Introduction

This document describes in detail the procedure used to select molecules having a potential inhibitory effect on the infection of cultured cells by covid-19.

Pre-publication in bioRxiv:

  • In vitro screening of a FDA approved chemical library reveals potential inhibitors of SARS-CoV-2 replication. Franck Touret, Magali Gilles, Karine Barral, Antoine Nougairede, Etienne Decroly, Xavier de Lamballerie, Bruno Coutard. bioRxiv 2020.04.03.023846. DOI 10.1101/2020.04.03.023846

Data

Viability measurements

Cell Titer Blue intensity (CTB)

The number of viable cells per well is measured by a colorimetric test. The primary measure is the Cell Titer Blue intensity (\(CTB\)).

#### Read the CTB values from the Excel workbook ####
message("Reading Cell Titer Blue (CTB) values from file ", supTableFile)
nbPlates <- 19
rowsPerPlate <- 8
columnsPerPlate <- 12

dataPerPlate <- list()

## Control 1: uninfected cells
cellControl <- data.frame(matrix(ncol = 8, nrow = nbPlates))
colnames(cellControl) <- LETTERS[1:rowsPerPlate]

## Control 2: untreated infected cells
virusControl <- data.frame(matrix(ncol = 6, nrow = nbPlates))
colnames(virusControl) <- LETTERS[3:rowsPerPlate]

## Prepare a table to store the raw data
inhibTable <- data.frame(matrix(ncol = 8, nrow = nbPlates*rowsPerPlate * columnsPerPlate))
colnames(inhibTable) <- c("ID", 
                          "Plate", 
                          "Row", 
                          "Column", 
                          "CTB", 
                          "cellControl", 
                          "virusControl",
                          "Chemical.name")

i <- 2 ## for quick test
for (i in 1:nbPlates) {
  message("\tLoading data from plate ", i)
  sheetName <- paste0("Plate", i)
  
  ## Raw measures
  # rawMeasures <- read.xlsx(file = supTableFile, 
  #                          sheetName = sheetName, 
  #                          rowIndex = 30:37,
  #                          colIndex = 2:13, header = FALSE)
  rawMeasures <- read_xlsx(path = supTableFile, col_names = FALSE, 
                           sheet = sheetName, 
                           range = "B30:M37", progress = FALSE)
  rawMeasures <- as.data.frame(rawMeasures)
  rownames(rawMeasures) <- LETTERS[1:nrow(rawMeasures)]
  colnames(rawMeasures) <- 1:ncol(rawMeasures)
  # dim(rawMeasures)
  # View(rawMeasures)

  ## Extract control values
  cellControl[i, ] <- as.vector(rawMeasures[,1])
  virusControl[i, ] <- as.vector(rawMeasures[3:8,12])
  platevc <- mean(unlist(virusControl[i, ]))
  platecc <- mean(unlist(cellControl[i, ]))

  ## Extract all values
  r <- 1
  for (r in 1:rowsPerPlate) {
    currentRowName <- LETTERS[r]
    currentValues <- unlist(rawMeasures[currentRowName,])
    id <- paste0(sprintf("%02d",i),
                 currentRowName, 
                 sprintf("%02d",1:columnsPerPlate))
    
    ## Compute the start index for the data table
    startIndex <- (i - 1) * (rowsPerPlate * columnsPerPlate) + (r - 1) * columnsPerPlate + 1
    # message(cat("\t\tIDs\t",  startIndex, id))
    indices <- startIndex:(startIndex + columnsPerPlate - 1)
    # length(indices)
    inhibTable[indices, "ID"] <- id
    inhibTable[indices, "Plate"] <- i
    inhibTable[indices, "Row"] <- currentRowName
    inhibTable[indices, "Column"] <- 1:columnsPerPlate
    inhibTable[indices, "CTB"] <- currentValues
    inhibTable[indices, "virusControl"] <- platevc
    inhibTable[indices, "cellControl"] <- platecc
  }
  
  dataPerPlate[[i]] <- list()
  dataPerPlate[[i]][["rawMeasures"]] <- rawMeasures
}

# dim(inhibTable)
# names(inhibTable)
# View(inhibTable)
# View(dataPerPlate)
# View(dataPerPlate[[1]][["rawMeasures"]])
# table(inhibTable$Row, inhibTable$Column) ## Check that there are 19 entries for each plate position

## Use the plate well ID as rowname
rownames(inhibTable) <- inhibTable$ID

## Check consistency between IDs in supplementary Touret Table 1
##  and those created here
touretIDs <- unlist(supTable$ID)
# length(touretIDs)
inhibIDs <- inhibTable$ID
# length(inhibIDs)

## Cell control: uninfected cells
cellControlIndices <- inhibTable$Column == 1
inhibTable[cellControlIndices, "Chemical.name"] <- "uninfected"

## Virus control: infected cells, no treatment
virusControlIndices <- (inhibTable$Column == 12) & (inhibTable$Row %in% LETTERS[3:8])
# table(virusControlIndices)
inhibTable[virusControlIndices, "Chemical.name"] <- "infected no treatment"

## Define the treatment type
wellType <- NA
wellType[cellControlIndices] <- "cellCtl"
wellType[virusControlIndices] <- "virusCtl"

## All the other ones are treated with a given molecule
wellType[!(virusControlIndices | cellControlIndices)] <- "treated"

inhibTable[, "wellType"] <- wellType


#### Retrieve fields from the bioRxiv supplementary Table 1 ####

for (field in c("Chemical.name",
                "Broad.Therapeutic.class",
                "Reported.therapeutic.effect",
                "Inhibition.Index")) {
  inhibTable[, field] <- NA
  inhibTable[inhibTable$ID %in% touretIDs, field] <- 
    as.vector(supTable[, field])
}


# ## Retrieve the molecule names from Table 1 of the bioRxiv workbook
# inhibTable$Chemical.name <- NA
# inhibTable[inhibTable$ID %in% touretIDs, "Chemical.name"] <- 
#   as.vector(supTable$Chemical.name)




kable(t(table(inhibTable$wellType)), caption = "Well types. cellCtl: no infection; virusCtl: infection without treatment; treated: inhected and treated with one molecule", )
Well types. cellCtl: no infection; virusCtl: infection without treatment; treated: inhected and treated with one molecule
cellCtl treated virusCtl
152 1558 114

The raw data contains 19 plates with 8 rows (indiced A to H) and 12 columns (indiced from 1 to 12. )

The raw data consists of CTB measurements in cell cultures.

Distribution of raw CTB values

Distributions of the CTB measures. Top: uninfected cells. Middle: infected cells without treatment. Bottom: infected cells treated with a specific molecule.

Distributions of the CTB measures. Top: uninfected cells. Middle: infected cells without treatment. Bottom: infected cells treated with a specific molecule.

  • Cell control.

    • The top panel (green) shows the distribution of CTB measurements in controls cultures, where the cells were neither infected by the virus nor treated with a drug.
    • Each plate contains 8 wells with uninfected cells (total = 152).

  • Virus control.

    • The middle panel (orange) shows the distribution of CTB measurements in infected cells without drug treatment
    • The virus control was performed on 6 wells per plate, total = 114).

  • Treated cells.

    • The bottom distribution (pale blue) shows the CTB values for cells infected and treated with a given drug.

    • Note that each drug was tested on a single well (no replicates). Indeed, in order to face the COVID-19 emergency, the study attempted to test as fast as possible a wide range of molecules. This first screening was thus performed without replicates. This has to be taken into account for the normalization, which should be done with no estimation of the variance for the individual drugs.

    • The distribution is strongly asymmetrical, and seems bi- or multi-modal. This distribution can be considered as a mixture between different distributions;

      • all the drugs that have no inhibitory effect (and are thus expected to have a CTB similar to the virus control);
      • various drugs that inhibit the action of the virus, each one with its specific level of inhibition. This probably corresponds to the widely dispersed values above the bulk of distribution (and above the virus control distribution)

Hydroxychloroquine sulfate

We assin a specific label to Hydroxychloroquine sulfate, which has a specific interest since it is one of the molecules tested in an European clinical trial.

CTB boxplots

Distribution of CTB values per plate. Top virus control (untreated infected cells); middle: treated cells; bottom: cell control (uninfected). Black plain circles: arbidol control duplicates.

Distribution of CTB values per plate. Top virus control (untreated infected cells); middle: treated cells; bottom: cell control (uninfected). Black plain circles: arbidol control duplicates.

