R/ReductiveHourglassTest.R

In HajkD/myTAI: Evolutionary Transcriptomics

#' @title Perform the Reductive Hourglass Test
#' @description The \emph{Reductive Hourglass Test} aims to statistically evaluate the
#' existence of a phylotranscriptomic hourglass 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 hourglass like shape. A p-value < 0.05 indicates that the corresponding phylotranscriptomics pattern does
#' indeed follow an hourglass (high-low-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 reductive hourglass 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_early - T_mid and D2 = T_late - T_mid 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 Hourglass 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 (high-low-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) Mol Biol Evol. 32 (5): 1221-1231 doi:10.1093/molbev/msv012
#'
#' Quint M et al. (2012). A transcriptomic hourglass in plant embryogenesis. Nature (490): 98-101.
#'
#' M. L. Delignette-Muller, R. Pouillot, J.-B. Denis and C. Dutang (2014), fitdistrplus: help to fit
#' of a parametric distribution to non-censored or censored data.
#'
#' Cullen AC and Frey HC (1999) Probabilistic techniques in exposure assessment. Plenum Press, USA, pp. 81-159.
#'
#' Evans M, Hastings N and Peacock B (2000) Statistical distributions. John Wiley and Sons Inc.
#'
#' Sokal RR and Rohlf FJ (1995) Biometry. W.H. Freeman and Company, USA, pp. 111-115.
#'
#' Juergen Gross and bug fixes by Uwe Ligges (2012). nortest: Tests for Normality. R package version
#' 1.0-2. 
#' 
#' http://CRAN.R-project.org/package=nortest
#'
#' Dallal, G.E. and Wilkinson, L. (1986): An analytic approximation to the distribution of Lilliefors' test for normality. The American Statistician, 40, 294-296.
#'
#' Stephens, M.A. (1974): EDF statistics for goodness of fit and some comparisons. Journal of the American Statistical Association, 69, 730-737.
#'
#' http://stackoverflow.com/questions/4290081/fitting-data-to-distributions?rq=1
#'
#' http://stats.stackexchange.com/questions/45033/can-i-use-kolmogorov-smirnov-test-and-estimate-distribution-parameters
#'
#' http://cran.r-project.org/doc/contrib/Ricci-distributions-en.pdf
#'
#' http://cran.r-project.org/doc/contrib/Ricci-distributions-en.pdf
#'   
#' @author Hajk-Georg Drost
#' @seealso \code{\link{rhScore}}, \code{\link{bootMatrix}}, \code{\link{FlatLineTest}},
#' \code{\link{ReverseHourglassTest}}, \code{\link{EarlyConservationTest}}, \code{\link{PlotSignature}},
#' \code{\link{LateConservationTest}}
#' @examples
#' 
#' data(PhyloExpressionSetExample)
#'
#' # perform the reductive hourglass 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
#' ReductiveHourglassTest(PhyloExpressionSetExample,
#'                        modules = list(early = 1:2, mid = 3:5, late = 6:7), 
#'                        permutations = 1000)
#'
#'
#' # use your own permutation matrix based on which p-values (ReductiveHourglassTest)
#' # shall be computed
#' custom_perm_matrix <- bootMatrix(PhyloExpressionSetExample,100)
#' 
#' ReductiveHourglassTest(PhyloExpressionSetExample,
#'                      modules = list(early = 1:2, mid = 3:5, late = 6:7),
#'                      custom.perm.matrix = custom_perm_matrix)
#'
#' 
#' @import foreach
#' @export

ReductiveHourglassTest <- 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 ReductiveHourglassTest.", call. = FALSE)
        
        if(length(modules) != 3)
                stop("Please specify three modules: early, mid, and late to perform the ReductiveHourglassTest.", 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(dplyr::select(ExpressionSet, 3:ncol(ExpressionSet))),as.vector(unlist(dplyr::select(ExpressionSet, 1))))
        ### compute the real reductive hourglass scores of the observed phylotranscriptomics pattern
        real_score <- rhScore(real_age,
                              early         = modules[[1]],
                              mid           = modules[[2]],
                              late          = modules[[3]],
                              method        = "min",
                              scoringMethod = "mean-mean",
                              profile.warn=T)
        options(warn=1)
        
        ### compute the bootstrap matrix 
        if (is.null(custom.perm.matrix)){
                resMatrix <- cpp_bootMatrix(as.matrix(dplyr::select(ExpressionSet, 3:ncol(ExpressionSet))),
                                            as.vector(unlist(dplyr::select(ExpressionSet, 1))),
                                            as.numeric(permutations))       
        }
        
        else if (!is.null(custom.perm.matrix)) {
                resMatrix <- custom.perm.matrix
        }
        
        ### compute the global phylotranscriptomics destruction scores foe each sampled age vector
        score_vector <- apply(resMatrix, 1 ,rhScore,early = modules[[1]],mid = modules[[2]],late = modules[[3]],method = "min",scoringMethod = "mean-mean")
        
        
        
        # parameter estimators using MASS::fitdistr
        param <- fitdistrplus::fitdist(score_vector,"norm", method = "mme")
        mu <- param$estimate[1]
        sigma <- param$estimate[2]
        
        if(plotHistogram == TRUE){
                # plot histogram of scores
                normDensity <- function(x){
                        
                        return(stats::dnorm(x,mu,sigma))
                        
                }
                
                if(lillie.test)
                        graphics::par(mfrow = c(2,2))
                if(!lillie.test)
                        graphics::par(mfrow = c(1,3))
                
                fitdistrplus::descdist(score_vector, boot = permutations)
                
                graphics::curve( expr = normDensity,
                                 xlim = c(min(score_vector,real_score),max(score_vector,real_score)),
                                 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 rh value
                graphics::abline(v = real_score, lwd = 5, col = "darkred")
                
                p.vals_vec <- vector(mode = "numeric", length = runs)
                lillie_vec <- vector(mode = "logical", length = runs)
                rht <- 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(ReductiveHourglassTest( 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){
                                        rht <- ReductiveHourglassTest( 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){
                                       
                                        rht <- ReductiveHourglassTest( 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] <- rht$p.value
                               
                               if(lillie.test)
                                        lillie_vec[i] <- rht$lillie.test
                                
#                                 if(runs >= 10){
#                                         # printing out the progress
#                                         setTxtProgressBar(progressBar,i)
#                                 }
                        }
                }
                
                #cat("\n")
                
                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_score >= 0)
        pval <- stats::pnorm(real_score,mean = mu,sd = sigma,lower.tail = FALSE)
        
        #if(real_score < 0)
        #pval <- pnorm(real_score,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 == FALSE)){
                        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))
}