CopulaREMADA (version 1.7.3)

imperfectCopulaREMADA: Maximum likelihood estimation of bivariate copula mixed models for meta-analysis of diagnostic accuracy studies without a gold standard

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

imperfectCopulaREMADA.norm(y11,y10,y01,y00,
gl,mgrid,qcond,tau2par,select.random,start)
                               
imperfectCopulaREMADA.beta(y11,y10,y01,y00,
gl,mgrid,qcond,tau2par,select.random,start)

Value

A list containing the following components:

LogLikelihood

the maximized log-likelihood

Estimates

the MLE

SE

the standard errors

Arguments

y11

the number of the test results where the index test outcome is positive and the reference test outcome is positive

y10

the number of the test results where the index test outcome is positive and the reference test outcome is negative

y01

the number of the test results where the index test outcome is negative and the reference test outcome is positive

y00

the number of the test results where the index test outcome is negative and the reference test outcome is negative

gl

a list containing the components of Gauss-Legendre nodes gl$nodes and weights gl$weights

mgrid

a list containing two matrices with the rows of the output matrix x are copies of the vector gl$nodes; columns of the output matrix y are copies of the vector gl$nodes

select.random

vector \((t_{1},t_{2})\), where \(1\leq t_1<t_2\leq 5\), that indicates the random effects

qcond

function for the inverse of conditional copula cdf

tau2par

function for maping Kendall's tau to copula parameter

start

starting values for the parameters

References

Nikoloulopoulos, A.K. (2024) Vine copula mixed models for meta-analysis of diagnostic accuracy studies without a gold standard. Submitted.

Examples

data(Pap)
attach(Pap)

nq=30
gl=gauss.quad.prob(nq,"uniform")
mgrid<- meshgrid(gl$n,gl$n)

tau2par=tau2par.bvn
qcond=qcondbvn

select.random=c(1,2)

start=c(rep(0.6,5),rep(0.5,2),-0.1)
est.norm=imperfectCopulaREMADA.norm(y11,y10,y01,y00,gl,mgrid,
qcond,tau2par,select.random,start)

detach(Pap)