Short Answer
Survival analysis is the statistical method that studies the time until an event occurs; it is used for events such as death, recurrence, complication, or treatment failure. When follow-up times are not equal, or when some patients leave the study before the event occurs (censoring), this method is needed instead of the classic t-test or ANOVA. The Kaplan-Meier curve shows survival probability according to a single factor, and groups are compared with the log-rank test; Cox regression, on the other hand, controls for more than one factor simultaneously and gives a hazard ratio for each. The most common mistake is coding censoring incorrectly (0 = censored, 1 = event); the second most common mistake is accepting the proportional hazards assumption in Cox regression without testing it. It is also frequently overlooked that median survival is only meaningful when at least half of the events have occurred.
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You are investigating the efficacy of a cancer drug. Half of the patients died before the follow-up period ended, some left the study, and the rest are still under follow-up. You cannot analyze these data with a standard t-test or ANOVA; because there is both an event time and censoring. This is exactly where survival analysis comes in.
When Is Survival Analysis Used?
Survival analysis is the statistical method that studies time-related events. The event does not have to be death; it can also be readmission to the hospital, development of a complication, disease recurrence, or treatment failure.
Survival analysis is used in the following situations:
- To compare the survival time of different treatments
- To determine prognostic factors in a disease
- In cohort studies with unequal follow-up times
What Is Censoring?
The fundamental concept of survival analysis is censoring. If a patient leaves the study before the follow-up period ends, or dies for another reason, that patient is considered "censored." The data of these patients is not removed from the analysis; the time up to the censoring point is included in the analysis.
Coding censoring correctly is vitally important. Coding as 0 = censoring, 1 = event is the most common approach.
Kaplan-Meier Analysis
The Kaplan-Meier method is used to visualize survival probability over time across different groups.
How is a Kaplan-Meier curve interpreted?
- Y axis: Survival probability (between 0 and 1)
- X axis: Time (days, months, years)
- Vertical drops: The moments when events occurred
- Small vertical lines (ticks): Censoring points
Whether the curves between two groups are statistically different is assessed with the log-rank test. If the p value is < 0.05, it means there is a significant difference between the groups.
Median survival: The time at which each group's survival probability drops to 50%. It is only meaningful if at least 50% of the events have occurred.
Cox Regression
While Kaplan-Meier examines a single factor, Cox regression allows you to control for more than one factor simultaneously.
Hazard Ratio (HR) interpretation:
- HR > 1: That factor increases the risk
- HR < 1: That factor decreases the risk (protective)
- If the 95% confidence interval does not include 1, it is statistically significant
The basic assumption for Cox regression is the proportional hazards assumption. If this assumption is violated; that is, if the risk difference between groups changes over time; alternative approaches such as a time-interaction model or separate survival curves are needed.
Kaplan-Meier with SPSS
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Where Do People Get Stuck Most in This Analysis?
- You coded the censoring incorrectly and did not notice, and the results are completely wrong.
- The proportional hazards assumption in Cox regression is violated, but you do not know its alternative.
- Median survival cannot be calculated because 50% of the events have not occurred.