#' Compute FDR for given F statistics based on true and
#' null dataset
#' 
#' @param df_out data frame containing results from analysis by
#' fitAndEvalDataset
#' @param df_null data frame containing results from analysis by
#' bootstrapNull
#' 
#' @return data frame annotating each protein with a FDR based on 
#' it's F statistic and number of observations
#' 
#' @examples 
#' data("simulated_cell_extract_df")
#' temp_df <- simulated_cell_extract_df %>% 
#'   filter(clustername %in% paste0("protein", 1:5)) %>% 
#'   group_by(representative) %>% 
#'   mutate(nObs = n()) %>% 
#'   ungroup 
#' example_out <- fitAndEvalDataset(temp_df)
#' example_null <- bootstrapNull(temp_df, B = 2/10)
#' computeFdr(example_out, example_null)
#'  
#' @export
#'
#' @import dplyr
computeFdr <- function(df_out, df_null){

    dataset <- nObs <- nObsRound <- F_statistic <- 
        is_decoy <- max_rank <- true_cumsum <- 
        null_cumsum <- representative <- clustername <- 
        dataset <- fdr <- NULL

    B <- max(as.numeric(
        gsub("bootstrap_", "", unique(df_null$dataset))))
  
    nrow_out <- nrow(df_out)
    out_df <- bind_rows(df_out %>% mutate(dataset = "true"),
                        df_null) %>%
        mutate(nObsRound = round(nObs/10)*10) %>%
        group_by(nObsRound) %>%
        arrange(desc(F_statistic)) %>%
        mutate(max_rank = n(),
               rank = dense_rank(desc(F_statistic)),
               is_decoy = ifelse(dataset != "true", 1, 0)) %>%
        mutate(true_cumsum = cumsum(!is_decoy),
               null_cumsum = cumsum(is_decoy)/(B/10)) %>% 
        mutate(pi = (nrow_out-true_cumsum)/(nrow_out-null_cumsum)) %>% 
        mutate(fdr = pi * null_cumsum/true_cumsum) %>% 
        ungroup()
    
    return(out_df)
}

#' Find hits according to FDR threshold
#' 
#' @param fdr_df data frame obtained from computeFdr
#' @param alpha significance threshold, default is set to 0.1
#' 
#' @return data frame of significant hits at FDR = alpha
#' 
#' @examples 
#' data("simulated_cell_extract_df")
#' temp_df <- simulated_cell_extract_df %>% 
#'   filter(clustername %in% paste0("protein", 1:5)) %>% 
#'   group_by(representative) %>% 
#'   mutate(nObs = n()) %>% 
#'   ungroup 
#' example_out <- fitAndEvalDataset(temp_df)
#' example_null <- bootstrapNull(temp_df, B = 2/10)
#' fdr_df <- computeFdr(example_out, example_null)
#' findHits(fdr_df, 0.1)
#' 
#' @export
#' 
#' @import dplyr
findHits <- function(fdr_df, alpha){
  
  nObsRound <- fdr <- max_rank_fdr <- 
    dataset <- min_rank_true <- NULL
  
  hits_df <- fdr_df %>% 
    group_by(nObsRound) %>% 
    mutate(min_rank_true = min(rank[dataset == "true"])) %>% 
    filter(rank >= min_rank_true) %>% 
    mutate(max_rank_fdr = min(rank[fdr > alpha], na.rm = TRUE)) %>% 
    filter(rank < max_rank_fdr) %>% 
    filter(dataset == "true") %>% 
    ungroup()
  
  return(hits_df)
}