XLSX with 300WSs added, INFO boxes added to OPTIMIZE

R/Global.R

@@ -1626,3 +1626,47 @@ bendFUN <- function(coeffsMR, coeffsMU) {
   )
   return(BPsMR_MU)
 }
+
+#' Fitting of Gumbel location and scale parameters, and plotting function
+#'
+#'
+#' @param H Histogram density results with the mid-points of the histograms.
+#' @returns A ggplot object and a table of Gumbel quantiles 0.95, 0.99, and 0.999.
+#' @export
+#' @examples
+#' suppressMessages(source("../../dev/setup.R"))
+#'
+#' H = structure(list(breaks = c(1.02, 1.04, 1.06, 1.08, 1.1, 1.12, 1.14),
+#' counts = c(2L, 12L, 11L, 4L, 0L, 1L), 
+#' density = c(3.33333333333333, 20, 18.3333333333333, 6.66666666666666, 0, 1.66666666666667), 
+#' mids = c(1.03, 1.05, 1.07, 1.09, 1.11, 1.13), xname = 'UppAsympt', 
+#' equidist = TRUE), class = "histogram")
+#' Titel <- "test"
+#'
+#' GumbPlotFUN(H)
+GumbPlotFUN <- function(H, Titel="Maximum deviation of confidence limit") {
+  
+  H_df <- data.frame(Density = H[[3]], Mids=H[[4]])
+  startlist <- list(mu = 1.1, b = 1)
+  
+  GuM <- gsl_nls(
+    fn = Density ~ 1/b*exp(-((Mids-mu)/b+exp(-(Mids-mu)/b))),
+    data = H_df,
+    start = startlist, # race=T,
+    control = gsl_nls_control(xtol = 1e-6, ftol = 1e-6, gtol = 1e-6)
+  )
+  SuGuM <- summary(GuM)$coefficients
+  X_gu <- seq(min(H[["breaks"]]), max(H[["breaks"]]), by=0.001)
+  DGu <- dgumbel(X_gu, loc=SuGuM[1,1], scale = SuGuM[2,1])
+  DGuDF <- data.frame(X = X_gu, Y = DGu)
+  Quantiles <- qgumbel(c(0.95,0.99,0.999),loc=SuGuM[1,1], scale = SuGuM[2,1] )
+  INV_Quantiles <- 1/Quantiles
+  
+  p_gu <- ggplot(H_df) +
+    geom_col(mapping=aes(x=Mids, y=Density)) +
+    geom_line(DGuDF, mapping=aes(x=X, y=Y), inherit.aes = F) +
+    geom_vline(xintercept = Quantiles, linetype=2, col="blue") +
+    ggtitle(Titel) +
+    theme_bw()
+  return(list(p_gu, data.frame(Probabilities= c(0.95,0.99,0.999), INV_Quantiles,Quantiles)))
+}

dev/app.R

@@ -374,9 +374,10 @@ server <- function(input, output, session) {
             h4("Settings for report"),
             useShinyjs(),
             actionButton("btn", "Download 4PL PDF report", icon = icon("download")),
+            
             downloadButton("downloadXLReport", style = "visibility: hidden;"),
-            #downloadButton("downloadXLReport", label = "Download 4PL PDF report", class = "butt"),
+            
-            tags$style(type = "text/css", "#downloadXLReport {background-color: orange; color: black;font-family: Courier New}"),
+            tags$style(type = "text/css", "#downloadXLReport {background-color: #4FCBD9; color: black;font-family: Courier New}"),
             downloadButton("downloadXLReportLin", label = "Download linear PLA PDF report", class = "butt"),
             tags$style(type = "text/css", "#downloadXLReportLin {background-color: #4FCBD9; color: black;font-family: Courier New}"),
             textInput("Author", "Author", value = ""),
@@ -604,7 +605,7 @@ server <- function(input, output, session) {
   #### UI wizard ----
   output$wizard <- renderUI({
     navbarPage(
-      title = "Dilution setting",
+      title = "Optimizing wizard",
       tabPanel(
         "Plots",
         sidebarLayout(
@@ -616,9 +617,12 @@ server <- function(input, output, session) {
                   title = "Upload multiple worksheets", status = "warning", solidHeader = TRUE, width = 12, "Please upload your EXCEL file here",
                   fileInput("MiFile", "", accept = ".xlsx")
               ),
+              conditionalPanel(condition="input.tabs3 == 'Dilution slider'",       
                                sliderInput("dilslider", "Adjust the dilutions(+-change in %)", min = -100,max=100, value=0, step=1, round=0),
                                #checkboxInput("fixupper","Fix highest concentration (if unticked, the center is fixed)",FALSE),
                                sliderInput("dilmover", "Move the dilutions(+-move in log-units)", min = -3,max=3, value=0, step=0.1, round=1),
+              ),    
+            
               numericInput("TolConf","confidence", value=0.95, step=0.01),
               numericInput("TolPop","population", value=0.9, step=0.01)
             )
@@ -626,7 +630,7 @@ server <- function(input, output, session) {
           mainPanel(
             tabsetPanel(
               id = "tabs3",
-              tabPanel("4pl",
+              tabPanel("Sigmoid fits",
                 
