report generation after new setup of repo; linearity XL report improved
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This commit is contained in:
2026-06-01 19:35:00 +02:00
parent cf1ce314e1
commit c480111552
7 changed files with 185 additions and 59 deletions
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+15 -23
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@@ -280,14 +280,14 @@ plot_f <- function(dat, TransFlag = F) { # sigmoid,det_sig,
s_mr <- MODLS[[1]] s_mr <- MODLS[[1]]
a <- s_mr$coefficients["a", 1] a <- s_mr$coefficients["a", 1]
b <- s_mr$coefficients["b", 1] b <- s_mr$coefficients["b", 1]
cs <- s_mr$coefficients["cs", 1] c <- s_mr$coefficients["cs", 1]
d <- s_mr$coefficients["d", 1] d <- s_mr$coefficients["d", 1]
r <- s_mr$coefficients["r", 1] r <- s_mr$coefficients["r", 1]
log_dose <- unique(all_l$log_dose) log_dose <- unique(all_l$log_dose)
seq_x <- seq(min(log_dose), max(log_dose), 0.1) seq_x <- seq(min(log_dose), max(log_dose), 0.1)
SAMPLE <- a + (d - a) / (1 + exp(b * ((cs - r) - seq_x))) SAMPLE <- a + (d - a) / (1 + exp(b * ((c - r) - seq_x)))
REF <- a + (d - a) / (1 + exp(b * ((cs) - seq_x))) REF <- a + (d - a) / (1 + exp(b * (c - seq_x)))
s_mu <- MODLS[[2]] s_mu <- MODLS[[2]]
@@ -310,16 +310,16 @@ plot_f <- function(dat, TransFlag = F) { # sigmoid,det_sig,
all_l2$readout[all_l2$readout < 0] <- 0.01 all_l2$readout[all_l2$readout < 0] <- 0.01
all_l2$readouttrans <- log(all_l2$readout) all_l2$readouttrans <- log(all_l2$readout)
slopeEC50 <- b * (d - a) / 4 slopeEC50 <- b * (d - a) / 4
Intercept <- a + (d - a) / 2 - b * (d - a) / 4 * cs Intercept <- a + (d - a) / 2 - b * (d - a) / 4 * c
# browser() # browser()
Xbendl3 <- cs - (1.5434 / b) Xbendl3 <- c - (1.5434 / b)
Xbendu3 <- cs + (1.5434 / b) Xbendu3 <- c + (1.5434 / b)
XbendlT <- cs - r - (1.5434 / b) XbendlT <- c - r - (1.5434 / b)
XbenduT <- cs - r + (1.5434 / b) XbenduT <- c - r + (1.5434 / b)
XasymplS <- cs - (3 / b) XasymplS <- c - (3 / b)
XasympuS <- cs + (3 / b) XasympuS <- c + (3 / b)
XasymplT <- cs - r - (3 / b) XasymplT <- c - r - (3 / b)
XasympuT <- cs - r + (3 / b) XasympuT <- c - r + (3 / b)
bendpoints <- c( bendpoints <- c(
bendREF_lower = round(Xbendl3, 3), bendREF_upper = round(Xbendu3, 3), bendREF_lower = round(Xbendl3, 3), bendREF_upper = round(Xbendu3, 3),
bendSAMPLE_lower = round(XbendlT, 3), bendSAMPLE_upper = round(XbenduT, 3), bendSAMPLE_lower = round(XbendlT, 3), bendSAMPLE_upper = round(XbenduT, 3),
@@ -362,7 +362,7 @@ plot_f <- function(dat, TransFlag = F) { # sigmoid,det_sig,
geom_vline(xintercept = c(XbendlT, XbenduT), col = "#C2173F", linetype = 2) + geom_vline(xintercept = c(XbendlT, XbenduT), col = "#C2173F", linetype = 2) +
geom_vline(xintercept = c(XasymplS, XasympuS), col = "#4545BABB", linetype = 3) + geom_vline(xintercept = c(XasymplS, XasympuS), col = "#4545BABB", linetype = 3) +
geom_vline(xintercept = c(XasymplT, XasympuT), col = "#C2173FBB", linetype = 3) + geom_vline(xintercept = c(XasymplT, XasympuT), col = "#C2173FBB", linetype = 3) +
annotate("text", x = cs, y = a + (d - a) / 2, label = "0", size = 5) + annotate("text", x = c, y = a + (d - a) / 2, label = "0", size = 5) +
geom_abline(slope = slopeEC50, intercept = Intercept) + geom_abline(slope = slopeEC50, intercept = Intercept) +
theme(legend.position = "none") theme(legend.position = "none")
Dat$p2 <- p2 Dat$p2 <- p2
@@ -419,16 +419,8 @@ plot_f <- function(dat, TransFlag = F) { # sigmoid,det_sig,
