# 3370 - Empirically calibrated summative synthesis

Documented rule `qa/calibrated_synthesis_20260929/3370_rule.json` (SHA-256 `129b568406ffd65edc95e5ab620a5f0caf2a6ed11143154fe47a56cd58e71fa5`, written 2026-09-29T21:25:41, before any calibration quantity was computed) and amendment 1 `qa/calibrated_synthesis_20260929/3370_amendment_1.json` (SHA-256 `81bae8f1e568875c0bbd01cfc6e0fcdc5d01c667cea8550150d1baa1ed52f69d`, written 2026-09-29T22:50:11) and amendment 2 `qa/calibrated_synthesis_20260929/3370_amendment_2.json` (SHA-256 `ccb779dc54c50838eff8138a2a9b0a64b6f69a610501458231302ff8c2bac2ec`, written 2026-09-30T03:30:30: a bug fix in the round-2 classifier, before any round-2 fit); what they change and what had been seen are in their files and below. Every output carries the rule hash; the script refuses to compute or report if the rule, the amendment or a frozen input changes, or if an NC input changes between the fits and the report. NC rounds read: 1, 2.

## The answer (documented)

**Conditional calibrated estimate: 0.871 (0.741-1.020)**: the common effect under the reported calibrated variant V1 (leave-one-NC-out coverage 0.93 >= 0.85, so V1 is the reported variant; log BF(common : heterogeneous) = 2.43 >= 0, so the rule takes the common effect), p20. P(RR > 1.05) = 0.010, P(> 1.10) = 0.002, P(> 1.25) = <0.001, P(> 1.50) = <0.001; excluded at 95%: RR 1.05, RR 1.10, RR 1.25, RR 1.50. Numerics: minimum relevant core ESS below 50 at p20 (flagged, as the rule prescribes); its two independent scrambles give 0.871 (0.740-1.022) and 0.871 (0.744-1.017); 97.5th-percentile difference 0.0048 on the log scale, within the amendment's 0.02 Monte Carlo threshold.

- **Against the documented primary** (assumed allowances, heterogeneous shared mean) 0.957 (0.599-1.517), log width 0.930: the calibrated V1 shared mean is 0.877 (0.696-1.102) (log width 0.459) and the calibrated common effect 0.871 (0.741-1.020) (log width 0.319); under the assumed allowances the common effect was 0.964 (0.637-1.455) (3350 A1, log width 0.826).
- **The assumption it rests on: autism's design bias in each context is exchangeable with the negative controls' biases in that context, contexts are exchangeable with each other, and an independent timing bias is measured by the placebo breakpoints.** A systematic error specific to autism series (for example diagnostic-practice or awareness trends that move autism identification but not injury, sensory or physical-disability counts) is not calibrated away.
- **What the controls measured.** 45 same-cell controls in 9 pooled contexts (Brazil maternal DTaP, Canada rotavirus (excl. Quebec), Colombia varicella, England rotavirus, Hong Kong PCV, Sweden PCV, Tanzania schedule, U.S. PCV, U.S. RotaShield): between-context bias SD sigma_b = 0.20 (0.03-0.47), within-context SD between outcomes omega = 0.02 (0.00-0.09), mean bias mu_b = +0.042 (-0.155 to +0.217; posterior SD 0.091). A context without its own controls (e.g. Japan MMR) therefore carries a predictive bias SD of 0.26 (the assumed floors were 0.35 / 0.70), and the shared component (mu_b) has SD 0.091 against the fixed 0.15 it replaces.
- **Why the calibrated interval is narrower than the primary's.** The primary's shared bias (SD 0.15) loads 1 on every context and cannot be learned from any data; it alone caps the common effect's upper limit near 1.33 (3350). Under calibration the shared component loads fully only on the 6 contexts without controls; a context with its own controls has its bias measured, and its loading on mu_b is Brazil maternal DTaP 0.44, Canada rotavirus (excl. Quebec) 0.55, Colombia varicella 0.21, England rotavirus 0.14, Hong Kong PCV 0.36, Sweden PCV 0.04, Tanzania schedule 0.44, U.S. PCV 0.33, U.S. RotaShield 0.80. The mean shifts matter too: the controls lean above 1 where autism leans above 1 (U.S. PCV) and below 1 where autism leans below 1 (Brazil), so calibration pulls the context estimates together.
- **Placebo-only calibration (V3) is not the defensible summary**: 0.972 (0.858-1.104) for the common effect (the 3350 decomposition). Placebo breakpoints measure only timing bias (tau 0.04-0.08); the controls show non-timing bias between contexts of sigma_b = 0.20, which V3 ignores.

## Results by variant

| Variant | Estimand | RR (95% CrI) | Log width | P>1.05 | P>1.10 | P>1.25 | P>1.50 | Excluded | Power | Min. ESS | Scramble 23091 | Scramble 23092 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Primary (assumed floors, shared 0.15) | shared mean | 0.957 (0.599-1.517) | 0.930 | 0.345 | 0.275 | 0.126 | 0.028 | none | 18 | 106 | | |
| 3350 A1 (assumed floors, shared 0.15) | common effect | 0.964 (0.637-1.455) | 0.826 | 0.343 | 0.265 | 0.108 | 0.018 | RR 1.50 | 18 | 181 | | |
| V1 Calibrated (NC + Placebo) | shared mean | 0.877 (0.696-1.102) | 0.459 | 0.055 | 0.026 | 0.004 | <0.001 | RR 1.25, RR 1.50 | 18 | 55.4 | 0.877 (0.693-1.107) | 0.877 (0.709-1.084) |
| V1 Calibrated (NC + Placebo) | common effect | **0.871 (0.741-1.020)** | 0.319 | 0.010 | 0.002 | <0.001 | <0.001 | RR 1.05, RR 1.10, RR 1.25, RR 1.50 | 20 | 16.4 (flag) | 0.871 (0.740-1.022) | 0.871 (0.744-1.017) |
| V2 Variance Only | shared mean | 0.934 (0.731-1.176) | 0.475 | 0.148 | 0.075 | 0.009 | <0.001 | RR 1.25, RR 1.50 | 18 | 71.6 | 0.934 (0.726-1.181) | 0.935 (0.748-1.160) |
| V2 Variance Only | common effect | 0.946 (0.806-1.111) | 0.322 | 0.102 | 0.033 | <0.001 | <0.001 | RR 1.25, RR 1.50 | 18 | 10.3 (flag) | 0.947 (0.805-1.114) | 0.945 (0.807-1.105) |
| V3 Placebo Only | shared mean | 0.945 (0.759-1.157) | 0.422 | 0.142 | 0.065 | 0.006 | <0.001 | RR 1.25, RR 1.50 | 18 | 61.5 | 0.946 (0.750-1.165) | 0.944 (0.779-1.136) |
| V3 Placebo Only | common effect | 0.972 (0.858-1.104) | 0.252 | 0.118 | 0.029 | <0.001 | <0.001 | RR 1.25, RR 1.50 | 20 | 43.0 (flag) | 0.973 (0.857-1.109) | 0.970 (0.859-1.095) |
| V4 NC Only | shared mean | 0.875 (0.699-1.095) | 0.449 | 0.049 | 0.023 | 0.003 | <0.001 | RR 1.10, RR 1.25, RR 1.50 | 18 | 42.9 (flag) | 0.875 (0.695-1.100) | 0.874 (0.711-1.076) |
| V4 NC Only | common effect | 0.868 (0.744-1.010) | 0.306 | 0.007 | 0.001 | <0.001 | <0.001 | RR 1.05, RR 1.10, RR 1.25, RR 1.50 | 18 | 1.0 (flag) | 0.868 (0.743-1.012) | 0.867 (0.746-1.005) |
| V5 With Secondary NCs | shared mean | 0.881 (0.697-1.115) | 0.470 | 0.063 | 0.031 | 0.005 | <0.001 | RR 1.25, RR 1.50 | 18 | 44.1 (flag) | 0.880 (0.693-1.119) | 0.886 (0.715-1.102) |
| V5 With Secondary NCs | common effect | 0.875 (0.748-1.022) | 0.312 | 0.011 | 0.002 | <0.001 | <0.001 | RR 1.05, RR 1.10, RR 1.25, RR 1.50 | 18 | 26.0 (flag) | 0.874 (0.746-1.023) | 0.876 (0.753-1.018) |
| S1 Context-Mean Only | shared mean | 0.877 (0.697-1.100) | 0.456 | 0.053 | 0.025 | 0.004 | <0.001 | RR 1.10, RR 1.25, RR 1.50 | 18 | 55.3 | 0.877 (0.693-1.105) | 0.876 (0.710-1.082) |
| S1 Context-Mean Only | common effect | 0.871 (0.742-1.019) | 0.317 | 0.010 | 0.002 | <0.001 | <0.001 | RR 1.05, RR 1.10, RR 1.25, RR 1.50 | 18 | 3.6 (flag) | 0.872 (0.741-1.021) | 0.870 (0.745-1.013) |

