Project: s41467-024-45838-3 | Function: RemoveDissimilarLipidsPcor (r)

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Complete the masked function based on the algorithm description.
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**DESCRIPTION:** Identifies and iteratively removes discordant lipid species between datasets based on partial correlation distance measures. Uses median absolute deviation thresholds for outlier detection.

**KEY TERMS:** {
  "pcor_dist": "partial correlation distance",
  "mat1/mat2": "reference and target datasets",
  "med_x_var": "median + k*MAD threshold",
  "frobenius_ave": "average Frobenius distance"
}

**CONTEXT CODE:** library("corpcor")

##############################################################################
##
##  Load saved working datasets 
##
##############################################################################

## Load saved composite datasets
ausdb_composite <- readRDS("data_derived/Ausdiab_composite_working_data_log_scale.rds") # reference data frame. variables: id, age, sex, bmi, chol_treat, 829 lipid species
lipid_composite <- readRDS("data_derived/LIPID_composite_working_data_log_scale.rds") # target data frame. variables: id, age, sex, bmi, treat_12, 307 lipid species

## Load splits of composite analysis lipid names 
Ausdiab_LIPID_lipid_names_collection <- readRDS('data_derived/Ausdiab_LIPID_lipid_names_collection.rds')

## Select matching variables needed here
ausdb307 <- ausdb_composite %>% select(id, all_of(Ausdiab_LIPID_lipid_names_collection$matching_307c))
lipid307 <- lipid_composite %>% select(id, all_of(Ausdiab_LIPID_lipid_names_collection$matching_307c))

## Make matrices for glmnet
ausdb307_mat <- as.matrix(ausdb307[,-1])
lipid307_mat <- as.matrix(lipid307[,-1])



###############################################################################
##
## Remove discrepant lipids between two datasets one-by-one based on differences 
## in their Partial correlation vectors. Run pcor after every removal, remove
## the most discrepant lipid, stop when there's no apparent outliers (3sd, 3mad)
##
###############################################################################


## Make a function for this task --------------------------------------------##

#' Identify and iteratively remove discordant lipid species based on partial correlations
#' 
#' @param mat1 Reference dataset matrix
#' @param mat2 Target dataset matrix
#' @param FUN Outlier detection function
#' @param num Threshold multiplier for outlier detection
#' @return List containing:
#'   - frobenius_ave: Series of average Frobenius distances after each exclusion
#'   - pcor_dist_series: Element-wise partial correlation differences
#'   - excluded: Vector of removed lipid names
#' @examples
#' # Usage: lipid_results <- RemoveDissimilarLipidsPcor(ausdb307_mat, lipid307_mat, mad, 3)
#' 
#' @export
RemoveDissimilarLipidsPcor <- function(mat1, mat2, FUN, num) {
  stop("Function implementation has been masked")
  # Validate inputs
  if (!identical(dim(mat1), dim(mat2)))
    stop("mat1 and mat2 must have same dimensions")

  n_cols <- ncol(mat1)

  # Return empty list for 0-1 columns
  if (n_cols <= 1) {
    return(list(
      frobenius_ave = numeric(0), 
      pcor_dist_series = list(),
      excluded = character()
    ))
  }

  # Compute initial partial correlations
  requireNamespace("corpcor", quietly = TRUE)
  pcor1 <- tryCatch(
    pcor.shrink(mat1, lambda = 0),
    error = function(e) stop("Partial correlation computation failed for mat1")
  )$cors
  pcor2 <- tryCatch(
    pcor.shrink(mat2, lambda = 0),
    error = function(e) stop("Partial correlation computation failed for mat2")
  )$cors

  # Set diagonal to 0 (as seen in example code)
  diag(pcor1) <- 0
  diag(pcor2) <- 0

  # Calculate initial differences and threshold
  initial_diff <- abs(pcor1 - pcor2)
  threshold <- num * do.call(FUN, list(initial_diff))
  warning(sprintf("Removal threshold set to: %.4f", threshold))

  # Initialize tracking variables
  frob_history <- numeric(0)
  pcor_diffs <- list()
  excluded_varnames <- character()
  var_id_to_name <- NULL

  # Helper to compute Frobenius norm
  compute_frobenius <- function(pcor1, pcor2) {
    as.numeric(norm(pcor1 - pcor2, type = "Frobenius"))
  }

  # Recursive removal process
  remove_one <- function(mat1, mat2, threshold, max_removals) {
    if (ncol(mat1) <= 1 || is.null(threshold) || max_removals <= 0)
      return(NULL)

    # Compute partial correlations
    pcor1 <- tryCatch(
      pcor.shrink(mat1, lambda = 0),
      error = function(e) stop("Partial correlation failed during iteration")
    )$cors
    pcor2 <- tryCatch(
      pcor.shrink(mat2, lambda = 0),
      error = function(e) stop("Partial correlation failed during iteration")
    )$cors

    diag(pcor1) <- 0
    diag(pcor2) <- 0

    # Record current state
    current_frob <- compute_frobenius(pcor1, pcor2)
    frob_history <<- c(frob_history, current_frob)

    # Compute column differences
    col_diffs <- numeric(ncol(pcor1))
    for(i in 1:ncol(pcor1)) {
      col_diffs[i] <- max(abs(pcor1[i, ] - pcor2[i, ]))
    }

    # Add to difference series (using list preserves structure)
    pcor_diffs <<- c(pcor_diffs, list(col_diffs))

    # Find candidate columns to remove
    max_diff_col <- which.max(col_diffs)
    cand_max_diff <- col_diffs[max_diff_col]

    # Only proceed if exceeds initial threshold
    if (cand_max_diff < threshold) {
      warning(sprintf("No more columns exceed threshold (%.4f)", threshold))
      return(NULL)
    }

    # Name resolution (first-time only)
    static <- !all(names(col_diffs) %in% names(pcor_diffs))
    if (any(static)) {
      var_id_to_name <- unlist(lapply(slot(mat1@Dimnames[[2]], "names"), paste)
      # Replace NULL names with empty strings
      namewise <<- if(all(namewise)) NULL else sapply(var_id_to_name, 
        function(x) if(is.null(x)) "" else x)
    }

    # Get actual variable name (resolve names if it's the first such event)
    cand_name <- if(is.null(var_id_to_name)) 


Complete the function implementation replacing "stop("Not implemented")".