 
                 column(12,
@@ -634,15 +638,33 @@ server <- function(input, output, session) {
                   # tableOutput("CIs"),
                   # "The confidence interval table is interactive for changes in: variability slider (%SD), potency of test-slider,
                   #                      and 'Adjust the dilutions'-slider",
-                  # tableOutput("optimalDils"),
                    plotOutput("sigPlotREF"),
-                  plotOutput("sigPlotTEST"),
+                  plotOutput("sigPlotTEST")),
+                box(title = "INFO for sigmiod plots", status = "info", solidHeader = TRUE, collapsible = TRUE, width = 12,collapsed=T,
+                  uiOutput('ExplTextOPTsigs'),
+                  
+                ),
+                
+                  column(8,
+                         plotOutput("GuPlotUA")),
+                column(4, tableOutput("GuTabUA")),
+                  column(8, plotOutput("GuPlotSLO")),
+                column(4,
+                      tableOutput("GuTabSLO")),
+                box(title = "INFO for histograms", status = "info", solidHeader = TRUE, collapsible = TRUE, width = 12,collapsed=T,
+                  uiOutput('ExplTextOPTGumbel'),
+                  br()
+                )
                   #selectInput(inputId = "scenario", label = "Select an 'optimal' scenario:", choices = c("scenario 2", "scenario 3", "scenario 6", "steep slope"))
 
-              )),
+              ),
               tabPanel("Dilution slider",
                        h4("Adjust the dilutions"),
                        plotOutput("plotfordilutions"),
+                       box(title = "INFO for sigmiod plots", status = "info", solidHeader = TRUE, collapsible = TRUE, width = 12,collapsed=T,
+                           uiOutput('ExplTextOPTdils'),
+                       ),
+                       
                        h5("Dilution factors"),
                        box(
                          title = "Adjusted dilutions", status = "primary", solidHeader = TRUE, width = 12, collapsible = TRUE,
@@ -655,10 +677,12 @@ server <- function(input, output, session) {
               tabPanel("Plots",
                 h4("Histograms of parameters"),
                 plotOutput("linerangeCIs"),
+                column(6,
                 plotOutput("ratioSlope"),
-                plotOutput("ratioLas"),
+                plotOutput("ratioLas")),
+                column(6,
                 plotOutput("ratioUas"),
-                plotOutput("widthCIs"),
+                plotOutput("widthCIs")),
                 column(6,
                       plotOutput("histEC50REF"), 
                       plotOutput("histLasREF"),
@@ -672,8 +696,7 @@ server <- function(input, output, session) {
                 
               ),
               tabPanel(
-                "Report",
+                "Download",
-                h4("Settings for report"),
                 #useShinyjs(),
                 #actionButton("btn2", "Download PDF report", icon = icon("download")),
                 downloadButton("downloadWizardData", label = "Download model and plots", class = "butt"),
@@ -748,19 +771,32 @@ server <- function(input, output, session) {
 #### input Wizard XL file ----
   observe({
     if (!is.null(input$MiFile)) {
+      withProgress(message = "You clicked this button.... Working...", value =0 , {
         MinFile <- input$MiFile
         ext <- tools::file_ext(MinFile$name)
         file.rename(MinFile$datapath, paste(MinFile$datapath, ".xlsx", sep = ""))
         t.filelocation <- gsub("\\\\", "/", paste(MinFile$datapath, ext, sep = "."))
         sheets <- openxlsx::getSheetNames(t.filelocation)
+        
+      incProgress(.25,message = "Reading from EXCEL.... Working...")
         dat <- lapply(sheets, openxlsx::read.xlsx, xlsxFile = t.filelocation)
+        
+      incProgress(.35, message = "All WS read.... Working...")
         names(dat) <- sheets
         Dat$Mws <- dat
         names(Dat$Mws) <- sheets
         Dat$Msheets <- sheets
         Dat$MFileName <- input$MiFile[["name"]]
+        
+        #output$downloadData
+      incProgress(1, message = "Calculating...COMPLETE!")
+      # Sys.sleep to show message 1 sec
+        Sys.sleep(1)
+      })
+      
     }
   })
+  observeEvent(input$MiFile, {showSpinner("sigPlotREF")})
 
