Predicting Permeability
Woodelyne Durosier
2025-04-05
Problem 6.2: Predicting Permeability
Introduction
Understanding a compound’s permeability is critical in pharmaceutical research since it helps anticipate whether it will be efficiently absorbed in the human body. A permeability prediction model can help save time, money, and resources. In this study, we use Partial Least Squares (PLS) to predict permeability based on chemical fingerprints.
Load library
library(AppliedPredictiveModeling)
library(caret)## Loading required package: ggplot2## Loading required package: latticelibrary(pls)##
## Attaching package: 'pls'## The following object is masked from 'package:caret':
##
## R2## The following object is masked from 'package:stats':
##
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## ✖ dplyr::lag() masks stats::lag()
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(readr)
library(dplyr)Load Data
data("permeability")
str(permeability)## num [1:165, 1] 12.52 1.12 19.41 1.73 1.68 ...
## - attr(*, "dimnames")=List of 2
## ..$ : chr [1:165] "1" "2" "3" "4" ...
## ..$ : chr "permeability"This data consist of permeability and fingerprints
Filtering Predictors with Low Frequency
nzv <- nearZeroVar(fingerprints)
filtered_fingerprints <- fingerprints[, -nzv]
ncol(filtered_fingerprints)## [1] 388Molecular fingerprints are largely zeros. Many predictors occur so infrequently that they add nothing to model performance and can lead to overfitting. The caret package’s nearZeroVar() method filters out such predictions. After filtering, 388 predictors remain, providing a more manageable and useful feature set.
Splitting Data and Training a PLS Model
set.seed(123)
trainIndex <- createDataPartition(permeability, p = 0.8, list = FALSE)
trainX <- filtered_fingerprints[trainIndex, ]
testX <- filtered_fingerprints[-trainIndex, ]
trainY <- permeability[trainIndex]
testY <- permeability[-trainIndex]# preprocessing and model tuning
pls_model <- train(
x = trainX,
y = trainY,
method = "pls",
tuneLength = 20,
trControl = trainControl(method = "cv", number = 10),
preProcess = c("center", "scale")
)
#optimal number of components
pls_model$bestTune## ncomp
## 6 6# Resampled R-squared
max(pls_model$results$Rsquared)## [1] 0.5335956We trained a PLS model with tenfold cross-validation. This model is useful when predictors are very collinear since it reduces dimensions to latent variables. The ideal number of latent variables was determined automatically. The resampled R² score indicates the model’s ability to accurately predict permeability during training.
Predictions on Test Set
pred_test <- predict(pls_model, testX)
# R-squated on test data
postResample(pred_test, testY)["Rsquared"]## Rsquared
## 0.3244542We trained a PLS model with tenfold cross-validation. This model is useful when predictors are very collinear since it reduces dimensions to latent variables. The ideal number of latent variables was determined automatically. The resampled R² score indicates the model’s ability to accurately predict permeability during training.
Problem 6.3: Improving Chemical Yield
In chemical production, boosting product yield is closely related to profit. Understanding how biological and manufacturing factors impact yield allows us to recommend modifications that increase production. We use a Random Forest model to discover essential traits and generate predictions.
Load Data
data("ChemicalManufacturingProcess")
head(ChemicalManufacturingProcess)## Yield BiologicalMaterial01 BiologicalMaterial02 BiologicalMaterial03
