Clayton-Oakes frailty model
ClaytonOakes(
formula,
data = parent.frame(),
cluster,
var.formula = ~1,
cuts = NULL,
type = "piecewise",
start,
control = list(),
var.invlink = exp,
...
)Arguments
- formula
formula specifying the marginal proportional (piecewise constant) hazard structure with the right-hand-side being a survival object (Surv) specifying the entry time (optional), the follow-up time, and event/censoring status at follow-up. The clustering can be specified using the special function
cluster(see example below).- data
Data frame
- cluster
Variable defining the clustering (if not given in the formula)
- var.formula
Formula specifying the variance component structure (if not given via the cluster special function in the formula) using a linear model with log-link.
- cuts
Cut points defining the piecewise constant hazard
- type
when equal to
two.stage, the Clayton-Oakes-Glidden estimator will be calculated via thetimeregpackage- start
Optional starting values
- control
Control parameters to the optimization routine
- var.invlink
Inverse link function for variance structure model
- ...
Additional arguments
Examples
set.seed(1)
d <- subset(simClaytonOakes(500,4,2,1,stoptime=2,left=2),truncated)
e <- ClaytonOakes(survival::Surv(lefttime,time,status)~x+cluster(~1,cluster),
cuts=c(0,0.5,1,2),data=d)
e
#> Estimate 2.5% 97.5%
#> log-Var:(Intercept) -0.92226 -1.16926 -0.6753
#> x 2.88805 2.58174 3.2307
#> (0,0.5] 1.07892 0.95530 1.2185
#> (0.5,1] 1.21696 1.06966 1.3845
#> (1,2] 1.16268 1.01451 1.3325
#>
#> Dependence parameters:
#> Variance 2.5% 97.5% Kendall's tau 2.5% 97.5%
#> (Intercept) 0.39762 0.31060 0.50902 0.16584 0.13442 0.2029
d2 <- simClaytonOakes(500,4,2,1,stoptime=2,left=0)
d2$z <- rep(1,nrow(d2)); d2$z[d2$cluster%in%sample(d2$cluster,100)] <- 0
## Marginal=Cox Proportional Hazards model:
ts <- ClaytonOakes(survival::Surv(time,status)~timereg::prop(x)+cluster(~1,cluster),
data=d2,type="two.stage")
## Marginal=Aalens additive model:
ts2 <- ClaytonOakes(survival::Surv(time,status)~x+cluster(~1,cluster),
data=d2,type="two.stage")
## Marginal=Piecewise constant:
e2 <- ClaytonOakes(survival::Surv(time,status)~x+cluster(~-1+factor(z),cluster),
cuts=c(0,0.5,1,2),data=d2)
e2
#> Estimate 2.5% 97.5%
#> log-Var:factor(z)0 -0.58294 -0.95495 -0.2109
#> log-Var:factor(z)1 -0.52286 -0.71031 -0.3354
#> x 2.57827 2.37165 2.8029
#> (0,0.5] 1.03878 0.94306 1.1442
#> (0.5,1] 1.00684 0.89868 1.1280
#> (1,2] 0.89075 0.78213 1.0144
#>
#> Dependence parameters:
#> Variance 2.5% 97.5% Kendall's tau 2.5% 97.5%
#> factor(z)0 0.55826 0.38483 0.80983 0.21822 0.16137 0.2882
#> factor(z)1 0.59282 0.49149 0.71505 0.22864 0.19727 0.2634
e0 <- ClaytonOakes(survival::Surv(time,status)~cluster(~-1+factor(z),cluster),
cuts=c(0,0.5,1,2),data=d2)
ts0 <- ClaytonOakes(survival::Surv(time,status)~cluster(~1,cluster),
data=d2,type="two.stage")
plot(ts0)
plot(e0,add=TRUE)
e3 <- ClaytonOakes(survival::Surv(time,status)~x+cluster(~1,cluster),cuts=c(0,0.5,1,2),
data=d,var.invlink=identity)
e3
#> Estimate 2.5% 97.5%
#> Var:(Intercept) 0.50280 0.37659 0.6290
#> x 3.07849 2.75254 3.4430
#> (0,0.5] 0.82748 0.73495 0.9317
#> (0.5,1] 0.97306 0.85420 1.1085
#> (1,2] 1.00635 0.87488 1.1576
#>
#> Dependence parameters:
#> Variance 2.5% 97.5% Kendall's tau 2.5% 97.5%
#> (Intercept) 0.50280 0.37659 0.62901 0.20090 0.15846 0.2393