I found the following study on the effectiveness of LDW on PubMed, I am copying the abstract here:
OBJECTIVE:
To evaluate the effects of lane departure warning (LDW) on single-vehicle, sideswipe, and head-on crashes.
CONCLUSIONS:
Lane departure warning is preventing the crash types it is designed to address, even after controlling for driver demographics. Results suggest that thousands of lives each year could be saved if every passenger vehicle in the United States were equipped with a lane departure warning system that performed like the study systems.
PRACTICAL APPLICATIONS:
Purchase of LDW should be encouraged, and, because drivers do not always keep the systems turned on, future efforts should focus on designing systems to encourage greater use and educating consumers about the benefits of using the systems.