st: Confidence intervals for rates (dependent events)

[Dirk Enzmann <dirk.enzmann@jura.uni-hamburg.de>]

This is not a specific stata question, but I don't know where to look 
for an answer to the following problem (perhaps it is too easy but I 
can't see it):

In a sample a part of the respondents have experienced victimizing 
events. Only a part of these events have been reported to the police. 
The rate of events reported to the police is

number of reported events / number of experienced events.

For example, 13 of 267 respondents have experienced a victimizing event, 
none of them did report it to the police, thus the rate of events 
reported is 0 % (here I am talking of events, not individuals!)

Because the events cannot be assumed to be independent (some victims 
have a high rate of vicitimization because they are more prone to become 
a victim) the construction of a confidence interval for the rate of 
events reported becomes difficult (to me).

Question 1: If nevertheless a use a binomial test to construct a 
confidence interval (say: 0 of 13 events reported, 95% CI = 0 to 24.7%), 
is it correct that the width of this interval is a lower bound and thus 
a conservative estimate?

Question 2: (a) My intuition tells me that multilevel modeling could be 
a solution to obtain a correct confidence interval by treating the 
events and the events reported as the first level and the victims as the 
second. Is this correct and how should I specify this model to obtain a 
confidence interval?

(b) Alternatively, could I treat the events (and events reported?) as 
coming from a negative binomial distribution and use this for 
constructing a confidence interval? How can this be done technically?

(Apart from constructing confidence intervals I would like to test the 
rate of reporting for different subgroups or different kind of events.)

Thanks in advance,
Dirk

*************************************************
Dr. Dirk Enzmann
Institute of Criminal Sciences
Dept. of Criminology
Schlueterstr. 28
D-20146 Hamburg
Germany

phone: +49-040-42838.7498 (office)
       +49-040-42838.4591 (Billon)
fax:   +49-040-42838.2344
email: dirk.enzmann@jura.uni-hamburg.de
www: 
http://www2.jura.uni-hamburg.de/instkrim/kriminologie/Mitarbeiter/Enzmann/Enzmann.html
*************************************************
*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/