myTAI: Evolutionary Transcriptomics

#' @title Perform Reductive Early Conservation Test
#' @description The \emph{Reductive Early Conservation Test} aims to statistically evaluate the
#' existence of a monotonically increasing phylotranscriptomic pattern based on \code{\link{TAI}} or \code{\link{TDI}} computations.
#' The corresponding p-value quantifies the probability that a given TAI or TDI pattern (or any phylotranscriptomics pattern) 
#' does not follow an early conservation like pattern. A p-value < 0.05 indicates that the corresponding phylotranscriptomics pattern does
#' indeed follow an early conservation (low-high-high) shape.
#' @param ExpressionSet a standard PhyloExpressionSet or DivergenceExpressionSet object.
#' @param modules a list storing three elements: early, mid, and late. Each element expects a numeric
#' vector specifying the developmental stages or experiments that correspond to each module. 
#' For example, \code{module} = list(early = 1:2, mid = 3:5, late = 6:7) devides a dataset 
#' storing seven developmental stages into 3 modules.
#' @param permutations a numeric value specifying the number of permutations to be performed for the \code{ReductiveHourglassTest}.
#' @param lillie.test a boolean value specifying whether the Lilliefors Kolmogorov-Smirnov Test shall be performed to quantify the goodness of fit.
#' @param plotHistogram a boolean value specifying whether a \emph{Lillifor's Kolmogorov-Smirnov-Test} 
#' shall be performed to test the goodness of fit of the approximated distribution, as well as additional plots quantifying the significance
#' of the observed phylotranscriptomic pattern.
#' @param runs specify the number of runs to be performed for goodness of fit computations, in case \code{plotHistogram} = \code{TRUE}.
#' In most cases \code{runs} = 100 is a reasonable choice. Default is \code{runs} = 10 (because it takes less computation time for demonstration purposes).
#' @param parallel performing \code{runs} in parallel (takes all cores of your multicore machine).
#' @param gof.warning a logical value indicating whether non significant goodness of fit results should be printed as warning. Default is \code{gof.warning = FALSE}.
#' @param custom.perm.matrix a custom \code{\link{bootMatrix}} (permutation matrix) to perform the underlying test statistic. Default is \code{custom.perm.matrix = NULL}.
#' @details The \emph{reductive early conservation test} is a permutation test based on the following test statistic. 
#'
#' (1) A set of developmental stages is partitioned into three modules - early, mid, and late - based on prior biological knowledge.
#'
#' (2) The mean \code{\link{TAI}} or \code{\link{TDI}} value for each of the three modules T_early, T_mid, and T_late are computed. 
#'
#' (3) The two differences D1 = T_mid - T_early and D2 = T_late - T_early are calculated.
#'
#' (4) The minimum D_min of D1 and D2 is computed as final test statistic of the reductive hourglass test.
#'
#'
#' In order to determine the statistical significance of an observed minimum difference D_min 
#' the following permutation test was performed. Based on the \code{\link{bootMatrix}} D_min 
#' is calculated from each of the permuted \code{\link{TAI}} or \code{\link{TDI}} profiles, 
#' approximated by a Gaussian distribution with method of moments estimated parameters returned by \code{\link[fitdistrplus]{fitdist}}, 
#' and the corresponding p-value is computed by \code{\link{pnorm}} given the estimated parameters of the Gaussian distribution. 
#' The \emph{goodness of fit} for the random vector \emph{D_min} is statistically quantified by an Lilliefors (Kolmogorov-Smirnov) test 
#' for normality.
#'
#'
#' In case the parameter \emph{plotHistogram = TRUE}, a multi-plot is generated showing:
#'        
#' (1) A Cullen and Frey skewness-kurtosis plot generated by \code{\link[fitdistrplus]{descdist}}. 
#' This plot illustrates which distributions seem plausible to fit the resulting permutation vector D_min. 
#' In the case of the \emph{reductive early conservation test} a normal distribution seemed plausible.
#'
#' (2) A histogram of D_min combined with the density plot is plotted. D_min is then fitted by a normal distribution. 
#' The corresponding parameters are estimated by \emph{moment matching estimation} using the \code{\link[fitdistrplus]{fitdist}} function.
#'
#' (3) A plot showing the p-values for N independent runs to verify that a specific p-value is biased by a specific permutation order.
#'
#' (4) A barplot showing the number of cases in which the underlying goodness of fit (returned by Lilliefors (Kolmogorov-Smirnov) test 
#' for normality) has shown to be significant (\code{TRUE}) or not significant (\code{FALSE}). 
#' This allows to quantify the permutation bias and their implications on the goodness of fit.
#' @return a list object containing the list elements:
#' 
#' \code{p.value} : the p-value quantifying the statistical significance (low-high-high pattern) of the given phylotranscriptomics pattern.
#'
#' \code{std.dev} : the standard deviation of the N sampled phylotranscriptomics patterns for each developmental stage S.
#' 
#' \code{lillie.test} : a boolean value specifying whether the \emph{Lillifors KS-Test} returned a p-value > 0.05, 
#' which indicates that fitting the permuted scores with a normal distribution seems plausible.
#' 
#' @references 
#' 
#' Drost HG et al. (2015) \emph{Evidence for Active Maintenance of Phylotranscriptomic Hourglass Patterns in Animal and Plant Embryogenesis}. Mol Biol Evol. 32 (5): 1221-1231 doi:10.1093/molbev/msv012.
#'
#' Quint M et al. (2012). \emph{A transcriptomic hourglass in plant embryogenesis}. Nature (490): 98-101.
#' 
#' Piasecka B, Lichocki P, Moretti S, et al. (2013) \emph{The hourglass and the early conservation models co-existing
#' patterns of developmental constraints in vertebrates}. PLoS Genet. 9(4): e1003476.
#' 
#' @author Hajk-Georg Drost
#' @seealso \code{\link{ecScore}}, \code{\link{bootMatrix}}, \code{\link{FlatLineTest}},\code{\link{ReductiveHourglassTest}} , \code{\link{PlotPattern}}
#' @examples
#' 
#' data(PhyloExpressionSetExample)
#'
#' # perform the early conservation test for a PhyloExpressionSet
#' # here the prior biological knowledge is that stages 1-2 correspond to module 1 = early,
#' # stages 3-5 to module 2 = mid (phylotypic module), and stages 6-7 correspond to
#' # module 3 = late
#' EarlyConservationTest(PhyloExpressionSetExample,
#'                        modules = list(early = 1:2, mid = 3:5, late = 6:7), 
#'                        permutations = 1000)
#'
#' 
#' # use your own permutation matrix based on which p-values (EarlyConservationTest)
#' # shall be computed
#' custom_perm_matrix <- bootMatrix(PhyloExpressionSetExample,100)
#' 
#' EarlyConservationTest(PhyloExpressionSetExample,
#'                        modules = list(early = 1:2, mid = 3:5, late = 6:7), 
#'                        custom.perm.matrix = custom_perm_matrix)
#'                        
#' @import foreach
#' @export

