Confidence Intervals for Small Proportions from a Complex Survey

[Bob Gerzoff]

I have a large complex survey (BRFSS) from which I need to calculate the proportion and confidence intervals of individuals having a particular outcome. The outcome is rare, typically less than 5% and often 1% or 2 %. I also need to calculate this proportion for many, many different cross classifications of demographics, e.g., state, race, age, sex, etc. In many instances, there will only be one individual in a particular cross classification. Further, I need to this unadjusted and age-adjusted.

The problem I am encountering is trying to calculate appropriate confidence intervals for the very small proportions. Other well known stat packages have options to do this but they are getting tripped up by the cells with only one observation (read fatal error) or can not handle the age adjustment.

I am wondering if STATA has a straight forward handle to handle this? My goal is to have a simple program that can be passed on to a entry level stat programmer.

Thanks for any advice or direction you might be able to provide.

Bob

[Steve Samuels]

I have no advice to offer. I do note that, according to this document, for BRFSS:

Estimates are considered statistically unreliable and are suppressed if the denominator is based on fewer than 50 sample cases.

[Phil Bromiley]

You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

In many Stata procedures, you can have Stata not crash on errors by using the capture prefix.

[Bob Gerzoff]

We do have an extensive set of suppression rules in places, both for reliability and privacy. With the large sample sizes, we can actually get publishable estimates with low rates.
Thanks.
Bob

[Steve Samuels]

Thanks, Bob. You asked a method for cells with one individual. In this case, cii or ci can get an exact CI for the unadjusted proportion under the binomial assumption, which now becomes crucial. With a sample size of 1, the confidence interval will be one-sided. I personally lower the confidence level to 90% or less in such situations.

. cii prop 1 1, level(80)
                                                         -- Binomial Exact --
    Variable |        Obs  Proportion    Std. Err.       [80% Conf. Interval]
-------------+---------------------------------------------------------------
             |          1           1           0              .1           1*

(*) one-sided, 90% confidence interval