Following is a response from DHS staff member, Tom Pullum:
Probably the closest you can come to what you want is the following:
gen NMR=0
replace NMR=1 if b7==0
svyset v001 [pweight=v005], strata(v023) singleunit(centered)
svy: logit NMR if v008-b3>=1 & v008-b3<=61
* Transform the constant term into the NMR with antilogit
matrix T=r(table)
matrix list T
scalar nmr=1000*exp(T[1,1])/(1+exp(T[1,1]))
* You can do the same thing to the lower and upper bounds of the 95% c.i.
* You can include covariates in the regression or restrict to subpopulations
This will not match exactly with the report or with syncmrates for the national rate because those estimates make some adjustments for exposure and deaths in the first and last months of the interval 1-60 months before the month of interview. However, this comes very close to an individual-level equivalent to the neonatal mortality rate.