Survival Analysis & Kaplan-Meier curve

Clinical trials describe how an outcome is affected by exposure. Incidence rates describe the effect of exposure on the outcome. The majority of clinical studies are designed in a way that enables reaching the desired endpoint in short enough time to ensure that all observations can be made with minimal dropout and an effect that is fairly constant over time. 

However, there are some cases in which either the final observed proportion of events in two treatment groups is identical or the desired outcome cannot be observed in the short term. In such cases, another technique that considers the time until an event occurs will develop much more clinical information than whether or not the event occurred. For example, if one group had all events occur shortly after randomization, while the other had no events until just before the end of follow-up then the two treatments would logically be considered to have different clinical effects despite the identical proportions at the end of follow-up. This is what survival analysis is all about.

Thus, we can define survival analysis as “a collection of statistical procedures for data analysis where the outcome variable of interest is the time until an event occurs”. To put it another way, measuring the time that passes between entering a study and a subsequent event. This statistical method has originated in the field of medical research for evaluating the impact of medicines or medical procedures on time until death which is the typical example of survival analysis. In fact, survival is not exclusively meaning survival from death; may be also applied to the time ‘survived’ from complete remission to relapse or progression.

The process of survival analytics can be explored through various techniques such as:

• Survivor and hazard function rates.
• Cox proportional hazards regression analysis.
• Parametric survival analytic models.
• Survival trees.
• Survival random forest.
• Life tables.
• Kaplan-Meier curve.

These analyses are often complicated due to mainly two reasons. First, the times of survival are most unlikely to be normally distributed. Second, the total survival time for some subjects cannot be accurately determined due to either negative reasons such as subjects drop out, loss of follow-up, or loss of data or conversely, something good happens, such as the study ends before the subject had the event of interest occur. This phenomenon is called censoring. 

In this article, we will illustrate briefly the Kaplan-Meier curve. The Kaplan-Meier curve is Visual representation of survival function that shows the probability of an event at a respective time interval. This statistical method perfectly matches effective cancer treatments. In this analysis, three assumptions are made. First, we assume that patients who are censored and those who are still being followed will always have the same chance of survival. Second, we assume that subjects recruited early and late in the study have comparable survival probabilities. Thirdly, we assume that the event occurs at the specified time. This creates problem in some conditions when the event would be detected at a regular examination. All we know is that the event happened between two examinations. By following up with individuals more frequently and for shorter periods of time, estimated survival can be calculated with greater accuracy; as brief as the recording accuracy allows, i.e., for one day (maximum).

On the Kaplan-Meier Curve, the survival duration for that interval is depicted by the horizontal line that runs along the X-axis of serial time. The interval is finished when the event of interest occurs. The vertical line along the Y-axis represents the survival rate.

We can look for gaps in these curves in a horizontal or vertical direction. A vertical gap, means that at a specific time point, one group had a greater fraction of subjects surviving. A horizontal gap indicates that a particular proportion of deaths occurred in one group more slowly than in another. However, a confidence interval of at least 95% is required to indicate a significant difference between the two groups. It is also recommended to calculate other statistical measures such as the P-value and the hazard ratio to confirm statistical significance.

References:

1. Clark TG, Bradburn MJ, Love SB, Altman DG. Survival analysis part I: basic concepts and first analyses. Br J Cancer. 2003 Jul 21;89(2):232-8. doi: 10.1038/sj.bjc.6601118. PMID: 12865907; PMCID: PMC2394262.
2. Fink SA, Brown RS Jr. Survival Analysis. Gastroenterol Hepatol (N Y). 2006 May;2(5):380-383. PMID: 28289343; PMCID: PMC5338193.
3. Goel MK, Khanna P, Kishore J. Understanding survival analysis: Kaplan-Meier estimate. Int J Ayurveda Res. 2010 Oct;1(4):274-8. doi: 10.4103/0974-7788.76794. PMID: 21455458; PMCID: PMC3059453.