If I understood you research question, it seems like you’re navigating a problem involving identifying molecules that are altered between two categorical classes while controlling for a continuous covariate.
1. Clarify Your Research Question:
My understanding of your research question is that you you want to determine if the concentration of each molecule differs between two categorical classes (eg, treatment vs. control) while accounting for the effect of a continuous covariate (eg, age, weight, etc).
Your goal is to find molecules where the categorical class has a significant effect on the concentration, after controlling for the covariate.
2. Model Selection:
- For each molecule, fit a linear regression model with the concentration as the response variable, and the categorical class and the continuous covariate as predictors.
- The formula for each model would be: Concentration ~ Class + Covariate.
3. Implementation in R:
- Ensure your data is in a suitable format, with molecules as columns and samples as rows, and include the class and covariate information:
# Example data format
data <- data.frame(
Class = factor(c('A', 'B', 'A', 'B')),
Covariate = c(23, 45, 21, 50),
Molecule1 = c(1.2, 3.4, 2.1, 4.3),
Molecule2 = c(2.2, 3.5, 1.9, 4.0)
# Add more molecules as needed
)
4. Running Multiple Models:
Loop through each molecule, fit the linear model, and store the results:
results <- list()
for (molecule in colnames(data)[-c(1, 2)]) { # Assuming first two columns are Class and Covariate
model <- lm(as.formula(paste(molecule, "~ Class + Covariate")), data = data)
results[[molecule]] <- summary(model)$coefficients
}
5. Extract Significant Results:
- Extract the p-values for the Class variable from each model and adjust for multiple comparisons using a method like Bonferroni or Benjamini-Hochberg:
p_values <- sapply(results, function(x) x['ClassB', 'Pr(>|t|)']) # Adjust if Class has different levels
p_adjusted <- p.adjust(p_values, method = "BH") # Benjamini-Hochberg adjustment
significant_molecules <- names(p_adjusted)[p_adjusted < 0.05]
6. Model Diagnostics:
Check the diagnostic plots for each model to ensure the assumptions of linear regression are met (linearity, homoscedasticity, normality of residuals):
for (molecule in significant_molecules) {
model <- lm(as.formula(paste(molecule, "~ Class + Covariate")), data = data)
par(mfrow = c(2, 2)) # May need to save the plots to disk in some environments
plot(model)
}
In case the plots do not display in your environment, we can save them to disk instead:
# Directory to save plots
plot_dir <- "diagnostic_plots"
if (!dir.exists(plot_dir)) {
dir.create(plot_dir)
}
for (molecule in significant_molecules) {
model <- lm(as.formula(paste(molecule, "~ Class + Covariate")), data = data)
# Create a file name for the plot
plot_file <- file.path(plot_dir, paste0(molecule, "_diagnostic.png"))
# Open a png device
png(filename = plot_file)
# Plot diagnostics
par(mfrow = c(2, 2))
plot(model)
# Close the device
dev.off()
# Optionally print a message indicating the plot was saved
cat("Diagnostic plot saved for", molecule, "as", plot_file, "\n")
}
7. Validation and Model Quality:
- It is important to validate your models. Splitting your data into training and testing sets and evaluating the performance can help. For linear models, prediction accuracy can be assessed using metrics like R-squared, RMSE (Root Mean Square Error), etc.:
library(caret)
set.seed(15)
trainIndex <- createDataPartition(data$Class, p = .8, list = FALSE, times = 1)
dataTrain <- data[trainIndex,]
dataTest <- data[-trainIndex,]
# Train models on training set and evaluate on test set
for (molecule in significant_molecules) {
model <- lm(as.formula(paste(molecule, "~ Class + Covariate")), data = dataTrain)
predictions <- predict(model, newdata = dataTest)
actuals <- dataTest[[molecule]]
print(paste(molecule, "R-squared:", summary(lm(predictions ~ actuals))$r.squared))
}
Additional Considerations:
- Residual Analysis: Check the residuals for normality, homoscedasticity, and independence.
- Assumption Checks: Ensure all assumptions of linear regression are tested (eg, linearity, no multicollinearity).
Summary:
- Clarify Research Question: Identify significant molecules controlling for covariate.
- Model Selection: Use linear regression models for each molecule.
- Implementation in R: Structure data and fit models.
- Extract Significant Results: Adjust p-values and identify significant molecules.
- Diagnostics: Check diagnostic plots to ensure model assumptions are met.
- Validation: Split data, train, and test models to ensure robustness.
This approach helps to ensure that your findings are statistically valid and robust, accounting for multiple comparisons and ensuring model quality through diagnostic checks and validation.
