Comparing CSC content among cytotoxic drugs across a range of spheroid viability index.
Krittiyabhorn Kongtanawanich
2025-02-25
Overview of R analysis for comparing CSC content among cytotoxic drugs across a range of spheroid viability index.
To compare CSC content under chemotherapies, we developed a method for comparing CSC index within a range of spheroid viability index (SVI) by calculating the normalized CSC index’s area under the curve (AUC). Briefly, a range of SVI is defined based on the SVI of all drugs, and then the drug concentrations of the SVIs are interpolated using a non-linear (exponential model fitting) approach. Next, interpolation of the CSC index of each SVI value is performed by linear interpolation between the nearby interpolated drug concentrations. To compare CSC content across a range of SVI, an AUC of the CSC index is calculated for each drug. The CSC index’s AUC is further normalized by the vehicle control. Statistical test is performed, and bar graphs are used for data visualization.
Figure 1: Overview of analysis for CSC content among cytotoxic drugs
across a range of SVI.
1. Analysis overview
Here, the analysis composed of 5 main sections below.
- Section 1: Define information of the dataset.
- Section 2: Load input data.
- Section 3: Create analysis pipeline.
- Part 3.1: Find SVIs of all drugs.
3.1.1 Find maximum and minimum SVI of each drug.
3.1.2 Define maximum and minimum of SVI across all drugs.
3.1.3 Define the range of SVI for AUC of the CSC index calculation.
- Part 3.2: Calculate drug concentration of each desired SVI by
interpolation.
- Part 3.3: Calculate the CSC index for each drug concentration by
interpolating from the interpolated drug concentrations.
3.3.1 Find nearest low/high drug concentration and CSC index from the interpolated drug concentration.
3.3.2 Interpolate CSC index from interpolated drug concentration.
- Part 3.4: Reconsider SVI range, according to NA value possibly
present.
3.4.1 Check whether NA present in the data.
3.4.2 Exclude SVI that contain NA values and define selected SVI range.
- Part 3.5: Find AUC of CSC index across the selected SVI range.
3.5.1 Calculate AUC of CSC index for vehicle control.
3.5.2 Calculate normalized CSC index’s AUC of each drug.
- Part 3.6: Create summary analysis.
- Part 3.1: Find SVIs of all drugs.
- Section 4: Statistical test
- Part 4.1: Normality test
- Part 4.2: Statistical test
- Part 4.1: Normality test
- Section 5: Data visualization
2. Inputs
The CSC index of each drug was created from the file name
DrugX_Input_forCSCindexAUC.csv from “Evaluating
CSC content and cytotoxicity under anti-cancer drug treatments for the
3D multi-spheroid model using 3D-SiSP analytical method.” which will
be used as input data for this analysis.
To compare the CSC index of cytotoxic drugs across a range of
spheroid viability index (SVI), we used drug A and drug B as
examples.
In the DrugX_Input_forCSCindexAUC.csv file contains 10
columns, which are described as below.
Drug= Name of the drug
Concentration_uM= Concentration of the drug (μM)
SVI= Spheroid viability index
CSCindex= Cancer stem cell index
Here, we provided a
set of example inputs which contained
A_Input_forCSCindexAUC.csv,
B_Input_forCSCindexAUC.csv for drug A and drug B,
respectively.
/
Figure 2: Double y-axis graphs show spheroid viability index (SVI) and
CSC index of drug A (left) and drug B(right).
Analysis for Comparing CSC content among cytotoxic drugs across a range of spheroid viability index.
Import R library
library(dplyr)
library(ggplot2)
library(nlme) # For non-linear regression
library(pracma) # For AUC calculation by trapezoidal rule
library(viridis) # For color library
library(ggpubr) # For statistical testSection 1: Define information of the dataset.
To define information of the dataset.
1.1 Define working directory: Output_Directory
1.2 Define input directory: Input_Directory
# Dataset example: drug A and drug B
## Output directory
Output_Directory <- 'path/to/directory'
setwd(Output_Directory)
## Input directory
Input_Directory <- 'path/to/directory'Section 2: Load the input data.
FileNames <- list.files(Input_Directory) # Get a list of .csv files in the input directory
FileNames <- as.list(FileNames) # Make .csv files as a listImport two .csv files for 2 drugs and then calculate the
required variable for further analysis.
# Create a blank list to store `Experimental_drug` information.
Experimental_list <- list()
# Calculate the required variable for all drugs for further analysis.
for (Drug_FileName in FileNames){
# Import each `.csv` file.
Drug_FilePath <- file.path(Input_Directory, Drug_FileName)
Experimental_DrugX <- read.csv(Drug_FilePath)
## Change all columns to numeric except the`Drug` column.
Experimental_DrugX[, -1] <- apply(Experimental_DrugX[, -1],
2,
as.numeric
)
Experimental_DrugX
# Rename the data frame to show the drug name.
## Extract the drug name.
Drug_Name <- sub("_.*", "", Drug_FileName)
## Rename the data frame.
Experimental_Data <- assign(paste0("Experimental_Drug", Drug_Name),
Experimental_DrugX
)
# Store the data frame into the list `Experimental_list`.
Experimental_list[[length(Experimental_list)+1]] <- Experimental_Data
}Observe the Experimental_Drug data
# The list which shows information of all drugs.
head(Experimental_list)## [[1]]
## Drug Concentration_pM log10_Concentration_pM SVI CSCindex Replicate
## 1 A 1e+06 6 0.5266515 1.1670821 1
## 2 A 1e+06 6 0.3727367 1.1439455 2
## 3 A 1e+06 6 0.3128734 1.1833153 3
## 4 A 1e+05 5 0.4753377 1.2614324 1
## 5 A 1e+05 5 0.2924306 1.3646002 2
## 6 A 1e+05 5 0.2619729 1.1668776 3
## 7 A 1e+04 4 0.7616551 1.6280216 1
## 8 A 1e+04 4 0.5151447 1.3951609 2
## 9 A 1e+04 4 0.5343289 1.3931141 3
## 10 A 1e+03 3 1.0047226 0.9452869 1
## 11 A 1e+03 3 1.0996911 1.0053784 2
## 12 A 1e+03 3 0.7377690 0.9074044 3
## 13 A 0e+00 0 0.8029457 0.9476974 1
## 14 A 0e+00 0 1.1784421 1.0611647 2
## 15 A 0e+00 0 1.0186123 0.9911379 3
##
## [[2]]
## Drug Concentration_pM log10_Concentration_pM SVI CSCindex Replicate
## 1 B 5e+07 7.7 0.4828559 0.9296289 1
## 2 B 5e+07 7.7 0.4610764 0.8759742 2
## 3 B 5e+07 7.7 0.3978878 0.7660433 3
## 4 B 5e+06 6.7 0.6813254 1.3671360 1
## 5 B 5e+06 6.7 0.6765575 1.3230907 2
## 6 B 5e+06 6.7 0.5448808 1.2561047 3
## 7 B 5e+05 5.7 0.5034974 1.4586134 1
## 8 B 5e+05 5.7 0.7315248 1.4095987 2
## 9 B 5e+05 5.7 0.7530513 1.4797003 3
## 10 B 5e+04 4.7 0.8363375 1.7513541 1
## 11 B 5e+04 4.7 0.9671786 1.8060602 2
## 12 B 5e+04 4.7 0.8248147 1.4299233 3
## 13 B 0e+00 0.0 1.0640481 1.0678026 1
## 14 B 0e+00 0.0 1.0720928 0.9787869 2
## 15 B 0e+00 0.0 0.8638591 0.9534105 3# Drug A
head(Experimental_DrugA)## Drug Concentration_pM log10_Concentration_pM SVI CSCindex Replicate
## 1 A 1e+06 6 0.5266515 1.167082 1
## 2 A 1e+06 6 0.3727367 1.143946 2
## 3 A 1e+06 6 0.3128734 1.183315 3
## 4 A 1e+05 5 0.4753377 1.261432 1
## 5 A 1e+05 5 0.2924306 1.364600 2
## 6 A 1e+05 5 0.2619729 1.166878 3# Drug B
head(Experimental_DrugB)## Drug Concentration_pM log10_Concentration_pM SVI CSCindex Replicate
## 1 B 5e+07 7.7 0.4828559 0.9296289 1
## 2 B 5e+07 7.7 0.4610764 0.8759742 2
## 3 B 5e+07 7.7 0.3978878 0.7660433 3
## 4 B 5e+06 6.7 0.6813254 1.3671360 1
## 5 B 5e+06 6.7 0.6765575 1.3230907 2
## 6 B 5e+06 6.7 0.5448808 1.2561047 3Section 3: Create analysis pipeline.
Part 3.1: Find SVI range for all drugs.