The boxplot of the CTB measurements highlights a plate effect, for the treated cells (middle barplots) but also for the untreated virus control (top boxplots) and uninfected cell control (bottom boxplots).

  • Treated:

    • The medians and interquartile ranges show strong variations between plates.
    • In particular, plate 1 (in red) has a the smallest median and a remarkably compact interquartile range. There are many statistical outliers (empty circles) in this plate, which might correspond to the molecules having a significant inhibitory effect.
    • In contrast, plates 11 to 15 show a high median and a wide dispersion of CTB measures, and there is not a single statistical outlier.

  • Virus control (\(vc\))

    • As expected, untreated infected cells generally gave a very small CTB, with small variations (very compact interquartile rectangles)
    • There is a problem for the virus control of plate 17, which shows a broad range of values, with a third quartile falling in the range of the uninfected cells. This suggests a problem with at least 2 of the 6 replicates (missed infection ?). However, the median of the virus controls for this plate falls in the same range as for the virus control of the other plates.

  • Cell control (\(cc\))

    • The cell control performs as expected in all the plates, with high CTB values.
    • Note however that the CTB of uninfected cells show inter-plate variations, with median values ranging from ~37,000 to ~53,000.

Importantly, there is a consistency between the inter-plate differences observed for virus control, treated cells and cell control, respectively. For example, plate 2 whose consistently higher value than the other plates for the three types of wells. This highlights the importances to perform a plate-wise standardization.

Plate-wise standardization

Plate-wise control points

Taking into account the above-reported results, we apply the following procedure to standardize the individual viability measures.

For each plate, we define two control values:

  • \(CTB_{cc,i}\): median CTB of the 8 cell controls (uninfected cells) of plate \(i\)
  • \(CTB_{vc,i}\): median CTB of the 6 virus controls (infected untreated cells) of plate \(i\)

These two values are deliberately estimated with the median measurement of the control replicate, in order to avoid the effect of outliers as denoted for the virus control of plate 17.

Plate-wise statistics on the CTB
plate CTBmean CTBsd CTBmedian CTBmin CTBmax CTBvc CTBcc
1 14968.79 9179.079 10568.5 7326 45194 10202.0 37197.5
2 21151.54 11359.022 17339.0 10069 55014 14018.0 51971.0
3 15561.16 8274.558 12261.0 8110 43083 10482.0 40016.0
4 20376.58 10986.807 15742.0 8648 46289 12241.0 44342.0
5 16882.96 9640.466 13660.5 7114 43824 9876.5 42012.0
6 15654.72 9488.589 11291.5 7389 43312 9942.0 38458.5
7 17024.33 9779.790 12338.0 8040 43221 10626.0 39375.0
8 16583.02 9286.450 12010.5 8033 43402 11185.5 38161.0
9 18603.48 9702.154 14293.5 9418 45126 12852.5 43904.5
10 18183.64 9574.292 14639.0 8690 45927 11993.0 42310.5
11 22241.27 10113.348 19335.0 5255 46301 12856.0 40742.5
12 21527.03 9444.469 19471.5 5248 43404 10781.5 40187.5
13 24039.02 10818.207 23996.5 5097 44821 11987.0 39596.5
14 23585.09 9364.788 23567.0 4263 42400 12083.0 36942.0
15 24082.91 10388.209 23327.0 4685 45445 11686.0 38995.5
16 19891.76 8991.913 19738.0 4483 45555 10090.0 34521.5
17 19518.59 9053.786 17587.0 4983 41762 12314.5 36445.0
18 21942.55 9706.601 19075.5 5173 44573 12623.0 40740.5
19 19526.67 9930.452 15299.5 4578 43712 10505.0 37360.5

Viability ratio and log2(ratio)

The viability ratio (\(R\)) associated to a given treatment with molecule \(m\) on a given plate \(i\) is defined as the ratio between

  • the \(CTB\) measured on infected cells treated with this molecule (\(CTB_{m,i}\)) and
  • the median \(CTB\) of 8 replicates of uninfected cells (denoted \(cc\) for cell control) on the same plate (\(CTB_{cc,i}\)).

\[R_{m,i} = \frac{CTB_{m,i}}{CTB_{cc, i}}\]

We further apply logarithmic transformation in order to normalise this ratio.

\[R_{m,i} = log2(R) = log2 \left( \frac{CTB_{m,i}}{CTB_{cc, i}} \right)\]

Viability ratio boxplots

par(mfrow = c(1,2))


#### Boxplots of viability ratios per plate ####

Rfloor <- floor(min(inhibTable$Vratio))
Rceiling <- max(inhibTable$Vratio) * 1.1

## Box plot per plate and well type
boxplot(Vratio ~ Plate + wellType, 
        main = "Viability ratio distribution",
        data = inhibTable, 
        las = 1, col = plateColor, 
        xlab = "R = CTB / CTBcc", 
        ylim = c(min(inhibTable$Vratio), Rceiling),
        cex.axis = 0.5, cex = 0.5,
        horizontal = TRUE)
abline(v = 1, col = "#00BB00")
abline(v = seq(from = Rfloor, to = Rceiling, by = 0.05), col = "#EEEEEE", lty = "dashed")
abline(v = seq(from = Rfloor, to = Rceiling, by = 0.2), col = "grey")
legend("topright", legend = names(plateColor), 
       title = "Plate", fill = plateColor, cex = 0.6)

## Add points to denote the arbidol controls
stripchart(Vratio ~ Plate, vertical = FALSE, 
           data = inhibTable[arbidolWells, ],
           method = "jitter", add = TRUE, cex = 0.7, 
           col = markColor["Arbidol"], pch = markPCh["Arbidol"])

legend("bottomleft", 
       title = "Markers", 
       legend = "Arbidol", 
       col = markColor["Arbidol"], 
       pch = markPCh["Arbidol"],
       cex = 0.8)


#### Boxplots of viability log(ratios) per plate ####

Lfloor <- floor(min(inhibTable$Vlog2R))
Lceiling <- ceiling(max(inhibTable$Vlog2R))

## Box plot per plate and well type
boxplot(Vlog2R ~ Plate + wellType, 
        main = "Viability log2(ratio) distribution",
        data = inhibTable, 
        las = 1, col = plateColor, 
        xlab = "L = log2(CTB / CTBcc)", 
        ylim = c(min(inhibTable$Vlog2R), Lceiling),
        cex.axis = 0.5, cex = 0.5,
        horizontal = TRUE)
abline(v = seq(from = Lfloor, to = Lceiling, by = 0.2), col = "#EEEEEE", lty = "dashed")
abline(v = seq(from = Lfloor, to = Lceiling, by = 1), col = "grey")
legend("topright", legend = names(plateColor), 
       title = "Plate", fill = plateColor, cex = 0.6)

## Add points to denote the arbidol controls
stripchart(Vlog2R ~ Plate, vertical = FALSE, 
           data = inhibTable[arbidolWells, ],
           method = "jitter", add = TRUE, cex = 0.7, 
           col = markColor["Arbidol"], pch = markPCh["Arbidol"])

legend("bottomleft", 
       title = "Markers", 
       legend = "Arbidol", 
       col = markColor["Arbidol"], 
       pch = markPCh["Arbidol"],
       cex = 0.8)
Distribution of the viability ratio (left) and log(ratio) (right) per plate. Top virus control (untreated infected cells); middle: treated cells; bottom: cell control (uninfected). Black plain circles: arbidol control duplicates.

Distribution of the viability ratio (left) and log(ratio) (right) per plate. Top virus control (untreated infected cells); middle: treated cells; bottom: cell control (uninfected). Black plain circles: arbidol control duplicates.

The barplots of log2-transformed viability measures show another indication for the possible existence of a plate bias: in plates 11 to 19, several molecules are associated to a much smaller viability than in any of the untreated cells. This might reflect a cytotoxic effect of the drug that would enforce the viral infection, but there is a priori no reason to expect such effects to be concentrated on the last plates.

Two-points scaling: defining a plate-wise relative viability (\(V_{m,i}\))

A plate-wise relative viability \(V_{m,i}\) is defined to indicate the viability of cells treated with a given molecule \(m\) relative to the two controls f their plate (\(i\)):

  • virus control (\(vc\)): infected untreated cells;
  • cell control (\(cc\)): uninfected cells.

It is computed as follows.

\[V_{m,i} = 100 \cdot \frac{L_{m,i} - L_{vc}}{L_{cc} - L_{vc}}\]

where \(L_{cc,i}\) and \(L_{vc,i}\) denote the median values of the log2(ratios) respectively obtained in cell controls and virus controls for plate \(i\).

