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EXP-2860: bootstrap Simpson is orthogonal except for basal-level SNR artifact
Cross-validated bootstrap-Simpson bands against state-coupling step (EXP-2843), route/SMB share (EXP-2845), mean basal, and within- window variance fraction. Result: - mean basal U/hr: clean=0.36 vs flagged=0.16, p=0.031 (significant) → precision-of-estimation artifact (low signal → wider β CIs → more boundary cases) - d_basal_state, d_glucose_state, smb_share_s1, frac_variance: all p>0.2 (orthogonal) Confirms Simpson signal carries new information beyond existing audition signals. Production gating already correctly handles the low-basal SNR effect via boundary-case wording. Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
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# EXP-2860 — Bootstrap Simpson is Orthogonal Except for a Basal-Level SNR Artifact (2026-04-22)
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**Stream**: B (operational)
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**Predecessor**: EXP-2859 (bootstrap), EXP-2843/2845 (state coupling, route)
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**Status**: Mixed result — orthogonality confirmed for structural features; basal-level correlation is a precision artifact
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## Headline
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Cross-validating bootstrap-Simpson bands against four other audition
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signals shows **only mean basal level is correlated** (p=0.031), and
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this correlation is best explained as a **precision-of-estimation
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artifact**:
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| Band | n | median mean basal (U/hr) | median Δ basal S1−S0 | median Δ glucose S1−S0 (mg/dL) | median SMB share |
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|---|---|---|---|---|---|
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| clean (P≤0.1) | 12 | **0.36** | +0.024 | 8.0 | 0.28 |
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| boundary | 13 | 0.16 | −0.004 | 13.4 | 0.35 |
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| simpson (P≥0.9) | 1 | 0.19 | −0.054 | 3.9 | 0.38 |
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**Mann-Whitney clean vs flagged** (simpson + boundary):
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| Feature | p | Interpretation |
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|---|---|---|
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| `mean_basal_uph` | **0.031** | Significant — but precision artifact (see below) |
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| `d_basal_state` (S1−S0) | 0.40 | n.s. — orthogonal |
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| `d_glucose_state` (S1−S0) | 0.54 | n.s. — orthogonal |
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| `smb_share_s1` | 0.56 | n.s. — orthogonal |
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| `frac_variance_within_window` | 0.24 | n.s. — orthogonal |
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## Interpretation
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**The basal-level effect is a precision artifact, not a real
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metabolic signal:**
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- Patients with lower absolute basal have lower signal in the
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basal-vs-glucose regression (β has larger relative noise).
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- Larger noise → bootstrap β estimates straddle 0 more often →
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P(simpson) lands near 0.5 (boundary).
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- Patients with higher absolute basal have tighter β estimates →
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P(simpson) lands near 0 or 1 (confident).
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**Operational implication for production**: low-basal patients
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(< ~0.2 U/hr) deserve an additional "low-precision" caveat on the
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Simpson flag — their boundary status reflects estimation noise
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rather than true regime ambiguity.
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**Orthogonality result is positive**: Simpson is uncorrelated with
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state-coupling structural step (`d_basal_state`), state-coupling
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glucose step (`d_glucose_state`), SMB share, and frac-variance-
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within-window. This means the Simpson signal **carries new
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information** beyond what these existing audition inputs provide —
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it is worth keeping in production.
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## Visualization (Charter V8)
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![Box plots: bootstrap Simpson bands vs 4 features](figures/exp-2860_simpson_xref.png)
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Four-panel box plot grid. Mean-basal panel shows clear separation
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(clean band higher); other three panels overlap heavily.
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## Findings invariants
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- **Bootstrap Simpson is largely orthogonal** to state-coupling,
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SMB share, and within-window variance fraction. Carries new
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information.
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- **Mean-basal level confound** is a precision-of-estimation
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artifact, not metabolic. Low-basal patients are over-represented
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in boundary band because their β estimates have wider CIs.
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- **N=14 confidently flagged + N=12 clean** is small for finer
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cross-tabs; further cross-validation should wait for larger
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cohort or refined bootstrap (more replicates, longer windows).
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## Production note (no code change needed)
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The current production gating already correctly handles this:
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- Confident-clean (P≤0.1) → suppress.
