Overall, it looks like you are trying to do two things:
- Get a better understanding of the accuracy and precision of your new bio-marker in comparison with another method that might not be very sensitive in identifying the true underlying disease (aka an imperfect gold standard).
Fortunately, imperfect gold standard are fairly common and there are some great resources on how to handle these situations:
For example, if you have three different (and decent) methods of measuring for the disease, you can run a latent class analysis to see where there is agreement to get an idea of where “truth” is.
Chapter 11 in Zhou’s Statistical Methods in Diagnostic Medicine by Zhou, Obuchowski, and McClish has some great information on handling imperfect gold standards and some great case examples.
Here is another very applicable manuscript on this exact topic (I might little biased because I do alot of testing around renal AKI/CKD biomarker analyses):
- Because you believe the new biomarker is more sensitive, the current understanding of the true incidence of the disease might be under-represented. Thus, you want to try and get a better understanding of what the incidence of the disease is when using your new biomarker.
It is my belief that understanding the performance of the new biomarker takes precedence over trying to find the new population incidence based off the new marker compared with the old one. In doing a comparison of the two markers, you might find that your new biomarker has a higher proportion of subjects above the disease cutoff (whether that be defined by ROC or reference interval etc…). I would caution against making a claim that your biomaker “finds more disease” and instead state something along the line of “finds more positive tests results” and then attempt to correct for the imperfect gold standard.
What would be an optimal way to calculate sample size for this study?
It is difficult to calculate a sample size without much prior information about the comparisons you are trying to make (this is why people tend to do pilot studies).
What you can do is reason what is the minimum effect size you would be willing to accept and then use this as the basis of your sample size calculation.