## 1 38.00 6.25 49.58 56.97
## 2 42.44 8.01 60.97 67.48
## 3 42.03 8.01 60.97 67.48
## 4 41.42 8.01 60.97 67.48
## 5 42.49 7.47 63.33 72.25
## 6 43.57 6.12 58.36 65.31
## BiologicalMaterial04 BiologicalMaterial05 BiologicalMaterial06
## 1 12.74 19.51 43.73
## 2 14.65 19.36 53.14
## 3 14.65 19.36 53.14
## 4 14.65 19.36 53.14
## 5 14.02 17.91 54.66
## 6 15.17 21.79 51.23
## BiologicalMaterial07 BiologicalMaterial08 BiologicalMaterial09
## 1 100 16.66 11.44
## 2 100 19.04 12.55
## 3 100 19.04 12.55
## 4 100 19.04 12.55
## 5 100 18.22 12.80
## 6 100 18.30 12.13
## BiologicalMaterial10 BiologicalMaterial11 BiologicalMaterial12
## 1 3.46 138.09 18.83
## 2 3.46 153.67 21.05
## 3 3.46 153.67 21.05
## 4 3.46 153.67 21.05
## 5 3.05 147.61 21.05
## 6 3.78 151.88 20.76
## ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03
## 1 NA NA NA
## 2 0.0 0 NA
## 3 0.0 0 NA
## 4 0.0 0 NA
## 5 10.7 0 NA
## 6 12.0 0 NA
## ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06
## 1 NA NA NA
## 2 917 1032.2 210.0
## 3 912 1003.6 207.1
## 4 911 1014.6 213.3
## 5 918 1027.5 205.7
## 6 924 1016.8 208.9
## ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess09
## 1 NA NA 43.00
## 2 177 178 46.57
## 3 178 178 45.07
## 4 177 177 44.92
## 5 178 178 44.96
## 6 178 178 45.32
## ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12
## 1 NA NA NA
## 2 NA NA 0
## 3 NA NA 0
## 4 NA NA 0
## 5 NA NA 0
## 6 NA NA 0
## ManufacturingProcess13 ManufacturingProcess14 ManufacturingProcess15
## 1 35.5 4898 6108
## 2 34.0 4869 6095
## 3 34.8 4878 6087
## 4 34.8 4897 6102
## 5 34.6 4992 6233
## 6 34.0 4985 6222
## ManufacturingProcess16 ManufacturingProcess17 ManufacturingProcess18
## 1 4682 35.5 4865
## 2 4617 34.0 4867
## 3 4617 34.8 4877
## 4 4635 34.8 4872
## 5 4733 33.9 4886
## 6 4786 33.4 4862
## ManufacturingProcess19 ManufacturingProcess20 ManufacturingProcess21
## 1 6049 4665 0.0
## 2 6097 4621 0.0
## 3 6078 4621 0.0
## 4 6073 4611 0.0
## 5 6102 4659 -0.7
## 6 6115 4696 -0.6
## ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24
## 1 NA NA NA
## 2 3 0 3
## 3 4 1 4
## 4 5 2 5
## 5 8 4 18
## 6 9 1 1
## ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27
## 1 4873 6074 4685
## 2 4869 6107 4630
## 3 4897 6116 4637
## 4 4892 6111 4630
## 5 4930 6151 4684
## 6 4871 6128 4687
## ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30
## 1 10.7 21.0 9.9
## 2 11.2 21.4 9.9
## 3 11.1 21.3 9.4
## 4 11.1 21.3 9.4
## 5 11.3 21.6 9.0
## 6 11.4 21.7 10.1
## ManufacturingProcess31 ManufacturingProcess32 ManufacturingProcess33
## 1 69.1 156 66
## 2 68.7 169 66
## 3 69.3 173 66
## 4 69.3 171 68
## 5 69.4 171 70
## 6 68.2 173 70
## ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36
## 1 2.4 486 0.019
## 2 2.6 508 0.019
## 3 2.6 509 0.018
## 4 2.5 496 0.018
## 5 2.5 468 0.017
## 6 2.5 490 0.018
## ManufacturingProcess37 ManufacturingProcess38 ManufacturingProcess39
## 1 0.5 3 7.2
## 2 2.0 2 7.2
## 3 0.7 2 7.2
## 4 1.2 2 7.2
## 5 0.2 2 7.3
## 6 0.4 2 7.2
## ManufacturingProcess40 ManufacturingProcess41 ManufacturingProcess42
## 1 NA NA 11.6
## 2 0.1 0.15 11.1
## 3 0.0 0.00 12.0
## 4 0.0 0.00 10.6
## 5 0.0 0.00 11.0
## 6 0.0 0.00 11.5
## ManufacturingProcess43 ManufacturingProcess44 ManufacturingProcess45
## 1 3.0 1.8 2.4
## 2 0.9 1.9 2.2
## 3 1.0 1.8 2.3
## 4 1.1 1.8 2.1
## 5 1.1 1.7 2.1
## 6 2.2 1.8 2.0 str(ChemicalManufacturingProcess)## 'data.frame': 176 obs. of 58 variables:
## $ Yield : num 38 42.4 42 41.4 42.5 ...
## $ BiologicalMaterial01 : num 6.25 8.01 8.01 8.01 7.47 6.12 7.48 6.94 6.94 6.94 ...
## $ BiologicalMaterial02 : num 49.6 61 61 61 63.3 ...
## $ BiologicalMaterial03 : num 57 67.5 67.5 67.5 72.2 ...
## $ BiologicalMaterial04 : num 12.7 14.7 14.7 14.7 14 ...
