Design on What Was Actually Done

Visual summary — data architecture & key evidence

Full statistical analysis plan (SAP) — longitudinal mediation with sequencing

1. Primary goal: estimate whether longitudinal changes in sequencing-derived mediators (taxon abundance, alpha diversity, community composition summaries) mediate the effect of time-varying exposures (clinical state / treatment / environmental exposure) on longitudinal clinical outcomes (e.g., FEV1%, PHQ score) while controlling for time-invariant and time-varying confounders.
2. Data inputs & preprocessing
   • Sequencing: denoised feature table (ASVs/OTUs) aggregated to genus or species as pre-specified; rare taxa filtering (present in >5% samples) to reduce multiplicity.
   • Normalize counts: use compositional-aware transforms (centered-log ratio) or variance-stabilizing transform depending on downstream model assumptions; retain raw read depth as covariate where relevant.
   • Diversity: compute Observed richness, Shannon, Simpson (phyloseq/scikit-bio). Prior example: observed richness mediated treatment/recovery in CF mSystems alpha diversity mediation
3. Modeling framework
   • Two-equation longitudinal mediation (SEM-style):
     Mediator model: M_it = f1(T_it, C_i, W_it, u_i) — mixed-effects model for mediator (taxon or diversity), with random intercepts (and slopes if warranted).
     Outcome model: Y_it = f2(T_it, M_it, C_i, W_it, v_i) — mixed-effects model for outcome with random effects. Indirect effect for mediator t estimated as δ_T × β_M (coefficient of T on M times coefficient of M on Y conditional on T), per mSystems approach mSystems mediation estimator.
   • High-dimensional mediators: apply penalized estimators (debiased lasso, MCP/elastic-net) to select candidate mediators, then refit low-bias mixed models for selected mediators for effect estimation and inference (de-biasing ensures valid CIs / p-values).
   • Bootstrap inference: nonparametric block bootstrap with subject-level resampling (3,000 resamples when feasible) computing BCa CIs for indirect effects (as in mSystems).
4. Confounding, covariates and identification assumptions
   • Pre-specify confounder sets for: exposure→mediator, mediator→outcome, and exposure→outcome paths. Include baseline demographics, site, antibiotic/medication exposure (time-varying), clinical covariates (baseline severity), and sequencing batch/read depth.
   • Assumptions to report explicitly: no unmeasured mediator–outcome confounding after adjustment; correct model specification; positivity (sufficient overlap across exposure/mediator strata); stable unit treatment value assumption (SUTVA) in observational longitudinal data. Discuss plausibility and sensitivity analyses (see below).
5. Multiplicity control & selection
   • Two-stage approach: (A) screening with false discovery rate (Benjamini–Hochberg) or penalized selection (elastic-net) to reduce mediator set; (B) targeted mediation estimation with bootstrap CIs; report both unadjusted and FDR-adjusted p-values.
6. Sensitivity analyses
   • Vary mediator aggregation (ASV / genus / pathway-level), inclusion/exclusion thresholds (present in >1%, 5%, 10%), and transformation (CLR vs log + offset).
   • Assess robustness to unmeasured confounding via bias formulas / E-values for indirect effects; perform negative-control mediator and outcome analyses where possible.
   • Time-lagged mediation: test lead-lag models where M_{t-1} mediates T_{t}→Y_{t+1} to better approximate causal temporality (as recommended in longitudinal causal frameworks) Causal guidance editorial.
7. Pre-specified primary & secondary outcomes
   • Primary: indirect effect of exposure (e.g., clinical state change) on outcome (e.g., FEV1% or PHQ) mediated by: (a) observed richness; (b) top selected taxa (pre-specified candidate taxa if known), tested separately with multiplicity control.
   • Secondary: mediation by beta-diversity axes (PCoA axes), community state types (enterotype-like clusters), and pathway-level features (metagenomic functional summaries if available).
8. Power and sample-size considerations
   • Because mediation indirect effects are products, power is lower than for direct effects. Use simulation-based power with your cohort's sampling schedule using realistic mediator–outcome covariance (informed by pilot data or literature e.g., mSystems sample/variance structure) to estimate detectable indirect effects. If sample sizes are small, emphasize estimation and CIs over hypothesis testing.
9. Software, reproducibility & workflow
   • Statistical libraries: R (lme4/nlme, mediation/medflex, glmnet, debiased lasso packages), or Python (statsmodels, pymer4, scikit-learn elastic-net), phyloseq / scikit-bio for microbiome processing. Use Snakemake or nf-core wrappers for pipeline reproducibility; containerize with Docker/Conda for exact environment.
   • Code and data-management: store all code in a versioned repository, use data dictionaries, and provide a reproducible vignette demonstrating the pipeline on the cohort (scripting for pre-processing → selection → estimation → bootstrap inference → sensitivity checks).
10. Reporting checklist
    • Report cohort flow, missingness patterns, per-subject sample counts (plot included above), mediator selection thresholds, full model specifications (fixed/random effects), bootstrap iterations, and multiple-testing corrections.
    • Explicitly discuss limitations: residual confounding (e.g., antibiotics), uneven sampling, sequencing platform depth, taxonomic resolution limits, and observational design (no definitive causality) as in prior work mSystems limitations.
11. Decision rules & interpretation
    • Prespecify thresholds for declaring a mediator as noteworthy (e.g., BCa 95% CI for indirect effect excluding zero and FDR-adjusted q < 0.10). Emphasize effect sizes and plausible biological magnitude over binary p-values.

Implementation checklist (concrete steps & code modules)

1. Data import & QC (reads, metadata, exposures/outcomes, timepoints). Output: cleaned anndata/phyloseq object.
2. Preprocess & transform microbial features (ASV→genus, CLR transform, rare taxa filter). Save transformed matrices.
3. Compute alpha/beta diversity; PCoA on Bray-Curtis; compute per-sample covariates (antibiotics windows, read depth).
4. Mediator screening: elastic-net logistic/linear models with cross-validation (subject-level CV) to rank mediators.
   Output: candidate mediator list (top K or those passing FDR threshold).
5. Mediation estimation: fit mixed-effects mediator & outcome models (random intercept per subject ± slope); compute indirect effects as product δ×β; obtain bootstrap BCa CIs with subject-level resampling (3,000 iterations where compute resources permit).
6. Sensitivity & robustness: time-lag models, negative control mediators/outcomes, E-value computations, alternative transforms/aggregations.
7. Report generation: forest plots of indirect effects, sample-count bar charts (above), PCoA ordination with state coloring, and table of mediator effect estimates with CIs and adjusted q-values.

Key references informing choices

• mSystems longitudinal mediation
• Causal inference editorial
• Bariatric longitudinal mediation example

Limitations & known blindspots (be explicit)

• Observational mediation can suggest but not prove causality; residual confounding (especially time-varying antibiotic use or treatment allocation) is a major threat — include sensitivity analyses and negative controls mSystems limitations.
• Taxonomic resolution (16S genus-level) may mask species-level mediator signals; metagenomics or targeted qPCR may be needed to validate candidate taxon mediators.
• Uneven sampling across timepoints reduces power for individual-specific trajectories; apply mixed models with appropriate random effects and consider subcohort analyses where repeated measures are dense.

What would falsify a mediation claim?

Replication in an independent longitudinal cohort with the same temporal ordering and control set failing to reproduce the indirect effect (point estimate near zero and CI covering zero), or showing that manipulating the mediator (randomized perturbation) does not change downstream outcome, would falsify the mediation hypothesis. This mirrors standard causal-testing recommendations in longitudinal mediation literature Causal testing guidance.