[R] Second-order effect in Parametric Survival Analysis

[David Winsemius]

On Nov 13, 2011, at 12:51 AM, ryusuke wrote:

> Thank you Dr. David.
>
> I try to summarize it.
> Assumes x and z are two covariates:
> x = dummy variable (1 or 0)
> z = factors (people name)
>
> x*z = x + z + x*z

Actually I said = x + z + x:z

And interaction formula of a two level dummy with a multi-level factor  
would produce and intercept (which would be for the first person's  
name), a coefficient for each of other names at level zero, a dummy  
coefficient (for the first person), and interaction coefficients of  
each person at the 1-level.

> therefore this is not a 2nd-order interactions, it should be (for an
> exponential survival regression):-
> h(t|(X=x,Z=z)) = exp(Beta0 + XZBeta1)

If Beta1 is not a vector in this instance, with a distinct value for  
each(x,z) pairing, then I am unable to make sense out of that model.  
The questin remains however whether you are also expecting Beta0 to  
also be distinct for each specific combination of covariates.

> #---------------------------------------------------
>
> I believe there is no 2nd-order interactions survival regression as I
> searched over www.rseek.org. While I tried to read through the codes  
> of
> survreg(), I stuck (cannot understand) at survreg6.c
>
> survreg6.c apply C Language which involves Cholesky decomposition
> multi-matrix (first-order interactions) calculation.
> 1) chinv2.c
> 2) cholesky3.c
> 3) chsolve2.c (only solve the equations of first-order interactions)

That level of implementation should be addressed to a person with  
higher levels of knowledge: Therneau or Lumley are the two names that  
immediately come to mind.

>
> If someone gives some idea or suggestion on these?
> Thank you.
>
>
> Best,
> Ryusuke
>
>
> --
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David Winsemius, MD
West Hartford, CT