In contrast to other regression methods, survival analysis takes into account so-called censored observations. These can arise when patients are removed from the analysis before experiencing the event of interest. The first case where this may happen is when a patient is ‘withdrawn alive' at the end of the study period; another case when one may censor survival time is when a patient was lost to follow-up. An important advantage of censoring is that it allows one to use information on the exact time an individual spent in the study without experiencing the event; we then for example know that, up until the time of loss to follow-up, this patient was alive. There is however one critical assumption that must be met, namely that the probability that the survival time of a patient is censored is unrelated to the probability of experiencing the event (non-informative censoring). It should therefore be ascertained that the loss to follow-up had nothing to do with e.g. a poor response to treatment, which is associated with an increased risk of death.

With the Kaplan-Meier method the survival probability can be calculated by considering time in many small intervals. The table provides an example of the calculation of cumulative survival in a group of 25 patients with a specific disease. In this table all survival times have been ordered and the censored observations have been indicated by a “+”. When a survival time is indicated as 5+ months, we know that this particular person has lived for at least 5 months after inclusion in the study, but we do not know how much longer.

Table: Cumulative survival table showing the first 10 months of follow-up in 25 patients

The table clearly shows the effect of censoring: during the first 5 months 2 patients were removed from the alive group without affecting the cumulative proportion of patients surviving. At 6 months 2 persons died, thus the cumulative proportion surviving is 0.9130. After a censored observation at 9 months (reducing the number of alive persons to 20) there were 2 deaths at 10 months. The proportion surviving at that time, 0.90, is then multiplied with 0.9130 resulting in a cumulative proportion survival of 0.8217 at 10 months. So, taking into account censored observations, proportions of persons surviving are multiplied, and therefore the result is called cumulative survival.

A way to visualize cumulative survival is to produce a Kaplan-Meier plot. The figure shows a plot based on the same data as in the table. Censored observations are shown as dots, whereas deaths make the survival curve shift downwards.

Figure: Kaplan-Meier graph showing cumulative survival in the same group of 25 patients

The Kaplan-Meier method is suitable for univariate analysis, studying the effect of one factor on survival. Statistical significance of differences can be shown using a log-rank test. A disadvantage of the Kaplan-Meier method is that an effect estimate like a relative risk cannot be obtained. Also, for the assessment of multiple factors on survival (multivariate analysis) we need other statistical techniques like Cox proportional hazards regression. This method will be discussed in the following newsletter.

For further reading

1. Swinscow TDV and Campbell MJ. Statistics at Square One. BMJ Books, 2002.

2. Campbell MJ. Statistics at Square Two: Understanding Modern Statistical Applications in Medicine. BMJ Books, 2001.

3. Rothman K. Epidemiology: an introduction. Oxford University Press, 2002.

4.  Jager K. Prognostic Studies in Nephrology: Survival Analysis and Beyond