[R] Looking for Post-hoc tests (a la TukeyHSD) or interaction-level independent contrasts for survival analysis.

From: Thomas Oliver <toliver_at_stanford.edu>
Date: Tue, 29 Apr 2008 14:12:33 -0700

Hello all R-helpers,

    I've performed an experiment to test for differential effects of elevated temperatures on three different groups of corals. I'm currently performing a cox proportional hazards regression with censoring on the survivorship (days to mortality) of each individual in the experiment with two factors: Temperature Treatment (2 levels: ambient and elevated) and experimental group (3 levels: say 1,2,3).

In my experiment, all three groups survived equally well in the ambient control treatment, but two of three of the groups succumbed to heat stress in the elevated temperature treatment. I can see that the third group had a small degree of mortality, but it appears to be significantly less than the other two and may be not significantly different from the ambient controls.

I would like to ask three questions: 1) Is group 3 different from controls? 2) Is group 3 different from group 1 and/or group 2 in the elevated treatment? and 3) are groups 1 and 2 different from each other in the elevated treatment?

   Because I'm testing for differential effects among the elevated temperature treatment group, and "I've seen the data" by now, the analysis would be easiest for me if I performed a responsible multiple comparisons test like TukeyHSD to see how each of the six Treatment:Group subgroups compared to each other. TukeyHSD does not appear to be defined for outputs from the function coxph -- (see survival library).

cph <- coxph(Surv(DayToMort, Censor) ~ Treatment*Group, data=subb)

--> Does anyone know of an implementation of TukeyHSD that would
work, or of another post-hoc multiple comparison test?

I believe that another responsible tack would be to clearly define the contrasts I'd like to make within the interaction term. However this has yet to work as fully as I'd like it.

  I've successfully set the contrasts matrix for the three-level factor "Group" following Crawley's The R Book.


By setting these contrasts and then looking at the interaction terms in the coxph model, this allows me to compare groups _within_ each separate treatment, and confirms both that #2) that groups 1 and 2 are not sig. different in the elevated treatment, and #3) the group3 corals survived significantly better than the other groups in the elevated treatment. BUT it does not allow me to say if the group3 survival is or is not different from its own control.(#1 above).

To make this comparison, I've tried setting the contrast matrix for the Treatment:Group interaction term, with no success. Whenever I attempt to do so, I run the code below:

cmat<-cbind(c(-1,0,0,1,0,0),c(0,-1,0,0,1,0),c(0,0,-1,0,0,1),c(0,0,0,-1,1,0),c(0,0,0,0,-1,1)) #Build a matrix
rownames(cmat)<-rownames(contrasts(subb$Treatment:subb$Group)) #give cmat the correct rownames
colnames(cmat)<-colnames(contrasts(subb$Treatment:subb$Group)) #give cmat the correct colnames
contrasts(subb$Treatment:subb$Group)<-cmat #try to assign cmat

and I get this error message:
Error in contrasts(subb$Treatment:subb$Group, ) <- cmat :

   could not find function ":<-"

Alternatively I could run:
options(contrasts=c("contr.sum","contr.poly")) where:

             [,1] [,2] [,3] [,4] [,5]

Con:1   1    0    0    0    0
Con:2    0    1    0    0    0
Con:3    0    0    1    0    0
Exp:1    0    0    0    1    0
Exp:2    0    0    0    0    1
Exp:3   -1   -1   -1   -1   -1

But even that doesn't appear to affect the output of :

cph <- coxph(Surv(DayToMort, Censor) ~ Treatment*Group, data=subb)

--> Is what I'm trying to do statistically invalid and R is trying to
quietly save me from statistical destruction, or it is just being a pain? Is there a way around it?

--> Any other suggestions?

Many Thanks in Advance,

Tom Oliver

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