Session 2: Longitudinal Trajectory Analysis

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Review: The Arivale Dataset

Price et al, Nat Biotechnol, 2018

Review: Frailty Index is a Fraction of Health Defects

• Self-Report FI (35 items)
• Disease (15 items)
• Activity (9 items)
• Satisfaction (6 items)
• Medication (3 items)
• Digestion (2 items)
• Lab FI (34 items)
• Blood test items (29 items)
• Blood pressure items (5 items)
• Combined FI (69 items)
• The combination of the above two

Session 2.1: DIABLO Analysis

• Session 1
• Trends in data (PCA)
• Multi-omic correlations
• Identified clusters
• Cluster eigenvalues
• Session 2.1
• Trends in the outcome
• Multi-omic model
• Cross-validation

DIABLO Overview

1. Data preparation
1. Outcome: self-reported frailty index
2. Baseline data only
3. Proteomics, metabolomics, and lab tests
2. sPLS-DA
• Proteomics
• Metabolomics
• Lab tests
3. Block sPLS-DA (all three ‘omics)
• Sparsity parameter optimization
• Model fitting

Frailty Index (FI): fraction of health deficits

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• Self-Report FI (35 items) – Baseline questionnaire (once)
• Disease (15 items)
• Activity (9 items)
• Satisfaction (6 items)
• Medication (3 items)
• Digestion (2 items)
• Lab FI (34 items) – Longitudinal, every 6 months
• Blood test items (29 items)
• Blood pressure items (5 items)
• Combined FI (69 items) Session 1 (baseline labs)
• The combination of the above two
• Comparison (Spearman’s rank correlation of quintiles)
• Self x Lab 0.367
• Self x Combined 0.730
• Lab x Combined 0.843

Frailty Index (FI): fraction of health deficits

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• Self-Report FI (35 items) – Baseline questionnaire (once) Session 2.1
• Disease (15 items)
• Activity (9 items)
• Satisfaction (6 items)
• Medication (3 items)
• Digestion (2 items)
• Lab FI (34 items) – Longitudinal, every 6 months Session 2.2
• Blood test items (29 items)
• Blood pressure items (5 items)
• Combined FI (69 items) Session 1 (baseline labs)
• The combination of the above two
• Comparison (Spearman’s rank correlation of quintiles)
• Self x Lab 0.367
• Self x Combined 0.730
• Lab x Combined 0.843

To the Notebook!

PCA of Baseline ‘Omics Data

Proteomics (274) Metabolomics (703) Clinical Tests (47)

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Color and shape: Frailty Index Quintile (e.g. Q5 are the most frail 20%)

sPLS-DA of Baseline ‘Omics Data

To the Notebook!

sPLS-DA of Baseline ‘Omics Data

Proteomics (274) Metabolomics (703) Clinical Tests (47)

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Block sPLS-DA

To the Notebook!

Block sPLS-DA

Visualizing DIABLO model components

DIABLO Model: Component 1

Proteins Lab Tests Metabolites

FABP4 0.930 INSULIN 0.689 hydroxyasparagine 0.522

LEP 0.347 HOMA-IR 0.533 N-stearoyl-sphinganine 0.438

LPIR 0.385 cortolone glucuronide 0.366

N-stearoyl-sphingosine 0.311

5-methylthioadenosine 0.275

1-carboxyethylphenylalanine 0.253

DIABLO Model: Component 2

Proteins Lab Tests Metabolites

AGRP -0.763 BUN/CREAT 0.561 DHEA-S -0.557

NT-proBNP 0.413 POTASSIUM -0.318 androstenediol(3b,17b)S2 -0.452

NPPB 0.354 ALBUMIN -0.453 pregnenediol-S -0.292

GDF15 0.242 GFR, MDRD -0.246 pregnenetriol-S2 -0.284

PROTEIN -0.232 pregnenediol-S2 -0.259

CREATININE -0.228 androstenediol(3a,17a)S -0.253

VIT D, 25-OH 0.227

EPA 0.124

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Session 2.2: Longitudinal Data Analysis

Session 2.2: Longitudinal Data Analysis

• Measurements repeated over time are often correlated, not independent
• Appropriate analytical methods depend on…
• Number of repetitions (as few as 2, as many as thousands, millions)
• Data type (categorical, counts, money, continuous) and missingness
• Synchronous (e.g. stock prices, EEG) vs asynchronous (e.g. blood tests) data collection
• Handling of collection failures (e.g. recollection of one failed tube out of 5 in a blood draw)
• Systems biology (‘omics) data can be expected to have a variety of data collection issues!
• Potential goals
• Predict future values
• Identify unknown correlations among measured analytes (systems analysis)
• Determine differences between groups (e.g. treated vs untreated patients; same treatment of different patient subgroups)
• Identify causal relationships (causes precede effects in time).

Generalized Linear Mixed-Effects Models (GLMMs)

• Generalized Linear Model (GLM): g(Y) ~ A + B + … + 𝝐
• Response Y may be binary, categorical, or continuous
• Link function g(x) maps Y to a continuous value
• Must be invertible: Y ~ g^-1(g(Y))
• g(x) = x (Identity), = 1/x (inverse), = log(x), = x / (1+x) (logit), = Pr{ N(0,1) < x } (Probit)
• Fixed effects ( A + B + … )
• Explicit parameters
• Error 𝝐 distribution may be any distribution in the Exponential family
• Gaussian, Poisson, Binomial, Negative Binomial, Bernoulli, Exponential, Gamma
• GLMM: g(Y) ~ A + B + … + (C + D + … | Grouping) + 𝝐
• Random effects ( C + D + … | Grouping )
• Identical within but independent across groups
• Implicit parameters (no point estimates; average over a distribution)

Additional information: https://stats.oarc.ucla.edu/wp-content/uploads/2022/03/generalized_linear_new.html#(1)

Frailty Index increases with age

FI ~ t₁ + t₂ + t₃ + Age + PC₁ + PC₂ + PC₃ + PC₄ + (1 + t₁ | client)

— spline — — AIC —

674 F

425 M

Frailty Index can be lowered by lifestyle changes

t₁

t₂

t₃

674 F

425 M

FI ~ t₁ + t₂ + t₃ + Age + PC₁ + PC₂ + PC₃ + PC₄ + (1 + t₁ | client)

— spline — — AIC —

Polygenic Risk Score for Longevity (dl90_cs_PRS)

Frailty, Age, and Longevity

Frailty and Longevity PRS

Frailty by Sex and Age

BREAK