[R] Test for multiple contrasts?

[Thomas Lumley]

On Thu, 8 Feb 2001, Kaspar Pflugshaupt wrote:

> Hello,
> 
> I've fitted a parametric survival model by
> 
> > survreg(Surv(Week, Cens) ~ C(Treatment, srmod.contr), 
> >    data = poll.surv.wo3)
> 
> where srmod.contr is the following matrix of contrasts:
> 
>      prep auto       poll self home
> [1,]    1    1  1.0000000  0.0    0
> [2,]   -1    0  0.0000000  0.0    0
> [3,]    0   -1  0.0000000  0.0    0
> [4,]    0    0 -0.3333333  1.0    0
> [5,]    0    0 -0.3333333 -0.5    1
> [6,]    0    0 -0.3333333 -0.5   -1
> 
> The summary of the model looks like this:
> 
> [snip]
>                                 Value Std. Error      z         p
> (Intercept)                    1.4644     0.0552 26.536 3.68e-155
> C(Treatment, srmod.contr)prep  0.2117     0.1268  1.669  9.50e-02
> C(Treatment, srmod.contr)auto  0.1490     0.1265  1.178  2.39e-01
> C(Treatment, srmod.contr)poll -0.7242     0.1639 -4.420  9.89e-06
> C(Treatment, srmod.contr)self -0.2960     0.1141 -2.593  9.51e-03
> C(Treatment, srmod.contr)home  0.0494     0.1068  0.462  6.44e-01
> Log(scale)                    -0.4451     0.0517 -8.609  7.36e-18
> 
> [snip]
> 
> Now, I'd like to test which of my contrasts are significantly different from 
> zero. I assume that the p values given by the summary are not corrected for 
> multiple testing. Thus, I might correct them with p.adjust(). But since the 
> contrasts are not independent, I'm not sure if the adjustment methods would 
> work here.

The adjustment procedures are valid for dependent p-values. They wouldn't
be much use otherwise.  To be precise, the Holm method is valid
universally, the Hochberg method can sometimes slightly exceed the nominal
type I error.

> On the other hand, I've come across a procedure called "Scheffe's multiple 
> comparisons" (or S test), which is said to be appropriate for multiple 
> contrasts like these. Before I try to implement it: Has anybody already done 
> that, or are there good reasons not to use it?

The Scheffe procedure maintains the Type I error over all possible
contrasts, making it more conservative. On the other hand, it uses the
estimated  covariance among the parameters, which might make it less
conservative.  


> BTW, I tried to extract the SEs of the contrasts by se.contrast(), but it 
> would not work for survival models. Would they be the same that appear in the 
> summary above? 

Yes, that's why they are there :)

	-thomas

Thomas Lumley			Asst. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle

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