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I have a dataset of subjects with a binary outcome (1=disease, 0=healthy), and a column with the time in which the levels of several biomarkers (continuous values) were measured at each time point for a given subject.

The number of time points corresponds to the number of samples. For example, if I have $50$ samples there are also $50$-time points. There is a problem with $p\gg n$. In fact, the number of predictors (biomarkers) is much higher than the number of samples ($n$). Finally, the samples of the two classes have a common time series (only one column). For example:

sample data

My questions are:

  1. It is possible to build a classifier to distinguish the two classes and considering that the levels of biomarkers show decreasing or increasing trends with the time? I don’t want to build a model without taking into account the information of the time. Because as said, it is possible that there is a relation between time and level of biomarkers.

  2. I would like to identify the most important variable derived from 1). What is the best model that can I use to analyze my data?

    I have found some models that could be useful approaches based on time series analysis (e.g. Arima) but I have also seen the application of machine learning approaches (e.g. random forest). I am looking mainly for something that I can implement in R.

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  • $\begingroup$ Do you have the outcome in time series form as well? $\endgroup$
    – Skander H.
    Commented Jun 5, 2020 at 6:43
  • $\begingroup$ Hi thanks for the question. I have reported an example of my dataset in my post. I have simplified the questions for reason of explanation. The classes and the time were obtained using other analysis and the output is this format. $\endgroup$
    – gitm
    Commented Jun 5, 2020 at 9:32
  • $\begingroup$ OK. You might want to try treating it as a VAR model, and then after predicting the outcome variable, apply a decision threshold to insure a binary outcome. In theory for this type of problem you could use LSTM as binary time series classifier, but because you have so few samples, LSTM won't work well. $\endgroup$
    – Skander H.
    Commented Jun 5, 2020 at 11:51
  • $\begingroup$ thanks! I will try to study VAR model to understand if it is suitable for my data. $\endgroup$
    – gitm
    Commented Jun 5, 2020 at 21:29

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I'm not sure if I am fully understanding you. I would have prefer to post as a comment, but I lack reputation to do so. May be it would be clearer if you post a little bit of your data.

If I understand properly it is mixed effects cox regression? Are your data somehow like data in this page (but you having much more columns)?

May be you want to check answer and comments to this question

As you talk about biomarkers I imagine you are in live sciences, may be you want consider creating a categorical variable containing if some biomarker increases or decreases (appart from the outcome variable) and testing it against the outcome. For instance, person A has increased values of biomarker X over time and person B has stable values. May be it could be helpful -depending on your data- to create a variable called Xincreasing being 1 for person A and 0 for person B.

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  • $\begingroup$ Hi thanks for your reply and suggestions. I have edited my post with an example of the data. Hope that this could be useful. $\endgroup$
    – gitm
    Commented Jun 5, 2020 at 9:31

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