   #### process XLSX file ----
   observe({
@@ -2251,7 +2287,7 @@ server <- function(input, output, session) {
   })
 
 
-  #### Meta plots all XL ---- 
+  #### Wizard plots all XL ---- 
   observe({ 
     if (!is.null(Dat$Mws)) {
 
@@ -2259,7 +2295,11 @@ server <- function(input, output, session) {
     AllXL <- Dat$Mws
     AllSheets <- Dat$Msheets
     
-    URMcoefsL <- RMcoefsL <- potEstL <- list()
+   
+      
+        
+    
+    URMcoefsL <- RMcoefsL <- potEstL <- UAciL <- SLOciL <- list()
     
     for (N_WS in 1:length(AllXL)) {
    
@@ -2283,7 +2323,7 @@ server <- function(input, output, session) {
         CORro <- COR_FUNC(datWS[, logI], datWS[, 3])
       }
       Dat$datWS2 <- datWS2
-      
+   #browser()   
       FITs <- Fitting_FUNC(datWS2, TransFlag = F, nameWS = nameWS)
       if (!is.character(FITs)) {
         pot_est <- FITs[[3]]
@@ -2295,6 +2335,10 @@ server <- function(input, output, session) {
         URMcoefs <- t(matrix(unlist(URMcoefs1[,1])))
         URMcoefs_ <- cbind(AllSheets[[N_WS]], URMcoefs)
         URMcoefsL[[N_WS]] <- URMcoefs_
+        URMV_V <- SU_mu$cov.unscaled
+        SEsRMSE <- sqrt(diag(URMV_V) * SU_mu$sigma^2)
+        UAciL[[N_WS]] <- ParamCI_F(URMcoefs[1,7], URMcoefs[1,3], SEsRMSE[7],SEsRMSE[3], CoVar=0, SU_mu$df[2], Conf = 0.975)
+        SLOciL[[N_WS]] <- ParamCI_F(URMcoefs[1,6], URMcoefs[1,2], SEsRMSE[6],SEsRMSE[2], CoVar=0, SU_mu$df[2], Conf = 0.975)
         
         SU_mr <- FITs[[1]]
         RMcoefs1 <- SU_mr$coefficients
@@ -2316,6 +2360,12 @@ server <- function(input, output, session) {
       }
     } #for N_WS
     
+    
+    
+    
+    
+    
+   
 #browser()   
     URMcoefsDF <- t(matrix(unlist(URMcoefsL),nrow=9))
     colnames(URMcoefsDF) <- c("WS name", "lowerAs REF","slope REF","upperAs REF","EC50 REF", "lowerAs TEST","slope TEST","upperAs TEST","EC50 Difference")
@@ -2337,6 +2387,31 @@ server <- function(input, output, session) {
     UasRatio <- UasTEST/UasREF
     ratioDF <- data.frame(WS_name = URMcoefsDF[,1], slopeRatio = slopeRatio, LasRatio = LasRatio, UasRatio = UasRatio)
     
