Cox Regression : Spline Coefficient Interpretation?

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Cox Regression : Spline Coefficient Interpretation?

kosmirnov
Hi,

I'm using a Cox-Regression to estimate hazard rates on prepayments.

I'm using the "pspline" function to face non-linearity, but I have no clue
how to interpret the result.
Unfortunately I did not find enough information on the "pspline" function
wether in the survival package nor using google..

I got following output:

* library(survival)*


>
>
>
>
>
>
>
>
>
>
>
>
>
> *> Option.test2<-coxph(Surv(START,STOP,ZEROBAL==1)~pspline(OPTION),
> data=FNMA)coxph(formula = Surv(START, STOP, ZEROBAL == 1) ~
> pspline(OPTION),     data = FNMA)> > Option.test2> Call:> coxph(formula =
> Surv(START, STOP, ZEROBAL == 1) ~ pspline(OPTION), >     data = FNMA)>
>                          coef  se(coef)       se2     Chisq   DF
>         p> pspline(OPTION), linear   -0.1334    0.0131    0.0131  104.4325
> 1.00 <0.0000000000000002> pspline(OPTION), nonlin
>     1747.1295 3.05 <0.0000000000000002> Iterations: 8 outer, 19
> Newton-Raphson>      Theta= 0.991 > Degrees of freedom for terms= 4 >
> Likelihood ratio test=2136  on 4.05 df, p=0  n= 3390429 >  *


Thanks,

KS

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Re: Cox Regression : Spline Coefficient Interpretation?

Bert Gunter-2
??

It is unclear to me what "How to interpret the result" means. Note that the
survival package is very well documented and there is a vignette
specifically on the topic of the use of "Spline terms in a Cox model." Have
you studied it?

If you want to discuss the statistical issues, e.g. of survival modeling
or the technical details of penalized smoothing splines, that is mostly OT
here: stats.stackexchange.com would probably be a better place to post for
that. This list is mostly about R programming rather than statistics,
although they do sometimes intersect.

If I have misunderstood your question, you might wish to clarify exactly
what it is that you are seeking in another post.

Finally, as you can see from the below, post in PLAIN TEXT ONLY, as html
can get mangled by the server on this plain text mailing list.

Cheers,
Bert



Bert Gunter

"The trouble with having an open mind is that people keep coming along and
sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )

On Wed, Nov 1, 2017 at 1:12 PM, Kosta S. <[hidden email]> wrote:

> Hi,
>
> I'm using a Cox-Regression to estimate hazard rates on prepayments.
>
> I'm using the "pspline" function to face non-linearity, but I have no clue
> how to interpret the result.
> Unfortunately I did not find enough information on the "pspline" function
> wether in the survival package nor using google..
>
> I got following output:
>
> * library(survival)*
>
>
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > *> Option.test2<-coxph(Surv(START,STOP,ZEROBAL==1)~pspline(OPTION),
> > data=FNMA)coxph(formula = Surv(START, STOP, ZEROBAL == 1) ~
> > pspline(OPTION),     data = FNMA)> > Option.test2> Call:> coxph(formula =
> > Surv(START, STOP, ZEROBAL == 1) ~ pspline(OPTION), >     data = FNMA)>
> >                          coef  se(coef)       se2     Chisq   DF
> >         p> pspline(OPTION), linear   -0.1334    0.0131    0.0131
> 104.4325
> > 1.00 <0.0000000000000002> pspline(OPTION), nonlin
> >     1747.1295 3.05 <0.0000000000000002> Iterations: 8 outer, 19
> > Newton-Raphson>      Theta= 0.991 > Degrees of freedom for terms= 4 >
> > Likelihood ratio test=2136  on 4.05 df, p=0  n= 3390429 >  *
>
>
> Thanks,
>
> KS
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/
> posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

        [[alternative HTML version deleted]]

______________________________________________
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Re: Cox Regression : Spline Coefficient Interpretation?

