[R] meaning of frailty estimates

[Thomas Lumley]

On Thu, 28 Oct 2004, Emanuela Rossi wrote:

> Here the output. "Specie" is the frailty variable, with four types of
> answer. I'm asking what's the meaning of gauss:1, ....gauss:4

They are hazard ratios. There is no reference group, instead the log 
hazard ratios sum to zero (hazard ratios multiply to 1).

 	-thomas

> ----------------------------------------------------------------------------
> ------------------------------
>
>>
> SURV1<-read.table("C:/LAVORO/MOBILE/survival/surv_n1.csv",header=TRUE,sep=",
> ")
>> fit_13_2_sp<-coxph(Surv(DATA_INI1,DATA_FIN1,EVENT1)~
> V1+V2+Z+G+dim+frailty.gaussian(specie)+cluster(ID),data=SURV1)
>> summary(fit_13_2_sp)
> Call:
> coxph(formula = Surv(DATA_INI1, DATA_FIN1, EVENT1) ~ V1 + V2 +
>    Z + G + dim + frailty.gaussian(specie) + cluster(ID), data = SURV1)
>
>  n= 233450
>                         coef       se(coef)   se2             Chisq  DF
> p
> V1                  0.04995   0.14021  0.145916    0.13  1.00  7.2e-01
> V2                 -0.79656   0.20483  0.197135  15.12 1.00  1.0e-04
> Z                    -0.00359  0.00067  0.000841   28.76 1.00  8.2e-08
> G                     0.08186  0.00583  0.005796 196.91 1.00  0.0e+00
> dim                  0.39410  0.06981  0.057294   31.87 1.00  1.6e-08
> frailty.gaussian(specie)                                    181.44 2.95
> 0.0e+00
>
>        exp(coef) exp(-coef) lower .95 upper .95
> V1          0.951      1.051     0.723     1.252
> V2          0.451      2.218     0.302     0.674
> Z           0.996      1.004     0.995     0.998
> G           1.085      0.921     1.073     1.098
> dim         1.483      0.674     1.293     1.700
> gauss:1     2.504      0.399     2.108     2.975
> gauss:2     1.799      0.556     1.457     2.221
> gauss:3     0.278      3.599     0.217     0.356
> gauss:4     0.799      1.252     0.641     0.996
>
> Iterations: 5 outer, 11 Newton-Raphson
>     Variance of random effect= 0.975
> Degrees of freedom for terms= 1 1 1 1 1 3
> Rsquare= 0.003   (max possible= 0.025 )
> Likelihood ratio test= 810  on 7.95 df,   p=0
> Wald test            = 600  on 7.95 df,   p=0,   Robust = 355  p=0
>
> ----------------------------------------------------------------------------
> -------------------------------------------
>
>
> Thanks
>
> Emanuela
>
>
> ----- Original Message -----
> From: "Thomas Lumley" <tlumley at u.washington.edu>
> To: "Emanuela Rossi" <emanuela.rossi at unimib.it>
> Cc: <r-help at stat.math.ethz.ch>
> Sent: Thursday, October 28, 2004 4:08 PM
> Subject: Re: [R] meaning of frailty estimates
>
>
>> On Thu, 28 Oct 2004, Emanuela Rossi wrote:
>>
>>> Hello,
>>>
>>> I'm trying to estimate a Cox's survival model with a random effect, so I
>>> have added the instruction frailty.gaussian (name variable) in the
>>> model.
>>>
>>> My frailty variable is a qualitative variable with four types of answer.
>>>
>>> In the resulting output there are the parameter estimates of all the
>>> variables, but there are also four estimates for each type of answer of
>>> the frailty variable. Which kind of estimates are they? Maybe hazard
>>> ratio? But which is the reference?
>>>
>>
>> Perhaps you could post this output so we know what you are talking about.
>>
>>   -thomas
>>
>
>

Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle