Does an analogy ever have "as" in it. I'm just trying to figure out figures of speech and I know Writeteacher told me "as" would be a simile but in the following:

My brother has grown a great deal in the last year. He is almost as tall as I am now. This can't be a simile correct because it's comparing two like things so would this be an analogy, then? Thank you for helping

If it was an analogy it would have to be two word pairs like

Chapter is to book as state is to nation??Correct?