Week 11: More advanced Methods - Survival Analysis Flashcards
Survival time includes:
- Time to an event
2. The time starting from a defined point to the occurrence of a given event
An event can be:
- Death
- Disease occurrence
- Disease recurrence
- Recovery
- Other experience of study interest such as adverse drug reaction, development of a new disease
Special Features in Survival Time Data:
- rarely normally distributed
- often skewed
- typically with many early events and relatively few late ones
Survival Time: Censored Observations -
Those who have not yet reached the terminal event by the end of the study
- patient has not (yet) experienced the event by the time of the close of the study
- a patient is lost to follow-up during the study period
- a patient experiences a different event that makes further follow-up impossible
Issues with the 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
T/F Special methods of analysis are needed to account for censored data
True
Collective term for the methods of analysis for survival data invented specifically to deal with time to an event problems
Survival analysis
Examples of survival analysis:
- hazard ratio
- Kaplan-Meier curve
- median survival time
- log-rank test
- Cox Model
Survival analysis answers questions relating to what?
- relating to time to an event such
ex: How long does it take for the patient to get better?
ex: Do patients get better faster under treatment A or under treatment B?
survival analysis provides the statistical methods that can be used to do what?
analyze the survival time data that are not normally distributed but skewed in the presence of censored observations
Kaplan-Meier Curve -
- widely used in clinical research to visualize the estimate of the survival over time
- shows what the probability of an event is at a certain time interval
What is on the x and y axis for a Kaplan-Meier Curve?
horizontal axis (x-axis) displays ‘time’; the vertical axis (y-axis) ‘proportion surviving’
What does it mean that a Kaplan-Meier Curve is a step function?
as the cumulative survival remains the same until the day another person experiences the event
What is on the x and y axis for a Kaplan-Meier Curve with censored data?
the horizontal axis (x-axis) displays ‘time’; the vertical axis (y-axis) ‘proportion surviving’
T/F Kaplan-Meier Curve with censored data is a step function.
True
How are censored observations indicated on the K-M curve?
As tick marks
T/F Censored observations terminate the interval.
False, they do not terminate the interval
Kaplan-Meier Curve for Two Groups -
- visualize the difference between two survival curves
- study a question like “Do patients get better faster under treatment A or under treatment B?”
Now is Median Survival Time estimated?
- estimated as the smallest survival time for which the survival function is less than or equal to 0.5
1. . finding the 50% mark on the proportion axis
2. drawing a horizontal line at 50% to find the crossing point with the K-M curve
3. drawing a vertical line at the crossing point down to the time axis to read time
How is mean survival time estimated?
as the area under the survival curve
Mean survival time may not be the best estimate for what type of samples?
for the samples of survival times are frequently highly skewed
Is mean or median survival time generally a better measure of central location?
Median survival time
Hazard rate -
- rate of a subject to experience a particular event at the time it has reached
- measure of how rapidly a subject gets to experience a particular event
How can hazard rate be estimated?
slope of a K-M curve
Hazard ratio -
measure of how often a particular event happens in one group compared to how often it happens in another group
How do you calculate hazard ratio?
ratio of the hazard rate in one group over the hazard rate in another group
Hazard ratio in clinical trials measures what?
measures the survival at any point in time in a group of patients who have been given a specific treatment compared to a control group
Interpret hazard ratios:
HR = 1
means that the event rates are the same in both groups
Interpret hazard ratios:
HR > 1
means that the event rate in the treatment group is faster than in the control group
Interpret hazard ratios:
HR < 1
means that the event rate in the treatment group is slower than in the control group
The farther the HR is from 1 -
larger the difference between the two groups
What test used to compare two or more independent groups with the time to an event data
Log-rank test
When will a log-rank test fail?
if the two curves cross (fail = no statistical power)
When is power of log-rank test at its best?
for proportional hazards
What 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
- cannot control for potential confounders
- cannot control for other potential risk factors
- cannot include interaction terms
What model used to compare two or more independent groups for the time to an event data controlling for a confounding variable
Cox Proportional Hazard Model (Cox Model)
Cox model can accommodate how many confounding variables?
Any number
Cox model provides estimate of what with its associated what?
the estimate of HR (hazard ratio) with its associated 95% CI
Assumption of Cox Proportional Hazard Model (Proportional hazard assumption):
The ratio of the hazard functions for any two observations does not vary with time
What statistical hypothesis tests would you consider to use when your study aim is to compare the mean blood pressure between men and women?
Independent t-test (mann-whitney U test is data is not parametric)
What statistical hypothesis tests would you consider to use when your study aim is to compare the mean blood pressure between members of three different groups of low, medium, and high BMI?
Analysis of variance (Kruskal-wallis H test when data is not parametric)
What statistical hypothesis tests would you consider to use when your study aim is to compare the mean age (time) of onset of colorectal cancer between the group who use aspirin and the group who use ibuprofen?
log-rank test
How many are the censored observations?
5
What graph would be the best to visualize the survival time for each treatment group?
Kaplan-Meier curve
Which statistical hypothesis tests would be appropriate to compare the two treatment groups with their survival time?
Log-rank test or cox proportional hazard model
What is the median survival time for treatment 1?
37 days
What is the median survival time for treatment 2?
5 days
Are the hazard rates of the two treatments proportional?
Yes, diverging lines
Which treatment shows the slower hazard rate?
Treatment 1
What statistical method would be appropriate to test the different survival time between the two treatments?
Log-rank test
What statistical method would be appropriate to test the different survival time between the two treatments controlling for a confounding variable ‘Age’?
Cox proportional hazard model
Example: association between body mass index (BMI) and time to incident cardiovascular disease (CVD), participants’ BMI was measured, at baseline, in four categories of underweight, normal, overweight, and obesity along with a known clinical risk factor for CVD, blood pressure. Participants were followed for up to 10 years for the development of CVD. Using ___, they found that the time to a CVD is significantly different between the different BMI groups after controlling for blood pressure. Which statistical technique would be a best choice?
Cox proportional hazard model
