In a statement from Jeopardy's Youtube Account:
Alex recently finished taping shows for Season 35 and has hosted 50 episodes of Jeopardy! since his diagnosis. His primary plan for the next few months is to concentrate on his health, and we are scheduled to be back in the studio in July to tape shows for Season 36 that will begin airing in September. He paused in the busy tape day to give fans and friends this update.
I'm pulling so hard for Alex. His optimism, however, is beautiful and inspiring. Stage 4 anything is never a good sign but Alex has filmed 50 episodes since his diagnosis! He deserves a much needed break to focus on his health and I am fully expecting to see him right back on set in July for more episodes and see him on my television screen for years to come. - @Traceahamilton