Bert Gunter-2
Always reply to the list. I do not do private consulting.
(I have cc'ed this to the list).

I still think this belongs on stackexchange, not r-help. I think you need
to read up on the mathematics of spline bases.

Cheers,
Bert



Bert Gunter

"The trouble with having an open mind is that people keep coming along and
sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )

On Thu, Nov 2, 2017 at 3:43 AM, Kosta S. <[hidden email]> wrote:

> Hi Bert,
>
> Maybe I should make this more clear.
> I get following output when I use the pspline function inside the coxph
> statement:
>
> * library(survival)*
>
>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> *> Option.test2<-coxph(Surv(START,STOP,ZEROBAL==1)~pspline(OPTION),
>> data=FNMA)coxph(formula = Surv(START, STOP, ZEROBAL == 1) ~
>> pspline(OPTION),    data = FNMA)> > Option.test2> Call:> coxph(formula =
>> Surv(START, STOP, ZEROBAL == 1) ~ pspline(OPTION),>     data = FNMA)>
>>                        coef  se(coef)       se2     Chisq   DF
>>       p> pspline(OPTION), linear   -0.1334    0.0131    0.0131  104.4325
>> 1.00 <0.0000000000000002> pspline(OPTION), nonlin
>>     1747.1295 3.05 <0.0000000000000002> Iterations: 8 outer, 19
>> Newton-Raphson>      Theta= 0.991> Degrees of freedom for terms= 4>
>> Likelihood ratio test=2136  on 4.05 df, p=0  n= 3390429*
>
>
>
> What I do not understand, and what I have not found either in the package
> documentation nor somewhere else is how to  interpret the output result:
>
>
>
>
>
>
>
> *>                              coef  se(coef)       se2     Chisq   DF
>                 p> pspline(OPTION), linear   -0.1334    0.0131    0.0131
>  104.4325 1.00 <0.0000000000000002> pspline(OPTION), nonlin
>               1747.1295 3.05 <0.0000000000000002> Iterations: 8 outer, 19
> Newton-Raphson>      Theta= 0.991> Degrees of freedom for terms= 4>
> Likelihood ratio test=2136  on 4.05 df, p=0  n= 3390429*
>
>
> What does it actually tell me? What does the "linear" and "nonlinear"
> mean? It differs from the usual coxph output. Is this a proof of
> non-linearity?
>
> This topic was also alreday asked on the cross validated board, but
> unfortunately without any answer, see https://stats.
> stackexchange.com/questions/280168/interpretation-of-coxph-pspline-terms
>
>
> Thanks,
>
> KS
>
>
>
>
>
>
>
>
> 2017-11-01 23:11 GMT+01:00 Bert Gunter <[hidden email]>:
>
>> ??
>>
>> It is unclear to me what "How to interpret the result" means. Note that
>> the survival package is very well documented and there is a vignette
>> specifically on the topic of the use of "Spline terms in a Cox model." Have
>> you studied it?
>>
>> If you want to discuss the statistical issues, e.g. of survival modeling
>> or the technical details of penalized smoothing splines, that is mostly OT
>> here: stats.stackexchange.com would probably be a better place to post
>> for that. This list is mostly about R programming rather than statistics,
>> although they do sometimes intersect.
>>
>> If I have misunderstood your question, you might wish to clarify exactly
>> what it is that you are seeking in another post.
>>
>> Finally, as you can see from the below, post in PLAIN TEXT ONLY, as html
>> can get mangled by the server on this plain text mailing list.
>>
>> Cheers,
>> Bert
>>
>>
>>
>> Bert Gunter
>>
>> "The trouble with having an open mind is that people keep coming along
>> and sticking things into it."
>> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
>>
>> On Wed, Nov 1, 2017 at 1:12 PM, Kosta S. <[hidden email]> wrote:
>>
>>> Hi,
>>>
>>> I'm using a Cox-Regression to estimate hazard rates on prepayments.
>>>
>>> I'm using the "pspline" function to face non-linearity, but I have no
>>> clue
>>> how to interpret the result.
>>> Unfortunately I did not find enough information on the "pspline" function
>>> wether in the survival package nor using google..
>>>
>>> I got following output:
>>>
>>> * library(survival)*
>>>
>>>
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> > *> Option.test2<-coxph(Surv(START,STOP,ZEROBAL==1)~pspline(OPTION),
>>> > data=FNMA)coxph(formula = Surv(START, STOP, ZEROBAL == 1) ~
>>> > pspline(OPTION),     data = FNMA)> > Option.test2> Call:>
>>> coxph(formula =
>>> > Surv(START, STOP, ZEROBAL == 1) ~ pspline(OPTION), >     data = FNMA)>
>>> >                          coef  se(coef)       se2     Chisq   DF
>>> >         p> pspline(OPTION), linear   -0.1334    0.0131    0.0131
>>> 104.4325
>>> > 1.00 <0.0000000000000002> pspline(OPTION), nonlin
>>> >     1747.1295 3.05 <0.0000000000000002> Iterations: 8 outer, 19
>>> > Newton-Raphson>      Theta= 0.991 > Degrees of freedom for terms= 4 >
>>> > Likelihood ratio test=2136  on 4.05 df, p=0  n= 3390429 >  *
>>>
>>>
>>> Thanks,
>>>
>>> KS
>>>
>>>         [[alternative HTML version deleted]]
>>>
>>> ______________________________________________
>>> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide http://www.R-project.org/posti
>>> ng-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>
>>
>

