Survival analysis

  • 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
AgeNumberDeaths Lost to FUProportion dyingProportion survivingProbability of survival
1-1010202/10 =
11-208111 / (8 – 0.5) = 0.130.870.8 x 0.87= 0.69
21-306222 / (6-1) = 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

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