# Joint vaccine contrasts without duplicated outcome records

Secondary common-center analysis of existing Brazil and Sweden data. The fifteen-context heterogeneous primary is unchanged. This extension is post hoc; none of its variants is a new independent study.

The expanded model with product-deviation SD 0.35 gives **0.980 (0.648-1.480)**, with P(common center > 1.25) = 0.124. Its log-interval width changes by -0.01% relative to the existing common-effect model. The added information does not materially increase precision.

## What is combined

| Country | Jointly modeled contrasts | Unique outcome cells |
|---|---|---:|
| Brazil | Rotavirus; PCV10/MenC 2010 composite; maternal DTaP | 108 |
| Sweden, existing ages | PCV; hepatitis B; rotavirus | 756 |
| Sweden, expanded ages | Same three contrasts, ages 0-14 | 1,122 |

Each Sweden version replaces the other; they are never multiplied together. The complete expanded secondary contains 19 represented context-vaccine/schedule contrasts in the same 15 contexts and 14 likelihood blocks, with 5,499 original cells (366 more than the primary). Four additional contrasts are estimated jointly, not counted as four independent experiments. Brazil is a 2022 census cross-section; Sweden measures annual main-diagnosis specialist-care use, not autism incidence. The 2010 Brazil coverage average is a composite exposure proxy, not an observed joint-receipt probability.

## Synthesis results

| Replacement | Receipt assumption | Product-deviation SD | Shared-bias SD | Common-center ratio (95% CrI) | P(>1.25) |
|---|---|---:|---:|---:|---:|
| baseline | baseline | 0.00 | 0.15 | 0.964 (0.637-1.455) | 0.108 |
| baseline | baseline | 0.00 | 0.30 | 0.968 (0.531-1.763) | 0.202 |
| Brazil | independent | 0.00 | 0.15 | 0.975 (0.645-1.471) | 0.118 |
| Brazil | independent | 0.00 | 0.30 | 0.977 (0.536-1.780) | 0.211 |
| Brazil | independent | 0.35 | 0.15 | 0.975 (0.645-1.471) | 0.119 |
| Brazil | independent | 0.35 | 0.30 | 0.978 (0.536-1.780) | 0.211 |
| Brazil | independent | 0.70 | 0.15 | 0.975 (0.644-1.473) | 0.119 |
| Brazil | independent | 0.70 | 0.30 | 0.978 (0.536-1.782) | 0.211 |
| Brazil | nested | 0.00 | 0.15 | 0.975 (0.645-1.471) | 0.119 |
| Brazil | nested | 0.00 | 0.30 | 0.978 (0.537-1.780) | 0.211 |
| Sweden_existing | independent | 0.00 | 0.15 | 0.972 (0.643-1.466) | 0.115 |