3.1.1 Find minimum SVI of each drug.
# Create a blank data frame to store `DrugX_minSVI` from the highest concentration of each drug.
Data_minSVI <- data.frame()
# Create a for loop to calculate the lowest SVI from the highest concentration of each drug.
for (Experimental_DrugX in Experimental_list){
# Find the highest concentration of the drug.
DrugX_MaxConc <- max(Experimental_DrugX$Concentration_pM)
# Filter only SVI of the highest drug concentration.
DrugX_minSVI <- Experimental_DrugX %>%
dplyr::filter(Concentration_pM == DrugX_MaxConc) %>%
select(Drug, SVI)
Data_minSVI <- rbind(Data_minSVI,
DrugX_minSVI
)
}
# Show the SVIs from the highest concentration of each drug.
head(Data_minSVI)## Drug SVI
## 1 A 0.5266515
## 2 A 0.3727367
## 3 A 0.3128734
## 4 B 0.4828559
## 5 B 0.4610764
## 6 B 0.39788783.1.2 Define maximum and minimum of SVI for all drugs.
Maximum SVI will be set to 1 which is the vehicle control.
# Define maximum of SVI.
HighestSVI_LastPoint <- 1
print(paste0("The last point (highest SVI) of the AUC range across all drugs is ", HighestSVI_LastPoint))## [1] "The last point (highest SVI) of the AUC range across all drugs is 1"Minimum SVI will be determined by the highest value among the minimum SVIs across all drugs, to further analyze the CSC index within the same range of SVI.”
# Find the lowest of SVI across all drugs.
minSVI <- max(Data_minSVI$SVI)
print(paste0("Minimum SVI of across all drugs is ", minSVI))## [1] "Minimum SVI of across all drugs is 0.526651533159554" Rounded_minSVI <- round(minSVI, digits = 2)
LowestSVI_1stPoint <- ceiling(Rounded_minSVI / 0.05) * 0.05
print(paste0("The 1st point (lowest SVI) of the AUC range across all drugs is ", LowestSVI_1stPoint))## [1] "The 1st point (lowest SVI) of the AUC range across all drugs is 0.55"3.1.3 Define the range of SVI to calculate AUC of the CSC index.
# Summarize the range of SVI.
SVI_Range <- c(HighestSVI_LastPoint,
LowestSVI_1stPoint
)
print(paste("The SVI range for calculating the AUC of the CSC index is between", HighestSVI_LastPoint, "and", LowestSVI_1stPoint))## [1] "The SVI range for calculating the AUC of the CSC index is between 1 and 0.55"# Define the SVI values between the SVI range with an increment of 0.05.
Desired_SVIvalues <- seq(SVI_Range[1],
SVI_Range[2],
by = -0.05
)
print(paste("Based on the SVI range, the AUC of the CSC index will be calculated within this range. Therefore, CSC index will be calculated at SVI values of", paste(Desired_SVIvalues, collapse = ", ")))## [1] "Based on the SVI range, the AUC of the CSC index will be calculated within this range. Therefore, CSC index will be calculated at SVI values of 1, 0.95, 0.9, 0.85, 0.8, 0.75, 0.7, 0.65, 0.6, 0.55"Part 3.2: Calculate drug concentration of each desired SVI by interpolation.
# Create a blank list to store `InterpolatedConc_DrugX` information.
InterpolatedConc_list <- list()
# Find drug concentration of each desired SVI.
for (Experimental_DrugX in Experimental_list){
DrugX_FindConc <- dplyr::select(Experimental_DrugX,
Drug,
log10_Concentration_pM,
SVI
)
# Define a nonlinear model (exponential decay).
Model_DrugX <- nls(SVI ~ exp(a + b * log10_Concentration_pM),
data = DrugX_FindConc,
start = list(a = 0, b = 0)
)
# Define a function to find `log10_Concentration_pM` form a given SVI (`SVI`).
find.DrugX.log10Conc.pM <- function(SVI)
{
uniroot(
function(log10_Concentration)
{
predict(Model_DrugX,
newdata = data.frame(log10_Concentration_pM = log10_Concentration)) - SVI
},
interval = range(DrugX_FindConc$log10_Concentration_pM),
extendInt = "yes"
)$root
}
# Predict `log10_Concentration_pM` from each SVI (`SVI`).
Desired_SVIvalues
Predicted_DrugX_log10_Conc_pM <- sapply(Desired_SVIvalues,
find.DrugX.log10Conc.pM)
# Summarize the interpolated output.
InterpolatedConc_DrugX <- data.frame(Drug = DrugX_FindConc$Drug[1],
SVI = Desired_SVIvalues,
log10_Concentration_pM = Predicted_DrugX_log10_Conc_pM,
Concentration_pM = 10^(Predicted_DrugX_log10_Conc_pM)
)
InterpolatedConc_DrugX
# Rename the data frame to show the drug name.
## Extract the drug name.
Drug_Name <- InterpolatedConc_DrugX$Drug[[1]]
## Rename the data frame
InterpolatedConc_DrugX_Data <- assign(paste0("InterpolatedConc_Drug", Drug_Name),
InterpolatedConc_DrugX
)
# Store the data frame into the list `InterpolatedConc_list`
InterpolatedConc_list[[length(InterpolatedConc_list)+1]] <- InterpolatedConc_DrugX_Data
}Observe the InterpolatedConc_Drug data.
# The list which shows information of all drugs.
head(InterpolatedConc_list)## [[1]]
## Drug SVI log10_Concentration_pM Concentration_pM
## 1 A 1.00 0.4658773 2.923326
## 2 A 0.95 0.8163205 6.551195
## 3 A 0.90 1.1856657 15.334361
## 4 A 0.85 1.5761514 37.683516
## 5 A 0.80 1.9903186 97.795429
## 6 A 0.75 2.4312231 269.912538
## 7 A 0.70 2.9025564 799.017714
## 8 A 0.65 3.4088326 2563.495571
## 9 A 0.60 3.9556517 9029.249693
## 10 A 0.55 4.5500784 35487.746764
##
## [[2]]
## Drug SVI log10_Concentration_pM Concentration_pM
## 1 B 1.00 0.5229577 3.333939e+00
## 2 B 0.95 1.1844042 1.528988e+01
## 3 B 0.90 1.8816524 7.614694e+01
## 4 B 0.85 2.6187342 4.156562e+02
## 5 B 0.80 3.4005238 2.514918e+03
## 6 B 0.75 4.2327854 1.709171e+04
## 7 B 0.70 5.1224883 1.325832e+05
## 8 B 0.65 6.0781535 1.197164e+06
## 9 B 0.60 7.1103569 1.289309e+07
## 10 B 0.55 8.2324125 1.707704e+08# DrugA
head(InterpolatedConc_DrugA)## Drug SVI log10_Concentration_pM Concentration_pM
## 1 A 1.00 0.4658773 2.923326
## 2 A 0.95 0.8163205 6.551195
## 3 A 0.90 1.1856657 15.334361
## 4 A 0.85 1.5761514 37.683516
## 5 A 0.80 1.9903186 97.795429
## 6 A 0.75 2.4312231 269.912538# DrugB
head(InterpolatedConc_DrugB)## Drug SVI log10_Concentration_pM Concentration_pM
## 1 B 1.00 0.5229577 3.333939
## 2 B 0.95 1.1844042 15.289883
## 3 B 0.90 1.8816524 76.146938
## 4 B 0.85 2.6187342 415.656151
## 5 B 0.80 3.4005238 2514.917842
## 6 B 0.75 4.2327854 17091.705307Part 3.3: Calculate the CSC index for each drug concentration by interpolating from the interpolated drug concentrations.
3.3.1 Find nearest low/high drug concentration and CSC index from the interpolated drug concentration.
# Create a blank list to store `NearestData_DrugX` information.
NearestData_list <- list()
for (InterpolatedConc_DrugX in InterpolatedConc_list){
# Extract the interpolated drug concentration.
DrugX_Conc <- InterpolatedConc_DrugX$Concentration_pM %>%
as.list()
# Extract the drug concentration which were used in wet lab experiment from `Experimental_list`.
## Extract the drug name from `InterpolatedConc_DrugX`
Drug_Name <- InterpolatedConc_DrugX$Drug[1]
## Iterate over the list of `Experimental_list` and select the data frame which the drug name matchs with `InterpolatedConc_DrugX`.
