In perfusion analysis, the patient is injected with some dose of medicine. A machine detects, over time, the dose of medicine in the patient's body. In other words, the data for each patient is time points $0=t_0 < t_1 < \cdots < t_N$ and doses $y_1, \ldots, y_N$, with $y_i \in [0, \infty)$ representing the amount of dose in patient's body at time $t_i$. (Typically, $y_i$ can also be some indirect measure of doses.) Depending on scenarios, there can be only one patient or several patients or patients divided in groups, etc. We stress only one assumption: given time $t$, the dose at time $t$ for any patient is random so that this is not a machine learning task.
When we plot all the pairs $(t_i,y_i)$, the shape usually looks like a probability density function of some distributions concentrated on $[0, \infty)$ (e.x. lognormal, Weibull, exponential, ...)
The statistician's task here is typically to investigate the trend, make inference of for instance when does the dose reach its peak, when the dose ascends, etc. One way of solving the problem is to talk to the client, fit a probability density function according to beliefs, and then look at the tasks.
For example, suppose that there is only one patient and we want to give an estimate of when the dose reaches the peak. We can say fit the data with the probability density function of lognormal distribution after discussing with client, with parameter chosen to say minimize least squares, and then look at the fitted maximum.
Question: what is the name of the statistician's task? Does such task count as a survival analysis? Time series analysis? I am leaning towards calling it survival analysis but I am uncertain, for typical tools in survival analysis seems unavailable at such a scenario.
