Chapter 11 Survival (time-to-event) analysis

Survival analysis (also called ‘time-to-event analysis’) is one of the problem-solving settings that separates biostatistics from pure statistics. Survival analysis research questions ask, “How long until (some event) happens?”. This is a messy question, especially in biomedical research contexts where the investigators do not observe what happens to every observational unit (e.g, every patient) in the study. A patient may come to the clinic once, receive treatment, and then never come back to the clinic again. Whatever outcome the investigators wanted to observe remains unknown for that patient – we would say the outcome for such a patient is censored.

The most-used methods in survival analysis are the log-rank test and the Cox proportional hazards model. The log-rank test is a conceptual analog to a Cochran-Mantel-Haenzel test in categorical data analysis. When working with a survival outcome and a single categorical predictor, the log-rank test can be used to test the null hypothesis: “there is no difference in survival between the groups being compared.” The Cox proportional hazards model is a multivariate regression approach in which the exponentiated coefficients are the hazard ratios.

11.1 Quick examples

Here are a few brief survival analysis scenarios:

  • Clinical trials: patients battling a chronic condition are randomized to either new drug B or the standard of care drug A. Patients have follow-up visits once per month for 1 year to monitor the time until their symptoms flare up again (e.g., time to relapse or time to recurrence).

  • Dentistry: electronic dental records are used to assess the time until re-intervention for crown margin repairs (CMRs). CMRs are compared to assess which materials last longer: glass ionomer, resin-modified glass ionomer, resin-based composite, and amalgam.

  • Industry/manufacturing: Suppose there are four machines on a factor floor, two from brand A and two from brand B. The time until next malfunction could be used to compare the two brands of machines.

11.2 R code tips

Packages to know about:

  • survival: a must-have for survival analysis
  • ggsurvfit: more options for for graphics
  • contsurvplot: great for visualizing effects of continuous covariates

11.3 References