PhenoAge & PCage

Saket Choudhary

saketc@iitb.ac.in

Computational Multi-omics of Ageing

DH 603

Lecture 07 || Wednesday, 2^nd April 2025

PhenoAge

3

dfdf

PhenoAge: Predictor for ageing and lifespan

Levine et al. 2018

dfdf

From last class: GrimAge uses plasma protein and smoking years as surrogates

Lu et al. 2019

dfdf

PhenoAge Steps

• Step1 : Use clinical data to estimate “phenotypic age” from “National Health and Nutrition Examination Survey (NHANES)”
• Step 2 : Elastic-net regression model to predict PhenoAge from CpG markers

​

​

​

​

​

​

• Step 3: Understand the biology of the 513 CpGs

https://www.cdc.gov/nchs/nhanes/index.html

What is NHANES?

https://www.cdc.gov/nchs/nhanes/index.html

dfdf

What is NHANES

• Nationally-representative sample, with over 23 years of mortality follow-up with biomarker data
• Fit a regression model to select variables of associated with phenotypic score (regress hazard of mortality on 42 clinical biomarkers)

dfdf

PhenoAge can predict mortality

dfdf

PhenoAge can also predict chronological age

PCAge

11

dfdf

PCAge

Higgins-Chen et al

dfdf

Intraclass correlation coefficient as a measure of reproducibility

Source

dfdf

CpG signal shows low reproducibility

Higgins-Chen et al

dfdf

Default clocks lack reproducibility

Higgins-Chen et al

dfdf

PCage uses PCA before running elastic-net regression

Higgins-Chen et al

dfdf

Epigenetic clocks trained from principal components are highly reliable

Higgins-Chen et al

dfdf

1D Principal Component Analysis (PCA)

Source

Goal: Reduce the dimensionality of data by projecting the data into lower dimensional space such that the reconstruction error is minimized

dfdf

Minimizing reconstruction error = Maximizing variance

Original point

Projected

point

Reconstruction error

Variance

How can we determine the direction of maximal variance?

dfdf

What does covariance matrix tell you about the data?

Data aligned with axes and covariance is diagonal

Data oblique wrt axies and covariance is diagonal

Gaussian cloud

dfdf

Covariance matrix captures the general extent of data

Different distributions with same covariance matrix

dfdf

PCA rotates the axes to diagonalize the covariance matrix

Singular value decomposition

• Input: A matrix
• Output: a set of numbers called singular values and two collections of vectors: a set of right singular vectors and another set of left singular vectors.

Source

Geometry of Singular value decomposition

• A given matrix M transforms the unit vectors into an ellipse
• This can be imagined as
• 1. Performing rotation of the unit vectors by V
• 2. Scaling these vectors by scaling factors (singular values of the matrix M)
• 3. Performing another rotation by U

Source

Singular value decomposition

• The matrix M is rectangular.�
• There are three non-zero singular values.�
• The rank of M is 3�
• UU^T = I and VV^T = I where I is the unit vector

Source

​

What are singular values?

• A m x n matrix M can be thought of as mapping a vector x from Rⁿ to R^m.
• A unit sphere in Rⁿ is mapped to an ellipsoid in R^m:����
• The non-zero singular values of M are the lengths of the semi-axes of the ellipsoid.

Principal Component Analysis - The recipe

• Start with a data matrix M.
• Center M by subtracting the column means (each column is a feature)
• Perform SVD of M → M = UΣV^T
• U and V are orthonormal
• Σ is a diagonal matrix of singular values
• V is made of eigenvectors that diagonalize the covariance matrix M^TM.
• Truncate V_k to retain the first k columns
• M_k = U_kΣV_k^T is a good low rank (k) approximation of M.
• “Project” the original matrix M onto V_k: MV_k
• This projection has two properties:
• It maximises the variance of projected points
• It results in minimum reconstruction error if the original matrix is to be reconstructed

dfdf

PCA: the optimization

PC1

PC2

28

Questions?