ic_par_copula: Copula regression models with parametric margins for...

Description Usage Arguments Details Value Source Examples

View source: R/ic_par_copula.R

Description

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

Usage

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

Arguments

data

a data frame; must have id (subject id), ind (1,2 for two units in each subject), Left (0 if left-censoring), Right (Inf if right-censoring), status (0 for right-censoring, 1 for interval-censoring or left-censoring), and covariates by column.

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 "Newton"; default is 300.

stepsize

size of optimization step when method is "Newton"; default is 1e-5.

hes

default is TRUE for hessian calculation.

control

a list of control parameters for methods other than "Newton"; see ?optim.

Details

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).

Value

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.

Source

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.

Examples

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# fit a Copula2-Weibull model
data(AREDS)
copula2_wb <- ic_par_copula(data = AREDS, copula = "Copula2",
                  m.dist = "Weibull",
                  var_list = c("ENROLLAGE","rs2284665"))
summary(copula2_wb)

CopulaCenR documentation built on March 1, 2021, 5:06 p.m.