# [R] Cumulative Incidence : Gray's test

K F Pearce k.f.pearce at newcastle.ac.uk
Mon Dec 15 10:48:33 CET 2008

```Hello everyone,

I am a very new user of R and I have a query about the cuminc function
in the package cmprsk. In particular I would like to verify that I am
interpreting the output correctly when we have a stratification
variable.

Hypothetical example:

group : fair hair, dark hair
fstatus: 1=Relapse, 2=TRM, 0=censored
strata: sex (M or F)

Our data would be split into:

Fair, male, relapse
Dark,male, relapse
Fair, female, relapse
Dark, female, relapse

Fair, male, TRM
Dark,male, TRM
Fair, female, TRM
Dark, female, TRM

Fair, male, censored
Dark,male, censored
Fair, female, censored
Dark, female, censored

Am I correct in thinking that the 2 "(Gray's) Tests" which will be
printed by R tell us (i) if there are significant differences between
those with fair hair and those with dark hair as regards cumulative
incidence of relapse [taking into account sex differences] (ii) if there
are significant differences between those with fair hair and those with
dark hair as regards cumulative incidence of TRM [taking into account
sex differences] ? The 'est'and 'var'values are the same regardless of
whether we include a stratification variable or not.

If we do not include a stratification variable the '(Gray's)tests'
results will be different to those when a stratification variable is
included and they test (i) if there are significant differences between
those with fair hair and those with dark hair as regards cumulative
incidence of relapse (ii) if there are significant differences between
those with fair hair and those with dark hair as regards cumulative
incidence of TRM.

Can I ask.....what happens when the "group" variable has say 3 levels?
I guess that the "(Gray's) Tests" output in R for each 'cause' (in our
case TRM and Relapse) would tell us the significance *overall* three-way
comparison of the groups?
What if I wanted to determine the significance of  pairwise comparisons
i.e.  so that we were comparing groups (i) 1&2,  (ii) 2&3 (iii) 1&3?

Many thanks for your help on this matter,
Kind Regards,

Kim

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