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Editorial
. 2020 Nov;36(6):668-672.
doi: 10.1007/s12055-020-01049-1. Epub 2020 Oct 2.

Survival analysis-part 1

Salil Vasudeo Deo  1   2 , Vaishali Deo  1 , Varun Sundaram  1
Affiliations
Editorial

Survival analysis-part 1

Salil Vasudeo Deo et al. Indian J Thorac Cardiovasc Surg. 2020 Nov.
No abstract available

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Conflict of interest statement

Conflict of interestThe authors declare that they have no conflict of interest.

Figures

Fig. 1
Fig. 1
This figure presents a hypothetical example of 4 patients included in a study to evaluate survival after coronary artery bypass grafting. As discussed in the paper, each patient may enter the study at different calendar time points, stay in the study for differing durations, and leave the study either because the patient dies or is alive at the end of follow-up. Briefly, these are the unique challenges inherent in the analysis of time-related information
Fig. 2
Fig. 2
These graphs depict the survival function [S(t)] and the corresponding hazard rate [h(t)] for the same data set. The line which depicts the survival changes according to the observed hazard rate at that time
Fig. 3
Fig. 3
These two graphs depict the survival function for very different group of patients. The patients in the first graph appear to die at very regular intervals. The initial line shows a pretty rapid decline demonstrating a high hazard rate, which then appears to reduce after approximately 400 days of follow-up. At the end of follow-up, approximately 10% patients are estimated to be living. The second graph depicts a very different picture. Here, survival appears to be good with a low hazard rate. The survival curve then declines faster after around 400 days, which may be due to an increasing hazard rate. At the end of follow-up, overall survival is still pretty good with approximately 60% surviving. Another important point to understand here is that the survival function [S(t)] is always limited between (1,0). As explained in the paper, it starts at 1 and then either remains constant or declines during the follow-up period
Fig. 4
Fig. 4
These graphs depict the corresponding hazard function [h(t)] for the same group of patients whose survival function [S(t)] is graphed in Fig. 3. As Fig. 3 shows, it is very clear how different these two groups of patients are with regard to their hazard function [h(t)]. Like the survival function [S(t)], the hazard rate h(t) is also always positive; however, unlike S(t), it can increase or decrease during the follow-up time
Fig. 5
Fig. 5
This figure with the accompanying Table 1 provides a better understanding regarding the Kaplan and Meier survival estimator. Patients are arranged according to their time spent in the study from smallest to largest time intervals. The time segments for patients that observed the event during follow-up are colored red, while those for censored patients are depicted in green. Calculations for the Kaplan and Meier estimate are performed at each time point that an event occurs. However, as demonstrated in the table, the survival estimate at the end of each time point is a product of the failure during that time interval and the survival estimate at the start of that time interval
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References

    1. Hosmer DW, Lemeshow S, May S. Applied survival analysis : regression modeling of time -to -event data. 2nd ed: Wiley Lifesciences; 2008.
    1. Kleinbaum DG, Klein M. Survival analysis. a self-learning text. 3rd ed: Springer Verlag; 2012.

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