+    UAciM <- t(matrix(unlist(UAciL),nrow=2))
+    SLOciM <- t(matrix(unlist(SLOciL),nrow=2))
+    colnames(UAciM) <- c("lowerCL_upperA", "upperCL_upperA")
+    colnames(SLOciM) <- c("lowerCL_Hslope","upperCL_Hslope")
+    UAciDF <- data.frame("lowerCL_upperA" =UAciM[,1], "upperCL_upperA" = UAciM[,2],"reciLowerCI"= 1/UAciM[,1])
+    UAciDF$MaxDeviation <- apply(UAciDF, 1,max)
+    SLOciDF <- data.frame("lowerCL_upperA" =SLOciM[,1], "upperCL_upperA" = SLOciM[,2],"reciLowerCI"= 1/SLOciM[,1])
+    SLOciDF$MaxDeviation <- apply(SLOciDF, 1,max)
+ #browser()   
+   H <-  hist(UAciDF[,4])
+   
+   GumbelL <- GumbPlotFUN(H, Titel="Histogram of max. deviation of upper asymptote ratio confidence limits")
+   p_gu <- GumbelL[[1]]
+   Gu_tab <- GumbelL[[2]]
+    output$GuPlotUA <- renderPlot({ p_gu })
+    output$GuTabUA <- renderTable({ Gu_tab }, digits=3)
+    
+    H_s <-  hist(SLOciDF[,4])
+    
+    GumbelL_s <- GumbPlotFUN(H_s, Titel="Histogram of max. deviation of Hill's slope ratio confidence limits")
+    p_gu_s <- GumbelL_s[[1]]
+    Gu_tab_s <- GumbelL_s[[2]]
+    output$GuPlotSLO <- renderPlot({ p_gu_s })
+    output$GuTabSLO <- renderTable({ Gu_tab_s }, digits = 3)
+    
     RMcoefsDF <- t(matrix(unlist(RMcoefsL),nrow=6))
     colnames(RMcoefsDF) <- c("WS name", "lower asymptote","Hill's slope","upper asymptote","log(EC50 ref)","logEC50 difference")
     Dat$URMcoefsDF <- URMcoefsDF
@@ -2376,10 +2451,12 @@ server <- function(input, output, session) {
           xlab("dilutions") +
           ggtitle("REF sample 4PL-fits (unrestricted model, gray vertical lines: EC50)") +
           theme_bw() +
+          { if (nrow(SIGrefDF)>30) theme(legend.position="none") } +
           theme(axis.text = element_text(face = "bold", size = 15),
                 plot.title = element_text(size = 15, face = "bold"),
                 plot.margin = unit(c(0.2, 0.2, 0.5, 0.5), "lines")) 
     
+  
     output$sigPlotREF <- renderPlot({ p1 })
     Dat$sigPlotREF <- p1
     
@@ -2396,6 +2473,7 @@ server <- function(input, output, session) {
       xlab("dilutions") +
       ggtitle("TEST sample 4PL-fits (unrestricted model, gray vertical lines: EC50)") +
       theme_bw() +
+      { if (nrow(SIGtestDF)>30) theme(legend.position="none") } +
       theme(axis.text = element_text(face = "bold", size = 15),
             plot.title = element_text(size = 15, face = "bold"))
 
@@ -2403,7 +2481,10 @@ server <- function(input, output, session) {
 
     Dat$sigPlotTEST <- p2
   
-    #### histograms right panel ----
+   
+    
+    
+    #### Wizard histograms ----
     
    
     
@@ -2424,23 +2505,26 @@ server <- function(input, output, session) {
       # scale_x_continuous(
       #   breaks=seq(trunc(min(all_lPot$Potency_and_CI, na.rm=T)*10)/10, max(all_lPot$Potency_and_CI, na.rm=T)*1.1, by=0.4),
       # ) +
+      xlab("Index of worksheets") +
       theme_bw() +
       theme(axis.text = element_text(face="bold", size=15),
             axis.text.x = element_text(angle=90),
-            plot.title= element_text(size=15, face="bold"))
+            plot.title= element_text(size=15, face="bold")) +
+      theme(legend.position="none")
     #P_linerangeCI
     output$linerangeCIs <- renderPlot({ P_linerangeCI })
     
-    P_widthCIs <- ggplot(CalcPotDF, aes(x=width_CI, fill="blue")) +
+    P_widthCIs <- ggplot(CalcPotDF, aes(x=width_CI, fill="red"), ) +
-      geom_histogram(color="#e9ecef", alpha=0.6, position = "identity") +
+      geom_histogram(aes(y = after_stat(density)), bins = 10, position = "identity", alpha=0.6) +
-      geom_density(alpha = 0.1) +
+      geom_density(alpha = 0.5) +
       #scale_fill_manual(values=c("darkgreen","darkblue","salmon2","tomato3")) +
       labs(title = "Histogram of width of CLs", subtitle = paste("with upper",input$TolConf,input$TolPop, "tolerance interval")) +
-      geom_vline(xintercept = widthCLTol[[5]]) +
+      geom_vline(xintercept = widthCLTol[[5]], linetype=2) +
       theme_bw() +
       theme(axis.text = element_text(face="bold", size=15),
             axis.text.x = element_text(angle=90),
-            plot.title= element_text(size=15, face="bold")) 
+            plot.title= element_text(size=15, face="bold")) +
+      theme(legend.position="none")
     
     output$widthCIs <- renderPlot({ P_widthCIs })
     
