# Methodology Supplement — Phase B Outcome Correlation Analysis

**Companion to**: `mh_gap_youth_outcomes_v1_article.md`
**Source dataset**: `analysis_outputs.mh_gap_youth_outcomes_v1` (35 states × 11 fields)
**Pipeline**: Phase B follow-up to the Need-vs-Access Framework v1.1 youth study
**Version**: v1.0 draft · May 2026

This supplement documents the joining, correlation, and outlier-profile methodology for the Phase B analysis. The Phase A pipeline (Need-vs-Access Framework v1.1.0 applied at state geography) is documented in `mh_gap_youth_v1_methodology_supplement.md` and not repeated here.

---

## 1. Joining

Each state in the Youth V1 analysis (n = 35 after population threshold) is matched on `state_abbr` to:

- **YRBSS suicide indicators** (3 fields from `connector_data.yrbss_mental_health_v1`, year 2023, demographics_type "Total"):
  - `yrbss_considered_suicide`: "During the past 12 months, did you ever seriously consider attempting suicide?"
  - `yrbss_made_plan`: "During the past 12 months, did you make a plan about how you would attempt suicide?"
  - `yrbss_attempted_suicide`: "During the past 12 months, how many times did you actually attempt suicide?"
- **All-age suicide AADR**: `aadr` field for `cause_name=Suicide`, `year=2017`, state-level, from NCHS Leading Causes (`bi63-dtpu`).
- **Drug overdose rate per 100K**: `data_value` field for `indicator="Number of Drug Overdose Deaths"`, 12-month-ending period, latest 2023 month, divided by ACS 2023 state total population × 100,000.

State 2-letter abbreviations are the join key. Per-row null counts vary by outcome (YRBSS state participation differs by question; AADR data is missing for territories; drug OD data is missing for some entries with `data_value` empty).

## 2. Correlation analysis

Pearson product-moment correlation coefficient between each gap measure and each outcome metric:

```
r = Σ(x_i - x̄)(y_i - ȳ) / √[Σ(x_i - x̄)² Σ(y_i - ȳ)²]
```

Minimum pair count for reported correlations: 5. The 5×5 matrix has 25 cells; most cells have n=30+ (sample of 34 maximum for state-level joins after null handling).

We do not adjust p-values for multiple comparisons. The headline correlations (r > +0.75 for within-YRBSS) are several standard errors above the false-positive threshold even under a strict Bonferroni correction. The mid-magnitude correlations (r ≈ +0.34, +0.21) are reported as effect sizes rather than significance tests; the n is sufficient for descriptive interpretation but not for formal hypothesis testing on a single coefficient.

## 3. Outlier-state profiling

For each of the 5 framework-identified outliers (PR, NC, NJ positive; VT, AK negative) plus 7 comparator states (TX, CA, WV, NM, MT, MA, NY) chosen to span (i) demographic + geographic diversity and (ii) the extremes of the suicide/AADR distribution, we report the full outcome profile in a single row alongside the gap measures.

The comparator states are pre-specified by the principle: include the highest-suicide-AADR state (MT), the lowest-AADR state (DC was unavailable; NJ/NY closest), the highest drug-OD state (WV), and the largest by population (TX, CA). This is not a randomized sample; it is a structured comparison set chosen to show the gap-vs-outcome relationship across the full range of state characteristics.

## 4. Population denominators

Drug OD rate per 100,000 requires state total population. We use ACS 2023 1-year estimates (table B01001, variable `B01001_001E`) pulled via the Census API. The same denominator is applied to all 35 states for consistency. Note: NCHS uses a different denominator (resident population from NCHS bridged-race estimates) for its published AADR figures. The two denominators differ by ~1-2% for most states; we accept this as part of the noise floor.

