VineCopulaREMADA: Maximum likelhood estimation for (truncated) vine copula...

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

Maximum likelhood estimation for (truncated) vine copula mixed models for diagnostic test accurracy studies accounting for disease prevalence and non-evaluable outcomes

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

VineCopulaREMADA.norm(TP,FN,FP,TN,gl,mgrid,
                               qcondcop12,qcondcop13,qcondcop23,
                               tau2par12,tau2par13,tau2par23,
                               NEP,NEN)
VineCopulaREMADA.beta(TP,FN,FP,TN,gl,mgrid,
                               qcondcop12,qcondcop13,qcondcop23,
                               tau2par12,tau2par13,tau2par23,
                               NEP,NEN)
tVineCopulaREMADA.norm(TP,FN,FP,TN,gl,mgrid,
                               qcondcop12,qcondcop13,
                               tau2par12,tau2par13,
                               NEP,NEN)
tVineCopulaREMADA.beta(TP,FN,FP,TN,gl,mgrid,
                               qcondcop12,qcondcop13,
                               tau2par12,tau2par13,
                               NEP,NEN)

Arguments

TP	the number of true positives
FN	the number of false negatives
FP	the number of false positives
TN	the number of true negatives
gl	a list containing the components of Gauss-Legendre nodes gl$nodes and weights gl$weights
mgrid	a list containing three-dimensional arrays. Replicates of the quadrature points that produce a 3-dimensional full grid
qcondcop12	function for the inverse of conditional copula cdf at the (1,2) bivariate margin
qcondcop13	function for the inverse of conditional copula cdf at the (1,3) bivariate margin
qcondcop23	function for the inverse of conditional copula cdf at the (2,3|1) bivariate margin
tau2par12	function for maping Kendall's tau at the (1,2) bivariate margin to copula parameter
tau2par13	function for maping Kendall's tau at the (1,3) bivariate margin to copula parameter
tau2par23	function for maping Kendall's tau at the (2,3|1) bivariate margin to the conditional copula parameter
NEP	the number of non-evaluable positives in the presence of non-evaluable subjects
NEN	the number of non-evaluable negatives in the presence of non-evaluable subjects

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. (2017) A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence. Statistical Methods in Medical Research, 26, 2270–2286. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/0962280215596769")}.

Nikoloulopoulos, A.K. (2020) An extended trivariate vine copula mixed model for meta-analysis of diagnostic studies in the presence of non-evaluable outcomes. The International Journal of Biostatistics, 16(2). \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1515/ijb-2019-0107")}.

See Also

rVineCopulaREMADA

Examples

nq=15
gl=gauss.quad.prob(nq,"uniform")
mgrid=meshgrid(gl$n,gl$n,gl$n,nargout=3)

data(OGT)
attach(OGT)
out=tVineCopulaREMADA.norm(TP,FN,FP,TN,gl,mgrid,
qcondbvn,qcondbvn,tau2par.bvn,tau2par.bvn)
detach(OGT)
############################################
# In the precence of non-evaluable results #
data(coronary)
attach(coronary)
out=tVineCopulaREMADA.norm(TP,FN,FP,TN,gl,mgrid,
qcondbvn,qcondbvn,tau2par.bvn,tau2par.bvn,NEP,NEN)
detach(coronary)

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