Survival Analysis

Question 1

You created a Kaplan-Meier curve (below) comparing study time until death (or censoring) in subjects with and without a DNR order in place (dnr1=Yes or dnr1=No). What can you conclude from the curve?

Answer 1

Those without a DNR have a higher survival rate than those with a DNR order but neither group contains more than 50 subjects that survive at least one year, according to the Kaplan-Meier curve.

Question 2

What are characteristics of a survival analysis?

Answer 2

• Used to analyze time-to-event data while accounting for censoring (typically right censoring)
• Survival data are not symmetrically distributed – often will be right skewed
• Should include a number at risk table below plot
• Median survival time will only be calculated if 50% or more of the subjects experience the event during the observation period
• Log rank test used to compare two survival curves, where the null hypothesis is the two survival functions are equal for all times (t)

Question 3

What is censoring in a survival analysis?

Answer 3

It is when we account for not knowing whether the event has occurred based on end of the observation period or patient lost to follow-up. We know that person survived at least up to a certain time.

patient followed 3 years without dying is censored at 3 years.

Question 4

In Kaplan-Meier estimate, what is the Survival fuction?

Answer 4

• probability of surviving until at least time t
• probability of not dying at time t conditional on the individual still being at risk at time t (conditional probability of the event if the subject does not have the event prior)

Question 5

What do the lines and crosses indicate on a Kaplan-Meier plot?

Answer 5

• Line indicates survival probability at each time point, crosses indicate time points where censoring has occurred, steps down indicate events

Question 6

What are characteristics of a cox proportional hazard regression?

Answer 6

• Cumulative hazard function H(t) describes the risk of “failure” in an interval after time t, conditional on the subject having survived to time t
• Exponentiated coefficient provides the hazard ratio holding all other variables constant
• Interpret hazard ratio as “hazard of <event> is X times that of…”</event>

Question 7

How do we check goodness of fit in a cox proportional hazard model?

Answer 7

• Concordance describes the probability that a prediction goes in the same direction as the actual data
• AIC and BIC also useful (lower the better)
• Cox and Snell pseudo-R2 reflects the improvement of the model over a model with the intercept alone; higher values better, not a percentage of anything

Question 8

What is the assumption of a proportional hazard model?

Answer 8

• Hazard ratio between any two individuals is constant over time
• i.e. the effect of a covariate (age. treatment) multiplies the baseline hazard but doesn’t change over time.
• Also may consider linearity of log hazard, independence no unmeasured confounders

Question 9

what do these plots for schoenfeld test show?

Answer 9

These plots show that the slope of residual against ime is consistantly close to zero (within dotted parameters). This means that there are no violations of the proportional hazard assumption.

Question 10

What does a value below p .05 tell you in a schoenfeld test?

Answer 10

• Reject the null. There is evidence that the proportional hazard assumption is violated. The effect of the covariate is not constant over time.
• Test can be done for each covariate separately and for global model.

Question 11

What can we do if the proportional hazard assumption fails on a categorical predictor?

Answer 11

• Fit a Cox model stratified by that predictor (likely an interaction between the covariate and time)
• Could use an extension of the Cox model that permites covariates to vary over time. (each subject has multiple rows each representing a time interval, reshape data into start-stop (1,0). this allows covariates to change across intervals so we can see the effect of predictor to change over time.

Question 12

What is survival analysis used for?

Answer 12

To analyze time-to-event data while accounting for censoring

Question 13

What type of censoring is typically accounted for in survival analysis?

Answer 13

Right censoring

Question 14

How is the distribution of survival data typically characterized?

Answer 14

Not symmetrically distributed, often right skewed

Question 15

What should be included below a survival plot?

Answer 15

A number at risk table

Question 16

When is median survival time calculated?

Answer 16

If 50% or more of the subjects experience the event during the observation period

Question 17

What test is used to compare two survival curves?

Answer 17

Log rank test

Question 18

What is the null hypothesis in a log rank test?

Answer 18

The two survival functions are equal for all times (t)