• Time to event (TTE) data
  • Analysis of data from a point in time until a particular event. In many oncological studies event is death or event is disease progression.
  • It is not normally distributed
  • It is continuous data

• Survival data/analysis is a type of TTE data/analysis

• Data may often be censored
  • Right censored – patients who have not reached end point of interest when they were last under follow up e.g. lost to follow up, still alive at end of mortality study.
  • Left censored – patients whose end point of interest occurred before the baseline/initial date of study. (for obvious reasons – survival data with event as death cannot be left censored)

e.g. If Event is “To Learn how to operate new chemo e-prescription system.” And time to event is time to first successful independent prescription of first chemotherapy regimen. Some registrars might already be competent and have completed a prescription (left censored), some might learn and complete and task during the study period (exact event time) and some might not learn / successfully complete task until the end of the study period (right censored).

Summarising survival data

• Summarising survival data:
  • Actuarial life table
  • Kaplan meier curve

• Actuarial life table
  • Tabulate total number of patients, number of events & number who are censored, to calculate:
    • Proportion dying
    • Proportion surviving
    • Probability of survival

Age	Number	Deaths	Lost to FU	Proportion dying	Proportion surviving	Probability of survival
1-10	10	2	0	2/10 = 0.2	0.8	0.8
11-20	8	1	1	1 / (8 – 0.5) = 0.13	0.87	0.8 x 0.87= 0.69
21-30	6	2	2	2 / (6-1) = 0.4	0.6	0.87 x 0.6= 0.41

• Kaplan Meier curve
  • Summarises survival data graphically
  • Probability of survival is plotted on Kaplan Meier curve (survival will only change when an endpoint occurs)
  • The bottom of the survival curve often has number at risk
  • The drops in a KM curve are events.

• Data which can be summarised from kaplan meier curves includes:
  • Median survival (as long as >50% have had event – if not then ‘median survival not reached’)
  • Estimated % surviving at fixed time points
  • If KP curve shows number at risk – how many have had event/been censored
• Kaplan meier (KM) curves assume several things:
  • Survival probability is the same in those who are censored vs remain
  • Survival probability is the same no matter where they are in the study timeline
  • Surviving proportion remains static between events

Comparing survival 

• Tests used to compare survival data/TTE data:
  • Log rank test
  • Hazard ratio
  • Cox proportional hazard regression

• Log-rank test
  • Use to compare ≥2 survival curves
  • Non-parametric method – tests null hypothesis
  • This calculates the log rank statistic, you then compare this with the Chi² (X²) distribution, this gives p value

• Hazard ratio
  • Used to compare 2 hazard rates – each group has a hazard rate which relates to KM curve
  • Hazard rate = probability of event per unit time

• Results: 
  • Hazard ratio (HR) <1 – less chance of dying in treatment group
  • HR >1 – more chance of dying in treatment group
  • Can also calculate CI – if crosses 1 –> not significant

• Cox proportional hazard regression
  • Used to compare effect of multiple variables on outcome
  • Cox regression – regression analysis where the outcome is a survival curve
  • Assumes hazard ratio remains constant over time
  • If curves crossover on kaplan meier curve, this means that the HR is non constant. You would therefore use cox non-proportional hazard regression instead
  • Results: 
    • HR <1 – decreasing chance of TTE with increasing X
    • HR >1 – increasing risk of TTE with increasing X