Can this be applied to Neyman-Pearson lemma?

Hi, I am working on a project. It is about to detect the beginning of a breath. One parameter is the air change rate (derivative) we monitor. The decision (right or wrong) is whether it is within a prescribed number (which may be determined in advance. A small change makes no big consequence.) Our manager want us to get a ROC curve. This is equivalent to type I and type II errors. The text book talks about Neyman-Pearson lemma is very simple: There is a parameter threshold to adjust. The derivative can also be as a threshold in Neyman-Pearson lemma? Furthermore, we have another parameter to include to make the decision robust. Can I say that it is a 2 dimension variable problem (although one variable is a derivative)? I look forward to your highlight on our problem. Thanks.