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Statistical Analysis Usage Guide

Overview

Statistical analysis decides which metabolites differ between conditions and whether a discriminant model is real. The two endemic failure modes it guards against are overfitting (in p >> n, supervised models separate pure noise -- a score plot proves nothing without permutation-validated Q2) and false-discovery inflation (thousands of correlated tests on small n yield long "significant" lists that do not replicate). It covers transformation/scaling as an explicit modeling choice, unsupervised structure (PCA/HCA for QC), validated PLS-DA/OPLS-DA, univariate testing with covariate adjustment, and dependence-aware multiple testing.

Prerequisites

# Python
pip install scipy statsmodels numpy pandas matplotlib scikit-learn

# R
BiocManager::install("ropls")
install.packages(c("mixOmics", "lme4", "qvalue"))

Conceptual prerequisites: decide the scaling (Pareto vs unit-variance is a hypothesis, not a default), know whether the normalization imposed closure (total-area/PQN), distinguish technical from biological zeros, and identify the experimental unit (the subject, not the injection) before any group test.

Quick Start

Tell your AI agent what you want to do: - "Run PCA with Pareto scaling and check whether my pooled QC samples cluster tightly" - "Fit an OPLS-DA model and permutation-test it -- I only trust it if pQ2 is small" - "Run Welch t-tests between case and control with explicit BH FDR and fold changes" - "Fit a linear mixed model per metabolite for my longitudinal design" - "Show me whether my top hits survive switching from Pareto to unit-variance scaling"

Example Prompts

Scaling and Unsupervised Structure

"Transform and Pareto-scale my feature table, run PCA, and color the scores by batch and injection order to check for drift." "Re-run the PCA with unit-variance scaling and tell me whether the top loadings change."

Validated Multivariate Models

"Build an OPLS-DA model between disease and control, run 1000 permutations, and report R2X, R2Y, Q2, and pQ2." "Put a PCA score plot next to my PLS-DA plot so I can see whether the separation is real or supervised-only." "Extract VIP scores but only after the model passes the permutation test, and cross-check them against my univariate hits."

Univariate Testing and FDR

"Run Welch t-tests in Python with Benjamini-Hochberg correction and report log2 fold changes." "Fit a per-metabolite linear model adjusting for age, sex, and BMI." "My features are heavily correlated -- use an effective-number-of-tests correction instead of Bonferroni."

Reproducibility

"Check whether my discriminant result survives changing the scaling and the imputation method." "I have a validation cohort -- estimate external performance, not just cross-validated discovery performance."

What the Agent Will Do

  1. Confirm the upstream state: normalization/closure, zero handling, and the experimental unit.
  2. Choose and report a transformation + scaling, and offer to run a second scaling as a robustness check.
  3. Run PCA for QC and structure (pooled-QC clustering, batch/outlier inspection) before any supervised model.
  4. Match the univariate test to the design (Welch/Mann-Whitney/ANOVA/paired/LMM), with covariate adjustment where needed.
  5. Apply BH FDR explicitly (defaults are not BH in R or statsmodels) and report fold change + CI; use a dependence-aware correction when features are strongly correlated.
  6. For any discriminant model, fit PLS-DA/OPLS-DA, raise permutations to >= 1000, and report pQ2 plus the validation checklist.
  7. Read VIP/S-plot only from a validated model and reconcile multivariate VIPs with univariate FDR.
  8. Generate a volcano plot and a results table; flag scaling-fragile or detection-rate-confounded hits.

Tips

References