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I have an ordinal variable related to an outcome that is comprised of many levels and I´d like to collapse the number of ordinal values as much as possible.

> require(ipred)
> require(party)
> data(GBSG2)
> head(GBSG2)
  horTh age menostat tsize tgrade pnodes progrec estrec time cens
1    no  70     Post    21     II      3      48     66 1814    1
2   yes  56     Post    12     II      7      61     77 2018    1
3   yes  58     Post    35     II      9      52    271  712    1
4   yes  59     Post    17     II      4      60     29 1807    1
5    no  73     Post    35     II      1      26     65  772    1
6    no  32      Pre    57    III     24       0     13  448    1
> table(GBSG2$tgrade)

  I  II III 
 81 444 161 
> ctree(Surv(time,cens)~tgrade,data=GBSG2) -> mn
> plot(mn)

enter image description here

Would it be correct to claim that tgrade here could be collapsed into two instead of three values?

edit:

Running the usual parametric analysis I get:

>     anova(i1,i2)
Analysis of Deviance Table
 Cox model: response is  Surv(time, cens)
 Model 1: ~ tgrade
 Model 2: ~ tgrade == "I"
   loglik  Chisq Df P(>|Chi|)  
1 -1776.0                      
2 -1778.1 4.3049  1     0.038 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
>     anova(i1,i3)
Analysis of Deviance Table
 Cox model: response is  Surv(time, cens)
 Model 1: ~ tgrade
 Model 2: ~ tgrade != "III"
  loglik  Chisq Df P(>|Chi|)    
1  -1776                        
2  -1784 16.033  1 6.225e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> anova(i2,i3)
Analysis of Deviance Table
 Cox model: response is  Surv(time, cens)
 Model 1: ~ tgrade == "I"
 Model 2: ~ tgrade != "III"
   loglik  Chisq Df P(>|Chi|)    
1 -1778.1                        
2 -1784.0 11.728  0 < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> extractAIC(i1)
[1]    2.000 3555.975
> extractAIC(i2)
[1]    1.00 3558.28
>   extractAIC(i3)
[1]    1.000 3570.008  

Hence the i1 model provides a better fit than i2 and i3, and i2 fits significantly better than i3. So now all three categories are warranted with respect to survival, which is at odds with the ctree approach. Can anyone explain this? Is this due to the conditional nature of ctree instead of the semiparametric nature of cox regression?

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    $\begingroup$ I notice that this post has gone awhile without an answer. For people like me, it would be easier to answer if you described your results fully in a paragraph rather than relying so much on this output that is unique to a single software application. (What is the "usual parametric analysis" exactly? What's anova got to do with Cox regression?) $\endgroup$
    – rolando2
    Dec 3 '11 at 12:55
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Collapsing categories based on associations with Y is an invalid statistical technique that will result in a failure to preserve type I error and confidence interval coverage. You have a hidden multiplicity problem.

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  • $\begingroup$ I see that preservation of type I errors and confidence intervals would be an issue if the collapsed categories were to be used for further analysis-however I´m more uncertain if the only intent is to show that a grading system is unnecessary complex. $\endgroup$
    – Misha
    Dec 3 '11 at 14:52
  • $\begingroup$ To show that you would need to show that the confidence intervals for the differences between levels excludes a small clinically relevant value. This would require an extremely large sample size (number of events). $\endgroup$ Jan 2 '12 at 17:49

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