## $ BiologicalMaterial05 : num 19.5 19.4 19.4 19.4 17.9 ...
## $ BiologicalMaterial06 : num 43.7 53.1 53.1 53.1 54.7 ...
## $ BiologicalMaterial07 : num 100 100 100 100 100 100 100 100 100 100 ...
## $ BiologicalMaterial08 : num 16.7 19 19 19 18.2 ...
## $ BiologicalMaterial09 : num 11.4 12.6 12.6 12.6 12.8 ...
## $ BiologicalMaterial10 : num 3.46 3.46 3.46 3.46 3.05 3.78 3.04 3.85 3.85 3.85 ...
## $ BiologicalMaterial11 : num 138 154 154 154 148 ...
## $ BiologicalMaterial12 : num 18.8 21.1 21.1 21.1 21.1 ...
## $ ManufacturingProcess01: num NA 0 0 0 10.7 12 11.5 12 12 12 ...
## $ ManufacturingProcess02: num NA 0 0 0 0 0 0 0 0 0 ...
## $ ManufacturingProcess03: num NA NA NA NA NA NA 1.56 1.55 1.56 1.55 ...
## $ ManufacturingProcess04: num NA 917 912 911 918 924 933 929 928 938 ...
## $ ManufacturingProcess05: num NA 1032 1004 1015 1028 ...
## $ ManufacturingProcess06: num NA 210 207 213 206 ...
## $ ManufacturingProcess07: num NA 177 178 177 178 178 177 178 177 177 ...
## $ ManufacturingProcess08: num NA 178 178 177 178 178 178 178 177 177 ...
## $ ManufacturingProcess09: num 43 46.6 45.1 44.9 45 ...
## $ ManufacturingProcess10: num NA NA NA NA NA NA 11.6 10.2 9.7 10.1 ...
## $ ManufacturingProcess11: num NA NA NA NA NA NA 11.5 11.3 11.1 10.2 ...
## $ ManufacturingProcess12: num NA 0 0 0 0 0 0 0 0 0 ...
## $ ManufacturingProcess13: num 35.5 34 34.8 34.8 34.6 34 32.4 33.6 33.9 34.3 ...
## $ ManufacturingProcess14: num 4898 4869 4878 4897 4992 ...
## $ ManufacturingProcess15: num 6108 6095 6087 6102 6233 ...
## $ ManufacturingProcess16: num 4682 4617 4617 4635 4733 ...
## $ ManufacturingProcess17: num 35.5 34 34.8 34.8 33.9 33.4 33.8 33.6 33.9 35.3 ...
## $ ManufacturingProcess18: num 4865 4867 4877 4872 4886 ...
## $ ManufacturingProcess19: num 6049 6097 6078 6073 6102 ...
## $ ManufacturingProcess20: num 4665 4621 4621 4611 4659 ...
## $ ManufacturingProcess21: num 0 0 0 0 -0.7 -0.6 1.4 0 0 1 ...
## $ ManufacturingProcess22: num NA 3 4 5 8 9 1 2 3 4 ...
## $ ManufacturingProcess23: num NA 0 1 2 4 1 1 2 3 1 ...
## $ ManufacturingProcess24: num NA 3 4 5 18 1 1 2 3 4 ...
## $ ManufacturingProcess25: num 4873 4869 4897 4892 4930 ...
## $ ManufacturingProcess26: num 6074 6107 6116 6111 6151 ...
## $ ManufacturingProcess27: num 4685 4630 4637 4630 4684 ...
## $ ManufacturingProcess28: num 10.7 11.2 11.1 11.1 11.3 11.4 11.2 11.1 11.3 11.4 ...
## $ ManufacturingProcess29: num 21 21.4 21.3 21.3 21.6 21.7 21.2 21.2 21.5 21.7 ...
## $ ManufacturingProcess30: num 9.9 9.9 9.4 9.4 9 10.1 11.2 10.9 10.5 9.8 ...
## $ ManufacturingProcess31: num 69.1 68.7 69.3 69.3 69.4 68.2 67.6 67.9 68 68.5 ...
## $ ManufacturingProcess32: num 156 169 173 171 171 173 159 161 160 164 ...
## $ ManufacturingProcess33: num 66 66 66 68 70 70 65 65 65 66 ...
## $ ManufacturingProcess34: num 2.4 2.6 2.6 2.5 2.5 2.5 2.5 2.5 2.5 2.5 ...
## $ ManufacturingProcess35: num 486 508 509 496 468 490 475 478 491 488 ...
## $ ManufacturingProcess36: num 0.019 0.019 0.018 0.018 0.017 0.018 0.019 0.019 0.019 0.019 ...
## $ ManufacturingProcess37: num 0.5 2 0.7 1.2 0.2 0.4 0.8 1 1.2 1.8 ...
## $ ManufacturingProcess38: num 3 2 2 2 2 2 2 2 3 3 ...
## $ ManufacturingProcess39: num 7.2 7.2 7.2 7.2 7.3 7.2 7.3 7.3 7.4 7.1 ...
## $ ManufacturingProcess40: num NA 0.1 0 0 0 0 0 0 0 0 ...
## $ ManufacturingProcess41: num NA 0.15 0 0 0 0 0 0 0 0 ...
## $ ManufacturingProcess42: num 11.6 11.1 12 10.6 11 11.5 11.7 11.4 11.4 11.3 ...
## $ ManufacturingProcess43: num 3 0.9 1 1.1 1.1 2.2 0.7 0.8 0.9 0.8 ...
## $ ManufacturingProcess44: num 1.8 1.9 1.8 1.8 1.7 1.8 2 2 1.9 1.9 ...
## $ ManufacturingProcess45: num 2.4 2.2 2.3 2.1 2.1 2 2.2 2.2 2.1 2.4 ...Handling Missing Data
#distinct predictors and response
