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I have performed consensus clustering on a data set (N=2500), which resulted in a best value of k=3. The data set is from the medical domain, and the features represent demographic (e.g. age, sex) and medical data (presence of comorbidities, medicines etc). I intend to define clusters within this data set that represent sub-phenotypes. These clusters should have some characteristics that define them, e.g. cluster 1 is defined by a high age and a high prevalence of Diabetes. The data consists of both numerical and categorical data.

Now, I have the clusters but I'm not sure how I would statistically validate these clusters. Should I just take all the features and check whether or not they significantly differ from the patients outside the cluster? E.g. for continuous/numeric variables like age, use the Mann-whitney test to test whether or not the ages from patients in cluster a significantly differ from all other clusters? And then test the categorical features with a Person's Chi-square test? Or is there a better way of doing this? Intuitively this makes sense to me, but there are probably caveats I'm not aware of.

I read about this local article about this topic. However, I think the answers to this post do not yet answer my questions. Bootstrapping sounds like a way to make things more robust, but I suppose I already am bootstrapping since I'm using consensus clustering. I also found this relevant, local article, but it has no answers.

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