Survival Analysis Flashcards
Survival Time
- Time to an event
- The time starting from a defined point to the occurrence of a given event
Events for the end of survival time include
death disease occurrence disease recurrence recovery other experience of interest
Special features in survival time data
- rarely normally distributed
- often skewed
- typically with many early events and relatively few late ones
Censored Observations
Those who have not yet reached the terminal event by the end of the study.
In censored observations, why might information about a pt’s survival time be incomplete?
- pt hasn’t experienced event by end of study
- pt lost to follow up during study period
- pt experiences different event to make further follow up impossible
Issues with censored observations in analysis
these censored survival times will underestimate the true (but unknown) time to the event because it will occur beyond the end of the study.
Kaplan-Meier Curve
- visualize estimate of survival over time
- shows probability of an event at a certain time interval
- x-axis for time, y-axis for ‘proportion surviving’
- step function, as the cumulative survival remains the same until the day another person experiences the event
Kaplan-Meier Curve Censored Data
x-axis: time
y-axis: ‘proportion surviving’
-step function
-censored observations indicated on K-M curve as “tick marks”
-censored observations do not terminate the interval
Kaplan-Meier Curve for 2 Groups
Visualizes the difference between two survival curves. Can be used to compare treatments.
Median Survival Time
estimated as small survival time for which survival function is less than or equal to 0.5
How can you estimate the Median Survival Time?
- find the 50% mark on the proportion axis
- drawing a horizontal line at 50% to find the crossing point with the K-M curve
- drawing a vertical line at the crossing point down to the time axis to read time
Mean Survival Time
- area under survival curve
- may not be best estimate for sample of survival times, highly skewed
- median typically better measure of central location than mean
Hazard Rate
- measure of how often an event happens in one group compared to another
- in clinical trials, measures survival point at any point in time in a group given treatment vs control
- can be estimated as being a slope of a K-M curve
Interpreting Hazard Ratio
HR = 1
the event rates are the same in both groups
Interpreting Hazard Ratio
HR >1
the event rate in the treatment group is faster than in the control group
Interpreting Hazard Ratio
HR < 1
event rate in treatment group is slower than in the control group
Log-Rank Test
Compares two or more samples with survival data in presence of censored observations
How can a log-rank test fail
if two curves cross (no statistical power)
Assumption of Log-Rank Test
Hazard Rates of the groups to compare must be proportional
Limitations of Log-Rank Test
- We can only test one variable at a time
- can’t control for potential confounders
- can’t control for other potential risk factors
- can’t include interaction terms
Cox Proportional Hazard Model
Most commonly used method comparing two or more samples with survival data in presence of censored observations
T/F: Cox model can accommodate only one confounding variable
False
can accommodate any number of confounding variables
T/F: Cox Model provides the estimate of Hazard Rate with its associated 95% Confidence Interval
True
Assumption of Cox Model
The ratio of the hazard functions for any two observations does not vary with time.
