Naomi was near full term when she was diagnosed with cancer. The doctors recommended that in order to qualify for an experimental treatment, she be given an immediate cesarean section as the fetus would not survive the treatment.
However, Naomi resisted. Unbeknownst to her husband, she had previously given birth to a child with infantile Alexander's disease and was afraid that a pre-term baby would suffer the same fate. However, she finally agreed to the procedure .As the doctors prepared for it, the operation was called off by the hospital's chairman of the board because he had found out she was trying to get into a clinical trial right after the surgery, which went against the protocol.
Soon thereafter, she develops a pulmonary embolism. House realizes that she can't be saved and convinces Sean to allow them to remove the fetus, which has a chance to survive. Baby Randolph turns out to be healthy.