sslcov: Semi-Supervised Estimation Of Covariance

#'Semi-supervised correlation estimation
#'
#'This function estimates the correlation between an outcome available only
#'for a small subset of the data and a covariate. The outcome is imputed to all
#'the data using a smoothed predictor learned thanks to a set of surrogate variables,
#'available for all the data.
#'
#'Smoothing over the CDF transformed data prevents some tail estimation issues when the new data are subsequently large.
#'
#'@param data the data. The first \code{nn} rows should be the labeled data, the
#'remaining rows should be the unlabeled data.
#'
#'@param nn the number of labeled data
#'
#'@param outcome_name a character string containing the name of the
#'column from data containing the partly missing outcome of interest
#'
#'@param covariate_name a character string containing the name of the
#'column from data containing the covariate to be related to the outcome of
#'interest
#'
#'@param surrogate_name a character string vector containing the name of the
#'column(s) from data containing the surrogate variable(s)
#'
#'@param bw the bandwidth to use
#'
#'@param cdf_trans a logical flag indicating wether the smoothing should be
#'performed on the data transformed with their cdf. Default is TRUE. See Details.
#'
#'@param weights a vector of weights in case a weighted version of the
#'correlation has to be computed. Default is \code{NULL}, in which case, no
#'additional weighting is done and regular perturbation is performed.
#'
#'@param ptb_beta logical flag indicating whether beta coefficient should be perturbed.
#'Dafault is \code{TRUE}.
#'
#'@param adjust_covariates_name optional vector of names of the covariates to adjust on during imputation and smoothing.
#'Default is \code{NULL}.
#'
#'@param do_interact logical flag indicating whether interactins between \code{x} and
#'covariates should be taken into account when imputing \code{y}. Default is \code{FALSE}.
#'
#'@param X perturbation index needed for sapply call. This is a purely artificial argument and is never
#'used in the functions (only needed for sapply to work). Default is \code{NULL}.
#'
#'@importFrom stats lm rbeta
#'
#'@return a list with the following elements:\itemize{
#'    \item rhat
#'    \item bw the bandwith used
#'    \item data_sup
#'    \item W_unlabel
#'    }
#'
#'
#'@seealso \code{\link{smooth_ssl}} \code{\link{rhat}}
#'
#'@export
rhat_ptb <- function(data, nn, outcome_name = NULL, covariate_name=NULL,
                     surrogate_name = NULL, bw, cdf_trans = TRUE,
                     weights = NULL, ptb_beta = TRUE, adjust_covariates_name = NULL,
                     do_interact = TRUE, X=NULL){

  outcome_colnum <- which(colnames(data)==outcome_name)
  NN <- nrow(data)
  stopifnot(length(weights)==nn)

  # compute the perturbation weights:
  #index = sample(1:nn,nn,replace=T)
  #Vij <- c(tabulate(index,nbins=nn),rep(1,NN-nn))
  Vij <-  rbeta(NN, 0.5, 1.5)*4 #does ptb_nolabel do anything?
  #Vij <- rexp(NN)
  #Vij <- c(rbeta(nn, 0.5, 1.5)*4, rep(1,NN-nn))

  if(is.null(weights)){
    weights <- rep(NN/nn, nn)
  }
  Vij_w <- Vij
  Vij_w[1:nn] <- Vij_w[1:nn]*weights
  Vi <- Vij_w[1:nn]
  

  #data_centered_ptb <- data[, covariate_name, drop=FALSE] - mean(data[, covariate_name]*Vij)/mean(Vij)
  data_centered_ptb <- data[, covariate_name, drop=FALSE] - mean(data[, covariate_name])
  data_all_ptb <- cbind(data[, outcome_colnum], data_centered_ptb, data[, surrogate_name])
  if(!is.null(adjust_covariates_name)){
    data_all_ptb <- cbind(data_all_ptb, data[, adjust_covariates_name])
  }
  if(do_interact){
    data_interact_ptb <- data_centered_ptb[, covariate_name]*data[, surrogate_name, drop=FALSE]
    data_all_ptb <- cbind(data_all_ptb, data_interact_ptb)
  }
  outcome_colnum <- 1
  covariate_colnum <- 2

  ncoef <- ncol(data_all_ptb)
  W_unlabel_ptb <- data_all_ptb[-(1:nn), -outcome_colnum]

  data_sup_ptb <- data_all_ptb[1:nn, ]
  
  yi_cen <- data_sup_ptb[, outcome_colnum] - mean(data_sup_ptb[, outcome_colnum]*Vi)/mean(Vi)
  
  ri_ptb <- yi_cen*data_sup_ptb[, covariate_colnum]
  rhat_ptb_sup <- mean(ri_ptb*Vi)/mean(Vi)
  
  if(ptb_beta){
    betptb <- lm(yi_cen~data_sup_ptb[, -outcome_colnum], weights=Vi)$coef[1:ncoef]
  }
  else{
    betptb <- lm(yi_cen ~ data_sup_ptb[, -outcome_colnum], weights = weights[1:nn])$coef[1:ncoef] #TODO ?
  }
  if(length(which(is.na(betptb)))>0){
    betptb[which(is.na(betptb))] <- 0 #TODO
  }
  fi_ptb <- c(cbind(1, data_sup_ptb[, -outcome_colnum])[, 1:ncoef]%*%betptb)*data_sup_ptb[, covariate_name]
  fj_ptb <- c(cbind(1, W_unlabel_ptb)%*%betptb)*W_unlabel_ptb[, covariate_name]
  ptb_ssl <- smooth_sslCPP(ri=ri_ptb, fi=fi_ptb, fnew=fj_ptb, rsup=rhat_ptb_sup, wgt=Vij_w, bw=bw, cdf_trans=cdf_trans)
  #rptb.ssl = mean(Vj*npreg(bws=bw,txdat=fi_ptb,tydat=ri_ptb*Vi,exdat=fj_ptb)$mean/
  #                  npreg(bws=bw,txdat=fi_ptb,tydat=Vi,exdat=fj_ptb)$mean,na.rm=T)/mean(Vj)
  return(c("Supervised"=rhat_ptb_sup,
           "NoSmooth"=mean(c(fi_ptb,fj_ptb)),
           "SemiSupervised"=ptb_ssl[1],
           "SemiSupervisedBC"=ptb_ssl[2])
  )
}