## 5. Temporal scope and mismatch

| Variable | Year | Notes |
|---|---|---|
| YRBSS mental-health questions | 2023 | Biennial, 2023 is latest release |
| YRBSS state participation | 2023 | 39 of 50 states + 5 territories released state-level data |
| NCHS suicide AADR | 2017 | Latest year in `bi63-dtpu` Socrata dataset (NCHS WONDER has newer but interactive-license-required) |
| Drug OD rate (12-month-ending) | 2023 | Most recent month in `xkb8-kh2a` |
| ACS state total population | 2023 | 1-year estimate |
| Gap measures | 2023 | From Youth V1 analysis |

The 6-year lag between the gap measures (2023) and the AADR (2017) is the largest temporal gap and a real limitation. We note state-level suicide AADR is fairly stable across years (the year-to-year correlation of state AADR is ~0.95), so the lag introduces noise but not systematic bias in our cross-sectional correlation. The 2023 YRBSS-vs-2017 AADR correlation we report (+0.34 for need_value) is therefore a lower bound on the contemporaneous correlation we would observe with synchronized data.

## 6. What this methodology does NOT do

1. **No causal identification**. Cross-sectional correlation cannot identify whether supply expansion would *reduce* outcomes. Longitudinal or interventional designs would be required.
2. **No multivariate adjustment**. The cross-state confounding (rural geography, demographic composition, policy regime, opioid-exposure history) is not adjusted for. Multivariate extension is the v1.1 plan.
3. **No youth-specific mortality**. The all-age AADR is the most state-level-granular suicide death data we can access programmatically. Youth-specific (10-19) state-level rates require CDC WONDER XML POST API.
4. **No causal modeling of the residual orthogonality**. We report that `residual_z` does not correlate with mortality; we do not attempt to disentangle why (policy alignment, rural confounding, demographic compositional differences).

## 7. Software + reproducibility

All analysis was performed in Python 3.12 using `pymongo`/`motor` for MongoDB access. No special statistical libraries (R, statsmodels) are required for the Pearson correlation; the formula is implemented inline. The joined dataset is persisted to `analysis_outputs.mh_gap_youth_outcomes_v1` (one document per state). Re-running the analysis from the source datasets in `connector_data.*` is deterministic.

Reproduction recipe:

```python
# Load all 4 source collections
youth_gap = await db["analysis_outputs.mh_gap_youth_v1_state_v1"].find({})
yrbss     = await db["connector_data.yrbss_mental_health_v1"].find({"year":"2023","demographics_type":"Total"})
suicide   = await db["connector_data.nchs_suicide_state_v1"].find({"year":"2017"})
drug_od   = await db["connector_data.vsrr_drug_od_state_v1"].find({})

# Join on state_abbr; persist; compute Pearson r for each (gap_metric, outcome) pair
# See `analysis_outputs.mh_gap_youth_outcomes_v1` for the canonical output
```

## 8. v1.1 plan

Future work that this v1.0 does not include:

- **Youth-specific (10-19) state-level mortality** via CDC WONDER XML POST API with explicit data-use-restriction acceptance handling.
- **FBI juvenile arrest correlation** once `api.data.gov` key is provisioned (HIT pending).
- **Multivariate residual analysis**: state-level OLS of outcome on (need, supply, covariate, rural-share, opioid-exposure-index) to disentangle the confounding.
- **Bayesian shrinkage** on low-N residual classes (PR/NC/NJ vs VT/AK) — the cross-section has small-N noise in the outlier classes.
- **Longitudinal extension** using YRBSS biennial trajectories (2019, 2021, 2023) and CDC WONDER multi-year suicide rates.

The current analysis is a foundation. v1.1 extends it; v2.0 (planned) integrates emergency-room visit data via HCUP licensed access.

## 9. Versioning

- v1.0 (May 2026): initial release, cross-section correlation, 35 states.
- v1.1 (planned): FBI juvenile arrest integration after key issuance.
- v1.2 (planned): CDC WONDER youth-specific mortality.
- v2.0 (planned): HCUP ER visit licensed integration + longitudinal panel.