@@ -2449,41 +2533,44 @@ server <- function(input, output, session) {
     UasTol <- normtol.int(x = UasRatio, alpha = 1-input$TolConf, P = input$TolPop, side = 2)
     
     P_ratioSlope <- ggplot(ratioDF, aes(x=slopeRatio, fill="turquoise")) +
-      geom_histogram(color="#e9ecef", alpha=0.6, position = "identity") +
+      geom_histogram(aes(y = after_stat(density)),color="#e9ecef", alpha=0.6, position = "identity",bins = 10) +
       geom_density(alpha = 0.1) +
       #scale_fill_manual(values=c("darkgreen","darkblue","salmon2","tomato3")) +
       labs(title = "Histogram of Hill's slope ratios ", subtitle = paste("with",input$TolConf,input$TolPop, "tolerance interval")) +
-      geom_vline(xintercept = c(SlopeTol[[4]], SlopeTol[[5]]), linetype=2, col="grey") +
+      geom_vline(xintercept = c(SlopeTol[[4]], SlopeTol[[5]]), linetype=2) +
       theme_bw() +
       theme(axis.text = element_text(face="bold", size=15),
             axis.text.x = element_text(angle=90),
-            plot.title= element_text(size=15, face="bold"))
+            plot.title= element_text(size=15, face="bold")) +
+      theme(legend.position="none")
     
     output$ratioSlope <- renderPlot({ P_ratioSlope })
     
     P_ratioLas <- ggplot(ratioDF, aes(x=LasRatio, fill="turquoise")) +
-      geom_histogram(color="#e9ecef", alpha=0.6, position = "identity") +
+      geom_histogram(aes(y = after_stat(density)),color="#e9ecef", alpha=0.6, position = "identity", bins = 10) +
       geom_density(alpha = 0.1) +
       #scale_fill_manual(values=c("darkgreen","darkblue","salmon2","tomato3")) +
       labs(title = "Histogram of lower asymptote ratios ", subtitle = paste("with",input$TolConf,input$TolPop, "tolerance interval")) +
-      geom_vline(xintercept = c(LasTol[[4]], LasTol[[5]]), linetype=2, col="grey") +
+      geom_vline(xintercept = c(LasTol[[4]], LasTol[[5]]), linetype=2) +
       theme_bw() +
       theme(axis.text = element_text(face="bold", size=15),
             axis.text.x = element_text(angle=90),
-            plot.title= element_text(size=15, face="bold"))
+            plot.title= element_text(size=15, face="bold")) +
+      theme(legend.position="none")
     
     output$ratioLas <- renderPlot({ P_ratioLas })
     
     P_ratioUas <- ggplot(ratioDF, aes(x=UasRatio, fill="turquoise")) +
-      geom_histogram(color="#e9ecef", alpha=0.6, position = "identity") +
+      geom_histogram(aes(y = after_stat(density)),color="#e9ecef", alpha=0.6, position = "identity", bins = 10) +
       geom_density(alpha = 0.1) +
       #scale_fill_manual(values=c("darkgreen","darkblue","salmon2","tomato3")) +
       labs(title = "Histogram of upper asymptote ratios ", subtitle = paste("with",input$TolConf,input$TolPop, "tolerance interval")) +
-      geom_vline(xintercept = c(UasTol[[4]], UasTol[[5]]), linetype=2, col="grey") +
+      geom_vline(xintercept = c(UasTol[[4]], UasTol[[5]]), linetype=2) +
       theme_bw() +
       theme(axis.text = element_text(face="bold", size=15),
             axis.text.x = element_text(angle=90),
-            plot.title= element_text(size=15, face="bold"))
+            plot.title= element_text(size=15, face="bold")) +
+      theme(legend.position="none")
     
     output$ratioUas <- renderPlot({ P_ratioUas })
     
@@ -2537,41 +2624,7 @@ server <- function(input, output, session) {
    Dat$newDils <- dils2
 
 
-    #sigmoid <- sigmoid()
    