Variants (documented; only the bias terms differ from the primary): V1 = NC predictive bias (beta_c + u_c: mean shift and variance) + placebo timing tau_c, shared component = posterior uncertainty of mu_b; V2 = V1 with every mean shift removed; V3 = placebo timing only, no shared term (the 3350 decomposition); V4 = V1 without timing; V5 = V1 with the secondary NCs in the error model; S1 = V1 with the context MEAN bias only (u_c omitted: the literal "posterior predictive of beta_c"; not defensible under exchangeability, never the answer). The country-group terms (UK 0.20, Canada 0.20, care bridge 0.25) are kept in every variant. Nodes: common effect (10, 6, 7) = 420 nodes, hierarchy (5, 3, 5) = 75 nodes (sigma_b x omega x mu_b).

log BF(common effect : heterogeneous hierarchy), same bias terms and nodes: V1 2.43; V2 2.11; V3 2.09; V4 2.40; V5 2.18; S1 2.44.

**Monte Carlo and the ESS rule (amendment 1).** In the calibrated variants many quadrature nodes give the U.S. and Japan core contexts small bias SDs, so their core integrals rest on few importance draws: the minimum relevant core ESS (column above) is often below 50 at p18, and p20 does not always lift it above 50. As amended, the p20 refit is applied to the reported variant (V1) and V3, and every variant x estimand is reported with its two independent scrambles; the other variants are p18 with the flag. The scramble columns above are the Monte Carlo diagnostic. Agreement between two scrambles is not an error bound and does not establish accurate small tail probabilities when local ESS is low.
p20 refits not cached on the full grid are evaluated on the centres carrying the p18 posterior (each side outside holds less than 1e-15 of the p18 mass, plus a 0.1 margin; the likelihood is set to zero outside): V1 common effect: log -0.935 to 0.575 (p18 mass outside 0.0e+00).

## Sensitivities of the summative estimate

| Row | Status | Common effect (95% CrI) | P>1.10 | P>1.25 | Scrambles |
|---|---|---|---|---|---|
| V1 (the summative estimate) | documented | 0.871 (0.741-1.020) | 0.002 | <0.001 | 0.871 (0.740-1.022) / 0.871 (0.744-1.017) |
| V2 Variance Only | sensitivity variant | 0.946 (0.806-1.111) | 0.033 | <0.001 | 0.947 (0.805-1.114) / 0.945 (0.807-1.105) |
| V3 Placebo Only | sensitivity variant | 0.972 (0.858-1.104) | 0.029 | <0.001 | 0.973 (0.857-1.109) / 0.970 (0.859-1.095) |
| V4 NC Only | sensitivity variant | 0.868 (0.744-1.010) | 0.001 | <0.001 | 0.868 (0.743-1.012) / 0.867 (0.746-1.005) |
| V5 With Secondary NCs | sensitivity variant | 0.875 (0.748-1.022) | 0.002 | <0.001 | 0.874 (0.746-1.023) / 0.876 (0.753-1.018) |
| S1 Context-Mean Only | sensitivity variant | 0.871 (0.742-1.019) | 0.002 | <0.001 | 0.872 (0.741-1.021) / 0.870 (0.745-1.013) |
| Rounds 1 + 2 without the amendment-2 bug fix | amendment 2 (reported both ways) | 0.872 (0.741-1.023) | 0.002 | <0.001 | 0.872 (0.740-1.026) / 0.871 (0.743-1.016) |
| Round-2 categories de-nested | post hoc | 0.876 (0.740-1.033) | 0.004 | <0.001 | 0.877 (0.739-1.036) / 0.875 (0.743-1.025) |
| Colombia without 2020-2021 school years (3371 R1 curve) | post hoc | 0.943 (0.802-1.105) | 0.028 | <0.001 | 0.946 (0.803-1.110) / 0.937 (0.800-1.089) |
| C_INJ controls (3330 set) under the 3370 error model | post hoc | 1.064 (0.711-1.564) | 0.428 | 0.207 | 1.063 (0.707-1.569) / 1.064 (0.721-1.546) |

The amendment-2 fix adds 4 round-2 rows (the 3381 all-injuries rows, whose label names T80-T88 only as excluded codes); without it the error model has 44 PRIMARY controls entering instead of 45.

## Where calibration moved each context

Own-data autism estimate of each pooled context (its own likelihood, prior N(0, log 2^2), no pooling), uncalibrated and calibrated; the bias column is the V1 predictive bias mean (SD) that is removed.

