[R] Frailty models and omnibus test

[Johannes Huesing]

This is very possibly not a question on R.

I was under the impression that the argument that gives rise to Fisher's
LSD method in ANOVA works in other situations with three-way comparisons
too, given that formal logic works the same ("if the omnibus test rejects,
only two of the three groups may be equal, and therefore only one hypothesis
can be rejected falsely").

However, when I applied the method to survival models with a frailty term,
it looks as if things are not that easy. With simulated data, the global
test of a categorical explanatory variable with three categories rejects
nicely at the .05 level, but the culprit cannot be found among the pairwise
tests:

Call:
coxph(formula = Surv(start, stop, obs) ~ I(interv == "PERSON") + 
    I(interv == "TAU") + frailty.gamma(subjid), data = cip)

                          coef  se(coef) se2   Chisq DF  p   
I(interv == "PERSON")TRUE 0.315 0.543    0.429  0.34 1.0 0.56
I(interv == "TAU")TRUE    0.481 0.624    0.499  0.59 1.0 0.44
frailty.gamma(subjid)                          10.96 7.4 0.16

Iterations: 6 outer, 31 Newton-Raphson
     Variance of random effect= 0.381   I-likelihood = -75.4 
Degrees of freedom for terms= 0.6 0.6 7.4 
Likelihood ratio test=20.9  on 8.66 df, p=0.0108  n= 35 

I know that there is no 1:1 relationship (ie. even Fisher's LSD in ANOVA
is not consonant), but this situation nowhere near uncovers any conspicuous
contrast.

Here are the data:

"state"	"subjid"	"interv"	"stop"	"obs"	"well"	"start"
"1"	4	20	"PERSON"	2.9011943146276	TRUE	FALSE	0
"4"	3	21	"PERSON"	64.2158729475923	FALSE	FALSE	47.8848496390479
"5"	3	22	"PERSON"	17.5619324029277	TRUE	FALSE	0
"9"	3	23	"PERSON"	43.2824713513494	TRUE	FALSE	37.7695873739113
"12"	5	24	"PERSON"	30.3701080739726	TRUE	FALSE	0
"15"	3	25	"PERSON"	14.0466975658663	TRUE	FALSE	0
"21"	5	27	"PERSON"	56.2151528587565	FALSE	FALSE	0
"23"	5	28	"PERSON"	107.008366594091	FALSE	FALSE	81.3506138393983
"24"	3	29	"PERSON"	2.37513876948506	TRUE	FALSE	0
"28"	5	30	"PERSON"	11.8558184784885	TRUE	FALSE	0
"32"	4	33	"PERSON"	3.9649403609025	TRUE	FALSE	0
"38"	4	35	"PERSON"	46.3451030540359	TRUE	FALSE	11.8777967304634
"41"	3	36	"PERSON"	1.31729328750322	TRUE	FALSE	0
"44"	3	37	"PERSON"	3.02546596184197	TRUE	FALSE	0
"46"	4	38	"PERSON"	0.107545536671634	TRUE	FALSE	0
"56"	3	42	"SUMIT"	58.7353880008292	TRUE	FALSE	0
"62"	5	43	"SUMIT"	89.7918344149282	TRUE	FALSE	0
"67"	3	45	"SUMIT"	24.7430207077919	TRUE	FALSE	0
"70"	3	46	"SUMIT"	6.27882742756157	TRUE	FALSE	0
"74"	3	48	"SUMIT"	17.0609614511906	TRUE	FALSE	0
"79"	4	50	"SUMIT"	38.4473846749763	TRUE	FALSE	13.3018767580903
"85"	4	53	"SUMIT"	4.29013653621078	TRUE	FALSE	0
"89"	3	55	"SUMIT"	11.6584881048097	TRUE	FALSE	0
"92"	3	56	"SUMIT"	13.8629879979001	TRUE	FALSE	0
"98"	5	58	"SUMIT"	10.0370180170905	TRUE	FALSE	0
"100"	3	58	"SUMIT"	37.2975347554063	TRUE	FALSE	36.5702401089113
"104"	3	60	"TAU"	126.334602409974	FALSE	FALSE	0
"109"	3	63	"TAU"	8.34004312096584	TRUE	FALSE	0
"113"	3	65	"TAU"	13.5353540650711	TRUE	FALSE	0
"117"	3	66	"TAU"	6.90264432503116	TRUE	FALSE	0
"119"	4	66	"TAU"	84.0982554651905	TRUE	FALSE	80.0934220365208
"123"	4	68	"TAU"	0.574347350398699	TRUE	FALSE	0
"138"	3	74	"TAU"	8.6319161108183	TRUE	FALSE	0
"140"	3	74	"TAU"	52.6563648282415	TRUE	FALSE	48.1392786201591
"143"	3	75	"TAU"	17.2904575851141	TRUE	FALSE	0

-- 
Johannes Hüsing               There is something fascinating about science. 
                              One gets such wholesale returns of conjecture 
mailto:johannes at huesing.name  from such a trifling investment of fact.                
http://derwisch.wikidot.com         (Mark Twain, "Life on the Mississippi")