# Sensitivity/Specificity: determining confidence intervals for a small sample size

#### figueiredo.analucia

##### New Member
I'm conducting a study to determine the validity of a diagnostic test, by comparing its results to a reference standard. The variables I'm dealing with are all categorical.
Sadly, I couldn't obtain a proper sample size since the prevalence of the disease is very low (about 6%).

When I first calculate the sample size for a CI of 95% and an antecipated sensitivity of 80%, through the following formula - TP+FN = [1,96^2 x sensitivity x (1-sensitivity)] / [0,05^2 x prevalência] -, I realized I would need a sample greater than 3907 individuals.
Now, I have a sample of 157 subjects, but I only have 2 people that have a positive result in the reference standard test (TP+FN).

My questions are:
1) Is there a way to calculate/estimate the exat confidence interval for sensitivity and specificity for a small sample size?

2) What about the calculation of likelihood ratio; can I infer about his meaning with such a small sample, or do I have to state the confidence intervals for this measure too?

3) Are there any other statistic analysis that I could do to improve my study?

Many thanks!