| Sweden_existing | independent | 0.00 | 0.30 | 0.975 (0.535-1.775) | 0.208 |
| Sweden_existing | independent | 0.35 | 0.15 | 0.970 (0.641-1.464) | 0.114 |
| Sweden_existing | independent | 0.35 | 0.30 | 0.973 (0.534-1.772) | 0.207 |
| Sweden_existing | independent | 0.70 | 0.15 | 0.968 (0.639-1.463) | 0.113 |
| Sweden_existing | independent | 0.70 | 0.30 | 0.972 (0.533-1.770) | 0.205 |
| Sweden_existing | nested | 0.00 | 0.15 | 0.972 (0.642-1.466) | 0.115 |
| Sweden_existing | nested | 0.00 | 0.30 | 0.975 (0.535-1.775) | 0.208 |
| Sweden_expanded | independent | 0.00 | 0.15 | 0.968 (0.640-1.461) | 0.112 |
| Sweden_expanded | independent | 0.00 | 0.30 | 0.971 (0.533-1.769) | 0.205 |
| Sweden_expanded | independent | 0.35 | 0.15 | 0.970 (0.641-1.464) | 0.113 |
| Sweden_expanded | independent | 0.35 | 0.30 | 0.973 (0.534-1.772) | 0.206 |
| Sweden_expanded | independent | 0.70 | 0.15 | 0.968 (0.640-1.463) | 0.113 |
| Sweden_expanded | independent | 0.70 | 0.30 | 0.972 (0.533-1.771) | 0.205 |
| Sweden_expanded | nested | 0.00 | 0.15 | 0.968 (0.640-1.461) | 0.112 |
| Sweden_expanded | nested | 0.00 | 0.30 | 0.971 (0.533-1.769) | 0.205 |
| Both_existing | independent | 0.00 | 0.15 | 0.982 (0.650-1.482) | 0.125 |
| Both_existing | independent | 0.00 | 0.30 | 0.984 (0.540-1.792) | 0.217 |
| Both_existing | independent | 0.35 | 0.15 | 0.981 (0.648-1.480) | 0.124 |
| Both_existing | independent | 0.35 | 0.30 | 0.983 (0.539-1.790) | 0.216 |
| Both_existing | independent | 0.70 | 0.15 | 0.980 (0.647-1.481) | 0.124 |
| Both_existing | independent | 0.70 | 0.30 | 0.982 (0.538-1.790) | 0.215 |
| Both_existing | nested | 0.00 | 0.15 | 0.983 (0.650-1.482) | 0.126 |
| Both_existing | nested | 0.00 | 0.30 | 0.984 (0.540-1.792) | 0.217 |
| Both_expanded | independent | 0.00 | 0.15 | 0.979 (0.647-1.476) | 0.122 |
| Both_expanded | independent | 0.00 | 0.30 | 0.981 (0.538-1.786) | 0.214 |
| Both_expanded | independent | 0.35 | 0.15 | 0.980 (0.648-1.480) | 0.124 |
| Both_expanded | independent | 0.35 | 0.30 | 0.983 (0.539-1.789) | 0.216 |
| Both_expanded | independent | 0.70 | 0.15 | 0.980 (0.647-1.481) | 0.124 |
| Both_expanded | independent | 0.70 | 0.30 | 0.982 (0.538-1.790) | 0.215 |
| Both_expanded | nested | 0.00 | 0.15 | 0.979 (0.648-1.477) | 0.122 |
| Both_expanded | nested | 0.00 | 0.30 | 0.981 (0.539-1.787) | 0.214 |