Experimental_DrugX <- do.call(rbind,
lapply(Experimental_list,
function(df) df[df$Drug == Drug_Name, ]))
## Sort the drug concentrations from `Experimental_DrugX` in ascending order.
Sorted_Conc <- sort(Experimental_DrugX$Concentration_pM)
# Create a blank list to store `NearestData_DrugX` and `CSCindex` information.
NearestData_DrugX <- data.frame()
for (Conc in DrugX_Conc){
# Find the nearest low and high concentrations.
NearestConc_Low <- max(Sorted_Conc[Sorted_Conc <= Conc])
NearestConc_High <- min(Sorted_Conc[Sorted_Conc >= Conc])
# Find `CSCindex` from the nearest low and high concentrations.
## The nearest low concentration
CSCindex_NearestLow <- Experimental_DrugX %>%
filter(Concentration_pM == NearestConc_Low) %>%
select(CSCindex) %>%
t %>%
as.vector()
CSCindex_NearestLow
## The nearest high concentration
CSCindex_NearestHigh <- Experimental_DrugX %>% filter(Concentration_pM == NearestConc_High) %>%
select(CSCindex) %>%
t %>%
as.vector()
CSCindex_NearestHigh
NearestValues_DrugX <- c(Experimental_DrugX$Drug[1], Conc,
NearestConc_Low, CSCindex_NearestLow,
NearestConc_High, CSCindex_NearestHigh
)
NearestData_DrugX <- rbind(NearestData_DrugX,
NearestValues_DrugX
)
}
# Rename columns.
colnames(NearestData_DrugX) <- c("Drug", "Concentration_pM",
"Nearest_Low_Concentration_pM",
"CSCindex_Low_r1", "CSCindex_Low_r2", "CSCindex_Low_r3",
"Nearest_High_Concentration_pM",
"CSCindex_High_r1", "CSCindex_High_r2", "CSCindex_High_r3")
# Attach the SVI values to the `NearestData_DrugX`.
NearestData_DrugX <- merge(NearestData_DrugX,
InterpolatedConc_DrugX,
by = c("Drug", "Concentration_pM"),
all = FALSE
)
# Reorder columns.
NearestData_DrugX <- NearestData_DrugX %>%
select(Drug,
SVI,
Concentration_pM,
log10_Concentration_pM,
everything()
)
# Sort the nearest values according to SVI.
NearestData_DrugX <- NearestData_DrugX[order(NearestData_DrugX$SVI), ]
# Change the values to numeric.
NearestData_DrugX[, -1] <- lapply(NearestData_DrugX[, -1], as.numeric)
# Rename the data frame to show the drug name.
## Extract the drug name.
Drug_Name <- InterpolatedConc_DrugX$Drug[1]
## Rename the data frame.
NearestData_DrugX_Data <- assign(paste0("NearestData_Drug", Drug_Name),
NearestData_DrugX
)
# Store the data frame into the list `NearestData_list`.
NearestData_list[[length(NearestData_list)+1]] <- NearestData_DrugX_Data
}## Warning in min(Sorted_Conc[Sorted_Conc >= Conc]): no non-missing arguments to
## min; returning Inf## Warning in rbind(deparse.level, ...): number of columns of result, 10, is not a
## multiple of vector length 7 of arg 2## Warning in lapply(NearestData_DrugX[, -1], as.numeric): NAs introduced by
## coercionObserve the NearestData_Drug data.
# The list which shows information of all drugs.
head(NearestData_list)## [[1]]
## Drug SVI Concentration_pM log10_Concentration_pM
## 5 A 0.55 35487.746764 4.5500784
## 9 A 0.60 9029.249693 3.9556517
## 3 A 0.65 2563.495571 3.4088326
## 8 A 0.70 799.017714 2.9025564
## 4 A 0.75 269.912538 2.4312231
## 10 A 0.80 97.795429 1.9903186
## 6 A 0.85 37.683516 1.5761514
## 1 A 0.90 15.334361 1.1856657
## 7 A 0.95 6.551195 0.8163205
## 2 A 1.00 2.923326 0.4658773
## Nearest_Low_Concentration_pM CSCindex_Low_r1 CSCindex_Low_r2 CSCindex_Low_r3
## 5 10000 1.6280216 1.395161 1.3931141
## 9 1000 0.9452869 1.005378 0.9074044
## 3 1000 0.9452869 1.005378 0.9074044
## 8 0 0.9476974 1.061165 0.9911379
## 4 0 0.9476974 1.061165 0.9911379
## 10 0 0.9476974 1.061165 0.9911379
## 6 0 0.9476974 1.061165 0.9911379
## 1 0 0.9476974 1.061165 0.9911379
## 7 0 0.9476974 1.061165 0.9911379
## 2 0 0.9476974 1.061165 0.9911379
## Nearest_High_Concentration_pM CSCindex_High_r1 CSCindex_High_r2
## 5 1e+05 1.2614324 1.364600
## 9 1e+04 1.6280216 1.395161
## 3 1e+04 1.6280216 1.395161
## 8 1e+03 0.9452869 1.005378
## 4 1e+03 0.9452869 1.005378
## 10 1e+03 0.9452869 1.005378
## 6 1e+03 0.9452869 1.005378
## 1 1e+03 0.9452869 1.005378
## 7 1e+03 0.9452869 1.005378
## 2 1e+03 0.9452869 1.005378
## CSCindex_High_r3
## 5 1.1668776
## 9 1.3931141
## 3 1.3931141
## 8 0.9074044
## 4 0.9074044
## 10 0.9074044
## 6 0.9074044
## 1 0.9074044
## 7 0.9074044
## 2 0.9074044
##
## [[2]]
## Drug SVI Concentration_pM log10_Concentration_pM
## 5 B 0.55 1.707704e+08 8.2324125
## 2 B 0.60 1.289309e+07 7.1103569
## 1 B 0.65 1.197164e+06 6.0781535
## 3 B 0.70 1.325832e+05 5.1224883
## 6 B 0.75 1.709171e+04 4.2327854
## 7 B 0.80 2.514918e+03 3.4005238
## 9 B 0.85 4.156562e+02 2.6187342
## 10 B 0.90 7.614694e+01 1.8816524
## 4 B 0.95 1.528988e+01 1.1844042
## 8 B 1.00 3.333939e+00 0.5229577
## Nearest_Low_Concentration_pM CSCindex_Low_r1 CSCindex_Low_r2 CSCindex_Low_r3
## 5 5e+07 0.9296289 0.8759742 0.7660433
## 2 5e+06 1.3671360 1.3230907 1.2561047
## 1 5e+05 1.4586134 1.4095987 1.4797003
## 3 5e+04 1.7513541 1.8060602 1.4299233
## 6 0e+00 1.0678026 0.9787869 0.9534105
## 7 0e+00 1.0678026 0.9787869 0.9534105
## 9 0e+00 1.0678026 0.9787869 0.9534105
## 10 0e+00 1.0678026 0.9787869 0.9534105
## 4 0e+00 1.0678026 0.9787869 0.9534105
## 8 0e+00 1.0678026 0.9787869 0.9534105
## Nearest_High_Concentration_pM CSCindex_High_r1 CSCindex_High_r2
## 5 Inf NA 1.707704e+08
## 2 5e+07 0.9296289 8.759742e-01
## 1 5e+06 1.3671360 1.323091e+00
## 3 5e+05 1.4586134 1.409599e+00
## 6 5e+04 1.7513541 1.806060e+00
## 7 5e+04 1.7513541 1.806060e+00
## 9 5e+04 1.7513541 1.806060e+00
## 10 5e+04 1.7513541 1.806060e+00
## 4 5e+04 1.7513541 1.806060e+00
## 8 5e+04 1.7513541 1.806060e+00
## CSCindex_High_r3
## 5 5.000000e+07
## 2 7.660433e-01
## 1 1.256105e+00
## 3 1.479700e+00
## 6 1.429923e+00
## 7 1.429923e+00
## 9 1.429923e+00
## 10 1.429923e+00
## 4 1.429923e+00
## 8 1.429923e+00# Drug A
head(NearestData_DrugA)## Drug SVI Concentration_pM log10_Concentration_pM
