Is there a more formal way of saying:
"In most western countries, such as the United States, an increased level of ... has been observed."
Or should such a sentence be rephrased completely?
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Some alternatives include:
There is a subtle difference between 'such as' and 'like'.
Most western countries, such as the US...
Most western countries, with the US being an example...
On the other hand
Most western countries like the US...
Could be interpreted as
Most western countries that are similar to the US
Which may not be what you mean.
I don't know about formality, but if you want to capitalise on the residual popularity of Miss Teen USA 2007 then you could do worse than follow the wonderful precedent set by Miss South Carolina, who responded to the question
“Recent polls have shown that a fifth of Americans can’t locate the US on a world map. Why do you think this is?”
with (emphasis added)...
I personally believe, that U.S. Americans, are unable to do so, because uh, some, people out there, in our nation don’t have maps. and uh… I believe that our education like such as in South Africa, and the Iraq, everywhere like such as… and, I believe they should uh, our education over here, in the U.S. should help the U.S. or should help South Africa, and should help the Iraq and Asian countries so we will be able to build up our future, for our [children].”
On the "rephrase completely" note, I would consider taking the center clause out:
In most western countries, an increased level of ... has been observed
The U.S. is now pretty much the archetype western country, so you're not providing additional information. If you want to emphasize the U.S. is included, then you could use:
In most western countries, including the United States, an increased level of ... has been observed