Survival Analysis – An introduction

Survival-WordleSurvival time refers to a variable which measures the time from a particular starting time (e.g., time initiated the treatment) to a particular endpoint of interest (time-to-event).

In biomedical applications, this is known as survival analysis, and the times may represent the survival time of a living organism or the time until a diseased is cured.


These methods can also applied to data from different areas like social sciences (time for doing some task), economics (time looking for employment) and engineering (time to a failure of some electronic component).

Areas of application:

– Clinical Trials (e.g., Recovery Time after heart surgery).

– Longitudinal or Cohort Studies (e.g., Time to observing the event of interest).

– Events may include death, injury, onset of illness, recovery from illness (binary variables) or transition above or below the clinical threshold of a meaningful continuous variable (e.g. CD4 counts).

Study Types:

– Clinical Studies

      Time origin = enrollment

      Time axis = time on study

      Right censoring common

– Epidemiological Studies

      Time axis = age

      Right censoring common

      Left truncation common

– Longitudinal or Cohort Studies (e.g., Time to observing the event of interest).

The main goals of survival analysis are estimate time-to-event for a group of individuals, compare time-to-event between two or more groups and assess the relationship of covariates to time-to-event, such as example, does weight, insulin resistance, or cholesterol influence survival time of MI patients?

The distinguishing feature of survival analysis is that it incorporates censoring. Censoring occurs when we have some information about individual survival time, but we don’t know the time exactly.

Truncation on survival data occurs when only those individuals whose event time lies within a certain observation window (YL,YR) are observed, those who enter the study at time t are a random sample of those in the population still at risk at t.

Truncation and Censoring:

Truncation is about entering the study

      Right: Event has occurred (e.g. Cancer registry)

      Left: “staggered entry”

– Censoring is about leaving the study

      Right: Incomplete follow-up (common)

      Left: Observed time > survival time

– Independence is key.

censoring-3Kaplan-Meier method and Cox regression are nonparametric techniques with wide applicability in survival analysis. They are appropriate when time-to-event data are analyzed as outcome measure. They are especially efficient when follow-up times vary, which is common in clinical research. The data needed are time to event or last follow-up, last status (e.g. experienced the event, under follow-up, lost to follow-up, died) and explanatory or confounding variables (e.g. sex, age, type of glaucoma). Subjects who did not experience the event are “censored” at last follow-up. Censoring must be independent of the probability of experiencing the event, and the subject must remain at risk of the event after censoring. Cox regression additionally requires that the hazard be proportional (i.e. hazard ratio is constant over time). Kaplan-Meier analysis produces stepped curves which show the cumulative probability of experiencing the event as a function of time by study group. Groups can be compared using the log-rank test or equivalent. Cox regression provides a numerical hazard ratio (e.g. increased or decreased risk of the study group to experience the event relative to the control group), which is adjusted for the effect of other variables included in the regression model.

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