## 5 A 0.55 35487.74676 4.550078
## 9 A 0.60 9029.24969 3.955652
## 3 A 0.65 2563.49557 3.408833
## 8 A 0.70 799.01771 2.902556
## 4 A 0.75 269.91254 2.431223
## 10 A 0.80 97.79543 1.990319
## Nearest_Low_Concentration_pM CSCindex_Low_r1 CSCindex_Low_r2 CSCindex_Low_r3
## 5 10000 1.6280216 1.395161 1.3931141
## 9 1000 0.9452869 1.005378 0.9074044
## 3 1000 0.9452869 1.005378 0.9074044
## 8 0 0.9476974 1.061165 0.9911379
## 4 0 0.9476974 1.061165 0.9911379
## 10 0 0.9476974 1.061165 0.9911379
## Nearest_High_Concentration_pM CSCindex_High_r1 CSCindex_High_r2
## 5 1e+05 1.2614324 1.364600
## 9 1e+04 1.6280216 1.395161
## 3 1e+04 1.6280216 1.395161
## 8 1e+03 0.9452869 1.005378
## 4 1e+03 0.9452869 1.005378
## 10 1e+03 0.9452869 1.005378
## CSCindex_High_r3
## 5 1.1668776
## 9 1.3931141
## 3 1.3931141
## 8 0.9074044
## 4 0.9074044
## 10 0.9074044# Drug B
head(NearestData_DrugB)## Drug SVI Concentration_pM log10_Concentration_pM
## 5 B 0.55 1.707704e+08 8.232412
## 2 B 0.60 1.289309e+07 7.110357
## 1 B 0.65 1.197164e+06 6.078153
## 3 B 0.70 1.325832e+05 5.122488
## 6 B 0.75 1.709171e+04 4.232785
## 7 B 0.80 2.514918e+03 3.400524
## Nearest_Low_Concentration_pM CSCindex_Low_r1 CSCindex_Low_r2 CSCindex_Low_r3
## 5 5e+07 0.9296289 0.8759742 0.7660433
## 2 5e+06 1.3671360 1.3230907 1.2561047
## 1 5e+05 1.4586134 1.4095987 1.4797003
## 3 5e+04 1.7513541 1.8060602 1.4299233
## 6 0e+00 1.0678026 0.9787869 0.9534105
## 7 0e+00 1.0678026 0.9787869 0.9534105
## Nearest_High_Concentration_pM CSCindex_High_r1 CSCindex_High_r2
## 5 Inf NA 1.707704e+08
## 2 5e+07 0.9296289 8.759742e-01
## 1 5e+06 1.3671360 1.323091e+00
## 3 5e+05 1.4586134 1.409599e+00
## 6 5e+04 1.7513541 1.806060e+00
## 7 5e+04 1.7513541 1.806060e+00
## CSCindex_High_r3
## 5 5.000000e+07
## 2 7.660433e-01
## 1 1.256105e+00
## 3 1.479700e+00
## 6 1.429923e+00
## 7 1.429923e+003.3.2 Interpolate CSC index from the interpolated drug concentration.
Create function to interpolate CSC index from the interpolated drug concentration.
Interpolate.CSCindex <- function(NearestData_DrugX)
{
# Change SVI to a list.
SVI <- as.list(NearestData_DrugX$SVI)
# Create a blank data frame to store `Result` information from 3 replicates.
Result_df <- data.frame()
# Calculate the required information (`NearestData`) for each SVI
for (i in SVI){
# Filter to use an SVI at each iteration of the loop.
df <- dplyr::filter(NearestData_DrugX, SVI == i)
# Define the drug name
Drug_Name <- NearestData_DrugX$Drug[1]
## Replicate 1---------------------------------------------
# Calculate the slope.
m1 <- (df$CSCindex_High_r1 - df$CSCindex_Low_r1) / (df$Nearest_High_Concentration_pM - df$Nearest_Low_Concentration_pM)
# Perform linear interpolation to find the interpolated y-value (`Interpolated_CSCindex`).
log10_Dose_Finding <- df$log10_Concentration_pM
Dose_Finding <- df$Concentration_pM
y1 <- df$CSCindex_Low_r1 + m1 * (Dose_Finding - df$Nearest_Low_Concentration_pM)
Rep1_Result <- c(NearestData_DrugX$Drug[1],
i,
Dose_Finding,
log10_Dose_Finding,
m1,
y1,
"1"
)
# Store the information in `Result_df` data frame
Result_df <- rbind(Result_df,
Rep1_Result
)
## Replicate 2---------------------------------------------
# Calculate the slope.
m2 <- (df$CSCindex_High_r2 - df$CSCindex_Low_r2) / (df$Nearest_High_Concentration_pM - df$Nearest_Low_Concentration_pM)
# Perform linear interpolation to find the interpolated y-value (`Interpolated_CSCindex`).
y2 <- df$CSCindex_Low_r2 + m2 * (Dose_Finding - df$Nearest_Low_Concentration_pM)
Rep2_Result <- c(NearestData_DrugX$Drug[1],
i,
Dose_Finding,
log10_Dose_Finding,
m2,
y2,
"2"
)
# Store the information in `Result_df` data frame
Result_df <- rbind(Result_df,
Rep2_Result
)
## Replicate 3---------------------------------------------
# Calculate the slope.
m3 <- (df$CSCindex_High_r3 - df$CSCindex_Low_r3) / (df$Nearest_High_Concentration_pM - df$Nearest_Low_Concentration_pM)
# Perform linear interpolation to find the interpolated y-value (`Interpolated_CSCindex`).
y3 <- df$CSCindex_Low_r3 + m1 * (Dose_Finding - df$Nearest_Low_Concentration_pM)
Rep3_Result <- c(NearestData_DrugX$Drug[1], i, Dose_Finding, log10_Dose_Finding, m3, y3, "3")
# Store the information in `Result_df` data frame
Result_df <- rbind(Result_df,
Rep3_Result
)
}
colnames(Result_df) <- c("Drug",
"SVI",
"Concentration_pM",
"log10_Concentration_pM",
"m_Slope",
"Interpolated_CSCindex",
"Replicate"
)
# Change the values to numeric
Result_df[, -1] <- lapply(Result_df[, -1],
as.numeric
)
print(Result_df)
# Write the `Result_df` data into a `.csv` file.
write.csv(Result_df,
paste0(Drug_Name, "_Raw_InterpolatedData.csv"), row.names = FALSE)
return(Result_df)
}Interpolate CSC indexes.
# Create a blank list to store `CSCindex` information
CSCindex_list <- list()
# Interpolate CSC indexes.
for (NearestData_DrugX in NearestData_list){
# Interpolate CSC indexes by the created function.
CSCindex_DrugX <- Interpolate.CSCindex(NearestData_DrugX)
CSCindex_DrugX
# Rename the data frame to show the drug name.
## Extract the drug name.
Drug_Name <- CSCindex_DrugX$Drug[1]
## Rename the data frame.
CSCindex_DrugX_Data <- assign(paste0("CSCindex_Drug", Drug_Name),
CSCindex_DrugX
)
