3.4.1. Survival Analysis

Question 1

What is a longitudinal study? (4 main points)

Answer 1

1. follow a group of people forward in time
2. from a specified starting point
3. for the purpose of characterizing how some event (e.g. death) is acquired
   d. for the purpose of characterizing how an outcome (e.g. SBP) evolves over time

Question 2

What are some key characteristics of a longitudinal study? (4 main points)

Answer 2

1. key outcome is time between two events (e.g. diagnosis and death)
2. patients may enter the study at different calendar times
3. patients may be followed up for different lengths of time
4. at the time of analysis, information about patient’s duration or survival status may be unknown

Question 3

What is the mean duration of survival? What is an issue with this calculation?

Answer 3

1. add up all “survival” times and divide by the number of subjects
   
   1. BUT approach assumes duration = follow up time (not necessarily true) and mean is biased DOWN

Question 4

How can censored observations arise in a longitudinal study?

Answer 4

1. the patient is known to still be alive when the trial analysis is carried out
2. the patient was known to be alive at some past follow-up, but the investigator has since lost trace of him or her
3. the patient has died of some cause totally unrelated to the disease in question

Question 5

What is the overall rate of survival?

Answer 5

1. surviving subjects/total subjects (surviving = not confirmed dead)
   
   1. BUT assumes that patients who withdrew from the study did not die and ignores duration of follow-up

Question 6

What is the N-year survival rate?

Answer 6

1. N-year survival rate = # surviving N years/ # in study (surviving = not confirmed dead)
   
   1. includes length of follow-up BUT how do you deal with those withdrawn or lost to follow-up before N years of observation?

Question 7

What is the person-years approach?

Answer 7

1. confirmed deaths/person-years of follow-up
   
   1. good because all censored observations contribute to denominator, BUT assumes risk of death is constant over time

Question 8

What do we use the kaplan-meier life table for?

Answer 8

To calculate risk of event (“death”) at each time point (# deaths / # at risk of death)

You could also say: used to describe the survival experience of the subjects

Question 9

What are the 3 basic assumptions of the kaplan-meier life table?

Answer 9

1. risk in withdrawn = risk in observed (withdrawn does not equal died later)
2. risk for early recruits = risk for later recruits
3. events happen at exact time indicated

Question 10

What does a kaplan-meier life table look like?

Question 11

How do we create a kaplan-meier life table?

Answer 11

1. Column 1: create column of exact times of event (e.g. death), in order, starting with the earliest
2. Column 3: number of deaths at each time t is 1 for this group of 15 patients, in larger studies multiple deaths at a particular point are common
3. Column 2: number at risk of death at each time t is all the patients known to be alive just prior to time t; = # known to be alive at time t + deaths at time t
4. Column 4: = deaths at each time t / # at risk at time t
5. Column 5: survival rate at time t = 1 - death rate at time t
6. Column 6: cumulative survival rate at time t is computed by multiplying p(t) by the survival rates at all previous times
7. Finally, plot column 6 against time to visualize cumulative survival (4)

Question 12

What are some common statistical inference tests used on survival curves?

No need to know these, just need to recognize what they are.

Answer 12

1. Log-rank Test (most popular)
   
   1. to compare the survival times of 2 groups
2. Gethan’s Generalized Wilcoxon Test
3. Cox-Mantel Test
4. Peto’s Generalized Wilcoxon Test
5. Cox’s F-Test
6. Mantel-Haeszel Chi-Square Test

Question 13

What is a hazard ratio?

Answer 13

hazard (instantaneous risk) in exposed group/(hazard in unexposed group)

Question 14

What regression do we use to get hazard ratios?

Answer 14

COX Proportional Hazards Regression: used to estimate hazards ratios

Question 15

What does it mean when a hazard ratio is =1? >1? What if a variable is continuous?

Answer 15

1. hazard ratio = 1 → risk of outcome equal in exposed and unexposed group
2. hazard ratio > 1 → risk of outcome is greater in exposed group than unexposed group
3. for continuous exposure, hazard ratio = proportional change in hazard corresponding to 1-unit difference in exposure

Question 16

What does it mean to say that the hazard ratio = 2.37 if the outcome of interest is death?

Answer 16

If the hazard ratio is calculated to be 2.37 for individuals with poor cognition and poor appetite (first example listed in class), the risk of death is 2.37 times higher in these exposed individuals

Question 17

If we have a survival curve, what do we use from that curve to calculate the hazards ratio?

Answer 17

hazard ratio isn’t computed at any one time point, but includes all data in the survival curve

Question 18

What is one weakness of hazard ratios?

Answer 18

1. since there is only one hazard ratio reported, it can only be interpreted if you assume that the population hazard ratio is consistent over time, and that any differences are due to random sampling
2. If the hazard ratio is not consistent over time, the estimated hazard ratio will not be useful

Question 19

For a survival curve, if we have a hazard ratio of two, does that mean the median survival time of our subjects is doubled?

Answer 19

Note that a hazard ratio of two does not mean that the median survival time is doubled. A hazard ratio of two means a patient in one group at a certain time point has twice the probability of having died by the next time point compared to a patient in the other treatment group

Question 20

Why do we have to be careful of bias in survival studies? Why are comparison groups important?

Answer 20

We can draw inappropriate conclusions from data if we don’t carefully avoid biases

Example: “immortal time bias”: Oscar winners live 4 years longer than non-winning actors (actually these actors are usually older than non-winning actors so have already reached a greater age than their non-winning counterparts)