The plate-wise relative viability \(V_{m,i}\) is measured on a scale where

  • 0 corresponds to the median of infected untreated cells (virus control), and
  • 100 to the median of uninfected cells (cell control).

Note that \(V_{m,i}\) values lower than 0 denote treatments with a lower viability than the untreated virus infection. This might result from various sources: experimental flucturations, cytotoxic effect of the drug or plate bias.

\(V_{m,i}\) can also take values higher than 100, denoting a highly efficient treatment.

Relative viability boxplots

Distribution of relative viability (I) values per plate. Top virus control (untreated infected cells); middle: treated cells; bottom: cell control (uninfected). Black plain circles: arbidol control duplicates.

Distribution of relative viability (I) values per plate. Top virus control (untreated infected cells); middle: treated cells; bottom: cell control (uninfected). Black plain circles: arbidol control duplicates.

The box plots show that the relative viability standardises the measures by positioning each treatment relative to two milestones of its own plate:

  • the median virus control (0)
  • the cell control (100)

The virus controls are well regrouped in the range of smaller \(v_r\) values, except for plate 17.

The cell controls occupy the high range (their first quartile is higher than 80) and are quite compactly grouped around 100.

However, we still observe a strong difference between plates 11-19 and the other plates:

  • their median is mich higher than for the plates 1 to 10;
  • they also show a much wider inter-quartile rectangle, denoting a wide dispersion of values on this plate;
  • for plates 11 and 13-19, this wider dispersion is even visible for the virus controls (untreated infected cells), and it is thus unlikely that it results from the particular molecules sampled on this second half of the plates.

We thus need a way to perform a between-plates standardization of the variance.

Dot plots: relative viability

#### Dot plots of the relative viability ####
VrFloor <- floor(min(inhibTable$Vrel / 10)) * 10
VrCeiling <- max(inhibTable$Vrel) * 1.1

## Virus control plots
par(mfrow = c(4,1))
plot(inhibTable[wellType == "virusCtl", "Vrel"],
     main = "Virus control (infected, untreated)",
     xlab = "Replicates, sorted per plate",
     ylab = "Vr = (R - Rvc) / (Rcc - Rvc)",
     col = inhibTable[wellType == "virusCtl", "color"],
     pch = inhibTable[wellType == "virusCtl", "pch"],
     xlim = c(0, (nbPlates * 6 * 1.05)),
     ylim = c(VrFloor, VrCeiling),
     panel.first = c(abline(h = 0, col = "red", lwd = 2), 
                     abline(h = 100, col = "#008800", lwd = 2),
                     abline(h = seq(VrFloor,VrCeiling, 10), col = "#DDDDDD"),
                     abline(v = (0:19) * 6, col = "#999999")
                     ),
     xaxt = "n",
     las = 1,
     cex = 0.5
     )
mtext(plateNumbers, at = (1:19) * 6 - 3, side = 1, col = plateColor)
legend("topright", 
       legend = names(plateColor), 
       col = plateColor, pch = 1, 
       cex = 0.7)

## Treated cells
plot(inhibTable[wellType == "treated", "Vrel"],
     main = "Relative viability (Vr)",
     xlab = "Molecules",
     ylab = "relative viability",
     col = inhibTable[wellType == "treated", "color"],
     pch = inhibTable[wellType == "treated", "pch"],
     xlim = c(0, (nbPlates * 80 * 1.05)),
     ylim = c(VrFloor, VrCeiling),
     panel.first = c(abline(h = 0, col = "red", lwd = 2), 
                     abline(h = 100, col = "#008800", lwd = 2),
                     abline(h = seq(VrFloor,VrCeiling, 10), col = "#DDDDDD"),
                     abline(v = (0:19) * 80, col = "#999999")
                     ),
     xaxt = "n",
     las = 1,
     cex = 0.5
     )
mtext(plateNumbers, at = (1:19) * 80 - 40, side = 1, col = plateColor)
legend("topright", 
       legend = names(plateColor), 
       col = plateColor, pch = 1, 
       cex = 0.6)

## Cell control
plot(inhibTable[wellType == "cellCtl", "Vrel"],
     main = "Cell control (uninfected)",
     xlab = "Replicates, sorted per plate",
     ylab = "relative viability",
     col = inhibTable[wellType == "cellCtl", "color"],
     pch = inhibTable[wellType == "cellCtl", "pch"],
     xlim = c(0, (nbPlates * 8 * 1.05)),
     ylim = c(VrFloor, VrCeiling),
     panel.first = c(abline(h = 0, col = "red", lwd = 2), 
                     abline(h = 100, col = "#008800", lwd = 2),
                     abline(h = seq(VrFloor,VrCeiling, 10), col = "#DDDDDD"),
                     abline(v = (0:19) * 8, col = "#999999")
                     ),
     xaxt = "n",
     las = 1,
     cex = 0.5
     )
mtext(plateNumbers, at = (1:19) * 8 - 4, side = 1, col = plateColor)
legend("topright", 
       legend = names(plateColor), 
       col = plateColor, pch = 1, 
       cex = 0.7)
# names(supTable)

## Rank plot
VrRank <- order(inhibTable$Vrel, decreasing = TRUE)
plot(inhibTable[VrRank, "Vrel"],
     main = "Ranked relative viability values",
     xlab = "Molecules (ranked by relative viability)",
     ylab = "relative viability",
     col = inhibTable[VrRank, "color"],
     pch = inhibTable[VrRank, "pch"],
     cex = 0.5,
     panel.first = grid(),
     xlim = c(0, length(VrRank) * 1.05)
     )
abline(h = 0, col = "red", lwd = 2)
abline(h = 100, col = "#008800", lwd = 2)
legend("topright", 
       legend = names(plateColor), 
       col = plateColor, pch = 1, 
       cex = 0.4)
Values of the plate-wise relative viability for all the tested molecules. Molecules are colored according to the plate number. A: virus control (infected untreated); B: treated cells; C: cell control (untreated cells); D: ranked values (all types). Plain triangles: virus control (untreated infected cells). Black plain circles: arbidol control duplicates per plate. Orange square: Hydroxychloroquine sulfate.

Values of the plate-wise relative viability for all the tested molecules. Molecules are colored according to the plate number. A: virus control (infected untreated); B: treated cells; C: cell control (untreated cells); D: ranked values (all types). Plain triangles: virus control (untreated infected cells). Black plain circles: arbidol control duplicates per plate. Orange square: Hydroxychloroquine sulfate.

IQR-based standardization

Plate-wise IQR-standardized viability

To take into account the between-plate differences in variance denoted above, we compute a z-scores from the original value.

  • centering: substract an estimator of the plate-wise mean \(\hat{\mu}\);
  • scaling: divide by an estimator of the plate-wise standard deviation (\(\hat{\sigma_i}\))

\[z_{c,i} = \frac{V_c - \hat{\mu_i}}{\hat{\sigma_i}}\]

where

  • \(V_c\) is the viability for molecule \(c\);
  • \(\hat{\mu_i}\) is the estimate for the mean viability of all the treated cells in plate \(i\);
  • \(\hat{\sigma_i}\) is the estimate for the standard deviation of all the treated cells in plate \(i\);

In classical statistics, the estimators of centrality and dispersion are derived from the sample mean and standard deviation, respectively:

  • the population mean is used as maximum likelihood estimator of the population: \(\hat{\mu} = \bar{x}\)
  • the population standard deviation (\(\sigma\)) is estimated with the sample standard deviation, corrected for the systematic bias: \(\hat{\sigma} = \sqrt{n/(n-1)} \cdot s\))

However, we must be careful because each plate supposedly contain a mixture of inactive (no inhibitory effect) and active (inhibitory) molecules. The previous histograms and box plots show that these inhibitory molecules appear as statistiacal outliers (with very high viability values) and would thus strongly bias the estimation of the background variance (the variance due to fluctuations in absence of treatment).

One possibility would be to use the standard deviation of the virus control to this purpose, but this would leat to instable estimators, since they would be based on 6 points per plate. In addition, the boxplots show that the variance among treated cells is higher than the virus control, suggesting some generic effect of the treatments.

Another strategy is to consider that the variance (and standard deviation) can be estimated from the bulk of treated cell viability measures themselves, and to use robust estimators of the central tendency (i.e. the plate-wise median) and dispersion (i.e. the plate-wise interquartile range).