| Context | Controls | Uncalibrated | V1 calibrated | Shift (log) | V1 bias mean (SD) | V2 (variance only) | V3 (placebo only) | V5 (+ secondary) |
|---|---|---|---|---|---|---|---|---|
| U.S. PCV | 4 | 1.165 (0.970-1.393) | 0.886 (0.630-1.238) | -0.274 | +0.285 (0.153) | 1.158 (0.823-1.619) | 1.164 (0.927-1.455) | 0.789 (0.576-1.078) |
| U.S. RotaShield | 3 | 0.872 (0.361-1.832) | 0.826 (0.339-1.849) | -0.054 | +0.101 (0.227) | 0.883 (0.356-1.960) | 0.876 (0.365-1.848) | 0.837 (0.337-1.924) |
| Japan MMR | 0 | 0.849 (0.279-2.322) | 0.840 (0.274-2.367) | -0.011 | +0.038 (0.271) | 0.852 (0.276-2.405) | 0.849 (0.279-2.329) | 0.869 (0.282-2.415) |
| Sweden PCV | 16 | 1.012 (0.786-1.555) | 0.963 (0.716-1.500) | -0.050 | +0.056 (0.077) | 1.015 (0.755-1.574) | 1.014 (0.764-1.568) | 0.989 (0.741-1.535) |
| Germany PCV | 0 | 1.034 (0.267-3.962) | 1.033 (0.267-3.957) | -0.001 | +0.038 (0.270) | 1.034 (0.267-3.961) | 1.034 (0.267-3.962) | 1.034 (0.267-3.963) |
| Hong Kong PCV | 2 | 0.892 (0.657-1.165) | 0.782 (0.529-1.128) | -0.131 | +0.145 (0.137) | 0.894 (0.603-1.289) | 0.892 (0.644-1.197) | 0.938 (0.652-1.322) |
| England rotavirus | 3 | 0.943 (0.864-1.021) | 0.923 (0.776-1.095) | -0.022 | +0.022 (0.077) | 0.943 (0.793-1.120) | 0.943 (0.841-1.052) | 0.983 (0.843-1.145) |
| Scotland rotavirus | 0 | 1.551 (0.376-5.315) | 1.525 (0.378-5.177) | -0.017 | +0.038 (0.272) | 1.529 (0.376-5.224) | 1.549 (0.376-5.305) | 1.519 (0.374-5.227) |
| Northern Ireland rotavirus | 0 | 1.012 (0.878-1.155) | 0.972 (0.600-1.609) | -0.040 | +0.038 (0.264) | 1.006 (0.619-1.660) | 1.011 (0.854-1.191) | 0.819 (0.485-1.322) |
| Canada rotavirus (excl. Quebec) | 1 | 0.992 (0.320-1.894) | 1.055 (0.326-2.235) | +0.061 | -0.149 (0.201) | 0.966 (0.317-2.015) | 0.987 (0.320-1.915) | 1.128 (0.331-2.430) |
| Quebec rotavirus | 0 | 1.067 (0.741-1.476) | 1.021 (0.579-1.791) | -0.043 | +0.038 (0.267) | 1.055 (0.597-1.846) | 1.066 (0.728-1.506) | 1.093 (0.561-2.116) |
| Czechia MMR | 0 | 1.035 (0.323-3.660) | 1.032 (0.317-3.659) | -0.003 | +0.038 (0.271) | 1.040 (0.320-3.675) | 1.036 (0.323-3.661) | 1.053 (0.323-3.709) |
| Brazil maternal DTaP | 9 | 0.766 (0.513-1.145) | 0.940 (0.565-1.580) | +0.205 | -0.221 (0.186) | 0.778 (0.467-1.308) | 0.768 (0.505-1.169) | 0.850 (0.533-1.356) |
| Colombia varicella | 6 | 0.764 (0.509-1.074) | 0.707 (0.454-1.054) | -0.079 | +0.091 (0.115) | 0.768 (0.492-1.144) | 0.766 (0.501-1.107) | 0.705 (0.454-1.052) |
| Tanzania schedule | 1 | 1.118 (0.543-1.687) | 1.082 (0.522-1.791) | -0.033 | +0.021 (0.153) | 1.101 (0.529-1.824) | 1.113 (0.540-1.721) | 1.106 (0.528-1.855) |

Shifted down by more than 0.05 on the log scale (predictive bias mean above 0: the context's own controls lean above 1 or, for a context without controls, the population mean bias mu_b is positive): U.S. PCV 1.165 -> 0.886, U.S. RotaShield 0.872 -> 0.826, Sweden PCV 1.012 -> 0.963, Hong Kong PCV 0.892 -> 0.782, Colombia varicella 0.764 -> 0.707. Shifted up (the context's own controls lean below 1): Canada rotavirus (excl. Quebec) 0.992 -> 1.055, Brazil maternal DTaP 0.766 -> 0.940. Contexts without their own controls move by the population mean bias mu_b (+0.042) and widen by its predictive SD. Every calibrated interval includes 1 unless the table shows otherwise.

## The negative-control error model

Round-1 rows listed in the rule before fitting: 23 PRIMARY, 98 SECONDARY, 993 EXCLUDED (each with its reason: claim-relevant outcomes such as speech/language, intellectual disability, other health impairment, learning disability, emotional disturbance, ADHD and the all-category composites; drowning; composites of fitted categories; duplicates; non-r-scale and non-block designs); round-2 rows are classified by amendments 1-2 (below). Entering after the prior-dominance rule (posterior log-SD at most 0.8 log 2), rounds 1, 2: 45 PRIMARY and 165 PRIMARY + SECONDARY. Unlisted round-1 rows at fit time: 0; listed rows missing: 0.

