\name{snp.imputation}
\alias{snp.imputation}
\title{Calculate imputation rules}
\description{
  Given two set of SNPs typed in the same subjects, this function
  calculates rules which can be used to impute one set
  from the other in a subsequent sample.
}
\usage{
snp.imputation(X, Y, pos.X, pos.Y, phase=FALSE, try=50, stopping=c(0.95, 4, 0.05),
               use.hap=c(0.95, 0.1), em.cntrl=c(50,0.01), minA=5)
}
\arguments{
  \item{X}{An object of class \code{"chopsticks"} or
    \code{"X.snp.matrix"} containing observations
    of the SNPs to be used for imputation ("regressor SNPs")}
  \item{Y}{An object of same class as \code{X} containing observations
  of the SNPs to be imputed in a future sample ("target SNPs")}
  \item{pos.X}{The positions of the regressor SNPs}
  \item{pos.Y}{The positions of the target SNPs}
  \item{phase}{See "Details" below}
  \item{try}{The number of potential regressor SNPs to be
    considered in the stepwise regression procedure around each target
    SNP . The nearest \code{try} regressor SNPs to each target SNP
    will be considered}
  \item{stopping}{Parameters of the stopping rule for the stepwise
    regression (see below)}
  \item{use.hap}{Parameters to control use of the haplotype imputation
    method (see below)}
  \item{em.cntrl}{Parameters to control test for convergence of EM
    algorithm for fitting phased haplotypes (see below)}
  \item{minA}{A minimum data quantity measure for estimating pairwise
    linkage disequilibrium (see below)}
}
\details{
  The routine first carries out a series of step-wise regression analyses in
  which each Y SNP is regressed on the nearest \code{try} regressor (X)
  SNPs. If
  \code{phase} is \code{TRUE}, the regressions will be calculated at the
  chromosome (haplotype) level, variances being simply  \eqn{p(1-p)} and
  covariances estimated 
  using the same algorithm used in \code{\link{ld.snp}} (this option is
  not yet implemented). Otherwise, the
  analysis is carried out at the genotype level based on  
  conventional variance and covariance estimates using the
  \code{"pairwise.complete.obs"} missing value treatment
  (see \code{\link{cov}}). New
  SNPs are added to the regression until either (a) the value of
  \eqn{R^2} exceeds the first parameter of \code{stopping}, (b) the
  number of "tag" SNPs has reached the maximum set in the second parameter of
  \code{stopping}, or (c) the change in \eqn{R^2} does not achieve the
  target set by the third parameter of \code{stopping}. If the third
  parameter of \code{stopping} is \code{NA}, this last test is replaced
  by a test for improvement in the Akaike information criterion (AIC). 

  If the prediction  as measure by  \eqn{R^2}, has not achieved a
  threshold (the first parameter of \code{use.hap})
  using more than one tag SNP, then a second imputation method is
  tried. Phased
  haplotype frequencies are estimated for the Y SNP plus the
  tag SNPs. The  \eqn{R^2} for prediction of the Y SNP using these
  haplotype frequencies is then calculated. If the \eqn{(1-R^2)} is reduced
  by a proportion exceeding the second parameter of \code{use.hap}, then
  the haplotype imputation rule is saved in preference to the faster
  regression rule. The argument \code{em.cntrl} controls convergence
  testing for the EM algorithm for fitting haplotype frequencies. The
  first parameter is the maximum number of iterations, and the second
  parameter is the threshold for the change in log likelihood
  below which the iteration is judged to have converged.

  All SNPs selected for imputation must have sufficient data for
  estimating pairwise linkage disequilibrium with each other and with
  the target SNP. The statistic chosen is based on the four-fold tables
  of two-locus haplotype frequencies. If the frequencies in such a table
  are labelled \eqn{a, b, c} and \eqn{d} then, if \eqn{ad>bc} then
  \eqn{t = min(a,d)} and, otherwise,  \eqn{t = min(b,c)}. The cell
  frequencies \eqn{t} must exceed \code{minA} for all pairwise
  comparisons.  
}
\value{
  An object of class
  \code{"snp.reg.imputation"}.
}
\references{
  Chapman J.M., Cooper J.D., Todd J.A. and Clayton D.G. (2003)
  \emph{Human Heredity}, \bold{56}:18-31.
}
\note{The \code{phase=TRUE} option is not yet implemented} 
\author{David Clayton \email{david.clayton@cimr.cam.ac.uk}}
\seealso{\code{\link{snp.reg.imputation-class}}, \code{\link{ld.snp}},
  \code{\link{imputation.maf}}, \code{\link{imputation.r2}}}
\examples{
# Remove 5 SNPs from a datset and derive imputation rules for them
library(chopsticks)
data(for.exercise)
sel <- c(20, 1000, 2000, 3000, 5000)
to.impute <- snps.10[,sel]
impute.from <- snps.10[,-sel]
pos.to <- snp.support$position[sel]
pos.fr <- snp.support$position[-sel]
imp <- snp.imputation(impute.from, to.impute, pos.fr, pos.to)
}
\keyword{models}
\keyword{regression}