The outcome of an upcoming oral argument involving Endo Pharmaceuticals Inc.'s patent on a claimed new treatment method for an existing opioid drug could shift the landscape for life sciences investment.

Branded drugmaker Endo Pharmaceuticals Inc. and generic maker Teva Pharmaceuticals USA Inc. are set to present dueling arguments at the U.S. Court of Appeals for the Federal Circuit Dec. 6 over whether certain method of treatment claims for already approved drugs are eligible for patents.

The question of what’s...