![Joint country contrasts and synthesis](08_figures/3376_joint_country_synthesis.svg)

Intervals are conditional on the stated likelihood and bias model; the same data appear in all replacement and sensitivity rows. Marginal product estimates below do not include the synthesis-level country bias allowance.

## Country diagnostics

| Country | Diagnostic | Ratio (95% CrI) |
|---|---|---:|
| BRA | actual | 0.956 (0.813-1.137) |
| BRA | future_3y | 0.908 (0.799-1.040) |
| SWE756 | actual | 1.240 (0.959-1.566) |
| SWE756 | future_3y | 1.036 (0.837-1.259) |
| SWE1122 | actual | 1.130 (0.897-1.432) |
| SWE1122 | future_3y | 1.037 (0.858-1.246) |

All twelve future-shift specifications include one, but shifted and actual exposures can remain correlated; this is not a proof of a valid counterfactual. The noise-free injected ratios 1, 1.25, 1.5 and 2 are monotonically recovered under every kernel summary. Brazil recovers a null as 1.066 and an injected 2 as 2.203, showing imperfect absolute calibration despite directional recovery. Sweden recovers those endpoints as 1.007/2.012 for existing ages and 1.002/2.002 for expanded ages. These are not power estimates.

| Country | Product | Joint marginal ratio (95% CrI) |
|---|---|---:|
| BRA | BRA_RV_census_autism | 0.899 (0.560-1.555) |
| BRA | BRA_SCHED2010_census_autism | 1.294 (0.777-2.486) |
| BRA | BRA_MDTPA_census_autism | 0.762 (0.504-1.149) |
| SWE756 | SWE_F84_allages_corrected | 1.007 (0.765-1.614) |
| SWE756 | SWE_HEPB_F84_allages | 1.489 (0.980-2.138) |
| SWE756 | SWE_RV_F84_allages | 1.083 (0.558-1.859) |
| SWE1122 | SWE_F84_allages_corrected | 0.994 (0.771-1.290) |
| SWE1122 | SWE_HEPB_F84_allages | 1.297 (0.940-1.738) |
| SWE1122 | SWE_RV_F84_allages | 1.292 (0.844-1.906) |

## Prior sensitivity

These eight additional post hoc summaries hold product-deviation SD at 0.35 and use expanded Sweden. The prior scales are log-scale SDs, not prior interval endpoints. No scenario is selected for closeness to one.

| Prior | Shared-bias SD | Common-center ratio (95% CrI) | P(>1.25) |
|---|---:|---:|---:|
| neutral_log2 | 0.15 | 0.980 (0.648-1.480) | 0.124 |
| neutral_log2 | 0.30 | 0.983 (0.539-1.789) | 0.216 |
| concentrated_log1.25 | 0.15 | 0.989 (0.727-1.345) | 0.068 |
| concentrated_log1.25 | 0.30 | 0.994 (0.689-1.432) | 0.109 |
| wide_log4 | 0.15 | 0.979 (0.637-1.500) | 0.131 |
| wide_log4 | 0.30 | 0.980 (0.512-1.874) | 0.231 |
| harm_centered | 0.15 | 1.025 (0.701-1.498) | 0.153 |
| harm_centered | 0.30 | 1.065 (0.638-1.775) | 0.269 |

## Model and verification

Under independent receipt, the cell log-rate shift is the sum of log(1 - p_j + p_j exp(theta_j)). The alternative nested-receipt model shares a uniform receipt rank across products and is evaluated only for equal effects. These are sensitivity assumptions about unobserved co-receipt, not estimated biological interaction models. Within a country theta_j = a + b_country + d_j; the independent d_j deviations have SD 0, 0.35 or 0.70. A single country bias remains outside that integration. Integrating d_j and then b_country is a marginal likelihood for a, not multiplication of product posteriors. The original Germany/Sweden care bridge, other countries and core likelihood are retained.

Six trend/serial-dependence kernels and all existing coverage scenarios are averaged at likelihood level. Brazil uses seven synchronized scenarios; Sweden uses 24 joint scenarios. Product-deviation Gaussian convolution uses zero padding; truncated mass is not renormalized. The interval is for a represented common center, not each product, every subgroup, all disabilities or a per-dose cumulative effect.

The existing common-effect summary is reproduced with maximum error 1.57e-13; independent posterior replay differs by at most 0. Fine/wide grid changes are at most 1.44e-06, below the specified 0.005 tolerance. The six unit tests cover exact alignment, quadratic/direct whitening, receipt special cases, analytic Gaussian convolution, baseline reproduction and direct core-factor substitution. Minimum relevant local core ESS across the 42 scenarios is 178.2; the largest two-scramble difference in a reported estimate/probability is 0.003485. Neither diagnostic is a proof of numerical or causal certainty.

## Reproduction

Run `python -X utf8 07_analysis_code/3376_joint_country_synthesis.py --points 121 --extent 6`, then `--points 161 --extent 6 --diagnostics`, then `--points 201 --extent 7.5`; finish with `python -X utf8 processed/report_joint_country_3376.py`. Each command uses one process. The original-cell inputs, per-grid results, all diagnostics, frozen synthesis likelihood and hashes are under `project_results/joint_country_3376/`. The code requires the existing project synthesis inputs. The compact independent replay requires only NumPy and SciPy and the frozen synthesis NPZ.

No new independent data source or calibrated-hierarchy refit is claimed. Survey augmentation, published-cohort total-evidence models and a fully joint heterogeneous product hierarchy remain separate extensions; this analysis does not certify that every possible synthesis has been exhausted.