# Store the data frame into the list `CSCindex_list`.
CSCindex_list[[length(CSCindex_list)+1]] <- CSCindex_DrugX_Data
}## Drug SVI Concentration_pM log10_Concentration_pM m_Slope
## 1 A 0.55 35487.746764 4.5500784 -4.073213e-06
## 2 A 0.55 35487.746764 4.5500784 -3.395635e-07
## 3 A 0.55 35487.746764 4.5500784 -2.513739e-06
## 4 A 0.60 9029.249693 3.9556517 7.585941e-05
## 5 A 0.60 9029.249693 3.9556517 4.330917e-05
## 6 A 0.60 9029.249693 3.9556517 5.396774e-05
## 7 A 0.65 2563.495571 3.4088326 7.585941e-05
## 8 A 0.65 2563.495571 3.4088326 4.330917e-05
## 9 A 0.65 2563.495571 3.4088326 5.396774e-05
## 10 A 0.70 799.017714 2.9025564 -2.410455e-06
## 11 A 0.70 799.017714 2.9025564 -5.578633e-05
## 12 A 0.70 799.017714 2.9025564 -8.373344e-05
## 13 A 0.75 269.912538 2.4312231 -2.410455e-06
## 14 A 0.75 269.912538 2.4312231 -5.578633e-05
## 15 A 0.75 269.912538 2.4312231 -8.373344e-05
## 16 A 0.80 97.795429 1.9903186 -2.410455e-06
## 17 A 0.80 97.795429 1.9903186 -5.578633e-05
## 18 A 0.80 97.795429 1.9903186 -8.373344e-05
## 19 A 0.85 37.683516 1.5761514 -2.410455e-06
## 20 A 0.85 37.683516 1.5761514 -5.578633e-05
## 21 A 0.85 37.683516 1.5761514 -8.373344e-05
## 22 A 0.90 15.334361 1.1856657 -2.410455e-06
## 23 A 0.90 15.334361 1.1856657 -5.578633e-05
## 24 A 0.90 15.334361 1.1856657 -8.373344e-05
## 25 A 0.95 6.551195 0.8163205 -2.410455e-06
## 26 A 0.95 6.551195 0.8163205 -5.578633e-05
## 27 A 0.95 6.551195 0.8163205 -8.373344e-05
## 28 A 1.00 2.923326 0.4658773 -2.410455e-06
## 29 A 1.00 2.923326 0.4658773 -5.578633e-05
## 30 A 1.00 2.923326 0.4658773 -8.373344e-05
## Interpolated_CSCindex Replicate
## 1 1.5242046 1
## 2 1.3865062 2
## 3 1.2892970 3
## 4 1.5543811 1
## 5 1.3531186 2
## 6 1.5164986 3
## 7 1.0638928 1
## 8 1.0730921 2
## 9 1.0260103 3
## 10 0.9457714 1
## 11 1.0165905 2
## 12 0.9892119 3
## 13 0.9470468 1
## 14 1.0461073 2
## 15 0.9904873 3
## 16 0.9474617 1
## 17 1.0557091 2
## 18 0.9909021 3
## 19 0.9476066 1
## 20 1.0590625 2
## 21 0.9910470 3
## 22 0.9476604 1
## 23 1.0603093 2
## 24 0.9911009 3
## 25 0.9476816 1
## 26 1.0607993 2
## 27 0.9911221 3
## 28 0.9476903 1
## 29 1.0610016 2
## 30 0.9911308 3
## Drug SVI Concentration_pM log10_Concentration_pM m_Slope
## 1 B 0.55 1.707704e+08 8.2324125 NA
## 2 B 0.55 1.707704e+08 8.2324125 0.000000e+00
## 3 B 0.55 1.707704e+08 8.2324125 0.000000e+00
## 4 B 0.60 1.289309e+07 7.1103569 -9.722378e-09
## 5 B 0.60 1.289309e+07 7.1103569 -9.935922e-09
## 6 B 0.60 1.289309e+07 7.1103569 -1.089025e-08
## 7 B 0.65 1.197164e+06 6.0781535 -2.032832e-08
## 8 B 0.65 1.197164e+06 6.0781535 -1.922399e-08
## 9 B 0.65 1.197164e+06 6.0781535 -4.968792e-08
## 10 B 0.70 1.325832e+05 5.1224883 -6.505348e-07
## 11 B 0.70 1.325832e+05 5.1224883 -8.810255e-07
## 12 B 0.70 1.325832e+05 5.1224883 1.106154e-07
## 13 B 0.75 1.709171e+04 4.2327854 1.367103e-05
## 14 B 0.75 1.709171e+04 4.2327854 1.654546e-05
## 15 B 0.75 1.709171e+04 4.2327854 9.530258e-06
## 16 B 0.80 2.514918e+03 3.4005238 1.367103e-05
## 17 B 0.80 2.514918e+03 3.4005238 1.654546e-05
## 18 B 0.80 2.514918e+03 3.4005238 9.530258e-06
## 19 B 0.85 4.156562e+02 2.6187342 1.367103e-05
## 20 B 0.85 4.156562e+02 2.6187342 1.654546e-05
## 21 B 0.85 4.156562e+02 2.6187342 9.530258e-06
## 22 B 0.90 7.614694e+01 1.8816524 1.367103e-05
## 23 B 0.90 7.614694e+01 1.8816524 1.654546e-05
## 24 B 0.90 7.614694e+01 1.8816524 9.530258e-06
## 25 B 0.95 1.528988e+01 1.1844042 1.367103e-05
## 26 B 0.95 1.528988e+01 1.1844042 1.654546e-05
## 27 B 0.95 1.528988e+01 1.1844042 9.530258e-06
## 28 B 1.00 3.333939e+00 0.5229577 1.367103e-05
## 29 B 1.00 3.333939e+00 0.5229577 1.654546e-05
## 30 B 1.00 3.333939e+00 0.5229577 9.530258e-06
## Interpolated_CSCindex Replicate
## 1 NA 1
## 2 0.8759742 2
## 3 NA 3
## 4 1.2903964 1
## 5 1.2446656 2
## 6 1.1793651 3
## 7 1.4444412 1
## 8 1.3961964 2
## 9 1.4655281 3
## 10 1.6976308 1
## 11 1.7333023 2
## 12 1.3762001 3
## 13 1.3014638 1
## 14 1.2615771 2
## 15 1.1870717 3
## 16 1.1021841 1
## 17 1.0203974 2
## 18 0.9877920 3
## 19 1.0734851 1
## 20 0.9856642 2
## 21 0.9590929 3
## 22 1.0688436 1
## 23 0.9800468 2
## 24 0.9544515 3
## 25 1.0680116 1
## 26 0.9790399 2
## 27 0.9536195 3
## 28 1.0678482 1
## 29 0.9788421 2
## 30 0.9534560 3Observe the CSCindex_Drug data.
# The list which shows information of all drugs.
head(CSCindex_list)## [[1]]
## Drug SVI Concentration_pM log10_Concentration_pM m_Slope
## 1 A 0.55 35487.746764 4.5500784 -4.073213e-06
## 2 A 0.55 35487.746764 4.5500784 -3.395635e-07
## 3 A 0.55 35487.746764 4.5500784 -2.513739e-06
## 4 A 0.60 9029.249693 3.9556517 7.585941e-05
## 5 A 0.60 9029.249693 3.9556517 4.330917e-05
## 6 A 0.60 9029.249693 3.9556517 5.396774e-05
## 7 A 0.65 2563.495571 3.4088326 7.585941e-05
## 8 A 0.65 2563.495571 3.4088326 4.330917e-05
## 9 A 0.65 2563.495571 3.4088326 5.396774e-05
## 10 A 0.70 799.017714 2.9025564 -2.410455e-06
## 11 A 0.70 799.017714 2.9025564 -5.578633e-05
## 12 A 0.70 799.017714 2.9025564 -8.373344e-05
## 13 A 0.75 269.912538 2.4312231 -2.410455e-06
## 14 A 0.75 269.912538 2.4312231 -5.578633e-05
## 15 A 0.75 269.912538 2.4312231 -8.373344e-05
## 16 A 0.80 97.795429 1.9903186 -2.410455e-06
## 17 A 0.80 97.795429 1.9903186 -5.578633e-05
## 18 A 0.80 97.795429 1.9903186 -8.373344e-05
## 19 A 0.85 37.683516 1.5761514 -2.410455e-06
## 20 A 0.85 37.683516 1.5761514 -5.578633e-05
## 21 A 0.85 37.683516 1.5761514 -8.373344e-05
## 22 A 0.90 15.334361 1.1856657 -2.410455e-06
## 23 A 0.90 15.334361 1.1856657 -5.578633e-05
## 24 A 0.90 15.334361 1.1856657 -8.373344e-05
## 25 A 0.95 6.551195 0.8163205 -2.410455e-06
## 26 A 0.95 6.551195 0.8163205 -5.578633e-05
## 27 A 0.95 6.551195 0.8163205 -8.373344e-05
## 28 A 1.00 2.923326 0.4658773 -2.410455e-06
## 29 A 1.00 2.923326 0.4658773 -5.578633e-05
## 30 A 1.00 2.923326 0.4658773 -8.373344e-05
## Interpolated_CSCindex Replicate
## 1 1.5242046 1
## 2 1.3865062 2
## 3 1.2892970 3
## 4 1.5543811 1
## 5 1.3531186 2
## 6 1.5164986 3
## 7 1.0638928 1
## 8 1.0730921 2
## 9 1.0260103 3
## 10 0.9457714 1
## 11 1.0165905 2
## 12 0.9892119 3
## 13 0.9470468 1
## 14 1.0461073 2
## 15 0.9904873 3
## 16 0.9474617 1
## 17 1.0557091 2
## 18 0.9909021 3
## 19 0.9476066 1
## 20 1.0590625 2
## 21 0.9910470 3
## 22 0.9476604 1
## 23 1.0603093 2
## 24 0.9911009 3
## 25 0.9476816 1
## 26 1.0607993 2
## 27 0.9911221 3
## 28 0.9476903 1
## 29 1.0610016 2
## 30 0.9911308 3
##
## [[2]]
## Drug SVI Concentration_pM log10_Concentration_pM m_Slope
## 1 B 0.55 1.707704e+08 8.2324125 NA
## 2 