cte <- Sum_u$coefficients["cs", 1] - Sum_u$coefficients["r", 1] cte <- Sum_u$coefficients["cs", 1] - Sum_u$coefficients["r", 1]
dst <- Sum_u$coefficients["ds", 1] dst <- Sum_u$coefficients["ds", 1]
dte <- Sum_u$coefficients["dt", 1] dte <- Sum_u$coefficients["dt", 1]
# } else {
# ast <- det_sig[5]
# ate <- det_sig[6]
# bst <- det_sig[1]
# bte <- det_sig[2]
# cst <- det_sig[7]
# cte <- det_sig[8]
# dst <- det_sig[3]
# dte <- det_sig[4]
# }
REFu <- ast + (dst - ast) / (1 + exp(bst * (cst - seq_x))) REFu <- ast + (dst - ast) / (1 + exp(bst * (cst - seq_x)))
SAMPLEu <- ate + (dte - ate) / (1 + exp(bte * (cte - seq_x))) SAMPLEu <- ate + (dte - ate) / (1 + exp(bte * (cte - seq_x)))
pl_df2 <- cbind(seq_x, SAMPLEu, REFu) pl_df2 <- cbind(seq_x, SAMPLEu, REFu)
@@ -20,6 +20,8 @@ params:
REP: NA REP: NA
REPlin: NA REPlin: NA
coeffsLin: NA coeffsLin: NA
NoP: NA
Assay: NA
author: "Author: `r params$author`" author: "Author: `r params$author`"
title: | title: |
| ![](logo.png){width=1in} | ![](logo.png){width=1in}
@@ -51,7 +53,7 @@ coeffsLin <- params$coeffsLin
all_l <- REP$all_l all_l <- REP$all_l
circles <- REPlin$circles circles <- REPlin$circles
ANOVAXLS <- REP$ANOVAXLS #ANOVAXLS <- REP$ANOVAXLS
SuModAB <- REPlin$SuModAB SuModAB <- REPlin$SuModAB
SuModABu <- REPlin$SuModABu SuModABu <- REPlin$SuModABu
LinTests <- REPlin$LinTests LinTests <- REPlin$LinTests
@@ -60,7 +62,8 @@ LinPotTab <- REPlin$LinPotTab
XLdat2 <- REP$XLdat2 XLdat2 <- REP$XLdat2
LinTests1 <- LinTests[,1:3]
ANOVAlin <- LinTests[,4:ncol(LinTests)]
``` ```
@@ -68,8 +71,8 @@ XLdat2 <- REP$XLdat2
# Introduction # Introduction
Bioassay potency estimation uses statistical methods to quantify the strength of a biological product or drug by comparing its response to that of a reference standard. Because biological responses are inherently variable, affected by assay conditions, cell systems or organisms, and measurement noise, the 4-parametric logistic regression is used to obtain reliable potency values. The variance for confidence interval calculation is coming from the regression procedure itself and is an excellent predictor for the variability of any future potency determinations. Bioassay potency estimation uses statistical methods to quantify the strength of a biological product or drug by comparing its response to that of a reference standard. Biological responses are inherently variable, affected by assay conditions, cell systems or organisms, and measurement noise. To control this variability, a linear regression approach is used to obtain reliable potency values. Three consecutive dilution steps showing the steepest slope are used for linear fitting.
USP<1034> recommends calculation of standard errors of ratios of the parameters using Fieller's theorem [Finney D.J. 1978] or using the "delta" method (for a discussion about the "delta" method see [Ver Hoef 2012]). However, the presented gradient approach using the differences on the log-scale is methematically more stable und thus preferable compared to any ratio approach ([Franz, V.H. 2007]). USP<1034> recommends calculation of standard errors of ratios of the parameters using Fieller's theorem [Finney D.J. 1978] or using the "delta" method (for a discussion about the "delta" method see [Ver Hoef 2012]). The present analysis calculated the relative potency with the "delta" method. The formula of the relative potency is in the Appendix.
