# [R] Trend test for hazard ratios

Göran Broström goran.brostrom at umu.se
Wed Apr 16 13:07:23 CEST 2014

```On 04/15/2014 10:51 PM, David Winsemius wrote:
>
> On Apr 15, 2014, at 6:32 AM, Therneau, Terry M., Ph.D. wrote:
>
>> You can do statistical tests within a single model, for whether
>> portions of it fit or do not fit.  But one cannot take three
>> separate fits and compare them.  The program needs context to know
>> how the three relate to one another.  Say that "group" is your
>> strata variable, trt the variable of interest, and x1, x2 are
>>
>> fit <- coxph(Surv(time,status) ~ trt * strata(group) + x1 + x2,
>> data=mydata)
>>
>> Will fit a model with a separate treatment coefficient for each of
>> the groups, and a separate baseline hazard for each.  One can now
>> create a contrast that corresponds to your trend test, using
>> vcov(fit) for the variance matrix and coef(fit) to retrieve the
>> coefficients.
>>
>
> I have at the moment on my workspace a dataset of breast cancer cases
> extracted from SEER that has a factor representing three grades of
> histology: \$Grade.abb. \$ Grade.abb     : Factor w/ 3 levels
> "Well","Moderate", "Poorly"
>
> It would be reasonable to test whether the grading has a "trend" in
> its effect when controlling for other factors (and it would be
> surprising to a medical audience if there were no effect.). So I
> compare across models using  AgeStgSiz.NG.Rad as my "linear" trend"
> model (with one df for an `as.numeric` version, AgeStgSizRad as my
> no-grade-included baseline, and AgeStgSiz.FG.Rad as my full factor
> version:

David, your problem is different from the original one; I think you can
solve yours by transforming the (unordered) factor to an ordered.

Try

SEER.historic.stage.A+ as.numeric(Size.cat) + ordered(Grade.abb)
+ Rgrp , data=BrILR)

and contrasts based on orthogonal polynomials are used for Grade.abb

see ?contr.poly

Göran B.
>
>> AgeStgSiz.NG.Rad <- coxph( Surv(Survmon,
>> Vital.status.recode..study.cutoff.used.=="Dead") ~ AgeDx+
>> SEER.historic.stage.A+ as.numeric(Size.cat) + as.numeric(Grade.abb)
>> + Rgrp , data=BrILR) AgeStgSizRad <- coxph( Surv(Survmon,
>> Vital.status.recode..study.cutoff.used.=="Dead") ~ AgeDx+
>> SEER.historic.stage.A+ as.numeric(Size.cat) + Rgrp , data=BrILR)
>> AgeStgSiz.FG.Rad <- coxph( Surv(Survmon,
>> Vital.status.recode..study.cutoff.used.=="Dead") ~ AgeDx+
>> SEER.historic.stage.A+ as.numeric(Size.cat) + Grade.abb + Rgrp ,
> [1] 5166.291
> [1] 5888.492
> [1] 5889.379
>
> So there is strong evidence that adding grade to the existing
> covariates improves the fit but that representing as separate factor
> values with one extra degree of freedom may not be needed. When I add
> grade as a stratum I get a very different 2*loglikelihood:
>
>> AgeStgSiz.SG.Rad <- coxph( Surv(Survmon,
>> Vital.status.recode..study.cutoff.used.=="Dead") ~ AgeDx+
>> SEER.historic.stage.A+ as.numeric(Size.cat) + strata(Grade.abb) +
>> Rgrp , data=BrILR) 2*diff(summary(AgeStgSiz.SG.Rad)[['loglik']])
> [1] 3980.908
>
>> dput( vcov(AgeStgSiz.SG.Rad) )
> structure(c(9.00241385282728e-06, -4.45446264398645e-07,
> 5.18927440846587e-07, 2.62020260612094e-07, 7.47434378232446e-07,
> -4.45446264398645e-07, 0.0046168537719431, 0.00445692601518848,
> -8.67833275051278e-07, -3.68093395861629e-05, 5.18927440846587e-07,
> 0.00445692601518848, 0.00464685164887969, -1.61616621634903e-05,
> -3.77256742079467e-05, 2.62020260612094e-07, -8.67833275051278e-07,
> -1.61616621634903e-05, 7.84049821976807e-06, 1.8221575745622e-06,
> 7.47434378232446e-07, -3.68093395861629e-05, -3.77256742079467e-05,
> 1.8221575745622e-06, 0.000313989310316303), .Dim = c(5L, 5L),
> .Dimnames = list(c("AgeDx", "SEER.historic.stage.ALocalized",
> "SEER.historic.stage.ARegional", "as.numeric(Size.cat)", "RgrpTRUE"),
> c("AgeDx", "SEER.historic.stage.ALocalized",
> "SEER.historic.stage.ARegional", "as.numeric(Size.cat)", "RgrpTRUE"
> )))
> structure(c(0.0393472050734995, 0.901971276489615, 1.46695753267995,
> 0.108860100649677, -0.273688779502084), .Names = c("AgeDx",
> "SEER.historic.stage.ALocalized", "SEER.historic.stage.ARegional",
> "as.numeric(Size.cat)", "RgrpTRUE" ))
>
> I'm not particularly facile with contrast construction with var-covar
> matrices, so hoping for a worked example. Also wondering of the
> cross-model comparisons are invalid or less powerful?
>
>
>> Terry T.
>>
>>
>>
>> On 04/15/2014 05:00 AM, r-help-request at r-project.org wrote:
>>> Hello,
>>>
>>> I have the following problem. I stratified my patient cohort into
>>> three ordered groups and performed multivariate adjusted Cox
>>> regression analysis on each group separately. Now I would like to
>>> calculate a p for trend across the hazard ratios that I got for
>>> the three groups. How can I do that if I only have the HR and the
>>> confidence interval? For example I got the following HRs for one
>>> endpoint:
>>>
>>> 1.09(0.68-1.74),	1.29(0.94-1.76) and 1.64(1.01-2.68).
>>>
>>> There is a trend but how do I calculate if it is significant?
>>>
>>> Best regards
>>>
>>> Marcus Kleber
>>>
>>
>> ______________________________________________ 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.
>
> David Winsemius Alameda, CA, USA
>
> ______________________________________________ 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.
>

```