Survival analysis

Question 1

What different types of right-censoring are there?

Answer 1

• Fixed type I censoring: occurs when a study is designed to end after T years of follow-up. Everyone who does not experience the event within T is censored at T years
• Random type I censoring: individuals drop randomly before the end time T. This is the most common type of right-censoring
• Type II censoring: Study ends when there a pre-specified number of observable events

Question 2

What do the survival and hazard function describe?

Answer 2

Survival

• The probability that an individual survives from the origin of time to a specific future time t.

Hazard

• The instantaneous rate at which events occur given no previous events
• Integrating h(t) gives the cumulative hazard H(t) which describes the accumulated risk up to time t

Question 3

There are three different ways to estimate the survival function, which ones? Describe them.

Answer 3

Kaplan-Meier

• This is by far the easiest approach
• Used when:
  
  • When we simply want a snapshot of those who are still alive at time T
  • When we don’t include any covariate

Semi-parametric via regression models like the Cox Proportional Hazards

• To estimate S(t) via a semi-parametric approach, we build a regression model
• Needed in situations in which several factors (the covariates) could affect the outcome
• Most common approach is the Cox Proportional Hazards model
  
  • Evaluates the effect of several factors on the survival time
  • stimates how a given factor affects the rate of a particular event
  • We call this rate hazard rate
  • Main assumption: ratio of the hazards for any two individuals is constant over time

(Fully) Parametric via regression models that requires the full distributional properties

Question 4

How is Accelerated Failure Time (AFT) different than proportional hazard?

Answer 4

• The PH assumes that the effect of a covariate is multiplicative to the hazard
• The AFT assumes that the effect of a covariate is multiplicative on the time
• In other words, a covariate can accelerate (decelerate) the passage of time that the individual is experiencing