"In the case of medical diagnostics, there is a cost associated with each medical procedure that provides additional information (blood test, x-ray, etc.)."
Should that end with "etc.).", "etc)." or "etc.)"?
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You are correct in this item from your example:
(blood test, x-ray, etc.).
The two marks of punctuation are actually different; the period following "etc" marks an abbreviation, and the period following the closing parenthesis is terminal punctuation. Each mark is doing a different job, so you need both of them.
Here's another example that arises frequently:
The tarantula crawled into the sleeping bag ... unnoticed.
In this case, the three periods are marks of ellipsis, here serving to create a dramatic pause. But, when the marks of ellipsis fall at the end of a sentence, you still require closing punctuation:
The surgeon raised the scalpel and leaned forward ....
Since c is not the last letter of cetera, you need a full stop after it (at least in formal situations). British usage is to put this before the bracket in all cases, though I believe American differs sometimes. And though, logically, you would need another full stop to end the sentence, I've never seen it used (probably to avoid ending with ?etc..)
So go with the third alternative, "...x-ray, etc.)"
There's an increasing tendency not to add a period after "etc", so if OP were to adopt that convention the problem would obviously go away. But you can't just drop the period in that one context unless you're happy to discard it everywhere else - consistency is more important than which particular usage you adopt.
If OP doesn't want to always write "etc" without a period, I suggest he should drop the period after the bracket. Many people are happy to let a sentence end with just a closing bracket, if it's immediately preceded by a period, exclamation mark, or question mark.
Haing said that, ending a sentence with "etc.)." doesn't seem particularly unacceptable to me. Unfortunately it's difficult to search for usage figures involving these characters, so I can't produce any evidence to show what people normally write. All I can say is it's a matter of style, not absolute rules of grammar.