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I am looking for some statistical solution to the problem of testing the similarity of curves. I am working with multiply time series (sort of survival curves). The curves are calculated as a separate curves for different values of a categorized continuous variable. For example:

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I want to test which of the curves are equal and can be combined in one curve. I know that there are some r packages that use distance measure to cluster curves, such as tsclust.

What i need is an algorithm that takes into account that only curves form adjacent intervals of a class variables can be matched. It needs to be automatic as i have many curves and many class variables.

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In a similar problem with pharmacokinetics curves, I used the standard k-means algorithm. I used it in an automatic way for analyse several datasets, and it worked very well. Each curve is an observation and the variables are the values in each time point (50 variables in this plot)

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    $\begingroup$ Thank you! In this way I can use many different standard clustering algorithms and treat each curve as one observation. I wonder how did you provide for specific clustering order. What if the levels of curves for subsequent classes do not follow the order? $\endgroup$
    – RobM
    Commented Jul 8, 2016 at 9:16
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    $\begingroup$ I don't see this is a problem. Survival curves of two subsequent classes can be crossed (this is a normal situation in survival analysis). The clustering will detect these 2 curves are near or far, but if they are near, for me it is not very important what it is down or up. The clustering summarizes what is the general situation $\endgroup$
    – Jesus Herranz Valera
    Commented Jul 8, 2016 at 9:27
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On such small data, hierarchical clustering is your best choice.

The bigger challenge is how to preprocess your data to account for different factors (such as group size) that you do not want to take into account.

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