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Twostage Survival Model Fitted by Pseudo MLE

Source: R/twostage.R
twostageMLE.Rd

Fits Clayton-Oakes clustered survival data using marginals that are on Cox form in the likelihood for the dependence parameter as in Glidden (2000).

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 could be a (pairs) \(\times\) (number of parameters) \(\times\) (max number random effects) matrix.

Link function for variance; if 1 then uses exponential link.

method

Type of optimizer; 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.

Value

An object of class "mets.twostage" containing:

theta

Estimated dependence parameters.

coef

Coefficients.

var.theta

Variance of theta parameters.

robvar.theta

Robust variance of theta parameters.

theta.iid

Influence functions for theta.

theta.iid.naive

Naive influence functions for theta.

loglike

Log-likelihood value.

Details

The dependence can be modelled via a regression structure for the independent 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 exponential when var.link=1.

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.

  • Glidden (2000), A Two-Stage estimator of the dependence parameter for the Clayton Oakes model, LIDA.

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"