# Raw data # Raw data
@@ -81,7 +84,7 @@ kable(XLdat2, format = "markdown", caption= "Uploaded data (test and reference)
``` ```
All data used linerar regression is shown in table 2. The linerar regression is calculated on the readout listed in table 2.
```{r Circles, echo=FALSE, warning=FALSE, results='asis'} ```{r Circles, echo=FALSE, warning=FALSE, results='asis'}
@@ -135,21 +138,37 @@ plot_grid(XLplotLin)
``` ```
The ANOVA of the unconstrained model is listed in table 3.
```{r anovaxls, echo=FALSE, warning=FALSE, results='asis'} The relative potency can be read from tbale 3.
kable(ANOVAXLS, format = "markdown", caption= "ANOVA table unrestricted", digits=3) ```{r LinPotTab, echo=FALSE, warning=FALSE, results='asis'}
kable(LinPotTab, format = "markdown", caption= "Potency table", digits=3)
``` ```
The assay suitability tests are shown in table 4.
The ANOVA of the unconstrained model is listed in table 4.
```{r anovaxls, echo=FALSE, warning=FALSE, results='asis'}
kable(ANOVAlin, format = "markdown", caption= "ANOVA table unrestricted", digits=3)
RMSE <- sqrt(ANOVAlin[5,4])
```
The standard deviation of the model is `r RMSE`.
The assay suitability tests are shown in table 5.
```{r SST_ergebn, echo=FALSE, cache=FALSE, warning=FALSE, message=FALSE, tidy=TRUE} ```{r SST_ergebn, echo=FALSE, cache=FALSE, warning=FALSE, message=FALSE, tidy=TRUE}
kable(LinTests, row.names = F, format = "markdown", caption="Assay suitability test results", digits=3) kable(LinTests1, row.names = F, format = "markdown", caption="Assay suitability test results", digits=3)
``` ```
@@ -159,15 +178,15 @@ The estimate is the p-value of the test.
F-tests on regression, significance of slopes, and preparation need to have a p-value <0.05 to pass. F-tests on regression, significance of slopes, and preparation need to have a p-value <0.05 to pass.
All other tests pass if p-value > 0.05. All other tests pass if p-value > 0.05.
0 ... test passed (for EQ tests: CI within limits); 0 ... test passed;
1 ... test failed (for EQ tests CI not within limits);
1 ... test failed);
(NOTE: F-tests are sensitive, when the residual variability of the method is small. On the other hand effects may not be detected if residual variability is high.)
## Fitting results ## Fitting results
The results of the linear fitting procedure for the restricted model is listed in table 5: The results of the linear fitting procedure for the restricted model is listed in table 6:
```{r SumCSSI, echo=FALSE, warning=FALSE, results='asis'} ```{r SumCSSI, echo=FALSE, warning=FALSE, results='asis'}
@@ -178,9 +197,10 @@ kable(SuModAB, format = "markdown", caption= "Restricted linear regression (CSSI
CSSI: common slope, separate intercept CSSI: common slope, separate intercept
The results of the linear fitting procedure for the unrestricted model is listed in table 6. The results of the linear fitting procedure for the unrestricted model is listed in table 7.