This approach relies on the assumption that, in each plate, the number of active molecule (statistical outliers). Since teach plate contains tests of 80 molecules, there are 19 molecules above the third quartile (\(Q3\)). However, it has to be noted that the plates were manufactured with some grouping of molecules of the same structural family. It might thus happen that some plates contain more than 19 molecules having an inhibitory effect. Such a situation would result in a loss of sensitivity, since the presence of active molecules in the inter-quartile range would lead to over-estimate the dispersion.

An alternative is to estimate the dispersion based on the range between the first quartile (\(Q1\)) and the median (\(\tilde{x}\)) of each plate.

In summary, we compute robust estimators, in order to avoid the effect of outliers (in this case, the suspected outliers are the molecules having an actual inhibitory effect). To this purpose, we use:

  • the median plate-wise relative viability for all the molecules (\(\tilde{I_i}\)) to estimate the mean
  • the plate-wise standardized inter-quantile range; (\(IQR_i\)) standardized by the normal \(IQR\) to estimate the standard deviation.
#### Compute plate-wise statistics ####
statPerPlate <- data.frame(
  Plate = plateNumbers,
  TrMean = as.vector(by(
    data = inhibTable[wellType == "treated", "Vrel"], 
    INDICES = inhibTable[wellType == "treated", "Plate"], 
    FUN = mean)),
  TrSD = as.vector(by(
    data = inhibTable[wellType == "treated", "Vrel"], 
    INDICES = inhibTable[wellType == "treated", "Plate"], 
    FUN = sd)),
  TrMedian = as.vector(by(
    data = inhibTable[wellType == "treated", "Vrel"], 
    INDICES = inhibTable[wellType == "treated", "Plate"], 
    FUN = median)),
  vcMedian = as.vector(by(
    data = inhibTable[wellType == "virusCtl", "Vrel"], 
    INDICES = inhibTable[wellType == "virusCtl", "Plate"], 
    FUN = median)),
  ccMedian = as.vector(by(
    data = inhibTable[wellType == "cellCtl", "Vrel"], 
    INDICES = inhibTable[wellType == "cellCtl", "Plate"], 
    FUN = median)),
  arbidolMean = as.vector(by(
    data = inhibTable[arbidolWells, "Vrel"], 
    INDICES = inhibTable[arbidolWells, "Plate"], 
    FUN = mean)),
  TrMin = as.vector(by(    
    data = inhibTable[wellType == "treated", "Vrel"], 
    INDICES = inhibTable[wellType == "treated", "Plate"], 
    FUN = min)),
  TrMax = as.vector(by(
    data = inhibTable[wellType == "treated", "Vrel"], 
    INDICES = inhibTable[wellType == "treated", "Plate"], 
    FUN = max)),
  TrQ1 = as.vector(by(
    data = inhibTable[wellType == "treated", "Vrel"], 
    INDICES = inhibTable[wellType == "treated", "Plate"], 
    FUN = quantile, probs = 0.25)),
  TrQ3 = as.vector(by(
    data = inhibTable[wellType == "treated", "Vrel"], 
    INDICES = inhibTable[wellType == "treated", "Plate"], 
    FUN = quantile, probs = 0.75)),
  TrIQR = as.vector(by(    data = inhibTable[wellType == "treated", "Vrel"], 
    INDICES = inhibTable[wellType == "treated", "Plate"], 
    FUN = IQR))
)
rownames(statPerPlate) <- statPerPlate$Plate

We define a plate-wise scaling factor from the interquantile range, standardized by the inter-quartile range of a Gaussian distribution.

\[S_i = \frac{Q3_N - Q1_N}{Q3_i - Q3_i} = \frac{1.349}{Q3_i - Q3_i}\]

Where \(Q1\) and \(Q3\) denote the first and third quartile, \(N\) the Normal distribution, and \(i\) is the plate number.

The relative viabilities of each plate are then multiplied by the corresponding scaling factor to obtain plate-wise standardized values (\(z\)), which will have the same inter-quartile range as the normal distribution.

\[z_{c,i} = \frac{I_{m,i} - \hat{\mu_i}}{\hat{\sigma_i}} = (I_{m,i} - \tilde{I_i}) \frac{Q3_N - Q1_N}{Q3_i - Q3_i} = (v_c - \tilde{v_i}) \cdot S_i\]

where

  • \(Q1_N\) and \(Q3_N\) are the first and third quartiles of the normal distribution,
  • \(Q1_i\) and \(Q3_i\) are the first and third quartiles of the relative viability for all the molecules tested on plate \(i\),

The table below indicates the plate-wise statistics and scaling factor.

Plate-wise statistics of treated cells. Column prefixes: Tr = treated cells; cc = cell control (uninfected cells); vc = virus control (infected, untreated cells).
Plate TrMean TrSD TrMedian vcMedian ccMedian arbidolMean TrMin TrMax TrQ1 TrQ3 TrIQR scaling
1 12.90684 28.85439 2.589052 0 100 86.95038 -25.59828 96.51344 -1.7821824 13.16103 14.94322 0.0902737
2 17.39446 27.93057 16.069910 0 100 83.09473 -25.25135 85.57929 -0.5736503 26.71207 27.28572 0.0494390
3 16.83370 18.63510 11.395323 0 100 75.08391 -19.15266 79.09630 6.5846565 21.89036 15.30570 0.0881358
4 24.81053 34.66755 18.942453 0 100 74.97339 -26.98529 95.77630 3.5136062 51.96317 48.44957 0.0278430
5 23.26384 29.05021 21.490158 0 100 77.77693 -22.65224 95.78776 6.7390393 37.13402 30.39498 0.0443816
6 17.43508 30.30878 8.006709 0 100 90.14721 -21.90392 93.95942 -0.8851005 33.63426 34.51936 0.0390789
7 21.08448 30.61298 11.384151 0 100 79.78517 -21.27708 107.11582 3.6549605 28.72765 25.07269 0.0538027
8 16.67873 30.63601 5.283791 0 100 89.77955 -26.97461 110.48853 -2.4830636 27.03439 29.51745 0.0457011
9 16.31472 25.35433 7.863786 0 100 85.92780 -25.29322 94.09538 2.5641306 19.27661 16.71248 0.0807169
10 19.42648 25.89632 14.943992 0 100 87.83983 -25.54365 94.03011 2.5522727 25.38238 22.83011 0.0590877
11 35.61332 39.56404 35.389084 0 100 95.99690 -76.49642 111.03708 14.4378585 62.68187 48.24401 0.0279616
12 43.11607 30.50020 44.454842 0 100 94.35243 -54.72326 102.67258 22.5882232 63.03681 40.44858 0.0333505
13 45.02793 47.46814 55.760669 0 100 92.00095 -71.05808 110.34226 27.3510609 78.39580 51.04474 0.0264274
14 48.84468 46.17014 58.970068 0 100 82.41156 -93.22169 112.33839 35.9895577 76.01952 40.02996 0.0336992
15 49.12716 41.55740 57.064352 0 100 85.30208 -75.32854 112.66365 28.9231837 83.82389 54.90071 0.0245713
16 43.91908 38.84888 53.967685 0 100 79.82340 -65.94913 122.55003 18.4567483 71.31749 52.86074 0.0255195
17 26.21813 40.33094 28.927309 0 100 81.93965 -82.28630 98.15012 5.1396817 53.96415 48.82447 0.0276292
18 35.81653 36.11849 34.146657 0 100 94.46603 -75.77164 107.65872 17.4846896 58.06189 40.57720 0.0332448
19 35.74937 37.27653 28.621896 0 100 87.94144 -65.45262 112.37523 15.1202507 62.11723 46.99698 0.0287035
Statistics of the plate-wise IQR-standardized viability
Stat
mean 0.1656308
sd 1.4587500
IQR 1.2842621
var 2.1279515
min -5.1287479
Q1 -0.5507888
median 0.0000000
Q3 0.7334733
max 8.4789023

Histograms of inter-quartile standardized viability

The histogram of plate-wise IQR-standardized viability shows a clear improvement: the median is much closer to the mode than with the raw or log-transformed II values.

Distribution of the plate-wise IQR-standardized viability (z-scores) Top: virus control (infected, untreated); middle: treated; bottom: cell control (untreated)

Distribution of the plate-wise IQR-standardized viability (z-scores) Top: virus control (infected, untreated); middle: treated; bottom: cell control (untreated)

Boxplots: inter-quartile standardized viability

Distribution of inter-quartile standardized viability (z) values per plate. Top virus control (untreated infected cells); middle: treated cells; bottom: cell control (uninfected). Black plain circles: arbidol control duplicates.

