R/gtoxObjHill.R

In GladiaTOX: R Package for Processing High Content Screening data

#####################################################################
## This program is distributed in the hope that it will be useful, ##
## but WITHOUT ANY WARRANTY; without even the implied warranty of  ##
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the    ##
## GNU General Public License for more details.                    ##
#####################################################################

#-------------------------------------------------------------------------------
# gtoxObjHill: Generate a hill model objective function to optimize
#-------------------------------------------------------------------------------

#' @rdname Models
#'
#' @examples 
#' 
#' ## Load level 3 data for an assay endpoint ID
#' dat <- gtoxLoadData(lvl=3L, type="mc", fld="aeid", val=3L)
#' 
#' ## Compute fitting log-likelyhood
#' gtoxObjHill(c(rep(0,3), 1e-3), dat$logc, dat$resp)
#'
#' @section Hill Model (hill):
#' \code{gtoxObjHill} calculates the likelyhood for a 3 parameter Hill model
#' with the bottom equal to 0. The parameters passed to \code{gtoxObjHill} by
#' \code{p} are (in order) top (\eqn{\mathit{tp}}), log AC50 
#' (\eqn{\mathit{ga}}), hill coefficient (\eqn{\mathit{gw}}), and the scale 
#' term (\eqn{\sigma}). The hill model value \eqn{\mu_{i}}{\mu[i]} for the 
#' \eqn{i^{th}}{ith} observation is given by:
#' \deqn{
#' \mu_{i} = \frac{tp}{1 + 10^{(\mathit{ga} - x_{i})\mathit{gw}}}
#' }{
#' \mu[i] = tp/(1 + 10^(ga - x[i])*gw)}
#' where \eqn{x_{i}}{x[i]} is the log concentration for the \eqn{i^{th}}{ith}
#' observation.
#'
#' @importFrom stats dt
#' @export

gtoxObjHill <- function(p, lconc, resp) {

    ## This function takes creates an objective function to be optimized using
    ## the starting hill parameters, log concentration, and response.
    ##
    ## Arguments:
    ##   p:     a numeric vector of length 4 containg the starting values for
    ##          the hill model, in order: top, log AC50, hill
    ##          coefficient, and log error term
    ##   lconc: a numeric vector containing the log concentration values to
    ##          produce the objective function
    ##   lresp: a numeric vector containing the response values to produce the
    ##          objective function
    ##
    ## Value:
    ##   An objective function for the hill model and the given conc-resp data

    mu <- p[1]/(1 + 10^((p[2] - lconc)*p[3]))
    sum(dt((resp - mu)/exp(p[4]), df=4, log=TRUE) - p[4], na.rm=TRUE)

}

#-------------------------------------------------------------------------------