[R] Test for multiple contrasts?
Thomas Lumley
tlumley at u.washington.edu
Thu Feb 8 17:34:10 CET 2001
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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