Distribution of inter-quartile standardized viability (z) values per plate. Top virus control (untreated infected cells); middle: treated cells; bottom: cell control (uninfected). Black plain circles: arbidol control duplicates.

The above boxplots show that the inter-quartile standardization efficiently corrects for the over-dispersion of the plates 11 to 19. However we may expect a lot of sensitivity for these plates. There are however still some weaknesses.

  • The virus control show good properties: in absence of treatment, infected cells have sligtly negative values, except for 2 outliers in plate 17.

  • The cell control box plots show wide variation in their medians and dispersion:

    • Uninfected cells (cell control) have much lower values in some plates (plates 4 and 11-19) than in other ones. This is not expected, since these cells should by definition have the same inhibition values.

    • Even for the plates where the cell controls have a high relative viability after IQR-based standardization, there are strong between-plates variations.

This standardization seems thus efficient to correct the apparent over-dispersion of plates 11 to 19, and thereby reduce the rate of likely false positives, but the wide between-plate variability of the untreated cells suggest that the resulting z-scores should not be interpreted as indicators of inhibition.

Dot plots: inter-quartile standardized viability

zceiling <- max(inhibTable$z) * 1.1
zRange <- c(zfloor, zceiling)

## Virus control
par(mfrow = c(4,1))
plot(inhibTable[wellType == "virusCtl", "z"],
     main = "Virus control (infected, untreated)",
     xlab = "Replicates, sorted per plate",
     ylab = "z",
     ylim = zRange,
     xlim = c(0, (19*6*1.1)),
     col = inhibTable[wellType == "virusCtl", "color"],
     pch = inhibTable[wellType == "virusCtl", "pch"],
     panel.first = c(
       abline(h = seq(from = zfloor, to = zceiling, by = 1), col = "#EEEEEE"),
       abline(h = seq(from = -5, to = zceiling, by = 5), col = "grey"),
       abline(v = (0:19) * 6, col = "#999999")
     ),
     xaxt = "n",
     cex = 0.5, 
     las = 1
     )
abline(h = 0)
abline(h = c(-1, 1), lty = "dotted")
mtext(plateNumbers, at = (1:19) * 6 - 3, side = 1, col = plateColor)
legend("topright", 
       legend = names(plateColor), 
       col = plateColor, pch = 1, 
       cex = 0.7)

## Treated cells
plot(inhibTable[wellType == "treated", "z"],
     main = "IQR-standardized viability (z)",
     xlab = "Molecules",
     ylab = "z",
     ylim = zRange,
     col = inhibTable[wellType == "treated", "color"],
     pch = inhibTable[wellType == "treated", "pch"],
     xaxt = "n",
     cex = 0.5, 
     las = 1,
     xlim = c(0, length(inhibTable[wellType == "treated", "z"])*1.1)
     )
abline(h = seq(from = zfloor, to = zceiling, by = 1), col = "#EEEEEE")
abline(h = seq(from = zfloor, to = zceiling, by = 5), col = "grey")
abline(h = 0)
abline(h = c(-1, 1), lty = "dotted")
abline(v = (0:19) * 82, col = "#999999")
mtext(plateNumbers, at = (1:19) * 82 - 41, side = 1, col = plateColor)
legend("right", 
       legend = names(plateColor), 
       col = plateColor, pch = 1, 
       cex = 0.6)
legend("topright", 
       title = "Markers", 
       legend = names(markColor), 
       col = markColor, 
       pch = markPCh,
       cex = 0.6)

## Cell control
plot(inhibTable[wellType == "cellCtl", "z"],
     panel.first = grid(),
     main = "Cell control (uninfected)",
     xlab = "Replicates, sorted per plate",
     ylab = "z",
     ylim = zRange,
     col = inhibTable[wellType == "cellCtl", "color"],
     pch = inhibTable[wellType == "cellCtl", "pch"],
     xaxt = "n",
     cex = 0.5, 
     las = 1
     )
abline(h = seq(from = zfloor, to = zceiling, by = 1), col = "#EEEEEE")
abline(h = seq(from = zfloor, to = zceiling, by = 5), col = "grey")
abline(h = 0)
abline(h = c(-1, 1), lty = "dotted")
abline(v = (0:19) * 8, col = "#999999")
mtext(plateNumbers, at = (1:19) * 8 - 4, side = 1, col = plateColor)
legend("topright", 
       legend = names(plateColor), 
       col = plateColor, pch = 1, 
       cex = 0.7)
# names(supTable)

## Rank plot
zrank <- order(inhibTable$z, decreasing = TRUE)
plot(inhibTable[zrank, "z"],
     main = "Ranked IQR-standardized viability values",
     xlab = "Molecules (ranked by z index)",
     ylab = "z",
     col = inhibTable[zrank, "color"],
     pch = inhibTable[zrank, "pch"],
     cex = 0.5, las = 1,
     panel.first = grid(),
     xlim = c(0, length(zrank) * 1.05)
     )
abline(h = seq(from = zfloor, to = zceiling, by = 1), col = "#EEEEEE")
abline(h = seq(from = zfloor, to = zceiling, by = 5), col = "grey")
abline(h = 0)
abline(h = c(-1, 1), lty = "dotted")
legend("topright", 
       legend = names(plateColor), 
       col = plateColor, pch = 1, 
       cex = 0.4)
Values of the plate-wise IQR-standardized relative viability ($z$) for all the tested molecules. Molecules are colored according to the plate number. A: virus control (infected untreated); B: treated cells; C: cell control (untreated cells); D: ranked values (all types). Plain triangles: virus control (untreated infected cells). Black plain circles: arbidol control duplicates per plate. Orange square: Hydroxychloroquine sulfate.

Values of the plate-wise IQR-standardized relative viability (\(z\)) for all the tested molecules. Molecules are colored according to the plate number. A: virus control (infected untreated); B: treated cells; C: cell control (untreated cells); D: ranked values (all types). Plain triangles: virus control (untreated infected cells). Black plain circles: arbidol control duplicates per plate. Orange square: Hydroxychloroquine sulfate.

The plot of IQR-standardized viability values (top panel) clearly shows that the plate-wise normalization suppressed the background bias. However it denotes a new problem: the cell controls show striking differences depending on the plates. Noticeably,they show very high values in plates 1 and 3, and very low values in plates 11 to 19, as well as in plate 4.

Significance of Arbidol after IQR-based standardisation

relative viabilities for the arbidol controls (2 replicates per plate)
Plate CTB Vratio Vrel z FDR sig
01A12 1 30140 0.8102695 83.73696 7.3255223 0.0000000 10.2090616
01B12 1 32753 0.8805162 90.16381 7.9056975 0.0000000 11.9838973
02A12 2 43022 0.8278078 85.57929 3.4364768 0.0095644 2.0193432
02B12 2 40310 0.7756249 80.61017 3.1908082 0.0179826 1.7451485
03A12 3 27158 0.6786785 71.07152 5.2596065 0.0000056 5.2500335
03B12 3 30240 0.7556977 79.09630 5.9668772 0.0000002 6.8041204
04A12 4 28768 0.6487754 66.39001 1.3210805 0.6399280 0.1938689
04B12 4 35882 0.8092102 83.55677 1.7990539 0.3966139 0.4016321
05A12 5 29898 0.7116538 76.50695 2.4417358 0.1279384 0.8929990
05B12 5 31018 0.7383129 79.04691 2.5544633 0.1022814 0.9902034
06A12 6 32760 0.8518273 88.15047 3.1319317 0.0214732 1.6681026
06B12 6 34579 0.8991250 92.14395 3.2879925 0.0140365 1.8527400
07A12 7 31481 0.7995175 82.92103 3.8488803 0.0023701 2.6252267
07B12 7 28998 0.7364571 76.64930 3.5114438 0.0076324 2.1173377
08A12 8 32999 0.8647310 88.15897 3.7874855 0.0029637 2.5281661
08B12 8 34338 0.8998192 91.40012 3.9356094 0.0017472 2.7576602
09A12 9 34990 0.7969570 81.53001 5.9461083 0.0000002 6.7837172
09B12 9 38983 0.8879044 90.32560 6.6560607 0.0000000 8.5044463
10A12 10 36991 0.8742747 89.35443 4.3967436 0.0002952 3.5299142
10B12 10 35605 0.8415169 86.32523 4.2177554 0.0005825 3.2347260
11A12 11 40557 0.9954470 99.62165 1.7960449 0.3966139 0.4016321
11B12 11 37285 0.9151378 92.37214 1.5933371 0.4843136 0.3148733
12A12 12 38378 0.9549736 96.50145 1.7357792 0.4170330 0.3798296
12B12 12 36268 0.9024697 92.20341 1.5924375 0.4843136 0.3148733
13A12 13 37554 0.9484172 95.58200 1.0523741 0.8170508 0.0877510
13B12 13 34465 0.8704052 88.41989 0.8630982 0.8917906 0.0497371
14A12 14 29114 0.7881003 78.69880 0.6648434 0.9330662 0.0300875
14B12 14 31633 0.8562882 86.12432 0.9150780 0.8732382 0.0588673
15A12 15 33124 0.8494313 86.49818 0.7232261 0.9199074 0.0362559
15B12 15 32180 0.8252234 84.10597 0.6644467 0.9330662 0.0300875
16A12 16 28576 0.8277740 84.63658 0.7826548 0.9060414 0.0428520
16B12 16 25385 0.7353388 75.01022 0.5369949 0.9330662 0.0300875
17A12 17 30476 0.8362190 83.61734 1.5110402 0.5361907 0.2706807
17B12 17 29380 0.8061462 80.26197 1.4183340 0.5798132 0.2367119
18A12 18 37191 0.9128754 92.23756 1.9312183 0.3203252 0.4944090
18B12 18 39189 0.9619175 96.69449 2.0793879 0.2549801 0.5934937
19A12 19 32305 0.8646833 88.54249 1.7199327 0.4239580 0.3726772
19B12 19 31816 0.8515946 87.34039 1.6854284 0.4339075 0.3626029

