It's a good question but shows that the concept of ROC analysis and AUC is not clear. AUC is calculated for categorical / logical outcome against a continuous variable. If you want to use the AUC/ROC analysis in serial measurement study as indicated by you, you can define a categorical outcome say hypertension or hypotension. Now if we are going to see the effect of time on the hypertension or hypotension induced by the drug then we will keep the time as the predictor variable and hypoertension/hypotension as the outcome variables and thus can derive a receiver operator curve which will ultimately give us AUC measures. Similarly, an outcome dosage evaluation for ROC can also be done to derive an AUC for dosage-outcome relationship.
Thus, it can be used in the study proposed by you.
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