Lecture 5 - Survival Analysis

Question 1

Survival Analysis

Answer 1

Key outcome in many trials
Essential for economic modelling
Shows where time is being gained or lost over the course of different time intervals

Question 2

Survival Data

Answer 2

Time to event (days/months)
With respect to an origin point
Values the variable takes on are non-negative and potentially not observed (censored)

Question 3

Origin point

Answer 3

The point at which you first randomise (first point at risk of outcome)

Question 4

Unobserved data

Answer 4

At end of trial, it can be unknown if participant dies or drops out of trial

Question 5

Right censoring

Answer 5

Someone is lost to follow-up, or trial shuts down early, so we know they haven’t experienced event, but unknown when

Question 6

Non-parametric survival analysis

Answer 6

Kaplan-Meier curves and associated log-rank test
Looking at survival, probability subject is still alive at time t
Log-rank test asks if survival times are statistically significantly different overall between groups
No assumptions about distribution of survival times made

Question 7

Number at risk

Answer 7

Captures the number of people still at risk of the outcome either because of death or because of censoring

Question 8

Survival time

Answer 8

Generally use median time of survival alongside 95% confidence intervals to illustrate
Censoring may prevent the median survival time from being observed
Rarely compare median survival times directly, so use log-rank test

Question 9

Median time of survival

Answer 9

Time point at which half of people on each treatment have died or are alive

Question 10

Semi-parametric survival analysis

Answer 10

Cox proportional hazards regression
Effect estimate is hazard ratio
Make assumption that hazards are proportional to each other
Very limited but very important assumptions about distribution of survival times relative to different groups

Question 11

Hazard function: definition

Answer 11

The instantaneous incidence rate of the event conditional on not having experienced the event
Sits above survival function and tells us how quickly an event is happening in a group

Question 12

Cox proportional hazards regression

Answer 12

Make assumption that hazard functions are proportional
If functions are not proportional, hazard ratio will not be an appropriate estimate of the effect of the intervention (time-varying hazard ratios)

Question 13

When do we know if proportional hazards assumption is not met

Answer 13

Survival curves have very different shapes

Survival curves cross or converge early

Question 14

Parametric survival analysis

Answer 14

Place a specific named distribution on the survival times
Generates a hazard ratio but makes more assumptions
Specific distribution is appropriate to describe all the survival curves in your analysis

Question 15

Accelerated failure time ratio

Answer 15

Ratio of the times of outcomes

Question 16

Distribution

Answer 16

Specific family of ‘shapes’ of a curve

Shapes described by one or two parameters (also known as scale parameters)

Question 17

Scale parameters

Answer 17

Numbers we plug into the survival distribution to make it as close to the survival analysis as possible

Question 18

Why do we do parametric survival analysis?

Answer 18

Have a “framework” of describing what the hazards look like
Easier to test, we are comparing two distribution rather than all the points on a curve
Easier to project into the future; this is also called extrapolation

Question 19

Common distributions

Answer 19

Exponential
Log logistic
Lognormal
Weibull