| Context | Control (source file) | Source r (95% CrI) | y (log) | s | Enters |
|---|---|---|---|---|---|
| U.S. PCV | tbi (3326) | 1.654 (0.765-4.285) | +0.842 | 0.568 | yes |
| U.S. RotaShield | tbi (3326) | 0.693 (0.199-2.212) | - | - | no: prior-dominated (posterior log-SD 0.615 > 0.8 log 2) |
| U.S. PCV | orthopedic (3326) | 1.430 (0.905-2.257) | +0.404 | 0.248 | yes |
| U.S. RotaShield | orthopedic (3326) | 0.967 (0.314-2.355) | -0.075 | 0.766 | yes |
| U.S. PCV | hearing (3326) | 1.407 (1.050-1.910) | +0.359 | 0.157 | yes |
| U.S. RotaShield | hearing (3326) | 1.408 (0.480-3.159) | +0.659 | 0.667 | yes |
| U.S. PCV | visual (3326) | 1.446 (0.736-2.724) | +0.480 | 0.381 | yes |
| U.S. RotaShield | visual (3326) | 1.144 (0.352-2.901) | +0.337 | 0.853 | yes |
| Brazil maternal DTaP | head_injury (3332) | 0.475 (0.185-1.104) | -1.313 | 0.605 | yes |
| Brazil maternal DTaP | fracture (3332) | 0.734 (0.397-1.292) | -0.381 | 0.334 | yes |
| Brazil maternal DTaP | burn (3332) | 1.473 (0.647-2.994) | +0.568 | 0.473 | yes |
| Brazil maternal DTaP | poisoning (3332) | 0.672 (0.237-1.653) | -0.812 | 0.709 | yes |
| Brazil maternal DTaP | foreign_body (3332) | 0.863 (0.279-2.518) | - | - | no: prior-dominated (posterior log-SD 0.561 > 0.8 log 2) |
| Brazil maternal DTaP | road_traffic (3332) | 1.132 (0.563-2.081) | +0.161 | 0.380 | yes |
| Brazil maternal DTaP | falls (3332) | 0.378 (0.146-0.863) | -1.699 | 0.598 | yes |
| Brazil maternal DTaP | dog_bite (3332) | 1.020 (0.289-3.391) | - | - | no: prior-dominated (posterior log-SD 0.629 > 0.8 log 2) |
| Colombia varicella | hearing (3337) | 0.977 (0.658-1.490) | -0.026 | 0.219 | yes |
| Colombia varicella | motor_physical (3338) | 0.866 (0.667-1.283) | -0.153 | 0.172 | yes |
| Colombia varicella | visual (3338) | 0.901 (0.584-1.271) | -0.114 | 0.207 | yes |
| Tanzania schedule | albinism (3339) | 1.004 (0.689-1.281) | +0.004 | 0.163 | yes |
| Hong Kong PCV | physical_disability (3342) | 1.783 (1.226-2.903) | +0.643 | 0.232 | yes |
| Hong Kong PCV | visual_impairment (3342) | 2.009 (0.560-6.058) | - | - | no: prior-dominated (posterior log-SD 0.607 > 0.8 log 2) |
| Hong Kong PCV | hearing_impairment (3342) | 0.986 (0.716-1.323) | -0.015 | 0.161 | yes |
| England rotavirus | primary (3380) | 1.002 (0.868-1.161) | +0.002 | 0.075 | yes |
| Scotland rotavirus | primary (3380) | 0.918 (0.255-3.047) | - | - | no: prior-dominated (posterior log-SD 0.632 > 0.8 log 2) |
| Scotland rotavirus | primary (3380) | 0.749 (0.217-2.417) | - | - | no: prior-dominated (posterior log-SD 0.615 > 0.8 log 2) |
| England rotavirus | ksi (3380) | 1.030 (0.782-1.337) | +0.030 | 0.139 | yes |
| England rotavirus | pedestrian (3380) | 1.037 (0.858-1.248) | +0.037 | 0.096 | yes |
| Scotland rotavirus | falls (3380) | 0.887 (0.249-2.936) | - | - | no: prior-dominated (posterior log-SD 0.629 > 0.8 log 2) |
| Scotland rotavirus | rti (3380) | 0.866 (0.245-2.851) | - | - | no: prior-dominated (posterior log-SD 0.626 > 0.8 log 2) |
| Scotland rotavirus | poisoning (3380) | 0.970 (0.268-3.211) | - | - | no: prior-dominated (posterior log-SD 0.634 > 0.8 log 2) |
| Scotland rotavirus | struck (3380) | 0.850 (0.239-2.799) | - | - | no: prior-dominated (posterior log-SD 0.628 > 0.8 log 2) |
| Scotland rotavirus | crushing (3380) | 0.899 (0.249-2.989) | - | - | no: prior-dominated (posterior log-SD 0.634 > 0.8 log 2) |
| Scotland rotavirus | scalds (3380) | 0.863 (0.238-2.930) | - | - | no: prior-dominated (posterior log-SD 0.640 > 0.8 log 2) |
| Scotland rotavirus | other (3380) | 0.951 (0.263-3.169) | - | - | no: prior-dominated (posterior log-SD 0.635 > 0.8 log 2) |
| Scotland rotavirus | ksi (3380) | 0.908 (0.253-2.930) | - | - | no: prior-dominated (posterior log-SD 0.625 > 0.8 log 2) |
| Germany PCV | INJ_ALL (3381) | 1.090 (0.309-3.913) | - | - | no: prior-dominated (posterior log-SD 0.648 > 0.8 log 2) |
| Sweden PCV | INJ_ALL (3381) | 1.056 (0.980-1.132) | +0.054 | 0.037 | yes |
| Germany PCV | HEAD_S00_S09 (3381) | 0.980 (0.278-3.515) | - | - | no: prior-dominated (posterior log-SD 0.647 > 0.8 log 2) |
| Germany PCV | S06 (3381) | 1.019 (0.280-3.740) | - | - | no: prior-dominated (posterior log-SD 0.661 > 0.8 log 2) |
| Germany PCV | FRACTURES (3381) | 1.216 (0.329-4.369) | - | - | no: prior-dominated (posterior log-SD 0.660 > 0.8 log 2) |
| Germany PCV | BURNS_T20_T32 (3381) | 0.844 (0.230-3.200) | - | - | no: prior-dominated (posterior log-SD 0.671 > 0.8 log 2) |
| Germany PCV | POISONING_T36_T65 (3381) | 0.684 (0.183-2.893) | - | - | no: prior-dominated (posterior log-SD 0.704 > 0.8 log 2) |
| Germany PCV | FOREIGN_BODY_T15_T19 (3381) | 0.897 (0.227-3.702) | - | - | no: prior-dominated (posterior log-SD 0.713 > 0.8 log 2) |
| Germany PCV | S02 (3381) | 1.118 (0.295-4.097) | - | - | no: prior-dominated (posterior log-SD 0.671 > 0.8 log 2) |
| Germany PCV | S22 (3381) | 0.993 (0.262-3.739) | - | - | no: prior-dominated (posterior log-SD 0.678 > 0.8 log 2) |
| Germany PCV | S42 (3381) | 1.073 (0.288-3.928) | - | - | no: prior-dominated (posterior log-SD 0.667 > 0.8 log 2) |
| Germany PCV | S52 (3381) | 1.258 (0.327-4.618) | - | - | no: prior-dominated (posterior log-SD 0.675 > 0.8 log 2) |
| Germany PCV | S62 (3381) | 0.878 (0.227-3.532) | - | - | no: prior-dominated (posterior log-SD 0.700 > 0.8 log 2) |
| Germany PCV | S72 (3381) | 0.981 (0.267-3.582) | - | - | no: prior-dominated (posterior log-SD 0.663 > 0.8 log 2) |
| Germany PCV | S82 (3381) | 1.000 (0.266-3.749) | - | - | no: prior-dominated (posterior log-SD 0.675 > 0.8 log 2) |
| Sweden PCV | HEAD_S00_S09 (3381) | 1.045 (0.945-1.154) | +0.044 | 0.051 | yes |
| Sweden PCV | S06 (3381) | 1.008 (0.910-1.121) | +0.008 | 0.053 | yes |
| Sweden PCV | FRACTURES (3381) | 1.044 (0.966-1.112) | +0.043 | 0.036 | yes |
| Sweden PCV | BURNS_T20_T32 (3381) | 1.161 (0.916-1.443) | +0.153 | 0.118 | yes |
| Sweden PCV | POISONING_T36_T65 (3381) | 1.376 (0.930-2.014) | +0.347 | 0.206 | yes |
| Sweden PCV | FOREIGN_BODY_T15_T19 (3381) | 1.177 (0.955-1.338) | +0.165 | 0.087 | yes |
| Sweden PCV | S02 (3381) | 1.156 (0.933-1.417) | +0.149 | 0.108 | yes |
| Sweden PCV | S22 (3381) | 0.946 (0.433-1.881) | -0.079 | 0.445 | yes |
| Sweden PCV | S32 (3381) | 2.018 (1.086-3.577) | +0.870 | 0.338 | yes |
| Sweden PCV | S42 (3381) | 1.124 (1.022-1.212) | +0.117 | 0.044 | yes |
| Sweden PCV | S52 (3381) | 1.002 (0.917-1.098) | +0.002 | 0.046 | yes |
| Sweden PCV | S62 (3381) | 1.063 (0.862-1.189) | +0.062 | 0.083 | yes |
| Sweden PCV | S72 (3381) | 1.259 (0.810-1.771) | +0.251 | 0.209 | yes |
| Sweden PCV | S82 (3381) | 0.918 (0.734-1.075) | -0.087 | 0.099 | yes |
| Sweden PCV | S92 (3381) | 0.980 (0.858-1.104) | -0.020 | 0.065 | yes |
| Brazil maternal DTaP | unintentional (3382) | 0.362 (0.150-0.792) | -1.627 | 0.538 | yes |
| Brazil maternal DTaP | road_traffic (3382) | 0.811 (0.336-1.659) | -0.320 | 0.503 | yes |
| Brazil maternal DTaP | falls (3382) | 1.260 (0.428-3.265) | +0.524 | 0.780 | yes |
| Brazil maternal DTaP | fire (3382) | 0.689 (0.198-2.378) | - | - | no: prior-dominated (posterior log-SD 0.634 > 0.8 log 2) |
| Brazil maternal DTaP | accidental_poisoning (3382) | 0.772 (0.228-2.583) | - | - | no: prior-dominated (posterior log-SD 0.619 > 0.8 log 2) |
| Canada rotavirus (excl. Quebec) | asthma_incidence (3384) | 0.707 (0.476-1.057) | -0.379 | 0.213 | yes |
| Colombia varicella | transport (3385) | 1.359 (0.991-1.928) | +0.326 | 0.175 | yes |
| Colombia varicella | accidental (3385) | 1.563 (0.930-3.974) | +0.625 | 0.438 | yes |
| Colombia varicella | transport_plus_accidental (3385) | 1.326 (1.012-1.962) | +0.300 | 0.174 | yes |

y and s remove the N(0, (log 2)^2) prior from the reported posterior (1/s^2 = 1/v - 1/log2^2, y = s^2 m / v).

