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

## Question
Re-express five printed treatment effects (`data/effects.json`) on the target definition stated for each item, using only quantities printed in the cited source extract and an explicit transformation; where this is impossible, state so and name the missing quantity.

## Data and exclusions
Inputs: `data/effects.json` (5 items) and four arXiv extracts (line counts in `n_input_rows`; SHA-256 verified against `data/README.md`). All five items were assessed (`n_analysed` = 5); no exclusions (`out/exclusions.csv`). Source anomalies are listed in `data_issues` (e.g. two different SEs for the same DCR ATT, 608 vs 640 control regions, the abstract's "fatal fall by 35%" vs Table 7, the minimum-wage note's "about 4%" vs the printed 0.047, the Benin headline 0.0855 coming from a table absent from the extract). None changes a harmonised value except where stated below.

## Method
Conventions from TASK.md, applied to printed numbers only (`harmonised.*.transformation`, `harmonised.*.locator`):
- E1 (log points → % of counterfactual): 100·(exp(b)−1), b = −0.431 (DCR Table 6, ATT, 5 km).
- E2 (pp → % of control mean): 100·Δ/p, Δ = 1.47 pp (Table 2 ATE), p = 75.0% (Table 2 Control).
- E3 (elasticity → % change for the observed MW rise): 100·η·g, η = −0.388, g = 0.047 (Table 2 rows "Employment elasticity w.r.t MW" and "% MW changes").
- E4 (log points → absolute change per 100,000): requires Y0·(exp(b)−1) with a baseline level Y0, which the extract does not print.
- E5 (0–1 probability → pp): 100·β, β = −0.0962 (Table 3, Treatment, col (4)).
`out/analysis.py` locates each input line by pattern, prints it, and writes `out/results.json`; no randomness (`random_seed` = null).

## Results
| id | harmonised value | unit | key |
|---|---|---|---|
| E1 | −35.01 | % of counterfactual hospitalisation rate | `harmonised.E1.value` |
| E2 | 1.96 | % of control-group mean reemployment | `harmonised.E2.value` |
| E3 | −1.824 | % change in employment | `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` |

`n_harmonised` = 4, `n_not_harmonisable` = 1, `feasibility` = "complete": every item has either a value or a justified statement of impossibility. E1 agrees with the paper's printed "% change" of −35.0% (`baseline_printed_conversions.E1_table6_pct_change_row_5km`). For E4, the relative change 100·(exp(−0.354)−1) ≈ −29.81% can be computed (noted in `harmonised.E4.transformation`), but the target is an absolute rate change, which needs the baseline level of the fatal drug-related hospitalisation rate per 100,000 in the 5 km treated regions (`harmonised.E4.missing_quantity`).

## Uncertainty
No standard errors or confidence intervals were propagated (none are required). Exactness of the conversions:
- E5 is exact: only the scale changes.
- E1 is exact under the log-point convention for the effect on the log rate. Interpreting it as the percent change in the rate *level* relies on the usual exp(b)−1 approximation, which ignores Jensen-type retransformation terms.
- E2 is approximate. The ATE adjusts for randomisation week, but the denominator is the raw aggregate control mean (75.0%), which only stands in for the counterfactual level. Rounding of the printed numbers also matters (1.47 pp, 75.0%).
- E3 is approximate. A constant elasticity is applied linearly to a discrete 4.7% change. g is printed to 3 decimals, and the table note's "about 4%" would give about −1.55% instead (see `data_issues`).

## Limitations and open issues
- E4 cannot be harmonised from the extract. The missing quantity is the baseline/counterfactual fatal drug-related hospitalisation rate per 100,000 in the 5 km treated regions. No value was guessed.
- The DCR abstract's "fatal … fall by 35%" does not match Table 7 (−0.354 → −29.8%); we used Table 7. The two SEs printed for the same E1 estimate (0.210 vs 0.218) do not affect point estimates.
- E3 follows the target definition and uses the printed table value 0.047. The table note describes the increase as "about 4%".
- For the Benin study, the abstract's 0.0855 / 18.79% refers to a different table (Table 2, not in the extract) and was not used.