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# Re: Subject: Re: st: Survival function of regression Cox model postestimation

 From "Airey, David C" To "statalist@hsphsun2.harvard.edu" Subject Re: Subject: Re: st: Survival function of regression Cox model postestimation Date Fri, 15 Jul 2011 17:39:32 -0500

```.

Following up one more time, I have to say that the Stata documentation is
excellent. Read it and you eventually find insight and laugh as well. For
example, I was concerned about continuous covariates without a 0, and I
read in the stcox_postestimation PDF the following, where the last line
was funny.

"For these reasons, covariate values of 0 must be meaningful if you are going
to specify the basechazard or basesurv option. As the baseline values move to
absurdity, the first problem you will encounter is a baseline survivor function
that is too hard to interpret, even though the baseline hazard contributions are
estimated accurately. Further out, the procedure Stata uses to estimate the
baseline hazard contributions will break down—it will produce results that are
exactly 1. Hazard contributions that are exactly 1 produce survivor functions
that are uniformly 0, and they will remain 0 even after adjusting for covariates.
This, in fact, occurs with the Stanford heart transplant data:

-output removed-

The hint that there are problems is that the values of ch are huge and the
values of s are close to 0. In this dataset, age (which ranges from 8 to 64
with a mean value of 45) and year (which ranges from 67 to 74) are the
problems. The baseline functions correspond to a newborn at the turn of the
century on the waiting list for a heart transplant!"

-Dave

> I've not much experience with survival models other than log-rank tests, but am reading more about them now.
>
> What's the interpretation of a continuous covariate if it doesn't include 0? A transformation can be done on an X covariate, e.g., X-#, to get the relative risk to when X=#. But if you don't do this transformation, and your data range doesn't naturally include 0, what happens to the interpretation? What do you do with a continuous covariate that varies from (-) to (+) values and you don't want the given 0 to be used?
>
> -Dave
>
> --- On Tue, Jul 12, 2011 at 6:40 PM, Mario Petretta wrote me privately:
>> Anyway, there is a rule for applying a non-linear transformation to a
>> continuous covariate in order to obtain a survival function of a Cox model
>> with that covariate obtained at its mean value not different from
>> baseline survival function of the Cox model without covariates?
>
> It is better to respond to the Statalist and not privately because if
> you find my answer unclear, chances are that other people following
> this thread may also find it unclear.
>
> No, Cox regression has a baseline hazard function not a baseline
> survival function, and the baseline hazard function is the hazards at
> different points in time when all explanatory/independent/x-variables
> are 0 not fixed at the mean.
>
> Hope this helps,
> Maarten

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