Is Chi-sqaure the right test for analysing these disease test results?

#1
Hi All!

I have three tests testing for three different strains of the same disease. Unfortunately the tests are not very specific since antibodies (and therefore positive results) to the three strains are common in most populations. If however, there is a true outbreak of the disease, then of the strains will typically have a much higher population prevalence than the other two.

We take many batches of samples from different populations to see if there is a dominant strain (and therefore outbreak of that strain.)

A sample of my data can look like this:

Sample size: 100 individuals
Positives for test1: 24/100
Positives for test2: 42/100
Positives for test3: 18/100

The question is now whether the apparent higher levels for test2 (equals strain 2 of the disease) is due to true disease or just chance. I've used a chi-squared test on the data and am very happy with my results (the stats confirm my intuition.) However, I am not sure if a chi-squared test is allowed, because my results are not independent. For example one individual can test positive for 1, 2 or 3 three of the different strains.

Thanks to all the helpful people out there!

Johann
 

Karabiner

TS Contributor
#2
You are right in that Chi² is inappropriate in case of dependent measures.
You can perform a global test using Cochran's Q . Pairwise comparisons
can be made using McNemar's test.

Kind regards

K.