CK030 - Cox Proportional Hazards Model Flashcards
What is the formula of the ‘Cox proportional hazards model’ ?
h(t) = h0(t) ‘times’ exp(b1x1 + b2x2 + …)
What is the interpretation of the coefficients in the ‘Cox proportional hazards model’ ?
A 1 unit change in x gives:
- A b change in the log hazard
- A HR of exp(b)
What are the assumptions of the ‘Cox proportional hazards model’ ?
- Linearity
- Additivity
- Proportional hazards
What is ‘proportional hazards’ ?
The effect of the covariates is constant over time
How to test for ‘proportional hazards’ for CATEGORICAL covariates?
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
How to test for ‘proportional hazards’ for CONTINUOUS covariates?
Plot the ‘scaled Schoenfeld residuals’ against time
What can you do when the ‘proportional hazards assumption’ is violated?
- 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
How to model nonlinearity in a ‘Cox proportional hazards model’ ?
- Orthogonal polynomials
- Natural cubic splines
What does the ‘stratified Cox model’ do?
It allows for multiple strata that divide subjects into disjoint groups
What are ‘exogenous time-dependent covariates’ ?
The value of the covariate at time t is NOT affected by occurence of an event at an earlier time point u
What are ‘endogenous time-dependent covariates’ ?
The value of the covariate at time t is affected by occurence of an event at an earlier time point u
What is the problem with ‘clustered event time data’ ?
The ‘estimated standard errors’ are incorrect
Which options are there to correct for ‘clustered event time data’ ?
- Grouped Jackknife method, also known as ‘marginal Cox model’
- Frailty terms, also known as ‘conditional Cox model’
What is the interpretation of coefficients of a ‘marginal Cox model’ ?
exp(b) = the HR for a 1 unit increase in x INDEPENDENTLY from the clusters
What is the interpretation of coefficients of a ‘conditional Cox model’ ?
exp(b) = the HR for a 1 unit increase in x for patients in the SAME cluster
What crucial distinction has to be made for ‘competing risks’ ?
- Independent (different endpoints are independent of eachother)
- Dependent (different endpoints are related)
When will ‘competing risks’ give biased estimates?
When the different endpoints are DEPENDENT
What models can be used for ‘competing risks’ ?
- Cause-specific hazard function
- Overall survival function
- Cumulative incidence function
What is the ‘cause-specific hazard function’ ?
The hazard of failing from endpoint K at time t
What is the ‘overall survival function’ ?
The probability of NOT having failed from ANY cause by time t
What is the ‘cumulative incidence function’ ?
The probability of failing from cause K BEFORE time t