```{r SuSSSI, echo=FALSE, warning=FALSE, results='asis'}
```{r SumSSSI, echo=FALSE, warning=FALSE, results='asis'}
kable(SuModABu, format = "markdown", caption= "Restricted linear regression (SSSI)", digits=3, row.names = F) kable(SuModABu, format = "markdown", caption= "Restricted linear regression (SSSI)", digits=3, row.names = F)
@@ -197,7 +217,7 @@ SSSI: separate slope, separate intercept
## Potency of linear PLA ## Potency of linear PLA
$$ $$
rel Potency = \frac{I_{ref} - I_{test}{k} rel Potency = \frac{I_{ref} - I_{test}}{k}
$$ $$
where: I... intercept of reference or test where: I... intercept of reference or test
k ... common slope k ... common slope
@@ -93,6 +93,7 @@ kable(XLdat2, format = "markdown", caption= "Uploaded data (test and reference)
```{r Over_all, echo=FALSE, comment=NA, warning=NA, message=NA} ```{r Over_all, echo=FALSE, comment=NA, warning=NA, message=NA}
# browser()
potFlag <- 0 potFlag <- 0
if (pottab4plXL["test_result"][[1]][1]==1) potFlag <- 1 if (pottab4plXL["test_result"][[1]][1]==1) potFlag <- 1
AnalysisFlag <- FALSE AnalysisFlag <- FALSE
+130 -17
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@@ -548,6 +548,8 @@ server <- function(input, output, session) {
) )
}) })
#### UI wizard ----
output$wizard <- renderUI({ output$wizard <- renderUI({
navbarPage( navbarPage(
title = "Dilution setting", title = "Dilution setting",
@@ -557,14 +559,12 @@ server <- function(input, output, session) {
sidebarPanel( sidebarPanel(
width = 3, width = 3,
fluidRow( fluidRow(
column( column(6,
6, box(title = "Upload multiple worksheets", status = "warning", solidHeader = T, width = 12, "Please upload your EXCEL file here",
numericInput( fileInput("MiFile", "", accept = ".xlsx"))
"Limits", p("limit to be >", bsButton("q4", label = "", icon = icon("info"), style = "primary", size = "extra-small")),
bsPopover(id = "q4", title = "", content = "The calculated limits ...")
)
) )
) )
), ),
mainPanel( mainPanel(
tabsetPanel( tabsetPanel(
@@ -575,8 +575,7 @@ server <- function(input, output, session) {
title = "ANOVA table", status = "primary", solidHeader = T, width = 12, title = "ANOVA table", status = "primary", solidHeader = T, width = 12,
tableOutput("Anovatab") tableOutput("Anovatab")
), ),
column( column(4,
4,
h3("Confidence intervals"), h3("Confidence intervals"),
tableOutput("CIs"), tableOutput("CIs"),
"The confidence interval table is interaactive for changes in: variability slider (%SD), potency of test-slider, "The confidence interval table is interaactive for changes in: variability slider (%SD), potency of test-slider,
@@ -584,8 +583,7 @@ server <- function(input, output, session) {
tableOutput("optimalDils"), tableOutput("optimalDils"),
selectInput(inputId = "scenario", label = "Select an 'optimal' scenario:", choices = c("scenario 2", "scenario 3", "scenario 6", "steep slope")) selectInput(inputId = "scenario", label = "Select an 'optimal' scenario:", choices = c("scenario 2", "scenario 3", "scenario 6", "steep slope"))
), ),
column( column(5,
5,
plotOutput("plotfordilutions"), plotOutput("plotfordilutions"),
h4("in grey: most extreme bend point lines of theoretical samples with 50% and 200% potency"), h4("in grey: most extreme bend point lines of theoretical samples with 50% and 200% potency"),
sliderInput("dilslider", "Adjust the dilutions(+-change in %)", min = -100, max = 100, value = 0, step = 1, round = 0), sliderInput("dilslider", "Adjust the dilutions(+-change in %)", min = -100, max = 100, value = 0, step = 1, round = 0),
@@ -595,8 +593,7 @@ server <- function(input, output, session) {
"Short guidance: wider dilution ranges increase the CIs of rel. potency, and decrease the CIs of upper and lower asymptote ratios, as well as Hill's slope ratios", br(), "Short guidance: wider dilution ranges increase the CIs of rel. potency, and decrease the CIs of upper and lower asymptote ratios, as well as Hill's slope ratios", br(),
"Narrower dilution ranges decrease the CIs of rel. potency, and increase the CIs of upper and lower asymptote ratios, ands Hill's slope ratios", "Narrower dilution ranges decrease the CIs of rel. potency, and increase the CIs of upper and lower asymptote ratios, ands Hill's slope ratios",
), ),
column( column(3,
3,
h3("Bend points"), h3("Bend points"),
tableOutput("bps"), tableOutput("bps"),
tableOutput("extremebps"), tableOutput("extremebps"),
@@ -670,6 +667,22 @@ server <- function(input, output, session) {
}) })
observe({
if (!is.null(input$MiFile)) {
MinFile <- input$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)
dat <- lapply(sheets, openxlsx::read.xlsx, xlsxFile = t.filelocation)
names(dat) <- sheets
Dat$Mws <- dat
names(Dat$Mws) <- sheets
Dat$Msheets <- sheets
Dat$MFileName <- input$MiFile[["name"]]
}
})
#### process XLSX file ---- #### process XLSX file ----
observe({ observe({
if (!is.null(input$iFile)) { if (!is.null(input$iFile)) {
@@ -1339,7 +1352,7 @@ server <- function(input, output, session) {
if (is.null(input$PureErr)) { if (is.null(input$PureErr)) {
return(NULL) return(NULL)
} }
if (!is.null(Dat$FITsFlag)) { if (Dat$FITsFlag) {
return(NULL) return(NULL)
} }
@@ -1974,10 +1987,12 @@ server <- function(input, output, session) {
#### 4pl potency table XL ---- #### 4pl potency table XL ----
observe({ observe({
if (is.null(Dat$EXCEL)) { if (is.null(Dat$EXCEL)) {
return(NULL) return(NULL)
} }
if (!is.null(Dat$FITsFlag)) { if (Dat$FITsFlag) {
return(NULL) return(NULL)
} }
ro_new <- Dat$EXCEL ro_new <- Dat$EXCEL
@@ -2025,7 +2040,7 @@ server <- function(input, output, session) {
colnames(pottab4_) <- c("model", "potency", "lower95%CI", "upper95%CI", "relative_lower95%CI", "relative_upper95%CI", "test_result") colnames(pottab4_) <- c("model", "potency", "lower95%CI", "upper95%CI", "relative_lower95%CI", "relative_upper95%CI", "test_result")
row.names(pottab4_) <- NULL row.names(pottab4_) <- NULL
REP$pottab4plXL <- pottab4_[1:2, ] REP$pottab4plXL <- pottab4_[1:2, ]
#browser()
output$pottab4plXL <- DT::renderDataTable({ output$pottab4plXL <- DT::renderDataTable({
dat <- datatable(pottab4_[1:2, ], dat <- datatable(pottab4_[1:2, ],
rownames = F, rownames = F,
@@ -2055,8 +2070,101 @@ server <- function(input, output, session) {
#### Dilutions Simulator ---- #### Dilutions Simulator ----
output$plotfordilutions <- renderPlot({ output$plotfordilutions <- renderPlot({
tab <- sim2() if (!is.null(Dat$Mws))
tab <- as.data.frame(tab) AllXL <- Dat$Mws
AllSheets <- Dat$Msheets
for (N_WS in 1:length(AllXL)) {
datWS <- as.data.frame(AllXL[[N_WS]])
cn <- colnames(datWS)
logI <- grep("log|ln", cn)
logDoseI <- grep("log_dose", cn)
if (length(logI) > 0 & length(logDoseI) == 0) {
datWS$log_dose <- datWS[, logI]
datWS2 <- datWS[, -logI]
CORro <- cor(datWS$log_dose, datWS[, 3])
} else if (length(logI) == 0 & length(logDoseI) == 0) {
Ind <- grep(".ilution|.ose|.onc", cn)
datWS$log_dose <- log(datWS[, Ind])
CORro <- cor(datWS[, Ind], datWS[, 3])
datWS2 <- datWS[, -Ind]