| Quantity (log scale) | Primary NCs (V1) | Primary + secondary (V5) |
|---|---|---|
| mu_b | 0.042 (-0.155-0.217) | -0.051 (-0.204-0.090) |
| sigma_b | 0.204 (0.028-0.466) | 0.319 (0.195-0.492) |
| omega | 0.025 (0.003-0.090) | 0.018 (0.003-0.060) |

| Context | beta_c from its controls (RR) | Autism-bias predictive, V1: mean (SD), log | Loading on mu_b | Assumed floor |
|---|---|---|---|---|
| U.S. PCV | 1.330 (1.045-1.718) | +0.285 (0.136) | 0.33 | 0.70 |
| U.S. RotaShield | 1.089 (0.739-1.753) | +0.101 (0.213) | 0.80 | 0.70 |
| Japan MMR | no controls: population predictive | +0.038 (0.261) | 1.00 | 0.70 |
| Sweden PCV | 1.057 (1.019-1.102) | +0.056 (0.043) | 0.04 | 0.70 |
| Germany PCV | no controls: population predictive | +0.038 (0.261) | 1.00 | 0.70 |
| Hong Kong PCV | 1.148 (0.934-1.468) | +0.145 (0.122) | 0.36 | 0.70 |
| England rotavirus | 1.023 (0.914-1.140) | +0.022 (0.068) | 0.14 | 0.35 |
| Scotland rotavirus | no controls: population predictive | +0.038 (0.261) | 1.00 | 0.35 |
| Northern Ireland rotavirus | no controls: population predictive | +0.038 (0.261) | 1.00 | 0.35 |
| Canada rotavirus (excl. Quebec) | 0.875 (0.586-1.156) | -0.149 (0.183) | 0.55 | 0.35 |
| Quebec rotavirus | no controls: population predictive | +0.038 (0.261) | 1.00 | 0.35 |
| Czechia MMR | no controls: population predictive | +0.038 (0.261) | 1.00 | 0.70 |
| Brazil maternal DTaP | 0.804 (0.571-1.077) | -0.221 (0.173) | 0.44 | 0.70 |
| Colombia varicella | 1.093 (0.946-1.277) | +0.091 (0.085) | 0.21 | 0.35 |
| Tanzania schedule | 1.027 (0.783-1.315) | +0.021 (0.135) | 0.44 | 0.35 |

**Leave-one-NC-out validation (documented).** Each of the 45 entering PRIMARY controls calibrated with the error model fitted without it: calibrated 95% intervals cover RR 1 in 0.933 of them (target about 0.95; adequacy threshold 0.85), against 0.867 uncalibrated. With the secondary controls as well (165): 0.933 calibrated vs 0.891 uncalibrated. Calibration is therefore ADEQUATE and V1 is the reported calibrated variant.
Uncalibrated intervals that exclude 1, and their calibrated intervals: U.S. PCV hearing 1.41 (1.05-1.91) -> 1.15 (0.72-1.72); Brazil maternal DTaP falls 0.38 (0.15-0.86) -> 0.41 (0.17-1.02); Hong Kong PCV physical_disability 1.78 (1.23-2.90) -> 1.75 (1.07-2.85); Sweden PCV S32 2.02 (1.09-3.58) -> 1.93 (1.06-3.51); Sweden PCV S42 1.12 (1.02-1.21) -> 1.07 (0.95-1.20); Brazil maternal DTaP unintentional 0.36 (0.15-0.79) -> 0.40 (0.17-0.93).

## Reconciliation with the 3330 C_INJ preview (post hoc, coordinator request; not documented)

3330's documented set C_INJ has five injury controls and a single-level estimator (m_i ~ N(mu, tau^2 + s_i^2) on posterior summaries). Reproduced here from the same five rows: exp(mu) = 0.96, tau = 0.48 (3330 reports 0.96 and 0.48). The eligibility differs member by member:

| C_INJ member | In 3370 | Why |
|---|---|---|
| U.S. PCV / IDEA TBI (3331 B1 = 3326 tbi) | PRIMARY | same cells, same model |
| U.S. rotavirus 2006 / IDEA TBI (same fit) | SECONDARY (V5 only) | U.S. rotavirus 2006 is untied: it is not a pooled context, so its bias never enters the synthesis; it informs mu_b / sigma_b only in V5 |
| Brazil maternal DTaP / all injuries (3332) | its categories are PRIMARY instead | the rule enters the fitted categories (head injury, fracture, burn, poisoning, road traffic, falls) rather than their union; dog bite and foreign body are prior-dominated and drowning is excluded for leakage |
| England rotavirus / all unintentional deaths (3333 S) | its categories are SECONDARY | national WHO deaths are not the autism cells (3330 counts them as the closest match); the categories enter V5 |
| Japan MMR / unintentional deaths (3341) | its categories are SECONDARY | national deaths for the same 9 cohorts, not the Kohoku cells; the categories enter V5 |

3370 also admits non-injury negative controls fitted on the same cells (IDEA hearing, orthopedic and visual impairment for the U.S. paths; Hong Kong SEN physical disability and hearing impairment; Colombia hearing, motor/physical and visual; Tanzania albinism), which C_INJ leaves to its sensitivity S3; and it models two levels (context bias beta_c with SD sigma_b, outcome dispersion omega within a context) on de-priored estimates, where C_INJ has one level on posterior summaries (its de-priored S5 gives tau 0.71).

Fitting the 3370 error model to the five C_INJ members instead (de-priored): sigma_b = 0.55 (0.06-1.13), omega = 0.21 (0.01-0.62), mu_b = -0.018 (-0.573 to +0.563); a context without controls would carry a predictive bias SD of 0.75. The common effect with the V1 construction under that calibration is 1.064 (0.711-1.564) (p18; scrambles 1.063 (0.707-1.569) and 1.064 (0.721-1.546)), against 0.871 (0.741-1.020) with the rule's PRIMARY set. With one control per context, sigma_b and omega are not separately identified there (the priors split them).

## Round-2 negative controls (manifest)

NC inputs come from the manifest `qa/calibrated_synthesis_20260929/3370_nc_manifest.json` (SHA-256 `a4d5bdfb24cc2fa44174390ccb4144aebfd8d8957621fad37162ea1a8c01f23a`): round 1 = the 3326 and 3331-3348 reports (classified by the rule); round 2 = files matching 338[0-5]_*.csv, classified by explicit manifest rows or, where the harmonized 3330 summary covers them, by the amendment's specified classifier; otherwise listed as UNCLASSIFIED and excluded. Rerun unchanged with `--nc-rounds 1,2` (the default).

