Fits Clayton-Oakes clustered survival data using marginals that are on Cox form in the likelihood for the dependence parameter as in Glidden (2000). The dependence can be modelled via a
Regression design on dependence parameter.
We allow a regression structure for the indenpendent gamma distributed random effects and their variances that may depend on cluster covariates. So $$ \theta = h( z_j^T \alpha) $$ where \(z\) is specified by theta.des . The link function can be the exp when var.link=1
Usage
twostageMLE(
margsurv,
data = parent.frame(),
theta = NULL,
theta.des = NULL,
var.link = 0,
method = "NR",
no.opt = FALSE,
weights = NULL,
se.cluster = NULL,
...
)Arguments
- margsurv
Marginal model from phreg
- data
data frame
- theta
Starting values for variance components
- theta.des
design for dependence parameters, when pairs are given this is could be a (pairs) x (numer of parameters) x (max number random effects) matrix
- var.link
Link function for variance if 1 then uses exp link
- method
type of opitmizer, default is Newton-Raphson "NR"
- no.opt
to not optimize, for example to get score and iid for specific theta
- weights
cluster specific weights, but given with length equivalent to data-set, weights for score equations
- se.cluster
specifies how the influence functions are summed before squared when computing the variance. Note that the id from the marginal model is used to construct MLE, and then these scores can be summed with the se.cluster argument.
- ...
arguments to be passed to optimizer
References
Measuring early or late dependence for bivariate twin data Scheike, Holst, Hjelmborg (2015), LIDA
Twostage modelling of additive gamma frailty models for survival data. Scheike and Holst, working paper
Shih and Louis (1995) Inference on the association parameter in copula models for bivariate survival data, Biometrics, (1995).
Glidden (2000), A Two-Stage estimator of the dependence parameter for the Clayton Oakes model, LIDA, (2000).
Examples
data(diabetes)
dd <- phreg(Surv(time,status==1)~treat+cluster(id),diabetes)
oo <- twostageMLE(dd,data=diabetes)
summary(oo)
#> Dependence parameter for Clayton-Oakes model
#> Variance of Gamma distributed random effects
#> $estimates
#> Coef. SE z P-val Kendall tau SE
#> dependence1 0.9526614 0.3543033 2.68883 0.007170289 0.322645 0.08127892
#>
#> $type
#> NULL
#>
#> attr(,"class")
#> [1] "summary.mets.twostage"
theta.des <- model.matrix(~-1+factor(adult),diabetes)
oo <-twostageMLE(dd,data=diabetes,theta.des=theta.des)
summary(oo)
#> Dependence parameter for Clayton-Oakes model
#> Variance of Gamma distributed random effects
#> $estimates
#> Coef. SE z P-val Kendall tau SE
#> factor(adult)1 0.9117633 0.4000030 2.279391 0.02264381 0.3131310 0.09435851
#> factor(adult)2 1.0570600 0.7014182 1.507032 0.13180233 0.3457767 0.15010636
#>
#> $type
#> NULL
#>
#> attr(,"class")
#> [1] "summary.mets.twostage"