Treatment of HIV is challenging in areas where medical clinics are often far away from home and not easily reached by patients, which makes refilling a prescription challenging. Filmão et al. (2019) followed HIV prescription pick-ups in clinics in Mozambique. Patients are requested to pick up their prescription on a regular schedule. The researchers recorded for each patient the number of days between the beginning of treatment and first occasion that the patient was late picking up their prescription. Their findings are recorded in the following figure.

a. What is the event measured in this survival analysis?

b. Notice the vertical tick marks that appear on the curve above. What do those likely represent (following the same conventions as in the main text)?

c. How long does it take for 50% of the patients to be late picking up their prescription for the first time? Estimate by eye.