ROC curve: small focused sample vs large sample Background
I'm currently reading the book Data ming: practical machine learning tools and techniques and came across the following ROC curve:

The text corresponding to this figure:

Method  A  excels  if  a  small, focused sample is sought; that is, if
  you are working toward the left-hand side of  the  graph. Clearly, if 
  you  aim  to  cover  just  40%  of  the  true  positives  you should
  choose method A, which gives a false positive rate of around 5%,
  rather than method B, which gives more than 20% false positives. But
  method B excels if you are planning a large sample: if you are
  covering 80% of the true positives, method  B  will  give  a  false 
  positive  rate  of  60%  as  compared  with  method  A’s 80%.


Question
How does a ROC curve relate to sample sizes? (in the context of the text mentioned above)
 A: A ROC graph does not relate to sample size directly; small or large samples can have the same ROC graph. The methods (classifiers) used to create the ROCs have different performances and these performance characteristics can relate to the samples size of the results as a proportion of the overall sample examined.
What the author tries to convey is that the performance of method A is "preferable" if we aim detect a subsample of sample with true positives and we want to strongly limit our number of false positive instances (e.g. patients suggested to have an invasive medical procedure). Similarly, if we want to ensure that vast majority the true positive instances is detected (even to the expense of having a substantial number of false positives), method B would be preferable (e.g. patients who are suggested to take a relatively inexpensive screening test).
Different applications may require an exchange between high recall and high precision. As @Frank Harrell correctly notes, if we have a well-defined utility function we can use to maximise our expected utility. If we do not have one (as in the case of this arbitrary ROC graphs) we can pick a methodbased on an overall goal (e.g. medical diagnostics (method A) vs medical screening (method B)).
