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Survival Analysis Using SAS®: A Practical Guide by Paul D. Allison

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Cox Models with Nonproportional Hazards

Earlier, I mentioned that the Cox model can be easily extended to allow for nonproportional hazards. In fact, we’ve just finished a lengthy discussion of one class of nonproportional models. Whenever you introduce time-dependent covariates into a Cox regression model, it’s no longer accurate to call it a proportional hazards (PH) model. Why? Because the time-dependent covariates will change at different rates for different individuals, so the ratios of their hazards cannot remain constant. As we’ve seen, however, that creates no real problem for the partial likelihood estimation method.

But suppose you don’t have any time-dependent covariates. How do you know if your data satisfy the PH assumption, and ...

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