,
. tab exposure,m
   exposure |      Freq.     Percent        Cum.
------------+-----------------------------------
         .5 |     92,635      100.00      100.00
------------+-----------------------------------
      Total |     92,635      100.00
shows that the exposure is constant.
Am I misunderstanding something?
Thanks,
Fred Wolfe
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