Survival Analysis

Question 1

What does survival analysis describe?

Answer 1

Time until something meaningful occurs
‘time to event outcomes’
eg. death, relapse
PFS, DFS
recovery diagnosis

Has two elements to it: time and did thing happen? Y/N

Not continuous or categorical - both together at the same time

Question 2

What does composite outcomes mean?

Answer 2

Some outcomes are a combination of events occuring

e.g.
PFS is death **or **progression - treated the same

Have to be careful with interpretation becuase the composite events may not be equally meaningful

Question 3

What are absorbing events?

Answer 3

Some events stop other events from happening

Question 4

What is all cause vs. cause specific mortality?

Answer 4

All-cause - death or not death due to anything

Cause specific - death or not death due to specific thing

Question 5

What are the issues with all-cause mortality?

Answer 5

Estimates could be biased by focussing on a specific thing that could be blocked from happening by something else

Question 6

What are the issues with cause-specific mortality?

Answer 6

are the composite events equally meaninful? as some information/nuance is lost in combing them

Question 7

Why is time-to-event special?

Answer 7

• Not binary or continuous - mixture
• Not normally distributed - tail on the curve
  could just apply a transformation to make it normally distributed

BUT
event might not happen for some people - ‘censoring’ if we stop following up early - could die in the future after we stop recording

Question 8

What are actuarial life tables?

Answer 8

• summary of time to death data
• probability of event (e.g. survival) at given time points

Question 9

How are actuarial life tables made?

Answer 9

1. Split the follow up time into equal intervals (assumes events occur in the middle of an interval)
   For each interval:
2. Sum all participants where event hasn’t happened
3. Sum all participants where event has happened
4. Sum up the total participants censored in the time period

Question 10

How is average at risk calculated?

Answer 10

at risk - (censored x 0.5)
treat censored people as though they had both outcomes - so half an outcome each

Question 11

How is the survival probability calculated?

Answer 11

(t) = proportion survived in current period x proportion survived in last period

• Cumulative survival - current survival x survival up to this point
• This should decrease over time as your chance of survival decreases (or stays the same if no one dies)
• Survival probabilities depend on interval width e.g. if shoren the interval fewer people will die and so the numbers will change
• Too difficult to calculate survival probability after each event so create a table with intervals

Question 12

How is proportion died calculated?

Answer 12

dead / average at risk

Question 13

How is proportion survived calculated?

Answer 13

1 - proportion died

Question 14

What are the features of a Kaplain-Meyer curve?

Answer 14

Y axis is survival probability (%)

X axis is time followed up

Stepwise graph made up of individual participant data
Survival probability is calculated after each vent

Lines on steps indicate censored/dropped out patients

Question 15

What assumptions have to be made for a Kaplain Meyer?

Answer 15

3 assumptions need to be made:
1. Censored participants (drop outs) have the same survival chance i.e. not a drug side effect

2. Survival probabilities are the same whenever they were recruited a.k.a day 0 is day of recruitment not a specific date, background cancer care looked very different in the 90s to now
3. Events happen at the time sepcified (no lag) - may not have the exact date of death for a participant

Question 16

How can Kaplain-Meyer curves be summarised and compared?

Answer 16

• Compare % survival at a meaningful time point e.g. 1 year (read up from x axis)
• Median survival time i.e. time at 50% survival (read down from y axis)

Question 17

What is a log-rank test?

Answer 17

Deterimines if there is a statisitically signficiant difference between two survival curves

• non-parametric (doesn’t assume a distribution or shape
• Can be applied to >2 groups (curves)

Question 18

What is the null hypothesis in a log rank test?

Answer 18

Survival rate variance between two groups (curves) = random variation

Question 19

How is log-rank statistic calculated?

Answer 19

1. Calculate number of expected events in each curve, assuming no difference between them
2. Compare this to what has been obseved, if this differenc eis big enough (the Chi-squared p-value), then reject null hypothesis

Question 20

What are the disadvantages of log-rank tests?

Answer 20

• Only compares survival overall not at each point
• Only gives a p-value - might want to read off at particular months i.e. is there a difference in survival at 6 months?
• Only describes a difference in ‘one or more’ if used for multiple curves - can’t say which ones are different or how many are different
• omnibus test

Question 21

What is a Hazard Ratio?

Answer 21

• Relative measure of survival between 2 groups
• probability of an event occuring at a given time point

Hazard rate in group 2/ hazard rate in group 1

if HR >1 risk of event is greater in group 2
if HR = 1 risk of event is equal
if HR < 1 risk of event greater in group 1

Question 22

COX / Proportional Hazards/Regression

Question 23

What is assumped for a Cox proportional hazard regression?

Answer 23

Presumes that the hazard rates are proportional over time

If the survival functions cross they aren’t proportional
- could separate out before and after cross and model separately
- could do a non proportional hazard analysis

Question 24

Which survival analyses are descriptive?

Answer 24

• Actuarial tables
• Kaplan-Meier curves

Question 25

Which survival analyses are inferential?

Answer 25

• Log-rank tests
• Hazard ratios
• Cox proportional hazard regression