Immediately after a heart transplant, patients are randomly assigned to two treatment therapies to improve recovery from the transplant, therapy 1 and therapy 2. The patients are then followed for up to 5 years after their surgery. Define the time-to-event random variable T as the time (in months) until recovery after a heart transplant. For each of the following study descriptions that involve T, sketch the graph of the survival curve (or curves) with as much detail as necessary. Parts A through D are independent of each other.
a. Therapy 1 is not very effective shortly after surgery, but everybody recovers before the study period is over.
b. Therapy 2 is very effective shortly after surgery, but becomes less effective after 3 years. Not every patient fully recovers by the end of the study period.
c. Two curves on the same plot: Therapy 1 is consistently more effective than therapy 2 over time.
d. Two curves on the same plot: Therapy 1 is more effective than therapy 2 for the first 2 1/2 years, and then therapy 2 is more effective than therapy 1 for the remaining duration of the study.