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st: Confidence intervals for rates (dependent events)

From   Dirk Enzmann <>
Subject   st: Confidence intervals for rates (dependent events)
Date   Wed, 09 Feb 2005 16:57:01 +0100

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,

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

phone: +49-040-42838.7498 (office)
+49-040-42838.4591 (Billon)
fax: +49-040-42838.2344
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