Is there any way to determine the compression ratio used to render an already burned DVD-R?

You might be able to get kind of close. What's the total length of the running video? what type of audio...AC3 or PCM (wav)? Most would be AC3 which give a smaller file and allows a higher bitrate for the video. Once you know the total run time of the video and knowing that a standard DVD-R is actually less than 4.34 gigs due to formatting of the disc you should be able to get close to the BR used.
For example if the total run time of the video is 105 minutes and the audio is AC3 then the average BR would probably be somewhere around 5,542,200 using a VBR. If the audio were PCM the average would be 4,167,000 so as you can see it's quite a difference. Also if you have a motion menu vs. a static menu you need to allow a bit of room for that.
As you can see,without knowing specifics it's kind of a somewhat educated guess at best.

You could try playing it back in Media Player Classic or VLC and using their info options to look at the data rate. You can also try placing a .vob file in to PremierePro and looking at the stats for the video file to see if it tells you what you want.

Andrew

Open corresponding *.VOB file in MediaInfo (http://mediaarea.net/) (text mode) and You will get something like

Bit rate mode : Variable
Bit rate : 3 458 Kbps
Maximum bit rate : 7 000 Kbps

and many other usefull information.