Authorship for paper with questionable statistical analysis
If you are to co-author a paper, you need to agree with its methodology and conclusions. You don't.
My advice, in general, is to offer to work with others to improve the paper to meet everyone's standards. You indicate that this might not be possible, which would be a fault of the PI. If you can't convince them to work with you, then I don't see a real way forward without saying that you won't be part of it in any way.
They can then go forward if they like, citing your past work properly. If they don't do that, it would be time to contact editors.