[R] interpreting coxph results

[Thomas Lumley]

On Mon, 21 Aug 2006, Thomas Hills wrote:

> I am having trouble understanding results I'm getting back from coxph
> doing a recurrent event analysis.  I've included the model below and
> the summary.  In some cases, with minor variations, the Robust
> variance and Wald tests are significant, but the individual
> covariates may or may not be significant.  My main question is:  If
> Wald and robust tests both take into account the clustering, then why
> are they so different and how do I make sense of them.

In your example below the coefficient for topslope1 appears to be 
infinite, so the Wald test (which uses standard errors computed at the 
estimate) will be unreliable. The score test uses standard errors computed 
at the null and so is ok.


>							  A second
> question is:  If Wald and Robust are both significant in the summary
> tests, but all individual covariates are insignificant (these are
> Wald, yes?), what do I make of that?  I recognize the questions are
> partly R related and partly statistical (if there is a better place
> to post this please let me know).

That would mean that you have good evidence that some of the variables 
affect the hazard, but not good evidence as to which ones do.

 	-thomas


> Call:
> coxph(formula = Surv(startt, stopt, rep(1, nrow(omfi))) ~ joof1 +
>     topslope1 * top1 + I(early.angle/late.angle) + spac.cov +
>     ave.angle + slopef.d + cluster(id) + strata(sequence), data =
> thedofile))
>
>   n= 174
>                              coef exp(coef) se(coef) robust se
> z    p
> joof1                     -0.2755  7.59e-01   0.1590    0.2998 -0.919
> 0.36
> topslope1                 30.9827  2.86e+13  23.2339   51.9948  0.596
> 0.55
> top1                       0.1165  1.12e+00   0.1901    0.3951  0.295
> 0.77
> I(early.angle/late.angle)  0.0449  1.05e+00   0.1165    0.1296  0.347
> 0.73
> spac.cov                   0.9815  2.67e+00   3.4104    5.5871  0.176
> 0.86
> ave.angle                  0.0396  1.04e+00   0.0156    0.0266  1.488
> 0.14
> slopef.d                  -0.3394  7.12e-01   0.4373    0.8891 -0.382
> 0.70
> topslope1:top1            -5.5673  3.82e-03   2.8198    6.7696 -0.822
> 0.41
>
>
> Rsquare= 0.18   (max possible= 0.898 )
> Likelihood ratio test= 34.5  on 8 df,   p=3.27e-05
> Wald test            = 23.5  on 8 df,   p=0.00276
> Score (logrank) test = 31.8  on 8 df,   p=0.000103,   Robust = 13.5
> p=0.097
>
>   (Note: the likelihood ratio and score tests assume independence of
>      observations within a cluster, the Wald and robust score tests
> do not).
>
> Thanks for any help,
>
> Thomas Hills
> Indiana University
>
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Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle