R help - Apr 2011 - Testing equality of coefficients in coxph model

Dear all,

I'm running a coxph model of the form:
coxph(Surv(Start, End, Death.ID) ~ x1 + x2 + a1 + a2 + a3)

Within this model, I would like to compare the influence of x1 and x2 on the
hazard rate.
Specifically I am interested in testing whether the estimated coefficient
for x1 is equal (or not) to the estimated coefficient for x2.

I was thinking of using a Chow-test for this but the Chow test appears to
work for linear regression only (see: http://en.wikipedia.org/wiki/Chow_test).
Another option I was thinking of is to estimate an alternative model in
which the coefficients for x1 and x2 are constraint to be equal and to
compare the fit of such a constraint model with the one of an unconstraint
one. But again I'm not sure how this can be done using coxph.

Could anyone help me out on this please?

Thanks,

Michael



Michael Haenlein
Associate Professor of Marketing
ESCP Europe
Paris, France

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Hi Michael,

One way to work out you problem is with bootstrap methods. The following is 
a toy example that may be help you for you:

# test data...
library(survival)

set.seed(1007)
x <- runif(50)

mu <- c(rep(1, 25), rep(2, 25))

test1 <- data.frame(Time = qsurvreg(x, mean = mu, scale= 0.5, distribution = 
"weibull"),
                    Status = rbinom(50,1,0.7),
                    tr = gl(2, 20)
                    )

mod1 <- survreg(Surv(Time, Status) ~ -1 + tr, data = test1)
summary(mod1)

# Bootstrap function...
boot.fun <- function(dat, Ind)
{
mod1 <- survreg(Surv(Time, Status) ~ -1 + tr, data = dat[Ind,])
b <- coef(mod1)
delta <- b[1] - b[2] # statistic of interest
delta
}

# Bootstraping ...
library(boot)
boot.res <- boot(test1, boot.fun, R = 1999)
boot.res
boot.ci(boot.res)
plot(boot.res, jack = TRUE)
# end ...

Cheers,

Pablo



----- Original Message ----- 
From: "Michael Haenlein" <haenlein at escpeurope.eu>
To: <r-help at r-project.org>
Sent: Tuesday, April 12, 2011 11:19 AM
Subject: [R] Testing equality of coefficients in coxph model

> Dear all,
>
> I'm running a coxph model of the form:
> coxph(Surv(Start, End, Death.ID) ~ x1 + x2 + a1 + a2 + a3)
>
> Within this model, I would like to compare the influence of x1 and x2 on 
> the
> hazard rate.
> Specifically I am interested in testing whether the estimated coefficient
> for x1 is equal (or not) to the estimated coefficient for x2.
>
> I was thinking of using a Chow-test for this but the Chow test appears to
> work for linear regression only (see: 
> http://en.wikipedia.org/wiki/Chow_test).
> Another option I was thinking of is to estimate an alternative model in
> which the coefficients for x1 and x2 are constraint to be equal and to
> compare the fit of such a constraint model with the one of an unconstraint
> one. But again I'm not sure how this can be done using coxph.
>
> Could anyone help me out on this please?
>
> Thanks,
>
> Michael
>
>
>
> Michael Haenlein
> Associate Professor of Marketing
> ESCP Europe
> Paris, France
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> 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.
>

Hi:

Another possible approach (untested) would be to compare the two models

m1 <- coxph(Surv(Start, End, Death.ID) ~ x1 + x2 + a1 + a2 + a3)
m0 <- coxph(Surv(Start, End, Death.ID) ~ I(x1 + x2) + a1 + a2 + a3)
anova(m0, m1)

This should be able to test H_0: beta_1 = beta_2. If you want to test that
they are both equal to a specified [nonzero] constant, that's a different
test entirely (e.g., beta_1 = 1 = beta_2) - in that case, offset() might be
useful.

HTH,
Dennis

On Tue, Apr 12, 2011 at 2:19 AM, Michael Haenlein
<haenlein@escpeurope.eu>wrote:
> Dear all,
>
> I'm running a coxph model of the form:
> coxph(Surv(Start, End, Death.ID) ~ x1 + x2 + a1 + a2 + a3)
>
> Within this model, I would like to compare the influence of x1 and x2 on
> the
> hazard rate.
> Specifically I am interested in testing whether the estimated coefficient
> for x1 is equal (or not) to the estimated coefficient for x2.
>
> I was thinking of using a Chow-test for this but the Chow test appears to
> work for linear regression only (see:
> http://en.wikipedia.org/wiki/Chow_test).
> Another option I was thinking of is to estimate an alternative model in
> which the coefficients for x1 and x2 are constraint to be equal and to
> compare the fit of such a constraint model with the one of an unconstraint
> one. But again I'm not sure how this can be done using coxph.
>
> Could anyone help me out on this please?
>
> Thanks,
>
> Michael
>
>
>
> Michael Haenlein
> Associate Professor of Marketing
> ESCP Europe
> Paris, France
>
>        [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help@r-project.org mailing list
> 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]]