How to calculate 95% CI for a proportion of 100%

[Lao_feng]

Dear all,

Does anyone know how to calculate the 95% CI for a proportion when the proportion is exactly 100% ? Thanks !

Feng Liang

[Ksharp]

data x;
 x=1;output;
 x=1;output;
run;
proc freq data=x;
table x/binomial cl;
run;

[Rick_SAS]

The problem is that if all trials resulted in 'success' then (to a frequentist) the standard error is 0 and the confidence interval collapses to [1, 1]. There are ways to adjust the CI. See the Hanley's 1983 JAMA paper

http://www.medicine.mcgill.ca/epidemiology/hanley/reprints/If_Nothing_Goes_1983.pdf

which suggests that you should use a 95% CI of [1 - 3/n, 1] for the rate, where n is the number of observations.

[StatDave]

You can get an exact lower confidence limit by using the EXACT BINOMIAL statement in PROC FREQ:

data a; input x w; datalines;
1 20
0 0
;
proc freq; table x; exact binomial; weight w; run;

[Lao_feng]

Thanks a lot for your help !

Regards,

Feng Liang