I've been keep a diary of epilepsy seizures, and would like to attempt prediction modelling as an help for better management of anti consultant therapy.

Could you help to suggest models that fit with observed behaviors, and that make sense given the number of datapoints I have ?

Please find below a description of available data, the pattern I've observed, what I've tried, what I am puzzling myself about.

Available data & pattern observed

54 events of seizures, keeping date and time (to the minute). I kept records of the intervals between seizures : I see that even after therapy the trend just kept going linearly; but what changed is that after therapy a periodic pattern is longer, but when seizures happened, they happened more than one in 24h (clusters).

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So there is a periodicity in data, but also the periods are becoming progressively shorter.

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Statistical description about the seizures intervals: median: 3.7 (days) mean: 4.59, std: 4.7

What I've tried and choices I've taken.

How could I forecast single seizures? How can I forecast cluster seizures, and try to prevent them ?

I helped myself with keeping track of how the z-score of new seizures moved from the mean of all the above events.

In this way I could see even better the sinusoidal trend.

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I initially thought to make use of moving average techniques, with models approximating forecasting by extracting a trend from the moving average of periodic intervals (which I chose to be as the median of the seizures ) and make regression with it.

The regression yielded an MSE of 1.5 - is it good ?

Since I don't have a clear periodic intervals expressed in terms of weekdays or seasons, so to predict what will happened the next monday, tuesday or next month, I come up with the idea to label the indexes of the datapoint with the z-score itself.

So how to predict the next z-scores ?

I helped myself by exploring a markov chain, both with binary states (single seizures and cluster seizures modelled as a sequence of 0 and 1) and as well with more states (about 10 different z-scores observed in the range of the events).

I then entered in a loop of questions thought - does it make sense ? how to estimate the likelihood of a markov chain sequence ?

I'd like to ask for your help and guidance in modelling this time series - I was also reading about Long short term memory, but any help in brainstorming and possibly attack the problem in less amateurish way would be appreciated.

Key points

  • periodic time series (like a sinusoidal), but period becoming progressively shorter.
  • two types of events: single seizures (the height of the sinusoidal) and cluster seizures (the bottom of the sinusoidal, when events are close in time)

research questions :

  • can I make a predictor better than using statistical description ?
  • can I prevent single and cluster seizures, within an interval of 6 hours ?
  • With which probability confidence ?

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