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Introduction to Survival Analysis Correspondence Address:
Construction of the Survival Curve Concept of censoring Censoring is a form of missing data problem in which the time to event is not observed for reasons, such as termination of the study before all recruited subjects have shown the event of interest or the subject has left the study before experiencing an event. Illustration by example We have a hypothetical study in which we want to know about patients with stroke who have a recurrence of stroke. The study started in 2016 and began taking patients who had presented with firstever stroke. The patients were recruited between 2016 and 2018. These patients were followed up 6monthly and the study ended in 2020. There were 200 patients enrolled in the study period. There were 20 recurrence strokes. However, there were also 50 coronary events and 30 deaths. Five died due to cancer. There were 20 patients who could not be contacted after variable periods of followup. Points related to censoring in this example are as follows: 20 patients had the outcome of interest. We have completed information of interest for these patientsThere are some patients without the event of interest (stroke recurrence) until the end of the study. These patients may have a stroke sometime later; however, for the purpose of the study, they do not have the event. Thus, they are right censoredThere are 30 deaths and the followup ends here – this would be informative censoringThere were 20 patients who could not be contacted – this would be noninformative censoringThere would also be patients who would have been excluded because they already had a recurrence of stroke when they were contacted. These were left censored. Kaplan–Meier analysis Now that we have understood the concepts of survival probability and censoring, we can understand the simple example provided below. There are eight patients who were followed up to 11time units. “+” represents censoring. Below represent the event times. 1 5+ 6 6 8+ 8 9 11+ Kaplan–Meier (KM) curve of this example is shown in [Figure 2]a. As we can see, the xaxis depicts the timeline while the yaxis depicts the probability of the event. The graph has a step function which is dependent on the events recorded at the progressive timeline. The “+” mark depicts censoring, which may be of various types as depicted above. [Figure 2]b confirms the computation we just did and that is listed in the “survival table.”{Figure 2} Interpretation of the Survival Curve Certain points to be kept in mind when interpreting survival curves are as follows: The vertical axis does not represent the actual percent surviving for an actual cohort but the estimated probability of surviving for members of a hypothetical cohort. Since the function of probability always lies between 0 and 1, the yaxis ranges between 0 and 1 (or 0%–100%) Often, the number of patients at risk at various points in time is shown below the horizontal axis. The estimates on the lefthand side of the curve are sound because more patients are at risk during this time. However, at the tail of the curve, on the right, the number of patients on whom the estimation is based is often small because fewer patients are available for followup for that length of time. As a result, the estimates of survival toward the end of the followup period are less precise than in the earlier period. The survival analysis methodology can be used to analyze not only time to death (=survival) but also timetoany event and the results can be presented as a “survival curve.” The events may be remission, recurrence, stroke, or acute myocardial infarction. Therefore, instead of survival analysis, we can also call it “timetoevent” analysis [Table 1].{Table 1} Survival curve can be used to describe the survival after any length of time – 1 year, 2 years, 3 years, or 5 years. This gives a more complete and detailed description of prognosis. When percent (probability) of having an event, rather than not having it, presented, the curve starts at “zero” and sweeps upward and to the right. Financial support and sponsorship Nil. Conflicts of interest There are no conflicts of interest. Further Reading Cox D, Oakes D. Analysis of Survival Data. London: Chapman & Hall; 1984.Kleinbaum D, Klein M. Survival AnalysisA SelfLearning Text. New York: SpringerVerlag; 2012.