X <- ChemicalManufacturingProcess[, -1]
Y <- ChemicalManufacturingProcess$Yield
library(RANN)
pre_proc <- preProcess(X, method = c("knnImpute", "center", "scale"))
X_imputed <- predict(pre_proc, X)Some predictors are missing values. We utilized k-nearest neighbors (kNN) imputation to substitute missing values based on their resemblance to other samples. This, together with centering and scaling, prepares the data for modeling.
#Train Test split and build a model
set.seed(123)
train_index <- createDataPartition(Y,p = 0.8, list = FALSE)
trainX <- X_imputed[train_index, ]
testX <- X_imputed[-train_index, ]
trainY <- Y[train_index]
testY <- Y[train_index]rf_model <- train(x = trainX,
y = trainY,
method = "rf",
tuneLength = 10,
trControl = trainControl(method = "cv", number = 10)
)# checking training performance
max(rf_model$results$Rsquared)## [1] 0.6695883rf_model$results## mtry RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 2 1.233680 0.6522971 0.9863157 0.2485274 0.1551006 0.1718425
## 2 8 1.155652 0.6671644 0.9161959 0.2584433 0.1593769 0.1883288
## 3 14 1.137068 0.6695883 0.9010009 0.2695379 0.1547402 0.1942868
## 4 20 1.144384 0.6555923 0.9033100 0.2668507 0.1547724 0.1918255
## 5 26 1.138767 0.6589172 0.8975126 0.2647536 0.1469744 0.1869694
## 6 32 1.144398 0.6496300 0.8955242 0.2641008 0.1466654 0.1841463
## 7 38 1.145372 0.6463166 0.8887278 0.2665143 0.1497733 0.1902730
## 8 44 1.141166 0.6418132 0.8844658 0.2706379 0.1474131 0.1863840
## 9 50 1.144820 0.6401705 0.8772522 0.2575995 0.1445322 0.1794379
## 10 57 1.144081 0.6370679 0.8749294 0.2512206 0.1438900 0.1701359We trained a Random Forest model, a strong ensemble approach that deals with complicated, nonlinear linkages and interactions. The resampled R² score shows how well the model fits the training data.
Predict and Compare Performance
pred_test_rf <- predict(rf_model, testX)
postResample(pred_test_rf, testY)## Warning in pred - obs: longer object length is not a multiple of shorter object
## length
## Warning in pred - obs: longer object length is not a multiple of shorter object
## length## RMSE Rsquared MAE
## 1.959969 NA 1.598057The test set R² value accurately represents real-world predicting performance. If it’s close to the training R², the model will generalize well. If it’s significantly lower, it might be overfitting.
#Feature Importance
importance_rf <-varImp(rf_model)
plot(importance_rf, top = 10)
This graphic depicts the top ten most important predictors of yield.
ManufacturingProcess32 is the most critical, indicating that it is a
primary driver of production. Several biological factors also score
highly, demonstrating that input quality can influence yield even when
it is not changing during manufacture.
#Explore Top Predictor Relationships
top_predictor <- rownames(importance_rf$importance)[1]
ggplot(data.frame(X = trainX[[top_predictor]], Y = trainY), aes(x = X, y = Y)) +
geom_point() +
geom_smooth(method = "lm") +
labs(title = paste("Top Predictor:", top_predictor), x = top_predictor, y = "Yield")## `geom_smooth()` using formula = 'y ~ x'
Here, we show how the top predictor (ManufacturingProcess32) corresponds
with yield. The geom_smooth() method creates a regression line to depict
the overall trend. This knowledge can be used to direct process
modifications; for example, raising or improving this process parameter
may increase future yields.
To Conclude
Both models provide information on how biological and structural factors influence results in pharmaceutical research and manufacture. While not perfect, these prediction models can improve decision-making by identifying compounds or runs that may succeed or fail, allowing for improved resource allocation and quality control.