Does the diagnostic odds ratio for a test increase, decrease or not change if there is a change in the prevalence of a disease?

Question

Does the diagnostic odds ratio of a test change if there is an outbreak of the particular disease in the population? If so, does it increase, decrease or just stay the same?

Answer 1

From Wikipedia:

The diagnostic odds ratio is defined mathematically as $$\text{Diagnostic odds ratio, DOR} = \dfrac{TP/FP}{FN/TN}$$ where $TP,FN,FP,TN$ are the number of true positives, false negatives, false positives and true negatives respectively.

...

The diagnostic odds ratio may be expressed in terms of the sensitivity and specificity of the test: $$\text{DOR} = \frac{\text{sensitivity}\times\text{specificity}}{\left(1-\text{sensitivity}\right)\times\left(1-\text{specificity}\right)}$$

So if the sensitivity and specificity stay the same then the diagnostic odds ratio should also stay the same