EarlyConservationTest <- function(ExpressionSet,
                                  modules            = NULL,
                                  permutations       = 1000, 
                                  lillie.test        = FALSE, 
                                  plotHistogram      = FALSE, 
                                  runs               = 10, 
                                  parallel           = FALSE,
                                  gof.warning        = FALSE,
                                  custom.perm.matrix = NULL){
        
        is.ExpressionSet(ExpressionSet)
        
        if(is.null(modules))
                stop("Please specify the three modules: early, mid, and late using the argument 'module = list(early = ..., mid = ..., late = ...)'.", call. = FALSE)
        
        if(any(table(unlist(modules)) > 1))
                stop("Intersecting modules are not defined for the EarlyConservationTest.", call. = FALSE)
        
        if(length(modules) != 3)
                stop("Please specify three modules: early, mid, and late to perform the EarlyConservationTest.", call. = FALSE)
        
        if(length(unlist(modules)) != (dim(ExpressionSet)[2] - 2))
                stop("The number of stages classified into the three modules does not match the total number of stages stored in the given ExpressionSet.", call. = FALSE)
        
        
        nCols <- dim(ExpressionSet)[2]
        score_vector <- vector(mode = "numeric",length = permutations)
        resMatrix <- matrix(NA_real_, permutations,(nCols-2))
        real_age <- vector(mode = "numeric",length = nCols-2)
        real_age <- cpp_TAI(as.matrix(ExpressionSet[ , 3:nCols]),as.vector(ExpressionSet[ , 1]))
        
        # compute the real early conservation of the observed phylotranscriptomics pattern
        # ecScore = early conservation score
        real_ecv <- ecScore(real_age,early = modules[[1]],mid = modules[[2]],late = modules[[3]])
                
        ### compute the bootstrap matrix 
        if (is.null(custom.perm.matrix)){
                resMatrix <- cpp_bootMatrix(as.matrix(ExpressionSet[ , 3:nCols]),as.vector(ExpressionSet[ , 1]),as.numeric(permutations))
        }
        
        else if (!is.null(custom.perm.matrix)){
                resMatrix <- custom.perm.matrix
        }
        
        ### compute the global phylotranscriptomics destruction scores for each sampled age vector
        score_vector <- apply(resMatrix, 1 ,ecScore,early = modules[[1]],
                              mid = modules[[2]],late = modules[[3]])
        
        
        # parameter estimators using MASS::fitdistr
        param <- fitdistrplus::fitdist(score_vector,"norm", method = "mme")
        mu <- param$estimate[1]
        sigma <- param$estimate[2]
        
        if(plotHistogram){
                
                if(runs < 1)
                        stop("You need at least one run...")
                
                if(lillie.test)
                        graphics::par(mfrow = c(2,2))
                if(!lillie.test)
                        graphics::par(mfrow = c(1,3))
                
                fitdistrplus::descdist(score_vector, boot = permutations)
                
                # plot histogram of scores
                normDensity <- function(x){
                        
                        return(stats::dnorm(x,mu,sigma))
                        
