Point estimates for sensitivity and specificity are based on proportions. Therefore, we can compute confidence intervals using binomial theory. See SAS Example (18.1_sensitivity_specifi.sas) below for a SAS program that calculates exact and asymptotic confidence intervals for sensitivity and specificity.

***********************************************************************
* This is a program that illustrates the use of PROC FREQ in SAS for  *
* determining an exact confidence interval for sensitivity and        *
* specificity.                                                        *
***********************************************************************;

proc format;
value yesnofmt 1='yes' 2='no';
run;

data sensitivity;
input positive count;
format positive yesnofmt.;
cards;
1 14
2 01
;
run;

proc freq data=sensitivity;
tables positive/binomial alpha=0.05;
weight count;
title "Exact and Asymptotic 95% Confidence Intervals for Sensitivity";
run;

data specificity;
input negative count;
format negative yesnofmt.;
cards;
1 91
2 08
;
run;

proc freq data=specificity;
tables negative/binomial alpha=0.05;
weight count;
title "Exact and Asymptotic 95% Confidence Intervals for Specificity";
run;

For the FNA study, only 15 women with cancer, as diagnosed by the gold standard, were studied. The rule for using the asymptotic confidence interval fails for sensitivity because np(1 - p) = 0.9765 < 5 (the rule does hold for specificity).

As the output shows below, the exact 95% confidence intervals for sensitivity and specificity are (0.680, 0.998) and (0.847, 0.965), respectively.

Sample Size = 15

Sample Size = 99