} else if (length(logI) > 0 & length(logDoseI) > 0) {
datWS2 <- datWS
CORro <- cor(datWS[, logI], datWS[, 3])
}
Dat$datWS2 <- datWS2
FITs <- Fitting_FUNC(datWS2, TransFlag = F)
pot_est <- FITs[[3]]
potU_est <- FITs[[4]]
# unrestricted
SU_mu <- FITs[[2]]
URMcoeffs <- SU_mu$coefficients
X <- seq(min(log(datWS23$log_dose)), max(log(datWS2$log_dose)), 0.1)
sigRef <- URMcoefs[1,1] + (URMcoefs1[4,1]-URMcoefs[1,1])/(1+exp(URMcoefs[2,1]*(URMcoefs[3,1]-X)))
sigTest1 <- URMcoefs[5,1] + (URMcoefs[8,1]-URMcoefs[5,1])/(1+exp(URMcoefs[6,1]*(URMcoefs[7,1]-X)))
dfPlotsigRef <- data.frame(X=X, sigRef = sigRef, Prod = pdfInd)
dfPlotsigTest <- data.frame(X=X, sigTest = sigTest1, Prod = AllSheets[[N_WS]])
if (!exists("SIGrefDF")) SIGrefDF <- dfPlotsigRef else SIGrefDF <- rbind(SIGrefDF, dfPlotsigRef)
if (!exists("SIGtestDF")) SIGtestDF <- dfPlotsigTest else SIGtestDF <- rbind(SIGtestDF,dfPlotsigTest)
EC50TEST <- as.numeric(c(URMcoefsDF[,8]))
# EC50TEST <- EC50TEST[!EC50TEST %in% boxplot.stats(EC50TEST)$out]
EC50REF <- as.numeric(URMcoefsDF[,4])
# EC50REF <- EC50REF[!EC50REF %in% boxplot.stats(EC50REF)$out]
UasREF <- as.numeric(URMcoefsDF[,5])
# UasREF <- UasREF[!UasREF %in% boxplot.stats(UasREF)$out]
LasREF <- as.numeric(URMcoefsDF[,2])
# LasREF <- LasREF[!LasREF %in% boxplot.stats(LasREF)$out]
#
# Dat$URMcoefsDF <- URMcoefsDF
# Dat$RestrM <- RestrM
# Dat$CalcPot <- CalcPot
#
#### sigmoid plots ----
Slope <- as.numeric(URMcoefsDF[1,3])
# if (Slope > 0) {
# x_UA <- max(X); x_LA <- min(X)
# } else { x_UA <- min(X); x_LA <- max(X) }
#
# p1 <- ggplot(SIGrefDF, aes(x_X, y=sigRef, col=as.factor(Prod))) +
# geom_line() +
# annotate("text", label="x", x=x_UA, y=UasREF, alpha=0.2) +
# annotate("text", label="o", x=x_LA, y=LasREF, alpha=0.2) +
# geom_vline(xintercept = EC50REF, alpha = 0.2) +
# xlab("dilutions") +
# ggtitle("Plot of all calculated reference fits (unrestricted model, in gray vertical lines: EC50)") +
# theme_bw() +
# theme(axis.text = element_text(face = "bold", size = 15),
# plot.title = element_text(size = 15, face = "bold"))
#
# output$sigPlotREF <- renderPlot({ p1 })
#
# PLOTS$sigPlotREF <- p1
#
# p2 <- ggplot(SIGtestDF, aes(x_X, y=sigTest, col=as.factor(Prod))) +
# geom_line() +
# #annotate("text", label="x", x=x_UA, y=UasREF, alpha=0.2) +
# #annotate("text", label="o", x=x_LA, y=LasREF, alpha=0.2) +
# geom_vline(xintercept = EC50TEST, alpha = 0.2) +
# xlab("dilutions") +
# ggtitle("Plot of all calculated reference fits (unrestricted model, in gray vertical lines: EC50)") +
# theme_bw() +
# theme(axis.text = element_text(face = "bold", size = 15),
# plot.title = element_text(size = 15, face = "bold"))
#
# output$sigPlotREF <- renderPlot({ p2 })
#
# PLOTS$sigPlotTEST <- p2
dils <- tab$log_dose dils <- tab$log_dose
min_y <- min(tab[, 1:3]) min_y <- min(tab[, 1:3])
max_y <- max(tab[, 1:3]) max_y <- max(tab[, 1:3])
@@ -2077,6 +2185,9 @@ server <- function(input, output, session) {
dils2 <- dils_avsc + av dils2 <- dils_avsc + av
dilfactors <- 1 / exp(dils2 - lag(dils2)) dilfactors <- 1 / exp(dils2 - lag(dils2))
} }
} #for N_WS
Dat$newDils <- dils2 Dat$newDils <- dils2
@@ -2538,6 +2649,8 @@ server <- function(input, output, session) {
params = list( params = list(
FileName = Dat$FileName, FileName = Dat$FileName,
author = Dat$Author, author = Dat$Author,
NoP = Dat$NoP,
Assay = Dat$Assay,
REP = REP, REP = REP,
REPlin = REPlin, REPlin = REPlin,
coeffsLin = Dat$coeffs_UN coeffsLin = Dat$coeffs_UN
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