Round-2 files present at this run: 3380_injury_negative_controls_uk_round2.csv, 3381_injury_negative_controls_europe_round2.csv, 3382_injury_negative_controls_brazil_sim.csv, 3383_injury_negative_controls_us_deaths.csv, 3384_negative_controls_canada.csv, 3385_injury_negative_controls_col_hkg_jpn_twn_round2.csv. Status: 3380_injury_negative_controls_uk_round2.csv: harmonized 3330 rows, amendment 1 classifier (29 PRIMARY/SECONDARY rows before the numerical rule); 3381_injury_negative_controls_europe_round2.csv: harmonized 3330 rows, amendment 1 classifier (71 PRIMARY/SECONDARY rows before the numerical rule); 3382_injury_negative_controls_brazil_sim.csv: harmonized 3330 rows, amendment 1 classifier (25 PRIMARY/SECONDARY rows before the numerical rule); 3383_injury_negative_controls_us_deaths.csv: harmonized 3330 rows, amendment 1 classifier (6 PRIMARY/SECONDARY rows before the numerical rule); 3384_negative_controls_canada.csv: harmonized 3330 rows, amendment 1 classifier (2 PRIMARY/SECONDARY rows before the numerical rule); 3385_injury_negative_controls_col_hkg_jpn_twn_round2.csv: harmonized 3330 rows, amendment 1 classifier (10 PRIMARY/SECONDARY rows before the numerical rule). Round-2 rows excluded by the classifier: 61; unclassified: 0.

**Round-2 classification sensitivity (post hoc; not the specified round-2 primary).** The specified harmonized classifier drops a round-2 union only when its source role says "composite", so it admits nested round-2 categories (for example Swedish S00-S09 beside S06 and S02, fractures beside the S-codes, STATS19 all casualties beside KSI and pedestrians, SIM unintentional deaths beside road traffic and falls), which the error model treats as independent controls. Applying the rule's own composite / nested definitions by hand (35 round-2 rows dropped; written before any round-2 fit) gives 38 PRIMARY controls in 9 contexts, sigma_b 0.158, omega 0.062, mu_b +0.054, and a V1 common effect of 0.876 (0.740-1.033) (p18; scrambles 0.877 (0.739-1.036) and 0.875 (0.743-1.025)), against 0.871 (0.741-1.020) with the specified classification.

## Does round 2 move the result?

Round 1 only (archived `project_results/calibrated_synthesis_3370/round1_report/3370_calibrated_synthesis.json`, rule and amendment unchanged) against rounds 1 + 2 (this report):

| Variant | Estimand | Round 1 | Rounds 1 + 2 | Shift in log median |
|---|---|---|---|---|
| V1 Calibrated (NC + Placebo) | shared mean | 0.871 (0.670-1.133) | 0.877 (0.696-1.102) | +0.007 |
| V1 Calibrated (NC + Placebo) | common effect | 0.864 (0.708-1.057) | 0.871 (0.741-1.020) | +0.008 |
| V2 Variance Only | shared mean | 0.938 (0.703-1.235) | 0.934 (0.731-1.176) | -0.004 |
| V2 Variance Only | common effect | 0.952 (0.770-1.170) | 0.946 (0.806-1.111) | -0.006 |
| V3 Placebo Only | shared mean | 0.945 (0.759-1.157) | 0.945 (0.759-1.157) | +0.000 |
| V3 Placebo Only | common effect | 0.972 (0.858-1.104) | 0.972 (0.858-1.104) | +0.000 |
| V4 NC Only | shared mean | 0.871 (0.674-1.127) | 0.875 (0.699-1.095) | +0.005 |
| V4 NC Only | common effect | 0.863 (0.712-1.048) | 0.868 (0.744-1.010) | +0.006 |
| V5 With Secondary NCs | shared mean | 0.921 (0.712-1.197) | 0.881 (0.697-1.115) | -0.044 |
| V5 With Secondary NCs | common effect | 0.910 (0.756-1.108) | 0.875 (0.748-1.022) | -0.039 |
| S1 Context-Mean Only | shared mean | 0.872 (0.672-1.131) | 0.877 (0.697-1.100) | +0.006 |
| S1 Context-Mean Only | common effect | 0.867 (0.709-1.065) | 0.871 (0.742-1.019) | +0.005 |

Summative estimate: round 1 0.864 (0.708-1.057) (common effect); rounds 1 + 2 0.871 (0.741-1.020) (common effect). Error model, round 1: sigma_b 0.256, omega 0.130, mu_b +0.066 (19 controls in 6 contexts); rounds 1 + 2: sigma_b 0.204, omega 0.025, mu_b +0.042 (45 controls in 9 contexts).

## Verification

- The primary reproduced at the assumed floors (same machinery, zero shifts, shared SD 0.15, p18): 0.957 (0.599-1.517); components differ from hierarchy_final_grid_p18.npz by at most 9.1e-13 (log), headline by 4.1e-15: PASS.
- 3350 A1 (common effect, floors): 0.964 (0.637-1.455); log-likelihood values vs 3350 fits/A1_p18.npz within 1.8e-12 on |a| <= 1; summary within 1.6e-13: PASS.
- 3350 decomposition without the shared bias: T1_A1 0.963 (0.705-1.310) (within 3.0e-14) and T1_A2 = V3's common effect 0.972 (0.858-1.104) (p20, within 1.3e-14): PASS.
- Quadrature: the hierarchy scheme applied to the V1 common effect differs from the common-effect scheme by at most 0.0009 on the log 2.5/50/97.5 percentiles (p18, tolerance 0.005): PASS.
- The calibrated likelihood is the hierarchy's own: global_hierarchy.product_inputs and .component are reproduced by this script's implementation to 1e-12 (with core shifts, per-context SDs and shifted curves; tests). The common-effect evaluator skips draws more than 70 nats below the best draw (exact to n e^-70 of the node maximum; checked against the unpruned sum); the reproductions are computed unpruned.
- Per-context calibrated estimates of the core contexts use the U.S.-alone / Japan-alone draws binned on a 0.0025 grid; the binned uncalibrated medians differ from the exact weighted-draw medians by at most 0.001 (log).