        [[alternative HTML version deleted]]

______________________________________________
[hidden email] mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
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Re: Cox Regression : Spline Coefficient Interpretation?

Kevin E. Thorpe
In reply to this post by kosmirnov
Your output is mangled beyond interpretation.

However, when it comes to interpreting splines in general, you cannot
easily convert the individual beta coefficients into, say HR by
exponenitating them. The collection of beta coefficients describe the
relationship between the continuous variable and the outcome.

Consider a simple case. Suppose you fit a model with x and x^2. You
cannot really interpret the x^2 coefficient in isolation from the x
coefficient. It is the same with splines only worse.

Graphical displays of the spline are often more informative.

Kevin

On 11/01/2017 04:12 PM, Kosta S. wrote:

> Hi,
>
> I'm using a Cox-Regression to estimate hazard rates on prepayments.
>
> I'm using the "pspline" function to face non-linearity, but I have no clue
> how to interpret the result.
> Unfortunately I did not find enough information on the "pspline" function
> wether in the survival package nor using google..
>
> I got following output:
>
> * library(survival)*
>
>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> *> Option.test2<-coxph(Surv(START,STOP,ZEROBAL==1)~pspline(OPTION),
>> data=FNMA)coxph(formula = Surv(START, STOP, ZEROBAL == 1) ~
>> pspline(OPTION),     data = FNMA)> > Option.test2> Call:> coxph(formula =
>> Surv(START, STOP, ZEROBAL == 1) ~ pspline(OPTION), >     data = FNMA)>
>>                           coef  se(coef)       se2     Chisq   DF
>>          p> pspline(OPTION), linear   -0.1334    0.0131    0.0131  104.4325
>> 1.00 <0.0000000000000002> pspline(OPTION), nonlin
>>      1747.1295 3.05 <0.0000000000000002> Iterations: 8 outer, 19
>> Newton-Raphson>      Theta= 0.991 > Degrees of freedom for terms= 4 >
>> Likelihood ratio test=2136  on 4.05 df, p=0  n= 3390429 >  *
>
>
> Thanks,
>
> KS
>


--
Kevin E. Thorpe
Head of Biostatistics,  Applied Health Research Centre (AHRC)
Li Ka Shing Knowledge Institute of St. Michael's Hospital
Assistant Professor, Dalla Lana School of Public Health
University of Toronto
email: [hidden email]  Tel: 416.864.5776  Fax: 416.864.3016

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