-    # BPs <- Dat$bendpoints
-    # EC50REF <- (BPs[2] + BPs[1]) / 2
-    # Einh <- abs((BPs[2] - BPs[1]) / 5)
-    # asyml <- EC50REF - 2 * (EC50REF - BPs[1])
-    # asymu <- EC50REF + 2 * (EC50REF - BPs[1])
-    # 
-    # det_sig <- Dat$coeffs_UN
-    # 
-    # if (is.null(Dat$coeffs_UN)) {
-    #   SAMPLE50 <- sigmoid[1] + (sigmoid[3] - sigmoid[1]) / (1 + exp(sigmoid[5] * ((sigmoid[7] + 0.693147) - dils2)))
-    #   SAMPLE200 <- sigmoid[1] + (sigmoid[3] - sigmoid[1]) / (1 + exp(sigmoid[5] * ((sigmoid[7] - 0.693147) - dils2)))
-    #   Xbend50l <- sigmoid[7] + 0.693147 - 1.5434 / sigmoid[5]
-    #   Xbend200l <- sigmoid[7] - 0.693147 - 1.5434 / sigmoid[5]
-    #   Xbend50u <- sigmoid[7] + 0.693147 + 1.5434 / sigmoid[5]
-    #   Xbend200u <- sigmoid[7] - 0.693147 + 1.5434 / sigmoid[5]
-    #   Xbend50 <- max(Xbend50l, Xbend50u)
-    #   Xbend200 <- min(Xbend200l, Xbend200u)
-    #   dummy <- plot_f(tab)
-    # } else {
-    #   SAMPLE50 <- det_sig[3] + (det_sig[5] - det_sig[3]) / (1 + exp(det_sig[1] * (det_sig[7] + 0.693147 - dils2)))
-    #   SAMPLE200 <- det_sig[3] + (det_sig[5] - det_sig[3]) / (1 + exp(det_sig[1] * (det_sig[7] - 0.693147 - dils2)))
-    #   Xbend50l <- det_sig[7] + 0.693147 - 1.5434 / det_sig[1]
-    #   Xbend200l <- det_sig[7] - 0.693147 - 1.5434 / det_sig[1]
-    #   Xbend50u <- det_sig[7] + 0.693147 + 1.5434 / det_sig[1]
-    #   Xbend200u <- det_sig[7] - 0.693147 + 1.5434 / det_sig[1]
-    #   Xbend50 <- max(Xbend50l, Xbend50u)
-    #   Xbend200 <- min(Xbend200l, Xbend200u)
-    #   dummy <- plot_f(tab)
-    # }
-    # 
-    # 
-    # pl_df <- cbind(dils2, SAMPLE50, SAMPLE200)
-    # 
 
     output$adjlogdil <- renderTable({
       adjlogdilfactors <- round(dilfactors, 3)
@@ -2620,6 +2673,8 @@ server <- function(input, output, session) {
       } # if (!is.null(p2))
     } # if !is.null Dat$Mws
 
+
+
   })
 
   #### Dilutions CI table ----
@@ -3057,6 +3112,28 @@ server <- function(input, output, session) {
         
       }, contentType = "application/zip"
     )
+    
+    output$ExplTextOPTsigs = renderUI({
+      HTML("<b>Note</b>: The plots above contain the sigmiod fits of all uploaded worksheets, separated for reference and test, as long as a fit was possible. 
+           The estimated upper and lower asymptotes are shown with a grey 'x' or 'o' at each side of the plots. 
+           The horizontal grey dashed lines indicate the tolerance interval of the asymptotes. 
+           Please note that the asymptotes are often not normally distributed, or contain different groups, when the assay setup was changed.
+           Therefore the tolerance interval should be seen as a gross surrogate.")
+    })
+    output$ExplTextOPTGumbel = renderUI({ 
+      HTML("<b>Note</b>: The histograms show the 'maximum deviation' of the confidence interval.
+      The 'maximum deviation' is either the upper confidence limit, or 1/lower confidence limit, whichever is greater.
+      The blue dashed lines are the 0.95, 0.99 and 0.999 quantiles of the distribution.
+    The tables on the right list the 0.95, 0.99 and 0.999 quantiles, and the inverses thereof, i.e. 1/quantiles. 
+    Thus, the number pairs are symmetric on a log-scale. Any of the number-pairs can be used to set the equivalence limits.")
+    })
+    output$ExplTextOPTdils = renderUI({ 
+      HTML("<b>Note</b>: All sigmoids of the test samples are shown, because the test samples contain a wider variability, with stability and forced degradation samples.
+           To adjust the width of the dilution range, draw the slider to the left to shrink or to the right to increase the range.
+           Once the width is set, move the dilution range to the right or to the left, using the 2nd slider.
+           The dilutions and the steps inbetween are annotated in red on the plot.
+           The table below shows again the dilution concentrations and the steps.")
+    })
 }
 
 shinyApp(ui, server)