In the wikipedia article on the Cox model, in the development of the partial likelihood, it is mentioned that the different subjects are treated "as if they were statistically independent." Is this in fact an assumption of the model, or just that the subjects be independent conditionally on the covariates? It seems the partial likelihood in the article is only using conditional distributions.
Eg if I'm looking at time to onset of some contagious disease. Events from individuals in the same house are probably dependent, and I would be inclined to include a term for "living in the same house" and impose an assumption of conditional independence. Is that appropriate in the Cox model setting?