# F4-conf-03 — Harmonising effect sizes reported under incompatible definitions

## Question
Five treatment effects from four arXiv extracts are printed under different definitions: log points, percentage points, an elasticity, and a linear-probability coefficient. For each one, I re-express the printed point estimate on the target definition given in `data/effects.json`. I use only quantities printed in the cited extract and an explicit transformation. Where the target cannot be reached, I say so and name the quantity that is missing.

## Data and exclusions
- Inputs (`n_input_rows`): `effects.json` (5 items), `README.md` (16 lines), and four source extracts: arxiv-2609.27732v1 (134 lines), arxiv-2606.14621v1 (58), arxiv-2505.04555v3 (66) and arxiv-2510.03658v1 (91). All SHA-256 hashes match `data/README.md` (see `out/state/data_audit.md`).
- No exclusions: all 5 items were assessed (`n_analysed` = 5; `out/exclusions.csv`: 5 → 5).
- Problems found in the inputs are listed in `data_issues` (7 entries). The ones that matter here are:
  - The Armendariz abstract says fatal hospitalisations "fall by 35%". Table 7 implies −29.8%, and Section 6.1 says "approximately 30%".
  - Kanayama et al.'s note to Table 2 says "about 4%", but the table row prints 0.047.
  - The Armendariz extract prints no level of the fatal hospitalisation rate.
  - Two smaller Armendariz discrepancies have no effect on the results: the standard errors and control-region counts in Table A19 differ from those in Table 6, and A19's % change row disagrees with exp(b) − 1 by 0.1 in the last digit.

## Method
I applied the conventions stated in TASK.md. Each item's formula and the printed inputs are recorded in `harmonised.<id>.transformation`, and line-level locators are in `harmonised.<id>.locator`. `out/analysis.py` parses the numbers directly from the table rows and prints every source line it uses.
- E1: 100·(exp(b) − 1), with b = −0.431 (Table 6, ATT, 5 km).
- E2: 100·Δ/p, with Δ = 1.47 pp (Table 2, Reemployment, Average treatment effect estimate) and p = 75.0% (Table 2, Control).
- E3: 100·η·g, with η = −0.388 (Table 2, Employment elasticity w.r.t MW) and g = 0.047 (Table 2, "% MW changes"; read as a proportion, consistent with the note's "about 4%").
- E4: the target would be Y0·(exp(b) − 1), with b = −0.354 (Table 7, Drug-related (fatal), 5 km). Y0 is the counterfactual fatal rate per 100,000 per year.
- E5: 100·β, with β = −0.0962 (Table 3, Treatment, column (4)).

As a baseline, the untransformed printed values in their original units are kept under `baseline_reported`.

## Results
| id | harmonised value | unit | key |
|---|---|---|---|
| E1 | −35.0141 | % change in the hospitalisation rate (matches the printed −35.0%) | `harmonised.E1.value` |
| E2 | 1.96 | % of the control-group reemployment mean | `harmonised.E2.value` |
| E3 | −1.8236 | % change in employment for the observed 4.7% MW increase | `harmonised.E3.value` |
| E4 | null (not harmonisable) | hospitalisations per 100,000 per year | `harmonised.E4.value`, `harmonised.E4.missing_quantity` |
| E5 | −9.62 | percentage points | `harmonised.E5.value` |

- Four items were harmonised (`n_harmonised` = 4) and one was not (`n_not_harmonisable` = 1).
- E4 cannot be expressed as an absolute change. The extract prints only log-point ATTs, standard errors and region counts; it gives no mean, baseline or counterfactual level of the fatal drug-related hospitalisation rate per 100,000. The missing quantity is that level for the 5 km treated regions (`harmonised.E4.missing_quantity`). The relative change that can be computed, −29.8133% (`baseline_reported.E4.computable_relative_change_percent`), is not the target definition.
- The task as a whole is `feasibility` = "complete": every item has either a value or a justified statement of impossibility.

## Uncertainty
- No standard errors or confidence intervals were propagated (none were required). The values are point estimates only.
- E5 is exact: it is a pure rescaling (×100).
- E1 is exact given the printed b. However, b is rounded to 3 decimals, so only about 3 significant digits are meaningful (≈ −35.0%). It is also the exp-transform of an average log effect, not necessarily the percent change in the mean rate.
- E2 is an exact ratio of printed numbers, but it is approximate as an estimand. The denominator is the raw aggregate control mean (75.0%, one decimal), while the ATE is adjusted for randomisation week. The printed numbers do not give an exact counterfactual level.
- E3 is a first-order (linear) approximation, η·g. It also depends on which MW change is used: with the note's "about 4%", the result would be about −1.55% instead of −1.82%. I used the table's 0.047, as the task instructs.

## Limitations and open issues
- E4 is blocked by a missing quantity (see Results). I did not substitute any external or remembered baseline rate. The time unit ("per year") is also not stated explicitly in the extract.
- The extracts contain internal inconsistencies (`data_issues`), most importantly the 35% vs ≈30% figure for the fatal outcome in the Armendariz abstract. I used the table values throughout.
- The harmonised effects come from different populations, estimators and estimands (ATT, ITT/ATE, elasticity, DiD-LPM). Putting them on a common scale does not make them directly comparable as causal quantities.