Clinical Trials

❘❙❚■ Chapter 21 | Analysis of Survival DataTable 3. Kaplan–Meier estimate of survival function for patients receiving treatment A in the pancreaticcancer trial.Survival time (months) t jNumber at risk at t jn jNumber of events at t jd jSurvival function at t jS(t j)2 18 0 1.0005 17 0 1.00010 16 1 0.93812 15 1 0.87515 14 0 0.87527 13 1 0.80836 12 0 0.80837 10 1 0.72738 9 0 0.72739 8 0 0.72741 7 0 0.72742 6 0 0.72744 5 0 0.72745 4 1 0.54546 3 0 0.54548 2 0 0.545Step 2:Step 3:Determine the number of individuals at risk and the number of eventsat each time. At each time t j, there are n jindividuals who are said tobe at risk of an event. ‘At risk’ means that they have not experiencedan event, nor have they been censored prior to time t j. Cases thatare censored at exactly time t jare also considered to be at risk at t j.Let d jbe the number of individuals who have an event at time t j.Calculate the KM estimator using the following formula:^( n 1)S(t 1) = 1 – d 1( n 2)S(t 2) = S(t 1) × 1 – d 2^^^^...( n j)S(t j) = S(t j–1) × 1 – d j240