You see, the liver is responsible for the generation of almost all the plasma proteins, including the clotting factors. Therefore, in liver failure, the INR will be prolonged.
The other common measure of the liver's synthetic ability is albumin, but this changes too slowly for it to be much use in acute liver failure.
The transaminases (AST, ALT) also come to mind, although on closer inspection they appear to be less useful. For their levels to be elevated, enough of the enzymes must be released into the bloodstream as the liver gets damaged. For this reason, falling transaminases may simply mean that so much of the liver has been destroyed that there isn't much AST or ALT left!
Of course, measuring the INR also reminds you about one of the major complications of acute liver failure: haemorrhage.