B 0.55 1.707704e+08 8.2324125 0.000000e+00
## 3 B 0.55 1.707704e+08 8.2324125 0.000000e+00
## 4 B 0.60 1.289309e+07 7.1103569 -9.722378e-09
## 5 B 0.60 1.289309e+07 7.1103569 -9.935922e-09
## 6 B 0.60 1.289309e+07 7.1103569 -1.089025e-08
## 7 B 0.65 1.197164e+06 6.0781535 -2.032832e-08
## 8 B 0.65 1.197164e+06 6.0781535 -1.922399e-08
## 9 B 0.65 1.197164e+06 6.0781535 -4.968792e-08
## 10 B 0.70 1.325832e+05 5.1224883 -6.505348e-07
## 11 B 0.70 1.325832e+05 5.1224883 -8.810255e-07
## 12 B 0.70 1.325832e+05 5.1224883 1.106154e-07
## 13 B 0.75 1.709171e+04 4.2327854 1.367103e-05
## 14 B 0.75 1.709171e+04 4.2327854 1.654546e-05
## 15 B 0.75 1.709171e+04 4.2327854 9.530258e-06
## 16 B 0.80 2.514918e+03 3.4005238 1.367103e-05
## 17 B 0.80 2.514918e+03 3.4005238 1.654546e-05
## 18 B 0.80 2.514918e+03 3.4005238 9.530258e-06
## 19 B 0.85 4.156562e+02 2.6187342 1.367103e-05
## 20 B 0.85 4.156562e+02 2.6187342 1.654546e-05
## 21 B 0.85 4.156562e+02 2.6187342 9.530258e-06
## 22 B 0.90 7.614694e+01 1.8816524 1.367103e-05
## 23 B 0.90 7.614694e+01 1.8816524 1.654546e-05
## 24 B 0.90 7.614694e+01 1.8816524 9.530258e-06
## 25 B 0.95 1.528988e+01 1.1844042 1.367103e-05
## 26 B 0.95 1.528988e+01 1.1844042 1.654546e-05
## 27 B 0.95 1.528988e+01 1.1844042 9.530258e-06
## 28 B 1.00 3.333939e+00 0.5229577 1.367103e-05
## 29 B 1.00 3.333939e+00 0.5229577 1.654546e-05
## 30 B 1.00 3.333939e+00 0.5229577 9.530258e-06
## Interpolated_CSCindex Replicate
## 1 NA 1
## 2 0.8759742 2
## 3 NA 3
## 4 1.2903964 1
## 5 1.2446656 2
## 6 1.1793651 3
## 7 1.4444412 1
## 8 1.3961964 2
## 9 1.4655281 3
## 10 1.6976308 1
## 11 1.7333023 2
## 12 1.3762001 3
## 13 1.3014638 1
## 14 1.2615771 2
## 15 1.1870717 3
## 16 1.1021841 1
## 17 1.0203974 2
## 18 0.9877920 3
## 19 1.0734851 1
## 20 0.9856642 2
## 21 0.9590929 3
## 22 1.0688436 1
## 23 0.9800468 2
## 24 0.9544515 3
## 25 1.0680116 1
## 26 0.9790399 2
## 27 0.9536195 3
## 28 1.0678482 1
## 29 0.9788421 2
## 30 0.9534560 3# Drug A
head(CSCindex_DrugA)## Drug SVI Concentration_pM log10_Concentration_pM m_Slope
## 1 A 0.55 35487.75 4.550078 -4.073213e-06
## 2 A 0.55 35487.75 4.550078 -3.395635e-07
## 3 A 0.55 35487.75 4.550078 -2.513739e-06
## 4 A 0.60 9029.25 3.955652 7.585941e-05
## 5 A 0.60 9029.25 3.955652 4.330917e-05
## 6 A 0.60 9029.25 3.955652 5.396774e-05
## Interpolated_CSCindex Replicate
## 1 1.524205 1
## 2 1.386506 2
## 3 1.289297 3
## 4 1.554381 1
## 5 1.353119 2
## 6 1.516499 3# Drug B
head(CSCindex_DrugB)## Drug SVI Concentration_pM log10_Concentration_pM m_Slope
## 1 B 0.55 170770357 8.232412 NA
## 2 B 0.55 170770357 8.232412 0.000000e+00
## 3 B 0.55 170770357 8.232412 0.000000e+00
## 4 B 0.60 12893086 7.110357 -9.722378e-09
## 5 B 0.60 12893086 7.110357 -9.935922e-09
## 6 B 0.60 12893086 7.110357 -1.089025e-08
## Interpolated_CSCindex Replicate
## 1 NA 1
## 2 0.8759742 2
## 3 NA 3
## 4 1.2903964 1
## 5 1.2446656 2
## 6 1.1793651 3Part 3.4: Reconsider SVI range, according to NA value possibly present.
According to the calculated CSC index derived from interpolation, values from some replicates may fall outside the interpolatable range. This could potentially lead to the occurrence of NA values. If NA values are present due to interpolation issues, they are likely to occur at the highest or lowest SVI. Therefore, SVIs with NA values can be excluded and replaced with a new SVI range using our pipeline below. However, NA values may also arise from other reasons, so it’s important to thoroughly check the data.
3.4.1 Check whether NA is present in the data.
# Create a blank vector to store SVI that contains removable NA.
SVI_wtNAremovable_vector <- vector()
# Check whether NA value is present in any SVI.
for (CSCindex_DrugX in CSCindex_list){
print(paste("Start SVI range re-considering analysis of drug", CSCindex_DrugX$Drug[1]))
if (anyNA(CSCindex_DrugX))
{
print(paste0("CSCindex_Drug", CSCindex_DrugX$Drug[1], " contains NA."))
# Show the rows that contain NA value.
DrugX_Rows_with_NA <- CSCindex_DrugX[!complete.cases(CSCindex_DrugX), ]
print(DrugX_Rows_with_NA)
# Show SVIs that contain NA value.
SVI_wtNA <- unique(DrugX_Rows_with_NA$SVI)
print(paste0("SVI = ", SVI_wtNA, " contains NA."))
# Check whether the occurrence of NA values is removable or if all results should be rechecked.
if (SVI_wtNA == min(SVI_Range) | SVI_wtNA == max(SVI_Range)){
# Change variable name to`SVI_wtNAremovable` for further analysis.
SVI_wtNAremovable <- SVI_wtNA
# If NA values occur in the highest or lowest SVI, this might be due to interpolate issue. Thus, the lowest/highest SVI can be excluded.
print(paste0("SVI = ", SVI_wtNAremovable, " contains NA at highest or lowest SVI, thus this SVI is removable."))
# Store removable SVIs into a created vector (`SVI_wtNAremovable_vector`).
SVI_wtNAremovable_vector <- c(SVI_wtNAremovable_vector,
SVI_wtNAremovable
)
}
else
{
# If NA values occur in other SVIs, the data should be rechecked.
print(paste0("SVI = ", SVI_wtNA, " contains NA, all data should be re-checked."))
}
}
else
{
print(paste0("CSCindex_Drug", CSCindex_DrugX$Drug[1], " does not contain NA"))
}
print(paste("Finish SVI range re-considering analysis of drug", CSCindex_DrugX$Drug[1]))
print("===========================================")
}## [1] "Start SVI range re-considering analysis of drug A"
## [1] "CSCindex_DrugA does not contain NA"
## [1] "Finish SVI range re-considering analysis of drug A"
## [1] "==========================================="
## [1] "Start SVI range re-considering analysis of drug B"
## [1] "CSCindex_DrugB contains NA."
## Drug SVI Concentration_pM log10_Concentration_pM m_Slope
## 1 B 0.55 170770357 8.232412 NA
## 3 B 0.55 170770357 8.232412 0
## Interpolated_CSCindex Replicate
## 1 NA 1
## 3 NA 3
## [1] "SVI = 0.55 contains NA."
## [1] "SVI = 0.55 contains NA at highest or lowest SVI, thus this SVI is removable."
## [1] "Finish SVI range re-considering analysis of drug B"
## [1] "==========================================="Observe the SVIs that contain NA values.
unique(SVI_wtNAremovable_vector)## [1] 0.553.4.2 Exclude SVI that contain NA values and define the selected SVI range.
# Define new SVI range and SVI values (without SVI that contain NA values).
noNA_SVI_Range <- Desired_SVIvalues[!Desired_SVIvalues %in% SVI_wtNAremovable]
print(paste0("New SVI values(no NA) are ", paste(noNA_SVI_Range, collapse = ", ")))## [1] "New SVI values(no NA) are 1, 0.95, 0.9, 0.85, 0.8, 0.75, 0.7, 0.65, 0.6"# Create a blank list to store `CSCindex_noNA` information.
