[R] coxph and ordinal variables?

[Peng, C]

I look at this question in a different angle. My understanding is:

1. If treat tumor_grade as a numerical variable, you assume the hazard ratio
is invariant between any two adjacent levels of the tumor grade (assuming
invariant covariate patterns of other risks);
2. If you treat the tumor_grade as factor, you don't assume the constant
hazard ratio between the levels (assuming invariant covariate patterns of
other risks).

I don't see the difference between continuous risk and discrete ordinal risk
in this case. 
If the tumor grade is the response, there will be a difference between
variables types (ordinal, continuous and nominal) since that information
will be used to select appropriate models.

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