                }
                
                graphics::curve( expr = normDensity,
                       xlim = c(min(score_vector),max(score_vector,real_ecv)),
                       col  = "steelblue",
                       lwd  = 5,
                       xlab = "Scores",
                       ylab = "Frequency" )
                
                graphics::hist( x      = score_vector,
                      prob   = TRUE,
                      add    = TRUE, 
                      breaks = permutations / (0.01 * permutations) )
                
                graphics::rug(score_vector)
                
                # plot a red line at the position where we can find the real ec value
                graphics::abline(v = real_ecv, lwd = 5, col = "darkred")
                
                #legend("topleft", legend = "A", bty = "n")
                
                p.vals_vec <- vector(mode = "numeric", length = runs)
                lillie_vec <- vector(mode = "logical", length = runs)
                ect <- vector(mode = "list", length = 3)
                
                #cat("\n")
                
                if(parallel){
                        
                        ### Parallellizing the sampling process using the 'doParallel' and 'parallel' package
                        ### register all given cores for parallelization
                        par_cores <- parallel::makeForkCluster(parallel::detectCores())
                        doParallel::registerDoParallel(par_cores)
                        
                        # perform the sampling process in parallel
                        parallel_results <- foreach::foreach(i              = 1:runs,
                                                             .combine       = "rbind",
                                                             .errorhandling = "stop") %dopar% {
                                
                               
                                        data.frame(EarlyConservationTest( ExpressionSet = ExpressionSet,
                                                                          permutations  = permutations,
                                                                          lillie.test   = TRUE,
                                                                          plotHistogram = FALSE, 
                                                                          modules       = modules )[c(1,3)])
                                        
                        }
                        
                        parallel::stopCluster(par_cores)
                        
                        colnames(parallel_results) <- c("p.value","lillie.test")
                        
                        p.vals_vec <- parallel_results[ ,"p.value"]
                        lillie_vec <- parallel_results[ ,"lillie.test"]
                        
                }
                
                if(!parallel){
                        
                        # sequential computations of p-values 
#                         if(runs >= 10){
#                                 # initializing the progress bar
#                                 #progressBar <- txtProgressBar(min = 1,max = runs,style = 3)
#                                 
#                         }
                        
                        for(i in 1:runs){
                                
                                if(lillie.test){
                                        
                                        ect <- EarlyConservationTest( ExpressionSet = ExpressionSet,
                                                                      permutations  = permutations,
                                                                      lillie.test   = TRUE, 
                                                                      plotHistogram = FALSE,
                                                                      modules       = list(early = modules[[1]],mid = modules[[2]],late = modules[[3]]),
                                                                      runs          = NULL ) 
                                }
                                
                                
                                if(!lillie.test){
                                        
                                        ect <- EarlyConservationTest( ExpressionSet = ExpressionSet,
                                                                      permutations  = permutations,
                                                                      lillie.test   = FALSE, 
                                                                      plotHistogram = FALSE,
                                                                      modules       = list(early = modules[[1]],mid = modules[[2]],late = modules[[3]]),
                                                                      runs          = NULL )
                                }
                                
                                p.vals_vec[i] <- ect$p.value
                                
                                if(lillie.test)
                                        lillie_vec[i] <- ect$lillie.test
                                
#                                 if(runs >= 10){
#                                         # printing out the progress
#                                         setTxtProgressBar(progressBar,i)
#                                 }
                        }
                }
                
                graphics::plot( x    = p.vals_vec,
                                type = "l" , 
                                lwd  = 6, 
                                ylim = c(0,1), 
                                col  = "darkblue", 
                                xlab = "Runs", 
                                ylab = "p-value" )

                graphics::abline(h = 0.05, lty = 2, lwd = 3)

                if(lillie.test){
                        tbl <- table(factor(lillie_vec, levels = c("FALSE","TRUE")))
                        
                        graphics::barplot( height    = tbl/sum(tbl) , 
                                           beside    = TRUE, 
                                           names.arg = c("FALSE", "TRUE"), 
                                           ylab      = "relative frequency", 
                                           main      = paste0("runs = ",runs) )
                }
        }
        
        
        #if(real_ecv >= 0)
        pval <- stats::pnorm(real_ecv,mean = mu,sd = sigma,lower.tail = FALSE)
        
        #if(real_ecv < 0)
        #pval <- pnorm(real_ecv,mean=mu,sd=sigma,lower.tail=TRUE)
        ### computing the standard deviation of the sampled TAI values for each stage separately
        sd_vals <- vector(mode = "numeric",length = nCols-2)
        sd_vals <- apply(resMatrix,2,stats::sd)
        
        if(lillie.test){
                # perform Lilliefors K-S-Test
                lillie_p.val <- nortest::lillie.test(score_vector)$p.value
                # does the Lilliefors test pass the criterion
                lillie_bool <- (lillie_p.val > 0.05)
                
                if(gof.warning & (lillie_p.val < 0.05) & (!plotHistogram)){
                        warning("Lilliefors (Kolmogorov-Smirnov) test for normality did not pass the p > 0.05 criterion!")
                }
        }
        
        if(lillie.test)
                return(list(p.value = pval,std.dev = sd_vals,lillie.test = lillie_bool))
        if(!lillie.test)
                return(list(p.value = pval,std.dev = sd_vals,lillie.test = NA))
        
        
}