CSCindex_noNA_list <- list()
# Exclude the removable SVI ('SVI_wtNAremovable') from `CSCindex` data frame.
for (CSCindex_DrugX in CSCindex_list){
# Exclude SVI that contains NA values
CSCindex_noNA_DrugX <- dplyr::filter(CSCindex_DrugX,
SVI != SVI_wtNAremovable
)
CSCindex_noNA_DrugX
# Rename the data frame to show the drug name.
## Extract the drug name.
Drug_Name <- CSCindex_noNA_DrugX$Drug[1]
## Rename the data frame.
CSCindex_noNA_DrugX_Data <- assign(paste0("CSCindex_noNA_Drug", Drug_Name),
CSCindex_noNA_DrugX
)
# Store the data frame into the list `CSCindex_noNA_list`.
CSCindex_noNA_list[[length(CSCindex_noNA_list)+1]] <- CSCindex_noNA_DrugX_Data
}Observe the CSCindex_noNA_Drug data.
# The list which shows information of all drugs.
head(CSCindex_noNA_list)## [[1]]
## Drug SVI Concentration_pM log10_Concentration_pM m_Slope
## 1 A 0.60 9029.249693 3.9556517 7.585941e-05
## 2 A 0.60 9029.249693 3.9556517 4.330917e-05
## 3 A 0.60 9029.249693 3.9556517 5.396774e-05
## 4 A 0.65 2563.495571 3.4088326 7.585941e-05
## 5 A 0.65 2563.495571 3.4088326 4.330917e-05
## 6 A 0.65 2563.495571 3.4088326 5.396774e-05
## 7 A 0.70 799.017714 2.9025564 -2.410455e-06
## 8 A 0.70 799.017714 2.9025564 -5.578633e-05
## 9 A 0.70 799.017714 2.9025564 -8.373344e-05
## 10 A 0.75 269.912538 2.4312231 -2.410455e-06
## 11 A 0.75 269.912538 2.4312231 -5.578633e-05
## 12 A 0.75 269.912538 2.4312231 -8.373344e-05
## 13 A 0.80 97.795429 1.9903186 -2.410455e-06
## 14 A 0.80 97.795429 1.9903186 -5.578633e-05
## 15 A 0.80 97.795429 1.9903186 -8.373344e-05
## 16 A 0.85 37.683516 1.5761514 -2.410455e-06
## 17 A 0.85 37.683516 1.5761514 -5.578633e-05
## 18 A 0.85 37.683516 1.5761514 -8.373344e-05
## 19 A 0.90 15.334361 1.1856657 -2.410455e-06
## 20 A 0.90 15.334361 1.1856657 -5.578633e-05
## 21 A 0.90 15.334361 1.1856657 -8.373344e-05
## 22 A 0.95 6.551195 0.8163205 -2.410455e-06
## 23 A 0.95 6.551195 0.8163205 -5.578633e-05
## 24 A 0.95 6.551195 0.8163205 -8.373344e-05
## 25 A 1.00 2.923326 0.4658773 -2.410455e-06
## 26 A 1.00 2.923326 0.4658773 -5.578633e-05
## 27 A 1.00 2.923326 0.4658773 -8.373344e-05
## Interpolated_CSCindex Replicate
## 1 1.5543811 1
## 2 1.3531186 2
## 3 1.5164986 3
## 4 1.0638928 1
## 5 1.0730921 2
## 6 1.0260103 3
## 7 0.9457714 1
## 8 1.0165905 2
## 9 0.9892119 3
## 10 0.9470468 1
## 11 1.0461073 2
## 12 0.9904873 3
## 13 0.9474617 1
## 14 1.0557091 2
## 15 0.9909021 3
## 16 0.9476066 1
## 17 1.0590625 2
## 18 0.9910470 3
## 19 0.9476604 1
## 20 1.0603093 2
## 21 0.9911009 3
## 22 0.9476816 1
## 23 1.0607993 2
## 24 0.9911221 3
## 25 0.9476903 1
## 26 1.0610016 2
## 27 0.9911308 3
##
## [[2]]
## Drug SVI Concentration_pM log10_Concentration_pM m_Slope
## 1 B 0.60 1.289309e+07 7.1103569 -9.722378e-09
## 2 B 0.60 1.289309e+07 7.1103569 -9.935922e-09
## 3 B 0.60 1.289309e+07 7.1103569 -1.089025e-08
## 4 B 0.65 1.197164e+06 6.0781535 -2.032832e-08
## 5 B 0.65 1.197164e+06 6.0781535 -1.922399e-08
## 6 B 0.65 1.197164e+06 6.0781535 -4.968792e-08
## 7 B 0.70 1.325832e+05 5.1224883 -6.505348e-07
## 8 B 0.70 1.325832e+05 5.1224883 -8.810255e-07
## 9 B 0.70 1.325832e+05 5.1224883 1.106154e-07
## 10 B 0.75 1.709171e+04 4.2327854 1.367103e-05
## 11 B 0.75 1.709171e+04 4.2327854 1.654546e-05
## 12 B 0.75 1.709171e+04 4.2327854 9.530258e-06
## 13 B 0.80 2.514918e+03 3.4005238 1.367103e-05
## 14 B 0.80 2.514918e+03 3.4005238 1.654546e-05
## 15 B 0.80 2.514918e+03 3.4005238 9.530258e-06
## 16 B 0.85 4.156562e+02 2.6187342 1.367103e-05
## 17 B 0.85 4.156562e+02 2.6187342 1.654546e-05
## 18 B 0.85 4.156562e+02 2.6187342 9.530258e-06
## 19 B 0.90 7.614694e+01 1.8816524 1.367103e-05
## 20 B 0.90 7.614694e+01 1.8816524 1.654546e-05
## 21 B 0.90 7.614694e+01 1.8816524 9.530258e-06
## 22 B 0.95 1.528988e+01 1.1844042 1.367103e-05
## 23 B 0.95 1.528988e+01 1.1844042 1.654546e-05
## 24 B 0.95 1.528988e+01 1.1844042 9.530258e-06
## 25 B 1.00 3.333939e+00 0.5229577 1.367103e-05
## 26 B 1.00 3.333939e+00 0.5229577 1.654546e-05
## 27 B 1.00 3.333939e+00 0.5229577 9.530258e-06
## Interpolated_CSCindex Replicate
## 1 1.2903964 1
## 2 1.2446656 2
## 3 1.1793651 3
## 4 1.4444412 1
## 5 1.3961964 2
## 6 1.4655281 3
## 7 1.6976308 1
## 8 1.7333023 2
## 9 1.3762001 3
## 10 1.3014638 1
## 11 1.2615771 2
## 12 1.1870717 3
## 13 1.1021841 1
## 14 1.0203974 2
## 15 0.9877920 3
## 16 1.0734851 1
## 17 0.9856642 2
## 18 0.9590929 3
## 19 1.0688436 1
## 20 0.9800468 2
## 21 0.9544515 3
## 22 1.0680116 1
## 23 0.9790399 2
## 24 0.9536195 3
## 25 1.0678482 1
## 26 0.9788421 2
## 27 0.9534560 3# Drug A
head(CSCindex_noNA_DrugA)## Drug SVI Concentration_pM log10_Concentration_pM m_Slope
## 1 A 0.60 9029.250 3.955652 7.585941e-05
## 2 A 0.60 9029.250 3.955652 4.330917e-05
## 3 A 0.60 9029.250 3.955652 5.396774e-05
## 4 A 0.65 2563.496 3.408833 7.585941e-05
## 5 A 0.65 2563.496 3.408833 4.330917e-05
## 6 A 0.65 2563.496 3.408833 5.396774e-05
## Interpolated_CSCindex Replicate
## 1 1.554381 1
## 2 1.353119 2
## 3 1.516499 3
## 4 1.063893 1
## 5 1.073092 2
## 6 1.026010 3# Drug B
head(CSCindex_noNA_DrugB)## Drug SVI Concentration_pM log10_Concentration_pM m_Slope
