twostep_SurvSurv: Fit survival-survival copula submodel with two-step estimator

Description

The twostep_SurvSurv() function fits the copula (sub)model for a time-to-event surrogate and true endpoint with a two-step estimator. In the first step, the marginal distribution parameters are estimated through maximum likelihood. In the second step, the copula parameter is estimate while holding the marginal distribution parameters fixed.

Usage

twostep_SurvSurv(
  X,
  delta_X,
  Y,
  delta_Y,
  copula_family,
  n_knots,
  method = "BFGS"
)

Value

A list with three elements:

ml_fit: object of class maxLik::maxLik that contains the estimated copula model.
marginal_S_dist: object of class fitdistrplus::fitdist that represents the marginal surrogate distribution.
copula_family: string that indicates the copula family

Arguments

X

(numeric) Possibly right-censored time-to-surrogate event

delta_X

(integer) Surrogate event indicator:

1L if surrogate event ocurred.
0L if censored.

Y

(numeric) Possibly right-censored time-to-true endpoint event

delta_Y

(integer) True endpoint event indicator:

1L if true endpoint event ocurred.
0L if censored.

copula_family

Copula family, one of the following:

"clayton"
"frank"
"gumbel"
"gaussian"

n_knots

Number of internal knots for the Royston-Parmar survival models for \(\tilde{S}_0\), \(T_0\), \(\tilde{S}_1\), and \(T_1\). If length(n_knots) == 1, the same number of knots are assumed for the four marginal distributions.

method

Optimization algorithm for maximizing the objective function. For all options, see ?maxLik::maxLik. Defaults to "BFGS".