Is it plagiarism to closely mimic the structure of a table in a publication? I am writing a paper on a topic closely related to previous literature (but in a different study population). As such, the statistical analysis is very similar to a previous publication and I really like the way the previous authors (which I have cited in the literature review) have structured a particular table. 

Would essentially copying this structure, but putting in my own results, be a form of plagiarism?
I doubt anyone would consider a table format as plagiarized when used to show new data. It would be akin to saying use of Tukey's box-and-whisker type plots would be plagiarism. The question is understandable, however, since someone could arguably claim some such structure as intellectual property. I think the key here lies in what is being copied. You are copying the structure but not the content. To protect the form would be quite pointless since no-one would buy the rights and it would be simple to make sufficient variations to argue it is not the same form. I am sure this could be discussed at length by lawyers.

Although, not within the scope of your question, most author's will be happy to see something they produce becoming reused and maybe even a standard. I had a figure in a paper that was picked up by IPCC and used to show something different than my original but still unequivocally based on my design.

So in the end, as suggested in comments to your question. you can pay homage to the original by acknowledging the idea of the table in your acknowledgement or by citing the paper and stating the table is based on their table. Which makes most sense, will depend on circumstances in your paper.