## 1 B 0.60 12893086 7.110357 -9.722378e-09
## 2 B 0.60 12893086 7.110357 -9.935922e-09
## 3 B 0.60 12893086 7.110357 -1.089025e-08
## 4 B 0.65 1197164 6.078153 -2.032832e-08
## 5 B 0.65 1197164 6.078153 -1.922399e-08
## 6 B 0.65 1197164 6.078153 -4.968792e-08
## Interpolated_CSCindex Replicate
## 1 1.290396 1
## 2 1.244666 2
## 3 1.179365 3
## 4 1.444441 1
## 5 1.396196 2
## 6 1.465528 3Part 3.5: Find AUC of CSC index according to the selected SVI range.
3.5.1 Calculate AUC of CSC index for vehicle control.
# Define information.
VehicleControl_df <- data.frame(Drug = "Control",
SVI = CSCindex_noNA_list[[1]]$SVI,
Interpolated_CSCindex = 1,
Replicate = CSCindex_noNA_list[[1]]$Replicate
)
# Calculate AUC of CSC index for each replicate.
AUC_Control <- VehicleControl_df %>%
group_by(Replicate) %>%
summarise(AUC_Control = trapz(SVI, Interpolated_CSCindex)) %>%
cbind(Drug = VehicleControl_df$Drug[1])
# VObserve the `AUC_Control` data.
AUC_Control## Replicate AUC_Control Drug
## 1 1 0.4 Control
## 2 2 0.4 Control
## 3 3 0.4 Control3.5.2 Calculate normalized CSC index’s AUC of each drug.
# Create a blank list to store `NormalizedAUC` information.
NormalizedAUC_list <- list()
# Calculate AUC of CSC index.
for (CSCindex_noNA_DrugX in CSCindex_noNA_list){
# Step 1: Calculate AUC of CSC index for each Replicate.
AUC_DrugX <- CSCindex_noNA_DrugX %>%
group_by(Replicate) %>%
summarise(AUC = trapz(SVI, Interpolated_CSCindex)) %>%
cbind(Drug = CSCindex_noNA_DrugX$Drug[1])
# Step 2: Calculate normalized CSC index's AUC by divided by AUC of the vehicle control.
## Add AUC of the vehicle control the data frame.
AUC_DrugX <- cbind(AUC_DrugX, AUC_Control = AUC_Control$AUC_Control)
NormalizedAUC_DrugX <- dplyr::mutate(AUC_DrugX,
Normalized_AUC = AUC/AUC_Control
)
## Reorder columns.
NormalizedAUC_DrugX <- select(NormalizedAUC_DrugX,
Drug,
Replicate,
everything()
)
# Rename the data frame to show the drug name.
## Extract the drug name.
Drug_Name <- NormalizedAUC_DrugX$Drug[1]
## Rename the data frame.
NormalizedAUC_DrugX_Data <- assign(paste0("NormalizedAUC_Drug", Drug_Name),
NormalizedAUC_DrugX
)
# Store the data frame into the list `NormalizedAUC_list`.
NormalizedAUC_list[[length(NormalizedAUC_list)+1]] <- NormalizedAUC_DrugX_Data
}Observe the NormalizedAUC_Drug data.
# The list which shows information of all drugs.
head(NormalizedAUC_list)## [[1]]
## Drug Replicate AUC AUC_Control Normalized_AUC
## 1 A 1 0.3999078 0.4 0.9997696
## 2 A 2 0.4289365 0.4 1.0723413
## 3 A 3 0.4111848 0.4 1.0279620
##
## [[2]]
## Drug Replicate AUC AUC_Control Normalized_AUC
## 1 B 1 0.4967591 0.4 1.241898
## 2 B 2 0.4733989 0.4 1.183497
## 3 B 3 0.4475083 0.4 1.118771# Drug A
head(NormalizedAUC_DrugA)## Drug Replicate AUC AUC_Control Normalized_AUC
## 1 A 1 0.3999078 0.4 0.9997696
## 2 A 2 0.4289365 0.4 1.0723413
## 3 A 3 0.4111848 0.4 1.0279620# Drug B
head(NormalizedAUC_DrugB)## Drug Replicate AUC AUC_Control Normalized_AUC
## 1 B 1 0.4967591 0.4 1.241898
## 2 B 2 0.4733989 0.4 1.183497
## 3 B 3 0.4475083 0.4 1.118771Part 3.6: Create summary analysis.
# Combine all drug into a data frame.
NormalizedAUC_AllDrugs <- bind_rows(NormalizedAUC_list)
write.csv(NormalizedAUC_AllDrugs,
paste0("RawResult", "_NormalizedCSC.AUC_AllDrugs.csv"), row.names = FALSE)
# Summarize the analysis.
Summary_NormalizedAUC_AllDrugs <- NormalizedAUC_AllDrugs %>%
group_by(Drug) %>%
summarise_at(vars(Normalized_AUC),
list(Mean_Normalized_AUC = mean,
SD_Normalized_AUC = sd)
)
# Write the `Summary_NormalizedAUC_AllDrugs` into a `.csv` file.
write.csv(Summary_NormalizedAUC_AllDrugs, "Summary_NormalizedCSC.AUC_AllDrugs.csv", row.names = FALSE)Observe the Summary_NormalizedCSCindexAUC_AllDrugs
data.
head(Summary_NormalizedAUC_AllDrugs)## # A tibble: 2 × 3
## Drug Mean_Normalized_AUC SD_Normalized_AUC
## <chr> <dbl> <dbl>
## 1 A 1.03 0.0366
## 2 B 1.18 0.0616Section 4: Statistical test
4.1 Normality test
To determine whether the data follows a normal distribution, the normality test should be performed.
shapiro.test(NormalizedAUC_AllDrugs$Normalized_AUC)##
## Shapiro-Wilk normality test
##
## data: NormalizedAUC_AllDrugs$Normalized_AUC
## W = 0.95952, p-value = 0.8161For the example dataset, the result showed that the data is normally distributed.
4.2 Statistical test
According to the normal distribution of the data, a t-test was used for statistical testing.
If your data does not follow a normal distribution, a non-parametric
test like the “Wilcoxon rank-sum test” should be used instead.
Here, we also provide the choice of statistical tests as shown
below.
# Wilcoxon rank-sum test
Stat_NormalizedAUC_Wilcox <- compare_means(Normalized_AUC ~ Drug,
data = NormalizedAUC_AllDrugs,
method = "wilcox.test"
)
# T-test
Stat_NormalizedAUC_Ttest <- compare_means(Normalized_AUC ~ Drug,
data = NormalizedAUC_AllDrugs,
method = "t.test"
)
# Write the `Stat_NormalizedAUC_Ttest` into a `.csv` file.
write.csv(Stat_NormalizedAUC_Ttest,
paste0("Stat", "_NormalizedCSC.AUC.csv"), row.names = FALSE)Observe the Stat_NormalizedAUC_Ttest data.
head(Stat_NormalizedAUC_Ttest)## # A tibble: 1 × 8
## .y. group1 group2 p p.adj p.format p.signif method
## <chr> <chr> <chr> <dbl> <dbl> <chr> <chr> <chr>
## 1 Normalized_AUC A B 0.0327 0.033 0.033 * T-testSection 5: Data visualization
Data visualization is presented as a bar graph in an object named
NormalizedAUC_plot and saved as a .png
file.
NormalizedAUC_plot <- ggplot(Summary_NormalizedAUC_AllDrugs, aes(x = Drug)) +
geom_bar(aes(y = Mean_Normalized_AUC, fill = Drug),
stat = "identity", alpha = 0.8) +
geom_errorbar(aes(ymin = Mean_Normalized_AUC - SD_Normalized_AUC,
ymax = Mean_Normalized_AUC + SD_Normalized_AUC),
width = 0.1, position = position_dodge(0.9)) +
scale_fill_viridis(discrete = TRUE, option = "H") +
scale_y_continuous(breaks = seq(0, (max(Summary_NormalizedAUC_AllDrugs$Mean_Normalized_AUC)+0.25),
by = 0.25)) +
labs(title = "Comparing CSC content among the drugs",
x = "Drugs",
y = "Normalized CSC index's AUC") +
theme_classic() +
theme(plot.title = element_text(hjust = 0.5)) +
theme(legend.position = "none")
# Manually annotate the statistical significance
NormalizedAUC_plot_wtStat <- NormalizedAUC_plot +
annotate("text",
x = 1.5,
y = 0.1 + max(Summary_NormalizedAUC_AllDrugs$Mean_Normalized_AUC),
label = "*",
size = 8)
# Save the plot as a `.png` file.
ggsave('NormalizedAUC_plot.png',
width = 4, height = 4,
dpi = 300, units = 'in')
print(paste0("The .png file was saved as '", "NormalizedAUC_plot.png'"))## [1] "The .png file was saved as 'NormalizedAUC_plot.png'"
Figure 3: Comparing CSC content among cytotoxic drugs across a range of
3D multi-spheroid’s dose-response.