Doctors say cancer is a game of odds, and that Mr. Chávez may yet stage a full recovery. “The one thing we do know is that we are not great at predicting,” said J. Randolph Hecht, director of gastrointestinal oncology at the University of California at Los Angeles. “Only in Hollywood do people know how long they have.”

Despite the secrecy surrounding the politician’s condition, however, intelligence analysts in the hemisphere and doctors who specialize in cancer say they can piece together a rough prognosis based on publicly available information—even though they have no direct knowledge of the case.

His latest operation suggest the president’s odds of survival are worsening, doctors say. The fact that his cancer has returned twice after undergoing four surgeries and treatment like radiation therapy and chemotherapy that Mr. Chávez has said he had indicates the cancer is aggressive and unlikely to be cured, the doctors say.