3.1 - 2: Survival Analysis

Question 1

Survival analysis: Definition

Answer 1

• Analysis of data in the form of times from some well-defined time origin to occurrence of some event or endpoint
• e.g. time of entry into trial, or of diagnosis etc -> death/onset of particular disease/recurrence

Question 2

What types of events may survival analysis consider?

Answer 2

• Positive e.g. discharge from hospital
• Adverse e.g. death or disease recurrence
• Neutral e.g. cessation of breast feeding

Question 3

Special features of survival data:

Answer 3

• Not amenable to standard methods of analysis…
• Positive continuous data
• Typically skewed
• Subject to censoring

Question 4

Types of censoring:

Answer 4

• Right: Event time exceeds last follow-up time (most common type)
• Left: Event time precedes the last follow-up time but is unknown
• Interval: The event time falls in some specified interval

Question 5

Why may right censoring occur?

Answer 5

• Period of observation ending prior to event occurring
• Loss to follow-up
• A competing event which precludes further follow-up (e.g. death)
• Event may not be inevitable (e.g. time to pregnancy)

Question 6

Two key assumptions surrounding right censoring and patient time:

Answer 6

• Patient prognosis does not depend upon time of entry into the study
• Patient lost to follow-up have the same prognosis as those remaining in the study (i.e. random censoring)

Question 7

Aims of survival analysis: (x5)

Answer 7

• Model survival times for a single group
• Compare survival distributions for two or more groups
• Assess affects of covariates on survival
• Make predictions
• Allowing for potential ties in the data caused by rounding

Question 8

Survivor function:

Answer 8

• See notes

Question 9

Hazard function:

Answer 9

• Specifies instantaneous rate of failure at T=t
• See notes

Question 10

How is the hazard function useful? Generic types?

Answer 10

• Tells us about the effect of time on probability of failure
• Informs on failure rates in particular strata
• Generic types: Increasing, decreasing, constant, bathtub

Question 11

Estimating survivor function non-parametrically:

Answer 11

• Empirical survivor function
• See notes

Question 12

Dealing with censoring when estimating survivor function:

Answer 12

• Kaplan Meier estimator
• a.k.a. product limit estimator
• See notes
• Notes: If there is no censoring, this is simply the empirical survivor function

Question 13

Greenwoods formula:

Answer 13

• Estimating variance for kaplan meier estimate
• Can give confidence bands <0 and >1
• See notes for formula

Question 14

Formal comparison between groups during survival analysis:

Answer 14

• Log-rank test
• Null hypothesis: survival distributions are equal for the sub-groups (i.e. no difference in survival)