## Simulation from copula mixed models for diagnostic test accuaracy studies

### Description

To simulate the data we have used the following steps:

1. Simulate the study size n from a shifted gamma distribution with parameters \alpha=1.2,\beta=0.01,lag=30 and round off to the nearest integer.

2. Simulate (u_1,u_2) from a parametric family of copulas 'cop'.

3. Convert to beta realizations or normal realizations.

4. Draw the number of diseased n_1 from a B(n,0.43) distribution.

5. Set n_2=n-n_1, y_j=n_jx_j and then round y_j for j=1,2.

### Usage

rCopulaREMADA.norm(N,p,si,tau,rcop,tau2par)


### Arguments

 N sample size p Pair (\pi_1,\pi_2) of sensitivity/specificity si Pair (\sigma_1,\sigma_2) of variability; normal margins g Pair (\gamma_1,\gamma_2) of variability; beta margins tau Kendall's tau value rcop function for copula generation tau2par function for mapping from Kendall's tau to copula parameter

### Value

A list containing the following simulated components:

 TP the number of true positives FN the number of false negatives FP the number of false positives TN the number of true negatives

### References

Nikoloulopoulos, A.K. (2015) A mixed effect model for bivariate meta-analysis of diagnostic test accuracy studies using a copula representation of the random effects distribution. Statistics in Medicine, 34, 3842–3865. doi:10.1002/sim.6595.

CopulaREMADA rcop

### Examples

nq=15
mgrid<- meshgrid(gl$n,gl$n)

N=20
tau=-0.5
p=c(0.7,0.9)
g=c(0.2,0.1)
TP=simDat$TP TN=simDat$TN
FP=simDat$FP FN=simDat$FN
TP=simDat$TP TN=simDat$TN
FP=simDat$FP FN=simDat$FN