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Module 7: Non-proportionality in Cox Models & Proc PHReg (Customized…
Module 7: Non-proportionality in Cox Models & Proc PHReg
Non-proportional Hazards
Cox regression with time-dependent covariates
Incorporate interaction of covariate and time in model
Add new variable to represent interaction: the product of the covariate X and time T
If beta2 is >0, the effect of X increases over time on the hazard
If beta2 is <0, the effect of X decreases over time on the
If beta2 is =0, the PH assumption holds, no need to check for interaction with time
Cox regression without time-dependent covariates
Use stratification to allow non-proportionality
Most useful when the covariate that interacts with time is categorical and not of direct interest
To estimate the model: 1: Get PL0 and PL1 for each group, multiply PL0 and PL1 together to get just PL, and choose values of beta that maximize the function PL
Assumes that observations are conditionally independent within cluster and coefficients of the covariates are the same across clusters
Testing for Non-Proportionality
When there are no time-dependent covariates
Martingale Residuals
Use ASSESS statement
We see the observed path compared to a large number of simulated paths. The percent of paths that have supremum larger than observed = probability PH assumption holds true
This changes slightly with different random seeds
Test is only for PH and does not say anything about the effect of the coefficient
Even when there are time dependent covariates
Schoenfeld Residuals
Use ResSch keyword and computer correlation using PROC CORR
Need to use counting process method with the tweaked data
For each covariate X_k, its expected value for a randomly selected person from a randomly selected person from n is
The residual calculation is the covariate value for the individual with event minus the expected value
There is a separate residual for each covariate for each individual, and it's only calculated for event observations
If the PH assumption holds, the residuals should be independent of time
For censored obs, ResSch are missing
Survivor Function in Cox Models
In Cox Models, after the betas are estimated by partial likelihood, we can get non-parametric estimates of S(t)
The estimates survival uses the mean of the covariates to get the estimated survival for an "average" subject
In PROC PHReg, the estimation of S(t) is accomplished with the BASELINE statement and the PLOTS options
Testing Linear Hypothesis
TEST statement and CONTRAST statement test any linear hypothesis about more than one coefficient
Customized Hazard Ratios
Hazard Ratio is the e^beta -> interpreted as % change of a 1-unit change in that covariate
Use hazardRatio statement
