CK030 - Cox Proportional Hazards Model

Question 1

What is the formula of the ‘Cox proportional hazards model’ ?

Answer 1

h(t) = h0(t) ‘times’ exp(b1x1 + b2x2 + …)

Question 2

What is the interpretation of the coefficients in the ‘Cox proportional hazards model’ ?

Answer 2

A 1 unit change in x gives:
- A b change in the log hazard
- A HR of exp(b)

Question 3

What are the assumptions of the ‘Cox proportional hazards model’ ?

Answer 3

• Linearity
• Additivity
• Proportional hazards

Question 4

What is ‘proportional hazards’ ?

Answer 4

The effect of the covariates is constant over time

Question 5

How to test for ‘proportional hazards’ for CATEGORICAL covariates?

Answer 5

Compare the transformed Kaplan-Meier curves of the groups:
- log(-log(S1(t)) = bx + log(-log(S2(t)), where x is the variable you want to test the assumption for

Question 6

How to test for ‘proportional hazards’ for CONTINUOUS covariates?

Answer 6

Plot the ‘scaled Schoenfeld residuals’ against time

Question 7

What can you do when the ‘proportional hazards assumption’ is violated?

Answer 7

• Incorporate covariates with nonproportional effects as stratification factors
• Partition (=subdivide) the time axis
• Model non-proportionality using time-dependent covariates
• Use nonproportional hazards models, such as AFT

Question 8

How to model nonlinearity in a ‘Cox proportional hazards model’ ?

Answer 8

• Orthogonal polynomials
• Natural cubic splines

Question 9

What does the ‘stratified Cox model’ do?

Answer 9

It allows for multiple strata that divide subjects into disjoint groups

Question 10

What are ‘exogenous time-dependent covariates’ ?

Answer 10

The value of the covariate at time t is NOT affected by occurence of an event at an earlier time point u

Question 11

What are ‘endogenous time-dependent covariates’ ?

Answer 11

The value of the covariate at time t is affected by occurence of an event at an earlier time point u

Question 12

What is the problem with ‘clustered event time data’ ?

Answer 12

The ‘estimated standard errors’ are incorrect

Question 13

Which options are there to correct for ‘clustered event time data’ ?

Answer 13

• Grouped Jackknife method, also known as ‘marginal Cox model’
• Frailty terms, also known as ‘conditional Cox model’

Question 14

What is the interpretation of coefficients of a ‘marginal Cox model’ ?

Answer 14

exp(b) = the HR for a 1 unit increase in x INDEPENDENTLY from the clusters

Question 15

What is the interpretation of coefficients of a ‘conditional Cox model’ ?

Answer 15

exp(b) = the HR for a 1 unit increase in x for patients in the SAME cluster

Question 16

What crucial distinction has to be made for ‘competing risks’ ?

Answer 16

• Independent (different endpoints are independent of eachother)
• Dependent (different endpoints are related)

Question 17

When will ‘competing risks’ give biased estimates?

Answer 17

When the different endpoints are DEPENDENT

Question 18

What models can be used for ‘competing risks’ ?

Answer 18

• Cause-specific hazard function
• Overall survival function
• Cumulative incidence function

Question 19

What is the ‘cause-specific hazard function’ ?

Answer 19

The hazard of failing from endpoint K at time t

Question 20

What is the ‘overall survival function’ ?

Answer 20

The probability of NOT having failed from ANY cause by time t

Question 21

What is the ‘cumulative incidence function’ ?

Answer 21

The probability of failing from cause K BEFORE time t