menbreg marginal mean rates w exposure variable?

[Brad Anderson]

Using version 15.1

Having trouble estimating 30-day marginal mean rates using margins command with expression

sid = subject identifier
week = panel identifier
drgdays = count outcome
expose2 = days at risk, days of exposure varies considerably from subject to subject and week of panel.

Example data:

* Example generated by -dataex-. To install: ssc install dataex
clear
input int sid float(week drgdays expose2)
1  1  0  13
1  4  0  48
1 12  0  49
1 24  0  59
2  1  0  11
2  4 11  11
2 12 58  70
2 24  1  86
3  1  0  10
3  4  3   4
3 12  2  59
3 24  1  90
4  1  7   7
4  4 26  27
4 12 57  57
5  1  0   7
5  4  0  17
5 12  0  42
5 24  0 134
6  1  0  16
end

Commands and output:
Simple model estimating an overall marginal rate:

. menbreg drgdays , exp(expose2) ///
> || sid:, vce(robust) irr nolog

Mixed-effects nbinomial regression Number of obs = 567
Overdispersion: mean
Group variable: sid Number of groups = 178

Obs per group:
min = 1
avg = 3.2
max = 4

Integration method: mvaghermite Integration pts. = 7

Wald chi2(0) = .
Log pseudolikelihood = -1238.2894 Prob > chi2 = .
(Std. Err. adjusted for 178 clusters in sid)
------------------------------------------------------------------------------
| Robust
drgdays | Inc. Rate Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | .0397512 .0096893 -13.23 0.000 .0246531 .0640958
ln(expose2) | 1 (exposure)
-------------+----------------------------------------------------------------
/lnalpha | .6354762 .1293867 .3818829 .8890696
-------------+----------------------------------------------------------------
sid |
var(_cons)| 6.919573 .9967897 5.217478 9.176942
------------------------------------------------------------------------------
Note: Estimates are transformed only in the first equation.

. margins

Predictive margins Number of obs = 567
Model VCE : Robust

Expression : Marginal predicted mean, predict()

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | 53.45887 18.36544 2.91 0.004 17.46327 89.45447
------------------------------------------------------------------------------

. margins, expression(predict(mu)/expose2)

Predictive margins Number of obs = 567
Model VCE : Robust

Expression : predict(mu)/expose2

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | 1.264494 .4344084 2.91 0.004 .4130689 2.115919
------------------------------------------------------------------------------

. margins, expression((predict(mu)/expose2)*30)

Predictive margins Number of obs = 567
Model VCE : Robust

Expression : (predict(mu)/expose2)*30

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | 37.93481 13.03225 2.91 0.004 12.39207 63.47756
------------------------------------------------------------------------------

.

If I just calculate a simple 30-day rate:
gen rate30 = (drgdays/expose2)*30

The overall mean is around 6.2

Am I specifying the expression incorrectly? Thanks.