Twostage survival model fitted by pseudo MLE

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

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).

Author

Thomas Scheike

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"