Comparison between viability scores

CTB versus viability

#### Dot plots to compare viability scores ####


# names(inhibTable)
# par(mfrow = c(2,2))

#### Dot plot: viability ratio versus relative viability ####
plot(inhibTable[, c("CTB", "Vrel")],
     main = "CTB vs relative viability",
     xlab = "Cell Titer Blue intensity (CTB)", 
     ylab = "Relative viability (I)", 
     col = inhibTable[, "color"],
     pch = inhibTable[, "pch"],
#     xlim = c(0, max(inhibTable$R)*1.1),
     cex = 0.5,
     las = 1)

## Mark cell controls
points(inhibTable[wellType == "cellCtl", c("CTB", "Vrel")], 
       col = markColor["cellCtl"], pch = markPCh["cellCtl"], cex = 0.5)
## Mark virus controls
points(inhibTable[wellType == "virusCtl", c("CTB", "Vrel")], 
       col = markColor["virusCtl"], pch = markPCh["virusCtl"], cex = 0.5)
## Mark arbidol controls
points(inhibTable[arbidolWells, c("CTB", "Vrel")], 
       col = markColor["Arbidol"], pch = markPCh["Arbidol"], cex = 0.5)
## Mark Hydroxychloroquine
points(inhibTable[HOClSindex, c("CTB", "Vrel")], 
       col = markColor["Hydroxychloroquine"], pch = markPCh["Hydroxychloroquine"], cex = 0.5)

## Grid + specific values for the selected metrics
abline(h = seq(from = -100, to = 150, by = 10), col = "#DDDDDD")
abline(h = 0, col = "red")
abline(h = 100, col = "#00BB00")
abline(v = seq(from = 0, to = max(inhibTable$CTB), by = 2000), col = "#DDDDDD")
abline(v = seq(from = 0, to = max(inhibTable$CTB), by = 10000), col = "#BBBBBB")
abline(v = 1)

## Legends
legend("bottomright", legend = names(plateColor), 
       title = "Plate", fill = plateColor, cex = 0.6)
legend("topleft", legend = names(markColor), 
       title = "Markers", 
       col = markColor, 
       pch = markPCh,
       cex = 0.6)
Comparison between viability scores. CTB versus relative viability ($V_{r}$). Diamonds: cell control (uninfected cells). Plain triangles: virus control (untreated infected cells). Black plain circles: arbidol control duplicates per plate. Orange square: Hydroxychloroquine sulfate.

Comparison between viability scores. CTB versus relative viability (\(V_{r}\)). Diamonds: cell control (uninfected cells). Plain triangles: virus control (untreated infected cells). Black plain circles: arbidol control duplicates per plate. Orange square: Hydroxychloroquine sulfate.

Relative versus IQR-standardised viability

#### Dot plot: IQR-standardized versus relative viability ####
plot(inhibTable[, c("Vrel", "z")],
     main = "Relative viability vs IQR-standardized viability",
     xlab = "Relative viability (I)",
     ylab = "IQR-standardized viability (z-score)",
     col = inhibTable[, "color"],
     pch = inhibTable[, "pch"],
     cex = 0.5,
     xlim = c(VrFloor, VrCeiling),
     panel.first = grid(),
     las = 1)

## Mark cell controls
points(inhibTable[wellType == "cellCtl", c("Vrel", "z")], 
       col = markColor["cellCtl"], pch = markPCh["cellCtl"], cex = 0.5)
## Mark virus controls
points(inhibTable[wellType == "virusCtl", c("Vrel", "z")], 
       col = markColor["virusCtl"], pch = markPCh["virusCtl"], cex = 0.5)
## Mark arbidol controls
points(inhibTable[arbidolWells, c("Vrel", "z")], 
       col = markColor["Arbidol"], pch = markPCh["Arbidol"], cex = 0.5)
## Mark Hydroxychloroquine
points(inhibTable[HOClSindex, c("Vrel", "z")], 
       col = markColor["Hydroxychloroquine"], pch = markPCh["Hydroxychloroquine"], cex = 0.5)

## Mark milestones for the selected metrics
abline(v = seq(-100, 150, 10), col = "#EEEEEE")
abline(v = seq(-100, 150, 50), col = "#BBBBBB")
abline(v = 0, col = "red")
abline(v = 100, col = "#00BB00")
abline(h = seq(-5, 10, 1), col = "#EEEEEE")
abline(h = seq(-5, 10, 5), col = "#BBBBBB")
abline(h = 0)
abline(h = c(-1, 1), lty = "dashed")

## Legends
legend("topleft", legend = names(plateColor), 
       title = "Plate", fill = plateColor, cex = 0.7)
legend("bottomright", legend = names(markColor), 
       title = "Markers", 
       col = markColor, 
       pch = markPCh,
       cex = 0.7)
Comparison between viability scores. Relative viability versus IQR-standardized viability (z-score). Diamonds: cell control (uninfected cells). Plain triangles: virus control (untreated infected cells). Black plain circles: arbidol control duplicates per plate. Orange square: Hydroxychloroquine sulfate.

Comparison between viability scores. Relative viability versus IQR-standardized viability (z-score). Diamonds: cell control (uninfected cells). Plain triangles: virus control (untreated infected cells). Black plain circles: arbidol control duplicates per plate. Orange square: Hydroxychloroquine sulfate.

FDR versus relative viability

Comparison between viability scores. Diamonds: cell control (uninfected cells). Plain triangles: virus control (untreated infected cells). Black plain circles: arbidol control duplicates per plate. Orange square: Hydroxychloroquine sulfate.

Comparison between viability scores. Diamonds: cell control (uninfected cells). Plain triangles: virus control (untreated infected cells). Black plain circles: arbidol control duplicates per plate. Orange square: Hydroxychloroquine sulfate.

Relative viability versus inhibition index

. We compare hereafter the values of the relative variability with the inhibition index defined in the bioRxiv publication (DOI 10.1101/2020.04.03.023846).

Comparison between viability scores. Diamonds: cell control (uninfected cells). Plain triangles: virus control (untreated infected cells). Black plain circles: arbidol control duplicates per plate. Orange square: Hydroxychloroquine sulfate.

Comparison between viability scores. Diamonds: cell control (uninfected cells). Plain triangles: virus control (untreated infected cells). Black plain circles: arbidol control duplicates per plate. Orange square: Hydroxychloroquine sulfate.