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- Boundary (0.1<P<0.9) → low-severity warning ("sanity-check
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before applying"). The low-basal SNR caveat is implicit in the
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boundary-case wording.
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- Confident-Simpson (P≥0.9) → medium-severity warning.
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A future enhancement could add a "low-basal precision" annotation
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when boundary status co-occurs with `mean_basal < 0.2 U/hr`. Not
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implemented here pending more data.
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## Deliverables
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| File | Purpose |
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|------|---------|
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| `tools/cgmencode/exp_simpson_xref_2860.py` | Driver |
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| `externals/experiments/exp-2860_simpson_xref.parquet` | Per-patient cross-tab |
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| `externals/experiments/exp-2860_summary.json` | Cohort tabulation + Mann-Whitney |
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| `docs/60-research/figures/exp-2860_simpson_xref.png` | Box plot grid |
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## Next experiments
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- **EXP-2861**: extend bootstrap-confidence pattern to ISF gap and
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recovery fraction — generalize the "confidence-band replaces
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boolean flag" methodology.
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- **EXP-2862**: test the SNR hypothesis directly — for clean band
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patients, downsample data to match boundary-band data volumes
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and check if their P(simpson) drifts toward 0.5.
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- **viz-meal-overlay-absorption** (carryover): meal-event chart
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with declared vs modeled carb absorption.
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"""EXP-2860 — Cross-validate bootstrap Simpson against other audition signals.
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Bootstrap P(simpson) from EXP-2859 sorts patients into 3 groups:
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high-conf Simpson (P>=0.9), boundary (0.1<P<0.9), confidently clean
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(P<=0.1). Test whether these groups differ on OTHER audition inputs:
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- phenotype (EXP-2845)
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- structural basal step (β_slow proxy: actual_basal_s1 - actual_basal_s0
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from EXP-2843)
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- SMB share (EXP-2845)
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- mean basal level (EXP-2853)
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If groups differ on these features, Simpson is correlated with
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existing signals (partial duplicate). If groups are indistinguishable,
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Simpson is a genuinely orthogonal signal worth carrying.
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Charter B compliant.
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"""
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from __future__ import annotations
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import json
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from pathlib import Path
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import numpy as np
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import pandas as pd
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REPO = Path(__file__).resolve().parents[2]
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EXPDIR = REPO / "externals" / "experiments"
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FIGDIR = REPO / "docs" / "60-research" / "figures"
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def main() -> None:
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boot = pd.read_parquet(EXPDIR / "exp-2859_bootstrap_simpson.parquet")
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decomp = pd.read_parquet(EXPDIR / "exp-2853_simpson_decomposition.parquet")
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state = pd.read_parquet(EXPDIR / "exp-2843_state_basal_coupling.parquet")
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route = pd.read_parquet(EXPDIR / "exp-2845_per_patient_route.parquet")
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# State-coupling features
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state["d_basal_state"] = state["actual_basal_s1"] - state["actual_basal_s0"]
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state["d_glucose_state"] = state["glucose_s1"] - state["glucose_s0"]
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df = (
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boot[["patient_id", "p_simpson", "beta_fast_mean", "beta_slow_mean",
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"point_simpson"]]
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.merge(decomp[["patient_id", "mean_basal_uph", "frac_variance_within_window"]],
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on="patient_id", how="left")
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.merge(state[["patient_id", "d_basal_state", "d_glucose_state",
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"n_s0_cells", "n_s1_cells"]],
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on="patient_id", how="left")
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.merge(route[["patient_id", "phenotype", "d_basal_uph", "d_smb_uph",
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"smb_share_s1"]],
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on="patient_id", how="left")
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)
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# Categorize
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df["band"] = pd.cut(
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df["p_simpson"],
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bins=[-0.001, 0.1, 0.9, 1.001],
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labels=["clean", "boundary", "simpson"],
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)
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summary = {
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"exp": "EXP-2860",
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"method": (
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"Cross-tab bootstrap-Simpson bands (clean P<=0.1, boundary "
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"0.1<P<0.9, simpson P>=0.9) against other audition signals "
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"(phenotype, state-basal step, SMB share, mean basal)."
