Interpretation of hierarchical clustering with bootstrapping

Question

I have data that includes 'cases' and 'controls' and have carried out hierarchical clustering.

I used the pvclust package in R to bootstrap the results and significant branches are highlighted with red rectangles (based on au>0.95):

What is clear is that no clustering occurs that separates 'cases' and 'controls', and this is in fact what we expected and want to show. We want to show that the measured variable does not distinguish between cases and controls.

1. List itemApart from saying visually no clear clusters emerge that distinguishes between cases and controls are there any objective measures that can be used to say no significant clustering occurs between two groups?
2. One observation I have here is that the AU values and the BP values are very different, even though both p-values should be interpreted in a similar fashion, am I missing something?
3. Perhaps pvclust (bootstrapping) is not the right option here, is there a better way of showing quantifiably that no significant clustering occurs between two groups? Perhaps some kind of supervised clustering (I am not sure what this even means in this context)?

Answer 1

Good question. You have performed the first step via unsupervised learning and AU bootstraps give great results, orthodox bootstraps give no significant (or very few) clusters. The contrast between these approaches is unusual because they should be somewhere close to each other. If you can resolve that, your analysis is fine. So at present IMO the unsupervised learning needs further investigation. ... deleted

... antibodies ... oh I see. Trees, like you've done, don't work here because of the cross-reactivity creates network phylogenies. This is the antonym of bifurcating trees. If someone has a robust bifurcating phylogeny with antibody data and gets good bootstraps .. utterly amazing. However, if you subject your data to a network analysis you'll find connections all over the place - in practical terms this really messes up bootstraps. Thats the likely reason for you results. There is no point doing a complex bifurcating tree analysis because the antibody cross-reactivity will mess it up. k-means has been implemented as unsupervised learning in these instances and would provide the starting point in using clustering to define a supervised learning problem.

Answer 2

I've got it. The question you are asking is homogeneity between you target group and your general population of patients. What you want to show is "complete" homogeneity between the two groups regardless of any sub-sampling, ie. if there is groups within groups that might break your hypothesis. K-means is perfect here. The issue with K-means is designating the number of groups, but here thats irrelevant because its not the question you are asking. You are asking homogeneity and if your hypothesis is true no matter how many groups you designate for K-means, e.g. 2,3,4,5,6,7,8,9,10 (or maybe a more reduced sampling) homogeneity between target (treatment?) and general population is observed. This would therefore be a definitive analysing ASSUMING that you don't encounter a group where there is exclusively one population and the other is absent. Obviously the number of K-mean groups can't exceed the number of treated/target patients.

It would be a really good application of k-means because it avoids the question, So why was that a priori selected?

Personally I would first present your preferred a priori group size and then say same result for all group sizes. Its simple, recognised and neat and easy for a reviewer to follow. There are ML solutions to K-means, but I think "keep it simple".