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I have an time series data with an appearance of a headache events over time. Each headache is characterized with intensity (1-5) and duration (in seconds).

Therefore, the signal is represented in 3D - intensity frequency and duration. I would like to have a metric per day - to represent a day with some "rank of headaches".

Any suggestions?

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You can simply sum the number of headache seconds per day, weighted in some way by the intensity. I'd be careful of any overly complex summary.

In choosing the weight function, you will need to implicitly decide whether one hour of headache at intensity 5 is worse or less bad than three hours at intensity 3.

It might be best to ask your study participants which one they would "prefer". Best to define a small set of possible combinations that cover your observation space and then discuss this with the patients.

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  • $\begingroup$ thanks, but the suggested approach doesn't cover the "frequency" dimension.. $\endgroup$ Nov 22, 2017 at 14:23
  • $\begingroup$ What do you mean by "frequency"? I only see it once in your question, and assumed it referred to one or more bouts per day, which you would address by adding the seconds within each day. $\endgroup$ Nov 22, 2017 at 14:38
  • $\begingroup$ I also want to quantify the interval between events, the data is time series. You can think of a simple example, of 2 different days, where you have one day with 10 short events vs. a day with 2 long events, and assume the sum in seconds is equal - Taking only the duration into consideration, you will result with similar rank. you'll' "lose" information. $\endgroup$ Nov 22, 2017 at 15:05

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