quadVineCopulaREMADA: Maximum likelihood estimation of quadrivariate D-vine copula...

In CopulaREMADA: Copula Mixed Models for Multivariate Meta-Analysis of Diagnostic Test Accuracy Studies

Maximum likelihood estimation of quadrivariate D-vine copula mixed models for joint meta-analysis and comparison of two diagnostic tests

Description

The estimated parameters can be obtained by using a quasi-Newton method applied to the logarithm of the joint likelihood. This numerical method requires only the objective function, i.e., the logarithm of the joint likelihood, while the gradients are computed numerically and the Hessian matrix of the second order derivatives is updated in each iteration. The standard errors (SE) of the ML estimates can be also obtained via the gradients and the Hessian computed numerically during the maximization process.

Usage

quadVineCopulaREMADA.norm(TP1,FN1,FP1,TN1,TP2,FN2,FP2,TN2,
                               gl,mgrid,qcond1,pcond1,tau2par1,
                               qcond2,pcond2,tau2par2)
                               
quadVineCopulaREMADA.beta(TP1,FN1,FP1,TN1,TP2,FN2,FP2,TN2,
                               gl,mgrid,qcond1,pcond1,tau2par1,
                               qcond2,pcond2,tau2par2) 
quadVineCopulaREMADA.norm.beta(TP1,FN1,FP1,TN1,TP2,FN2,FP2,TN2,
                               gl,mgrid,qcond1,pcond1,tau2par1,
                               qcond2,pcond2,tau2par2)              

Arguments

TP1	the number of true positives for test 1
FN1	the number of false negatives for test 1
FP1	the number of false positives for test 1
TN1	the number of true negatives for test 1
TP2	the number of true positives for test 2
FN2	the number of false negatives for test 2
FP2	the number of false positives for test 2
TN2	the number of true negatives for test 2
gl	a list containing the components of Gauss-Legendre nodes gl$nodes and weights gl$weights
mgrid	a list containing four-dimensional arrays. Replicates of the quadrature points that produce a 4-dimensional full grid
qcond1	function for the inverse conditional copula cdf at the (1,2) bivariate margin
pcond1	function for the conditional copula cdf at the (1,2) bivariate margin
tau2par1	function for maping Kendall's tau at the (1,2) bivariate margin to copula parameter
qcond2	function for the inverse conditional copula cdf at the (3,4) bivariate margin
pcond2	function for the conditional copula cdf at the (3,4) bivariate margin
tau2par2	function for maping Kendall's tau at the (3,4) bivariate margin to copula parameter

Value

A list containing the following components:

minimum	the value of the estimated minimum of the negative log-likelihood
estimate	the MLE
gradient	the gradient at the estimated minimum of of the negative log-likelihood
hessian	the hessian at the estimated minimum of the negative log-likelihood
code	an integer indicating why the optimization process terminated
iterations	the number of iterations performed

For more details see nlm

References

Nikoloulopoulos, A.K. (2019) A D-vine copula mixed model for joint meta-analysis and comparison of diagnostic tests. Statistical Methods in Medical Research, 28(10-11):3286–3300. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/0962280218796685")}.

Examples

nq=15
gl=gauss.quad.prob(nq,"uniform")
data(mgrid15)

data(arthritis)
attach(arthritis)

qcond1=qcondcln270
pcond1=pcondcln270
tau2par1=tau2par.cln270

qcond2=qcondfrk
pcond2=pcondfrk
tau2par2=tau2par.frk

out<-quadVineCopulaREMADA.norm(TP1,FN1,FP1,TN1,TP2,FN2,FP2,TN2,
gl,mgrid15,qcond1,pcond1,tau2par1,qcond2,pcond2,tau2par2)

detach(arthritis)

CopulaREMADA documentation built on Oct. 18, 2024, 1:08 a.m.