Description Usage Arguments Details Value Source Examples

View source: R/ic_par_copula.R

Fits a copula model with parametric margins for bivariate interval-censored data.

1 2 3 | ```
ic_par_copula(data, var_list, copula, m.dist = "Weibull",
method = "BFGS", iter = 300, stepsize = 1e-05, hes = TRUE,
control = list())
``` |

`data` |
a data frame; must have |

`var_list` |
the list of covariates to be fitted into the copula model. |

`copula` |
Types of copula model. |

`m.dist` |
baseline marginal distribution. |

`method` |
optimization method (see ?optim); default is "BFGS"; also can be "Newton" (see ?nlm). |

`iter` |
number of iterations when method is |

`stepsize` |
size of optimization step when method is |

`hes` |
default is |

`control` |
a list of control parameters for methods other than |

The input data must be a data frame. with columns `id`

(sample id),
`ind`

(1,2 for the two units from the same id),
`Left`

(0 if left-censoring), `Right`

(Inf if right-censoring),
`status`

(0 for right-censoring, 1 for interval-censoring or left-censoring),
and `covariates`

. The function does not allow `Left`

== `Right`

.

The supported copula models are `"Clayton"`

, `"Gumbel"`

, `"Frank"`

,
`"AMH"`

, `"Joe"`

and `"Copula2"`

.
The `"Copula2"`

model is a two-parameter copula model that incorporates `Clayton`

and `Gumbel`

as special cases.
The parametric generator functions of copula functions are list below:

The Clayton copula has a generator

*φ_{η}(t) = (1+t)^{-1/η},*

with *η > 0* and Kendall's *τ = η/(2+η)*.

The Gumbel copula has a generator

*φ_{η}(t) = \exp(-t^{1/η}),*

with *η ≥q 1* and Kendall's *τ = 1 - 1/η*.

The Frank copula has a generator

*φ_{η}(t) = -η^{-1}\log \{1+e^{-t}(e^{-η}-1)\},*

with *η ≥q 0* and Kendall's *τ = 1+4\{D_1(η)-1\}/η*,
in which *D_1(η) = \frac{1}{η} \int_{0}^{η} \frac{t}{e^t-1}dt*.

The AMH copula has a generator

*φ_{η}(t) = (1-η)/(e^{t}-η),*

with *η \in [0,1)* and Kendall's *τ = 1-2\{(1-η)^2 \log (1-η) + η\}/(3η^2)*.

The Joe copula has a generator

*φ_{η}(t) = 1-(1-e^{-t})^{1/η},*

with *η ≥q 1* and Kendall's *τ = 1 - 4 ∑_{k=1}^{∞} \frac{1}{k(η k+2)\{η(k-1)+2\}}*.

The Two-parameter copula (Copula2) has a generator

*φ_{η}(t) = \{1/(1+t^{α})\}^{κ},*

with *α \in (0,1], κ > 0* and Kendall's *τ = 1-2ακ/(2κ+1)*.

The supported marginal distributions are `"Weibull"`

(proportional hazards),
`"Gompertz"`

(proportional hazards) and `"Loglogistic"`

(proportional odds).
These marginal distributions are listed below
and we assume the same baseline parameters between two margins.

The Weibull (PH) survival distribution is

*\exp \{-(t/λ)^k e^{Z^{\top}β}\},*

with *λ > 0* as scale and *k > 0* as shape.

The Gompertz (PH) survival distribution is

*\exp \{-\frac{b}{a}(e^{at}-1) e^{Z^{\top}β}\},*

with *a > 0* as shape and *b > 0* as rate.

The Loglogistic (PO) survival distribution is

*\{1+(t/λ)^{k} e^{Z^{\top}β} \}^{-1},*

with *λ > 0* as scale and *k > 0* as shape.

Optimization methods can be all methods (except `"Brent"`

) from `optim`

, such as
`"Nelder-Mead"`

, `"BFGS"`

, `"CG"`

, `"L-BFGS-B"`

, `"SANN"`

.
Users can also use `"Newton"`

(from `nlm`

).

a `CopulaCenR`

object summarizing the model.
Can be used as an input to general `S3`

methods including
`summary`

, `print`

, `plot`

, `lines`

,
`coef`

, `logLik`

, `AIC`

,
`BIC`

, `fitted`

, `predict`

.

Tao Sun, Yi Liu, Richard J. Cook, Wei Chen and Ying Ding (2019).
Copula-based Score Test for Bivariate Time-to-event Data,
with Application to a Genetic Study of AMD Progression.
*Lifetime Data Analysis* 25(3), 546-568.

Tao Sun and Ying Ding (In Press).
Copula-based Semiparametric Regression Model for Bivariate Data
under General Interval Censoring.
*Biostatistics*. DOI: 10.1093/biostatistics/kxz032.

1 2 3 4 5 6 |

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