## Negative-control inputs used (SHA-256)

The coordinator reported that the round-1 NC workflow completed at 21:57 (3326 and 3331-3348 final for that round) and later that every round-2 output (3380-3385) exists. Round-1 files are compared with their hashes when the rule was written (21:25); all hashes below were re-taken before this report and matched the fits. V1's entering controls come from 3326, 3332, 3337, 3338, 3339, 3342, 3380, 3381, 3382, 3384, 3385 (every 3331 row repeats a 3326 outcome, is off the r scale or is not a block design). No round-1 NC file changed since the rule was written, so none was mid-repair for this result.

| File | SHA-256 | Modified |
|---|---|---|
| 3326_us_core_negative_control_outcomes.csv | `75dccf6fb207b6f2ca726500c25c7c60a2af8799b349d919cfacc7f28c7e1086` | 2026-09-25T14:39:03 |
| 3326_us_core_negative_control_outcomes.md | `be7b896e9046a126aa6c953752b6be8202242484ca4a5930adcc5c8fefe6e21b` | 2026-09-25T14:39:03 |
| 3331_injury_negative_controls_us.csv | `96f101c8ccbf50e3e6bd7804f420b7ee23f62094623b7a5379c8b8023b02f49a` | 2026-09-29T21:07:24 |
| 3331_injury_negative_controls_us.md | `ccf93052b8c114c8a20d98d9938a9996ffed393926e6fe5487bd8a37a66b7c03` | 2026-09-29T21:07:46 |
| 3332_injury_negative_controls_brazil.csv | `5a76227163272c234ba68c47faf7176e3ccadc1c4f8e1517d49fa3a8a4dca1d0` | 2026-09-29T20:31:41 |
| 3332_injury_negative_controls_brazil.md | `9ab93de066eefcbd66fc5ed763929e254c6c2c74e00cb7a6a0caaa10d80d929e` | 2026-09-29T20:31:42 |
| 3333_injury_negative_controls_uk.csv | `8cbe3419f727bb75e6bbc7557e3bb7c92ed97364451beb6c32df8b818b6a665a` | 2026-09-29T20:01:46 |
| 3333_injury_negative_controls_uk.md | `a71deb0eea7d3685d9c8fb728c66ab7f1b956b2196f1d40e30863f046f916d9e` | 2026-09-29T20:01:46 |
| 3334_injury_negative_controls_europe.csv | `704c8107ef3e9ea55f575e6d11e19f3f6e70c8f3089b925607eca082c5599440` | 2026-09-29T20:38:16 |
| 3334_injury_negative_controls_europe.md | `1c423312bfe6b59c339e7f5d98b4735d68881123daa804c5b3eb412ffb1e1b66` | 2026-09-29T20:38:17 |
| 3335_injury_negative_controls_chile_deis.csv | `a8fabdaa9e610f7d7f5d86c71cb7f2dfd3f5f871d297bac701598426eef7636c` | 2026-09-29T16:56:26 |
| 3335_injury_negative_controls_chile_deis.md | `3f674e7569f330659dd3fd18997f352a7088e58abad329afa943ddfd258354b2` | 2026-09-29T16:56:27 |
| 3336_injury_negative_controls_chile_deis.csv | `a0d327e320b0e073a9cebaceccffb197ab42662ccefbbe056f846e72f78e6373` | 2026-09-29T19:59:27 |
| 3336_injury_negative_controls_chile_deis.md | `9d04cb8dc1706a6fb2856bc5b4368604d07e0fa0b1ee26631dbdedc46f0b75c8` | 2026-09-29T19:59:29 |
| 3337_injury_negative_controls_colombia_dane_school.csv | `9299dc94b51be054328bebd9f27001e021d04930bf4a44579c00707472b50249` | 2026-09-29T16:58:59 |
| 3337_injury_negative_controls_colombia_dane_school.md | `409a1984a3f15d0bafd2f569b6e54facfe8e9785a8e41f30af9af5a1f2ed624f` | 2026-09-29T19:51:32 |
| 3338_injury_negative_controls_colombia_dane_school_census.csv | `1aa9cb627e02a3ed995c6eeacc5f60f8988385afa45af70b524f6688140f10be` | 2026-09-29T20:03:57 |
| 3338_injury_negative_controls_colombia_dane_school_census.md | `529f08c8f0a0aac86e4513bb2d16b56012c9c9be1914a5e5b22545e662031ee5` | 2026-09-29T20:03:57 |
| 3339_injury_negative_controls_tanzania_best.csv | `1a15104d672597e0a1d10ac6b85073f88e483280c6779689a3e4a73b25715075` | 2026-09-29T20:04:31 |
| 3339_injury_negative_controls_tanzania_best.md | `1021a07881175eeb34d0db32069f2c219b00d908f06693f778ab219a590f223d` | 2026-09-29T20:04:31 |
| 3340_injury_negative_controls_japan_mext.csv | `47949ef4c1736fd21001c7721869851918890dd8524ae2591a52a988540c97c3` | 2026-09-29T20:36:06 |
| 3340_injury_negative_controls_japan_mext.md | `c4680be35575baca64a7364ff19bff3102dae5438215322d9717c54fcf4bf09d` | 2026-09-29T20:36:07 |
| 3341_injury_negative_controls_japan_who_mdb.csv | `b269d4b81a261a219965ffaa559da92acf77e0d988b0d82b70e8aabc55910806` | 2026-09-29T20:24:09 |
| 3341_injury_negative_controls_japan_who_mdb.md | `76ea2d56059988d368d95c048e5888a19f21c1b6f4cbfa4d405d4a364b07b0b0` | 2026-09-29T20:24:10 |
| 3342_injury_negative_controls_hkg_edb_sen.csv | `cb4cf5e53fcd871f1b70b7d42ca7258d49c3d2387fa223a8ca4e1b9cbd936510` | 2026-09-29T20:07:47 |
| 3342_injury_negative_controls_hkg_edb_sen.md | `5df07a54d595b1b6dfedd92de8d630be7a81708b4ed8a07c8c1b5b125d9462eb` | 2026-09-29T20:07:47 |
| 3343_injury_negative_controls_hkg_who_mdb.csv | `9ce81b29fb6457c8f222c123378b2924a0065d54d741e20ab75b25b2ac7d2558` | 2026-09-29T20:11:27 |
| 3343_injury_negative_controls_hkg_who_mdb.md | `8ce055b53dac491601a0da23854bc002da4c2d5b1aee07f20ac6bc59a8375230` | 2026-09-29T20:11:29 |
| 3344_injury_negative_controls_korea_nise.csv | `30a00f43572eb2f83fcbc007c3516dbc2f061d09804406f98febb1a65567ac01` | 2026-09-29T20:23:38 |
| 3344_injury_negative_controls_korea_nise.md | `7ded7c03b80719e3840db81d7d52aa6240c5dba683b0480a09bbd3a3ce8c5f75` | 2026-09-29T20:23:38 |
| 3345_injury_negative_controls_korea_who_mdb.csv | `857e1dee8f6a65c193f81346e409673306d861809230e1552e7c03db7d9da8a9` | 2026-09-29T19:58:07 |
| 3345_injury_negative_controls_korea_who_mdb.md | `dafec982874e53745b965186be12278a0d42e2a6b08c1bca16d49662d3324191` | 2026-09-29T19:58:09 |
| 3346_injury_negative_controls_taiwan.csv | `f66226b52a17f4676d7027e95f3ef8cb91234c06ebbe123d45757b18db408250` | 2026-09-29T20:02:48 |
| 3346_injury_negative_controls_taiwan.md | `47926595586cff75b5853c87ac59a931f40f9b6dfdcf4dde1d82866aa80f7a9e` | 2026-09-29T20:02:48 |
| 3347_injury_negative_controls_global_mortality.csv | `592a6587ebf61ce786207efbdc29a9e621de8dab4ba1168267e623823e78ffba` | 2026-09-29T20:39:01 |
| 3347_injury_negative_controls_global_mortality.md | `9f541fce9f885514ce589538b0b7c0ddff4119bcece63e3a6ec98b6c07c11346` | 2026-09-29T20:39:02 |
| 3348_injury_negative_controls_germany_destatis.csv | `2773574719cdb8a21534bc91626b79e7a9540ebf679491d04ca6be4a6420ae53` | 2026-09-29T20:08:13 |
| 3348_injury_negative_controls_germany_destatis.md | `529d7f4a41e2ae4e4b68996af5683a12d4cd17f57cb4beb0ac943359695ed107` | 2026-09-29T20:08:14 |
| 3380_injury_negative_controls_uk_round2.csv | `dd4df9e68b750f51dd7a110b300d9f3f52eb0f9aaffdc79d6c9a89f57022dbc5` | 2026-09-29T23:09:04 |
| 3380_injury_negative_controls_uk_round2.md | `647526aeae00490e69d743f739c7c12463531939cbafd8e951bdd6c23d7914bb` | 2026-09-29T23:09:04 |
| 3381_injury_negative_controls_europe_round2.csv | `a7db789fd4fd3472ee0ac5dff948546e50b2142f1724cbad15c19c0222b4cae5` | 2026-09-30T02:35:48 |
| 3381_injury_negative_controls_europe_round2.md | `da3312d1273c1f1f9f78f6996067a84915157af387dfa941f3de23e005b482b9` | 2026-09-30T02:35:51 |
| 3382_injury_negative_controls_brazil_sim.csv | `b2fb514ffd464aec05f8148e6b65e68e8fdca243d007705eabd26453ec343bf1` | 2026-09-29T22:28:17 |
| 3382_injury_negative_controls_brazil_sim.md | `04c00bee21fc1745b6dbba04f1e95afb46615109cddf719ff8d5ab5d311e3fb2` | 2026-09-29T22:28:19 |
| 3383_injury_negative_controls_us_deaths.csv | `768aa414e9f123f46fa9df667d65f1f8ee65b3e9a8773d8913a9718ca8955aaf` | 2026-09-29T22:54:59 |
| 3383_injury_negative_controls_us_deaths.md | `529822db389b93a884d8d46f18411c1f2f3414aa1ecd0fcd113bb48c73e902e2` | 2026-09-29T22:55:05 |
| 3384_negative_controls_canada.csv | `37eb39a8e52a8dd426015184ce938541886794e241b37a3eafeb0a7a4848a1b5` | 2026-09-29T22:29:02 |
| 3384_negative_controls_canada.md | `d6191f071d3ad57c44b22a40d14e72139217e3bdeff9c7ca7ba29cd310c45beb` | 2026-09-29T22:29:02 |
| 3385_injury_negative_controls_col_hkg_jpn_twn_round2.csv | `5a97dfd8456f61086b501ebdfb01c7a0254ffc6daca7aaecb0a04a2d6f3d8a45` | 2026-09-29T22:44:42 |
| 3385_injury_negative_controls_col_hkg_jpn_twn_round2.md | `1c8da673a40e64165da1ce96ee0349db446f13f0fa96992a1a46af188851901a` | 2026-09-29T22:44:45 |
| 3330_negative_control_summary.csv | `bba9f96b57117cc3652781db1e13571c134a8c74b65d052a7d493d6a2167683f` | 2026-09-30T03:14:35 |
| qa/calibrated_synthesis_20260929/3370_nc_manifest.json | `a4d5bdfb24cc2fa44174390ccb4144aebfd8d8957621fad37162ea1a8c01f23a` | 2026-09-29T22:50:11 |

