Clinical Trials

❘❙❚■ Chapter 21 | Analysis of Survival Datain a step function: the curve is horizontal at all times at which there is no event,with a vertical drop corresponding to the change in the survival function at eachtime, t j, when an event occurs.In reports, KM curves are usually displayed in one of two ways. The curves candecrease with time from 1 (or 100%), denoting how many people survive (or remainevent-free). However, in general it is recommended that the increase in event rates^is shown starting from 0 (or 0%) subjects with an increasing curve (1 – S[t]), unlessthe event rate is high [3]. Placing the curves for different treatment groups on thesame graph allows us to graphically review any treatment differences.Limitations of the Kaplan–Meier methodThe KM method has some limitations, however. As survival rates are calculatedthroughout the study, a decreasing number of subjects will be available forfollow-up as the curve progresses with time. Therefore, near the end of the study,when we have a relatively small number of subjects who have survived and are stillat risk, the data are less representative of the overall effect and some sensiblecut-off is needed in order to represent the data.For this reason, a well-presented chart will also include a table to show the numberof people available to the study and event-free at each point in time, as shown inFigure 1, which allows an appreciation of the censored data [3]. In addition, the KMmethod is a descriptive statistical approach and therefore does not estimate thetreatment effect. To establish whether there is any significant statistical differencein the survival rates between the treatment groups, a statistical test is required.Log-rank testFor the two KM curves by treatment group shown in Figure 1, the obviousquestion to ask is: “Did the new treatment make a difference in the survivalexperience of the two groups?” A natural approach to answering this question isto test the null hypothesis that the survival function is the same in the two groups:that is H 0: S 1(t) = S 2(t) for all t, where 1 and 2 represent the new treatment andthe standard treatment, respectively.The above hypothesis can be assessed by performing a log-rank test [1,2,4]. Themain purpose of this test is to calculate the number of events expected in eachtreatment group, and to compare this expected number of events with theobserved number of events in each treatment group if the null hypothesis is true.The log-rank statistic can be computed by the following steps:Step 1:Pool the two groups and sort the event times in ascending order.Suppose there are r distinct event times, t 1< t 2< … < t r.242