Statistics: The Next Generation
Eamonn Mallon
2025-02-27
Today’s lecture
- An ad for BS2004
- You can now understand machine learning (my research as an example)
BS2004: Contemporary Techniques in Biological Data Analysis
- Optional 15 credit second year course
- 11 x (Online lectures, Discussion sessions, Practicals, Help sessions)
- Second semester
Do I not know all the stats?
- What we taught you is a good basis
- If your experiments are simple, they will be fine
- multiway ANOVAs (with interactions), nested ANOVAs, ANCOVAs etc. etc
- You could learn these piecemeal as required or
BS2004: Contemporary Techniques in Biological Data Analysis
- General and generalised linear models
General and generalised linear models
- t-tests, ANOVA, ANCOVA, and regressions are types of General linear models
- The difference between general and generalised linear models is simply how error is handled
- General linear models assume errors are independent and follow a normal distribution
- Generalized linear models can use a wide range of distributions
- i.e. your data doesn’t have to be normal (bye bye non-parametric tests)
- lm is the R command for General linear models
- glm is the R command for Generalised linear models
Epigenetic ageing
Ageing
DNA methylation
How to build an epigenetic clock
Horvath used machine learning to select methylated parts of the genome that best predict age, an epigenetic clock
How LMs fit into machine learning
Penalised net regression
The penalized net regression equation is \[ \underset{\beta}{\text{minimize}} \sum_{i=1}^{n} \left(y_i - X_i \beta \right)^2 + \lambda_1 \sum_{j=1}^{p} |\beta_j| + \lambda_2 \sum_{j=1}^{p} \beta_j^2 \]
Build your own epigenetic clock
# Load necessary package
library(glmnet)
# Set seed for reproducibility
set.seed(42)
# Simulate toy methylation data (10 samples, 5 CpG sites)
CpG_sites <- matrix(runif(10 * 5, 0, 1), nrow = 10, ncol = 5) # 0-1 methylation beta values
colnames(CpG_sites) <- paste0("CpG_", 1:5) # Name CpG sites
# Simulate chronological age (true age)
true_age <- seq(30, 75, length.out = 10) + rnorm(10, sd = 2) # Add slight noise
# Fit Elastic Net Regression model (alpha = 0.5 for Elastic Net)
fit <- cv.glmnet(CpG_sites, true_age, alpha = 0.5) # Cross-validation to find best lambda
# Extract the best model
best_lambda <- fit$lambda.min
model_coefs <- coef(fit, s = best_lambda)
# Predict epigenetic age
epigenetic_age <- predict(fit, newx = CpG_sites, s = best_lambda)
# Combine results into a data frame
results <- data.frame(Sample = 1:10, Chronological_Age = true_age, Epigenetic_Age = as.numeric(epigenetic_age))
# Load ggplot2 for visualization
library(ggplot2)
# Create scatter plot with regression line
ggplot(results, aes(x = Chronological_Age, y = Epigenetic_Age)) +
geom_point(color = "blue", size = 3) + # Scatter points
geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") + # Perfect correlation line
labs(title = "Epigenetic Age vs. Chronological Age",
x = "Chronological Age",
y = "Epigenetic Age") +
theme_minimal()Results
Epigenetic clocks are plastic
We need an insect model
- Insects as an intermediary model between simple cell lines and complex vertebrate systems.
- Unlike cell lines, insects allow the study of multicellular interactions, tissues, and whole-organism processes.
- Compared to mice, insects excel in cost-effectiveness, rapid generation time, and ethical feasibility.
- Insects’ suitability for high-throughput behavioural and lifespan analysis provides unique insights that neither cell lines nor mice can easily achieve.
- Drosophila and C.elegans don’t have DNA methylation
Nasonia vitripenis has DNA methylation
Diapause as a test
The insect epigenetic clock is plastic
What did I learn today
- None of this new stuff is on the exams
See you next year
Lecture 7