## What this cannot establish

- It rests on exchangeability: an autism-specific systematic error that none of the controls share is not calibrated away. The controls calibrate what they share with autism: reporting systems, denominators, exposure reconstruction and trends.
- Only 9 of the 15 pooled contexts have same-cell controls that enter; the other 6 get the population predictive, so their calibration is only as good as the exchangeability of contexts; sigma_b is estimated from 9 contexts and is correspondingly uncertain.
- Control estimates enter through a Gaussian approximation of their reported posteriors (prior removed); overlapping categories (Brazil external-cause and nature-of-injury groups) are treated as distinct outcomes; U.S. PCV and RotaShield controls come from one joint fit and are treated as separate contexts.
- The narrow calibrated nodes leave the core integrals Monte Carlo limited (low local ESS); the two scrambles diagnose sensitivity but do not bound numerical error. Small tail probabilities remain numerically qualified pending stronger integration checks.
- Everything else is the primary's: its likelihood curves, exposure paths, gate decisions, the individual-scale mixture conversion, the country-group terms and the heterogeneity prior. Subgroup, short-latency and product-specific effects outside the pooled contexts are not addressed.

## Addendum: final review (2026-09-30, qa/fable_review_20260930/REVIEW_E_final.md)

- **U.S. PCV is settled here by assumption.** V1 reads the U.S. PCV controls’ lean as drift shared with autism (bias mean +0.285, SD 0.153) and moves that context from 1.165 (0.970-1.393) to 0.886 (0.630-1.238), the largest calibration move; the documented negative-control verdict for that context was MIXED. Without any mean shift (V2) the common effect is 0.946 (0.806-1.111): the exclusion of RR 1.25 does not depend on that reading, the exclusions of 1.05 and 1.10 do.
- **Monte Carlo threshold.** The 0.02 threshold (amendment 1) was specified after the round-one p18 scrambles, which differed by 0.011, had been seen; the reported p20 scrambles differ by 0.005. Applied to the shared mean, the same threshold would flag V1 (0.021), V3 (0.025), V4 (0.023) and S1 (0.021) as Monte Carlo limited; their scrambles agree on every exclusion call except RR 1.10, where for V1, V4 and S1 one scramble's 97.5th percentile lies below 1.10 and the other's above it.
- **Nesting.** The row amendment 2 restores, the Swedish all-injury union, is a union of Swedish category rows that also enter, which the rule’s composite definition would exclude (the harmonized source roles do not mark it as a composite). The de-nested sensitivity applies that definition by hand and is the rule-literal version (post hoc): 0.876 (0.740-1.033).
- **Leave-one-out gate.** Uncalibrated intervals already cover the held-out control in 0.867 of cases, above the 0.85 threshold, so the gate tests only that calibration does not worsen coverage; calibration repairs three of the six uncalibrated misses (U.S. PCV hearing, Brazil falls, Sweden S42) and leaves three.
- "Most precise defensible summative estimate" is the rule’s term: the reported calibrated variant chosen by the leave-one-out test, applied to the estimand the data do not disfavour (log BF >= 0).

## Files

- `07_analysis_code/3370_calibrated_synthesis.py` (one command: `python -X utf8 07_analysis_code/3370_calibrated_synthesis.py --workers 1`; round-1 report: add `--nc-rounds 1`); tests `07_analysis_code/test_3370_calibrated_synthesis.py`.
- `3370_calibrated_synthesis.csv` (summative, variants, references, per-context, error model, LOO, every NC row, post hoc rows; each row carries the rule hash and the combined NC-input hash), `3370_calibrated_synthesis.json` (everything, with nodes, scrambles, hashes and checks), `08_figures/3370_calibrated_synthesis.png` (Calibrating the Vaccine-Autism Synthesis with Negative Controls).
- Rule `qa/calibrated_synthesis_20260929/3370_rule.json` (writer `qa/calibrated_synthesis_20260929/write_3370_rule.py`), amendment `qa/calibrated_synthesis_20260929/3370_amendment_1.json` and manifest `qa/calibrated_synthesis_20260929/3370_nc_manifest.json` (writer `qa/calibrated_synthesis_20260929/write_3370_amendment_1.py`); node fits in `project_results/calibrated_synthesis_3370/fits/`. No pre-existing project file was modified (nothing snapshotted).