R Under development (unstable) (2023-08-12 r84939 ucrt) -- "Unsuffered Consequences"
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> options(na.action=na.exclude) # preserve missings
> options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type
> library(survival)
> 
> # Tests using the rats data
> #
> #  (Female rats, from Mantel et al, Cancer Research 37,
> #    3863-3868, November 77)
> 
> rfit <- coxph(Surv(time,status) ~ rx + frailty(litter), rats,
+ 	     method='breslow', subset= (sex=='f'))
> rfit
Call:
coxph(formula = Surv(time, status) ~ rx + frailty(litter), data = rats, 
    subset = (sex == "f"), method = "breslow")

                  coef se(coef)    se2  Chisq   DF     p
rx               0.906    0.323  0.319  7.882  1.0 0.005
frailty(litter)                        16.888 13.8 0.253

Iterations: 6 outer, 25 Newton-Raphson
     Variance of random effect= 0.474   I-likelihood = -181.1 
Degrees of freedom for terms=  1.0 13.9 
Likelihood ratio test=36.3  on 14.8 df, p=0.001
n= 150, number of events= 40 
> 
> rfit$iter
[1]  6 25
> rfit$df
[1]  0.975943 13.854864
> rfit$history[[1]]
$theta
[1] 0.4742849

$done
c.loglik 
    TRUE 

$history
         theta    loglik  c.loglik
[1,] 0.0000000 -181.8451 -181.8451
[2,] 1.0000000 -168.3683 -181.5458
[3,] 0.5000000 -173.3117 -181.0788
[4,] 0.3090061 -175.9446 -181.1490
[5,] 0.4645720 -173.7590 -181.0775
[6,] 0.4736210 -173.6431 -181.0773

$c.loglik
[1] -181.0773

> 
> rfit1 <- coxph(Surv(time,status) ~ rx + frailty(litter, theta=1), rats,
+ 	     method='breslow', subset=(sex=="f"))
> rfit1
Call:
coxph(formula = Surv(time, status) ~ rx + frailty(litter, theta = 1), 
    data = rats, subset = (sex == "f"), method = "breslow")

                            coef se(coef)    se2  Chisq   DF      p
rx                         0.918    0.327  0.321  7.851  1.0 0.0051
frailty(litter, theta = 1                        27.245 22.7 0.2324

Iterations: 1 outer, 6 Newton-Raphson
     Variance of random effect= 1   I-likelihood = -181.5 
Degrees of freedom for terms=  1.0 22.7 
Likelihood ratio test=50.7  on 23.7 df, p=0.001
n= 150, number of events= 40 
> 
> rfit2 <- coxph(Surv(time,status) ~ frailty(litter), rats, subset=(sex=='f'))
> rfit2
Call:
coxph(formula = Surv(time, status) ~ frailty(litter), data = rats, 
    subset = (sex == "f"))

                coef se(coef) se2 Chisq   DF    p
frailty(litter)                      18 14.6 0.24

Iterations: 6 outer, 22 Newton-Raphson
     Variance of random effect= 0.504   I-likelihood = -184.8 
Degrees of freedom for terms= 14.6 
Likelihood ratio test=30  on 14.6 df, p=0.01
n= 150, number of events= 40 
> 
> proc.time()
   user  system elapsed 
   0.87    0.09    0.96