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I want to see if a treatment brings patients closer to controls using multiple dependent variables. Can I do kmeans and see if the controls are separate from the patients before treatment, but cluster together after treatment? Could I report this, or is the fact that the observations are not independent mean I can't use clustering?

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K-means is a solution to an optimization problem. So, even if controls and patients cluster together, there is no quantitative measure of the treatment's effectiveness.

To address this, you need a reliable indicator, such as statistical significance. In your case, applying biostatistical procedures, such as statistical tests on the mean and/or variance of each variable, assuming a plausible a priori probability density function (p.d.f.) for those variables, seems appropriate.

If some of the variables are discrete, the analysis may become more challenging, as academic literature may not cover these cases as comprehensively.

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