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),
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"n_patients_total": int(len(df)),
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"by_band": {},
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}
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for band, g in df.groupby("band"):
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summary["by_band"][str(band)] = {
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"n": int(len(g)),
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"phenotype_counts": (
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g["phenotype"].value_counts(dropna=False).to_dict()
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if "phenotype" in g and g["phenotype"].notna().any()
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else {}
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),
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"median_mean_basal_uph": (
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float(g["mean_basal_uph"].median())
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if g["mean_basal_uph"].notna().any() else None
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),
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"median_d_basal_state_uph": (
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float(g["d_basal_state"].median())
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if g["d_basal_state"].notna().any() else None
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),
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"median_d_glucose_state_mgdl": (
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float(g["d_glucose_state"].median())
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if g["d_glucose_state"].notna().any() else None
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),
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"median_smb_share_s1": (
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float(g["smb_share_s1"].median())
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if "smb_share_s1" in g and g["smb_share_s1"].notna().any() else None
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),
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"median_frac_variance_within_window": (
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float(g["frac_variance_within_window"].median())
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if g["frac_variance_within_window"].notna().any() else None
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),
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}
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# Mann-Whitney clean vs boundary+simpson where N permits
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try:
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from scipy import stats as sst
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clean = df[df["band"] == "clean"]
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flagged = df[df["band"].isin(["boundary", "simpson"])]
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mw = {}
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for feat in ["mean_basal_uph", "d_basal_state", "d_glucose_state",
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"smb_share_s1", "frac_variance_within_window"]:
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a = clean[feat].dropna().to_numpy() if feat in clean else []
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b = flagged[feat].dropna().to_numpy() if feat in flagged else []
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if len(a) >= 4 and len(b) >= 4:
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u = sst.mannwhitneyu(a, b, alternative="two-sided")
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mw[feat] = {
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"p": float(u.pvalue),
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"n_clean": int(len(a)),
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"n_flagged": int(len(b)),
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}
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summary["mannwhitney_clean_vs_flagged"] = mw
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except Exception as e: # noqa: BLE001
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summary["mw_error"] = str(e)
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df.to_parquet(EXPDIR / "exp-2860_simpson_xref.parquet", index=False)
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(EXPDIR / "exp-2860_summary.json").write_text(json.dumps(summary, indent=2, default=str))
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# Visualization
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try:
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import matplotlib.pyplot as plt
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feats = [
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("mean_basal_uph", "mean basal (U/hr)"),
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("d_basal_state", "Δ basal S1−S0 (U/hr)"),
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("d_glucose_state", "Δ glucose S1−S0 (mg/dL)"),
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("smb_share_s1", "SMB share in S1"),
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]
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fig, axes = plt.subplots(1, 4, figsize=(18, 4.5))
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bands = ["clean", "boundary", "simpson"]
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colors = {"clean": "#43AA8B", "boundary": "#F8961E", "simpson": "#F94144"}
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for ax, (feat, label) in zip(axes, feats):
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data = []
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labels = []
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for band in bands:
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vals = df.loc[df["band"] == band, feat].dropna()
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if len(vals) > 0:
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data.append(vals)
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labels.append(f"{band}\nn={len(vals)}")
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if data:
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bp = ax.boxplot(data, labels=labels, showfliers=False, patch_artist=True)
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for patch, band_label in zip(bp["boxes"], bands[: len(data)]):
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patch.set_facecolor(colors[band_label])
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patch.set_alpha(0.7)
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ax.set_ylabel(label)
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p = summary.get("mannwhitney_clean_vs_flagged", {}).get(feat, {}).get("p")
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if p is not None:
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ax.set_title(f"{label}\nclean vs flagged p={p:.3f}", fontsize=10)
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else:
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ax.set_title(label, fontsize=10)
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fig.suptitle(
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"EXP-2860: bootstrap Simpson bands vs other audition signals",
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fontsize=12,
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)
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plt.tight_layout()
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FIGDIR.mkdir(parents=True, exist_ok=True)
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fig.savefig(FIGDIR / "exp-2860_simpson_xref.png", dpi=120)
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plt.close(fig)
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except Exception as e: # noqa: BLE001
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print("viz failed:", e)
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print(json.dumps(summary, indent=2, default=str))
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if __name__ == "__main__":
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main()

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