Hit molecules selected by the different criteria

Contingency table of the molecules selected by different criteria. Columns: inhibition index >= 1. Rows: Vrel > arbidol mean.
0 1
0 1397 89
1 50 22

Selected hits

Number of tests declared positive with FDR < 0.05
FALSE TRUE
1486 72
Candidate moecules sorted by significance after plate-wise normalization.
ID Chemical.name Reported.therapeutic.effect Inhibition.Index Vratio Vrel z sig +FDR +ii +arbidolMean +FDRandArbidol +FDRorArbidol +FDRonly +ArbidolOnly
01F08 Benoxinate hydrochloride Local anesthetic 1.1929 0.9559 96.5134 8.4789 13.7518 1 1 1 1 1 0 0
01B12 Arbidol NA NA 0.8805 90.1638 7.9057 11.9839 1 NA 1 1 1 0 0
01A12 Arbidol NA NA 0.8103 83.7370 7.3255 10.2091 1 NA 0 0 1 1 0
01H07 Dibucaine Local anesthetic 0.9095 0.7935 82.1224 7.1798 9.8665 1 0 0 0 1 1 0
01A06 Atracurium besylate Curarizing 0.8693 0.7705 79.8475 6.9744 9.3559 1 0 0 0 1 1 0
09F04 Promazine hydrochloride Antipsychotic 1.1610 0.9300 94.0954 6.9603 9.3559 1 1 1 1 1 0 0
09B12 Arbidol NA NA 0.8879 90.3256 6.6561 8.5044 1 NA 1 1 1 0 0
09D04 Opipramol dihydrochloride Antidepressant ’Antipsychotic 1.0521 0.8708 88.7401 6.5281 8.1880 1 1 1 1 1 0 0
01D05 Triamterene Antihypertensive ’Diuretic 0.7586 0.7071 73.2080 6.3750 7.8004 1 0 0 0 1 1 0
01D08 Pyrimethamine Antimalarial ’Antiprotozoal ’Antineoplastic 0.7421 0.6977 72.1695 6.2813 7.5824 1 0 0 0 1 1 0
01H05 Amitryptiline hydrochloride Antidepressant 0.7185 0.6841 70.6535 6.1444 7.2454 1 0 0 0 1 1 0
03B12 Arbidol NA NA 0.7557 79.0963 5.9669 6.8041 1 NA 1 1 1 0 0
09A12 Arbidol NA NA 0.7970 81.5300 5.9461 6.7837 1 NA 0 0 1 1 0
01H03 Imipramine hydrochloride Antidepressant 0.6546 0.6475 66.4013 5.7606 6.3312 1 0 0 0 1 1 0
09G07 Chlorcyclizine hydrochloride Antiemetic ’Antihistaminic ’Sedative 0.8573 0.7648 78.1773 5.6755 6.1438 1 0 0 0 1 1 0
03G08 Clemizole hydrochloride Antibacterial ’Antifungal ’Antihistaminic ’Antipruritic 1.0073 0.7205 75.5343 5.6529 6.1147 1 1 1 1 1 0 0
03H10 Orphenadrine hydrochloride Antihistaminic ’Antiparkinsonian 0.9732 0.7051 73.9193 5.5106 5.7855 1 0 0 0 1 1 0
09G08 Diphenylpyraline hydrochloride Antihistaminic ’Antipruritic ’Sedative 0.8198 0.7444 75.9759 5.4978 5.7788 1 0 0 0 1 1 0
01G11 Tolnaftate Antifungal ’Antifungal 0.5943 0.6129 62.1630 5.3780 5.5102 1 0 0 0 1 1 0
03A12 Arbidol NA NA 0.6787 71.0715 5.2596 5.2500 1 NA 0 0 1 1 0
07G07 Pregnenolone Anabolic ’Anti-inflammatory 1.6589 1.0977 107.1158 5.1506 5.0163 1 1 1 1 1 0 0
01H04 Sulindac Analgesic ’Anti-inflammatory ’Antipyretic 0.5382 0.5808 58.0051 5.0026 4.6984 1 0 0 0 1 1 0
08E11 Hydroxychloroquine sulfate Antimalarial 1.4327 1.1373 110.4885 4.8080 4.2870 1 1 1 1 1 0 0
01C05 Norethynodrel Contraceptive 0.5082 0.5636 55.6771 4.7925 4.2718 1 0 0 0 1 1 0
10G08 Merbromin disodium salt Antibacterial ’Antineoplastic 1.1210 0.9274 94.0301 4.6730 4.0339 1 1 1 1 1 0 0
03B05 Alverine citrate salt Antispastic 0.7629 0.6101 63.1168 4.5585 3.8115 1 0 0 0 1 1 0
07G09 Chloroquine diphosphate Anti-inflammatory ’Antimalarial ’Antiprotozoal 1.3510 0.9436 95.5713 4.5295 3.7681 1 1 1 1 1 0 0
01E08 Ticlopidine hydrochloride Anticoagulant ’Antiplatelet 0.4552 0.5333 51.4019 4.4065 3.5342 1 0 0 0 1 1 0
10A12 Arbidol NA NA 0.8743 89.3544 4.3967 3.5299 1 NA 1 1 1 0 0
09G09 Benzethonium chloride Antibacterial ’Antiseptic ’Antineoplastic 0.6042 0.6272 62.0279 4.3720 3.4952 1 0 0 0 1 1 0
07B04 Omeprazole Antiulcer 1.2487 0.8924 91.3149 4.3005 3.3683 1 1 1 1 1 0 0
01G06 Diphenhydramine hydrochloride Antiemetic ’Antihistaminic ’Antitussive ’Sedative 0.4338 0.5210 49.6043 4.2442 3.2725 1 0 0 0 1 1 0
10B12 Arbidol NA NA 0.8415 86.3252 4.2178 3.2347 1 NA 0 0 1 1 0
08D06 Exemestane Antineoplastic 1.0965 0.9392 94.8887 4.0950 3.0145 1 1 1 1 1 0 0
10D08 Chlorotrianisene Antineoplastic 0.9163 0.8098 83.2823 4.0380 2.9208 1 0 0 0 1 1 0
09D02 Dydrogesterone Progestogen 0.5447 0.5947 57.7090 4.0233 2.9060 1 0 0 0 1 1 0
08B12 Arbidol NA NA 0.8998 91.4001 3.9356 2.7577 1 NA 1 1 1 0 0
08H03 Dipivefrin hydrochloride Antiglaucoma 1.0095 0.8879 90.3132 3.8859 2.6799 1 1 1 1 1 0 0
07A12 Arbidol NA NA 0.7995 82.9210 3.8489 2.6252 1 NA 1 1 1 0 0
08A12 Arbidol NA NA 0.8647 88.1590 3.7875 2.5282 1 NA 0 0 1 1 0
07H07 Mirtazapine Antidepressant 1.0320 0.7840 81.4249 3.7684 2.5056 1 1 1 1 1 0 0
10H10 Pridinol methanesulfonate salt Antiparkinsonian 0.8315 0.7612 78.3641 3.7474 2.4796 1 0 0 0 1 1 0
03F02 Piroxicam Analgesic ’Anticoagulant ’Anti-inflammatory ’Antiplatelet ’Antipyretic ’Uricosuric 0.5726 0.5241 51.7713 3.5586 2.1704 1 0 0 0 1 1 0
09G04 Famprofazone Analgesic ’Antipyretic 0.4661 0.5520 51.6373 3.5333 2.1386 1 0 0 0 1 1 0
07B03 Nitrofural Antibacterial ’Antidotes 0.9359 0.7359 76.5940 3.5085 2.1173 1 0 0 0 1 1 0
07B12 Arbidol NA NA 0.7365 76.6493 3.5114 2.1173 1 NA 0 0 1 1 0
07F02 Pirenperone Anxiolytic 0.9157 0.7258 75.5356 3.4515 2.0344 1 0 0 0 1 1 0
02A12 Arbidol NA NA 0.8278 85.5793 3.4365 2.0193 1 NA 1 1 1 0 0
07H10 Tazarotene Antipsoriatic ’Antiacneic 0.9001 0.7180 74.7110 3.4072 1.9815 1 0 0 0 1 1 0
07C10 Bromperidol Antipsychotic 0.8959 0.7159 74.4893 3.3952 1.9715 1 0 0 0 1 1 0
09F10 Hexestrol Antineoplastic 0.4442 0.5401 49.8616 3.3899 1.9715 1 0 0 0 1 1 0
08H02 Alendronate sodium Antiosteoporetic 0.8169 0.7743 79.1607 3.3763 1.9583 1 0 0 0 1 1 0
06D11 Epiandrosterone Anabolic 1.0748 0.9215 93.9594 3.3589 1.9393 1 1 1 1 1 0 0
09A09 Nilvadipine Antianginal ’Antihypertensive 0.4331 0.5341 48.9538 3.3167 1.8813 1 0 0 0 1 1 0
05A10 Tacrine hydrochloride CNS Stimulant 1.4422 0.9408 95.7878 3.2975 1.8595 1 1 1 1 1 0 0
06B12 Arbidol NA NA 0.8991 92.1439 3.2880 1.8527 1 NA 1 1 1 0 0
07C03 Biperiden hydrochloride Antiparkinsonian ’Antineoplastic 0.8495 0.6927 71.9731 3.2599 1.8172 1 0 0 0 1 1 0
09G02 Trihexyphenidyl-D,L hydrochloride Antiparkinsonian 0.4224 0.5282 48.0568 3.2443 1.8009 1 0 0 0 1 1 0
06H02 Vatalanib Antineoplastic 0.9984 0.8745 90.0896 3.2077 1.7578 1 0 0 0 1 1 0
10A08 Liranaftate Antifungal 0.6869 0.6782 69.2049 3.2062 1.7578 1 0 0 0 1 1 0
02B12 Arbidol NA NA 0.7756 80.6102 3.1908 1.7451 1 NA 0 0 1 1 0
02C08 Pioglitazone NA 0.9499 0.7751 80.5590 3.1883 1.7451 1 0 0 0 1 1 0
06A12 Arbidol NA NA 0.8518 88.1505 3.1319 1.6681 1 NA 0 0 1 1 0
10E06 Ethoxyquin Antifungal ’Antineoplastic 0.6516 0.6579 66.7968 3.0639 1.5752 1 0 0 0 1 1 0
07H06 Nifuroxazide Antibacterial ’Antineoplastic 0.7750 0.6554 67.7468 3.0325 1.5365 1 0 0 0 1 1 0
03E06 Tolfenamic acid Analgesic ’Anti-inflammatory 0.4812 0.4828 45.6459 3.0187 1.5234 1 0 0 0 1 1 0
02B04 Azacyclonol Antipsychotic 0.8837 0.7400 77.0208 3.0134 1.5223 1 0 0 0 1 1 0
08G02 Mizolastine Antihistaminic 0.6881 0.6984 70.7524 2.9920 1.4982 1 0 0 0 1 1 0
08E07 Rimantadine hydrochloride Antiviral 0.6754 0.6909 69.8764 2.9520 1.4479 1 0 0 0 1 1 0
08B06 Tenatoprazole Antiulcer 0.6656 0.6851 69.1905 2.9206 1.4103 1 0 0 0 1 1 0
07D09 Budesonide Anti-inflammatory ’Antineoplastic 0.7260 0.6309 64.8405 2.8761 1.3548 1 0 0 0 1 1 0
06F06 Mebhydroline 1,5-naphtalenedisulfonate Antihistaminic 0.8344 0.7736 81.0329 2.8538 1.3303 1 0 0 0 1 1 0

