\name{epi.occc}

\alias{epi.occc}
\alias{print.epi.occc}
\alias{summary.epi.occc}

\title{
Overall concordance correlation coefficient (OCCC)
}

\description{
Overall concordance correlation coefficient (OCCC) for agreement on a continuous measure based on Lin (1989, 2000) and Barnhart et al. (2002).
}

\usage{
epi.occc(dat, na.rm = FALSE, pairs = FALSE)

\method{print}{epi.occc}(x, ...)

\method{summary}{epi.occc}(object, ...)
}

\arguments{
  \item{dat}{a matrix, or a matrix like object. Rows correspond to cases/observations, columns corresponds to raters/variables.}
  \item{na.rm}{logical. Should missing values (including \code{NaN}) be removed?}
  \item{pairs}{logical. Should the return object contain pairwise statistics? See Details.}
  \item{x, object}{an object of class \code{epi.occc}.}
  \item{\dots}{further arguments passed to \code{print} methods.}
}

\details{
The index proposed by Barnhart et al. (2002) is the same as the index suggested by Lin (1989) in the section of future studies with a correction of a typographical error in Lin (2000).
}

\value{
An object of class \code{epi.occc} with the following list elements (notation follows Barnhart et al. 2002):

\itemize{
  \item{\code{occc}: }{the value of the overall concordance correlation coefficient (\eqn{\rho_{o}^{c}}{rho.o^c}),}
  \item{\code{oprec}: }{overall precision (\eqn{\rho}{rho}),}
  \item{\code{oaccu}: }{overall accuracy (\eqn{\chi^{a}}{chi^a}),}
  \item{\code{pairs}: }{a list with following elements (only if \code{pairs = TRUE}, otherwise \code{NULL};
    column indices for the pairs (j,k) follow lower-triangle column-major rule
    based on a \code{ncol(x)} times \code{ncol(x)} matrix),
    \itemize{
        \item{\code{ccc}: }{pairwise CCC values (\eqn{\rho_{jk}^{c}}{rho_jk^c}),}
        \item{\code{prec}: }{pairwise precision values (\eqn{\rho_{jk}}{rho_jk}),}
        \item{\code{accu}: }{pairwise accuracy values (\eqn{\chi_{jk}^{a}}{chi_jk^a}),}
        \item{\code{ksi}: }{pairwise weights (\eqn{\xi_{jk}}{ksi_jk}),}
        \item{\code{scale}: }{pairwise scale values (\eqn{v_{jk}}{v_jk}),}
        \item{\code{location}: }{pairwise location values (\eqn{u_{jk}}{u_jk}),}
    }
  }
  \item{\code{data.name}: }{name of the input data \code{dat}.}
}
}

\references{
Barnhart H X, Haber M, Song J (2002). Overall concordance correlation coefficient for evaluating agreement among multiple observers. Biometrics 58: 1020 - 1027.

Lin L (1989). A concordance correlation coefficient to evaluate reproducibility. Biometrics 45: 255 - 268.

Lin L (2000). A note on the concordance correlation coefficient. Biometrics 56: 324 - 325.
}

\seealso{
  \code{\link[epiR]{epi.ccc}}
}

\author{
Peter Solymos, solymos@ualberta.ca.
}

\examples{
## Generate some artificial ratings data:
set.seed(1234)
p <- runif(10, 0, 1)
x <- replicate(n = 5, expr = rbinom(10, 4, p) + 1)

rval <- epi.occc(dat = x, pairs = TRUE)
print(rval); summary(rval)

}
\keyword{htest}
