# Diagnostic device hypothesis testing for superiority to a fixed value

I am designing a study to demonstrate that a diagnostic medical device is more sensitive than a fixed performance goal of 70%. Currently I am attempting to determine the appropriate sample size. My hypotheses are:

H0: u <= u0
H1: u > u0

u - Sensitivity of the device under test
u0 - Performance goal sensitivity = 70%

So typically we would observe a bunch of subjects with the target disease (all positive for the disease) and get a positive (+) or negative (-) test result from the test device.

Say we take 36 subjects and get 31 + results with the test. We could use the binomial test to determine the one tailed test result:

binom.test(31, 36, (7/10), alternative ="greater")

However, in my case I will be obtaining a Sensitivity of the test from each subject and then estimating the mean and variance Sensitivity of the test device from my group of subjects.

Subject - Test Result
1 - 85%
2 - 77%
3 - 50%
4 - 55%
5 - 90%
...
n - Xi

What would be the appropriate test statistic for this design?

• How can you get a sensitivity for each subject?! Using the device multiple times on the same subject? If so, one could use a Bernoulli repeated measures (GLMM) model. – Björn May 20 '16 at 5:09
• I should have explained better. You are exactly correct, our device is an imaging device, and we calculate the disease state of each pixel in the image. So from one image we obtain 1 million pixels and perform 1 million tests to classify each pixel as disease state + or -. One issue with this is that each pixel in the image cannot be considered independent. Therefore, I wish to know from how many subject we should collect images, and then how to perform the above hypothesis test. – jeffalltogether May 20 '16 at 14:20