Hits per plate

ii arbidolMean FDR FDRandArbidol FDRorArbidol FDRonly ArbidolOnly
1 1 2 14 2 14 12 0
2 0 1 4 1 4 3 0
3 1 2 7 2 7 5 0
4 7 9 0 0 9 0 9
5 3 4 1 1 4 0 3
6 1 2 5 2 5 3 0
7 4 5 13 5 13 8 0
8 3 4 9 4 9 5 0
9 2 3 12 3 12 9 0
10 1 2 7 2 7 5 0
11 3 4 0 0 4 0 4
12 2 3 0 0 3 0 3
13 9 10 0 0 10 0 10
14 14 15 0 0 15 0 15
15 16 17 0 0 17 0 17
16 9 11 0 0 11 0 11
17 3 4 0 0 4 0 4
18 3 4 0 0 4 0 4
19 8 9 0 0 9 0 9
Total 90 111 72 22 161 50 89 
[1] "ii"            "arbidolMean"   "FDR"           "FDRandArbidol" "FDRorArbidol"  "FDRonly"       "ArbidolOnly"
Number of candidate molecules per plate depending on the method.

Number of candidate molecules per plate depending on the method.

Result files

#### Export result tables ####

## Define output file names
outFiles <- list(
  "All results (tsv)" =  
    file.path(dir["results"], "result_table_all-molecules.tsv"),
  "All results (xlsx)" =  
    file.path(dir["results"], "result_table_all-molecules.xlsx"),
  "FDR-based hits (xlsx)" =  
    file.path(dir["results"], "result_table_FDR-hits.xlsx"),
  "Arbidol-based hits (xlsx)" =  
    file.path(dir["results"], "result_table_arbidol-hits.xlsx"),
  "High confidence hits (xlsx)" =  
    file.path(dir["results"], "result_table_HiConfidence-hits.xlsx")
)

# View(inhibTable) # check before exporting
write.table(x = inhibTable, 
            file = outFiles$`All results (tsv)`,  
            sep = "\t", quote = FALSE, 
            row.names = FALSE, col.names = TRUE)

write.xlsx2(x = inhibTable, 
            file = outFiles$`All results (xlsx)`, 
            row.names = FALSE, col.names = TRUE)

# table(!is.na(inhibTable$selected.FDR) & (inhibTable$selected.FDR == 1))
# View(inhibTable[!is.na(inhibTable$selected.FDR) & (inhibTable$selected.FDR == 1), ]) # check before exporting
write.xlsx2(x = inhibTable[!is.na(inhibTable$selected.FDR) & (inhibTable$selected.FDR == 1), ], 
            file = outFiles$`FDR-based hits (xlsx)`, 
            row.names = FALSE, col.names = TRUE)

# View(inhibTable[!is.na(inhibTable$selected.FDR) & (inhibTable$selected.arbidolMean), ])
write.xlsx2(x = inhibTable[!is.na(inhibTable$selected.FDR) & (inhibTable$selected.arbidolMean), ], 
            file = outFiles$`Arbidol-based hits (xlsx)`, 
            row.names = FALSE, col.names = TRUE)

# View(inhibTable[!is.na(inhibTable$selected.FDR) & (inhibTable$selected.FDRandArbidol), ])
write.xlsx2(x = inhibTable[!is.na(inhibTable$selected.FDR) & (inhibTable$selected.FDRandArbidol), ], 
            file = outFiles$`High confidence hits (xlsx)`, 
            row.names = FALSE, col.names = TRUE)

# system(paste("open", dir["results"]))

## Prepare a data frame with the relative links to output files
fileLinks <- data.frame(
  name = names(outFiles),
  path = unlist(outFiles),
  basename = basename(unlist(outFiles))
)

fileLinks$link <- paste0("<a href='", fileLinks$path, "'>", fileLinks$basename, "</a>")

kable(fileLinks[, c("name", "link")], row.names = FALSE, caption = "Links to the result tables. ")
Links to the result tables.
name link
All results (tsv) result_table_all-molecules.tsv
All results (xlsx) result_table_all-molecules.xlsx
FDR-based hits (xlsx) result_table_FDR-hits.xlsx
Arbidol-based hits (xlsx) result_table_arbidol-hits.xlsx
High confidence hits (xlsx) result_table_HiConfidence-hits.xlsx

Libraries and versions

For the sake of reproducibility, we list hereafter the R libraries used to generate this report, as well as their versions.

R version 3.6.1 (2019-07-05)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Mojave 10.14.6

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] grid      stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] vioplot_0.3.4       zoo_1.8-7           sm_2.2-5.6          fitdistrplus_1.0-14 npsurv_0.4-0        lsei_1.2-0          survival_3.1-11     MASS_7.3-51.5       limma_3.40.6        VennDiagram_1.6.20  futile.logger_1.4.3 knitr_1.28          readxl_1.3.1        xlsx_0.6.3         

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.4           highr_0.8            pillar_1.4.3         cellranger_1.1.0     compiler_3.6.1       formatR_1.7          futile.options_1.0.1 tools_3.6.1          digest_0.6.25        evaluate_0.14        tibble_3.0.0         lifecycle_0.2.0      lattice_0.20-40      pkgconfig_2.0.3     
[15] rlang_0.4.5          Matrix_1.2-18        cli_2.0.2            yaml_2.2.1           xfun_0.12            rJava_0.9-12         stringr_1.4.0        vctrs_0.2.4          xlsxjars_0.6.1       glue_1.3.2           rematch_1.0.1        fansi_0.4.1          tcltk_3.6.1          rmarkdown_2.1       
[29] lambda.r_1.2.4       magrittr_1.5         htmltools_0.4.0      ellipsis_0.3.0       splines_3.6.1        assertthat_0.2.1     stringi_1.4.6        crayon_1.3.4