# Chapter 7 Survival Analysis

In this chapter, you will learn how to:

• Identify a time-to-event outcome;
• Identify types and mechanisms of censoring;
• Interpret the survival and hazard functions;
• Use the Kaplan-Meier method to estimate the survival function;
• Use the log-rank test to compare survival between groups;
• Visualize the Kaplan-Meier estimate of the survival function;
• Visualize the estimated hazard function;
• Fit a Cox proportional hazards regression model, including the following:
• Write and interpret the Cox regression equation;
• Estimate the probability that an event has not yet occurred as of a given time;
• Estimate the hazard of an event relative to a reference group;
• Visualize the Cox regression estimate of the survival function;
• Test interactions between predictors;
• Incorporate time-varying predictors;
• Check the proportional hazards assumption;
• Allow non-proportional hazards using a time interaction or stratification;
• Check the linearity assumption, examine outliers, and identify influential observations; and
• Appropriately summarize the methods and results.

To use the code in this chapter, first load the tidyverse and survival packages.

library(tidyverse)
library(survival)

### References

Terry M. Therneau, and Patricia M. Grambsch. 2000. Modeling Survival Data: Extending the Cox Model. New York: Springer.
Therneau, Terry M. 2023. Survival: Survival Analysis. https://github.com/therneau/survival.