The survival function

Survival Analysis in R

Heidi Seibold

Statistician at LMU Munich

Survival Analysis in R

Survival analysis questions

  • What is the probability that a breast cancer patient survives longer than 5 years?
  • What is the typical waiting time for a cab?
  • Out of 100 unemployed people, how many do we expect to have a job again after 2 months?
Survival Analysis in R

Survival function

Theory

$$S(t) = 1 - F(t) = P(T > t)$$

Interpretation

Probability that duration is longer than $t$.

Survival Analysis in R

Survival function

Theory

$$S(t) = 1 - F(t) = P(T > t)$$

Interpretation

Probability that duration is longer than $t$.

Examples:

  • Probability to survive beyond time point $t$.
  • Probability that the cab takes more than $t$ minutes to arrive.
Survival Analysis in R

Survival function

Interpretation

The median duration is $t$.

Examples:

  • The median survival time is $3.7$ years.
  • Median time until the cab arrives is $3.7$ minutes.
Survival Analysis in R

Survival function

Interpretation

$100 \cdot \hat{S}(t)$ percent of durations are longer than $t$.

Examples:

  • 37 percent of all patients survive longer than $4$ years. 63 percent die within the first $4$ years.
  • Out of 100 cabs, 37 take more than 4 minutes to arrive.
Survival Analysis in R

Let's practice!

Survival Analysis in R

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