David Letterman Weighs in on Alex Trebek's Treatment Amid Cancer Battle

David Letterman has weighed in on Alex Trebek's treatment amid the game show host's cancer battle.

A TMZ cameraman caught up to Letterman and revealed to him that Trebek's tumors have shrunk by about 50 percent since he began treatment.

"That's great," the former late night talk show host said, then confirming that he "of course" believes in "the power of positive thought."

Trebek announced his cancer diagnosis earlier this year, saying in a record statement, "Hi everyone, I have some news to share with all of you and it's in keeping with my longtime policy of being open and transparent with our Jeopardy! fan base. I also wanted to prevent you from reading or hearing some overblown or inaccurate reports regarding my health. So therefore, I wanted to be the one to pass along this information"

"Now, just like 50,000 other people in the United States each year, this week I was diagnosed with stage 4 pancreatic cancer," he continued his statement. "Now normally, the prognosis for this is not very encouraging, but I'm going to fight this, and I'm going to keep working. And with the love and support of my family and friends and with the help of your prayers also, I plan to beat the low survival rate statistics for this disease."

"Truth told, I have to! Because under the terms of my contract, I have to host Jeopardy! for three more years! So help me. Keep the faith and we'll win. We'll get it done," Trebek's statement concluded. "Thank you."

Recently, the Jeopardy! host spoke to PEOPLE and revealed the news that his tumors have begun to shrink.

"It's kind of mind-boggling," Trebek explained. "The doctors said they hadn't seen this kind of positive result in their memory…some of the tumors have already shrunk by more than 50 percent."

He then went on to credit his loving and dedicated fanbase for all of their support and well-wishes as being part of what has helped him endure.

"I've got a couple million people out there who have expressed their good thoughts, their positive energy directed towards me and their prayers," Trebek stated. "I told the doctors, this has to be more than just the chemo, and they agreed it could very well be an important part of this."

"I've got a lot of love out there headed in my direction and a lot of prayer, and I will never ever minimize the value of that," he then said.

Trebek remains the host of Jeopardy! at this time, with no current plans to step down.