{
 "title": "ROBUSTNESS_A5: A5 robustness battery for the per-child relative-risk conversion",
 "generated_by": "07_analysis_code/9710_a5_battery.py (9700-9703)",
 "version_label": "work_v5c_v5e",
 "date": "2026-10-15",
 "root": "E:\\MigratedFromC\\C\\Users\\14787\\Documents\\Research\\Miscellaneous\\Substack\\Codex\\vaccine_autism_event_study\\qa\\claude_summative_20261008\\work_v5c_v5e",
 "spec": "scaled | linear | w66 | all; RE by country tau 0.33; declared allowance = RE + 0.15^2 (A5 battery)",
 "headline_replication_max_abs_diff": 0.0,
 "loader": "9500 driver",
 "interpretation": {
  "rule": "per-child label supported if P1-P4 allowance intervals overlap the headline, M1 intercept CI includes 0, M2 Q p > 0.05, no O3 exclusion leaves the headline allowance interval",
  "supported": false,
  "n_pass": 6,
  "n_total": 7,
  "failing": [
   "m1"
  ],
  "criteria": [
   {
    "key": "p1",
    "criterion": "P1 measured-p and modeled-p stacks: allowance intervals overlap the headline",
    "verdict": "PASS",
    "numbers": "measured 0.934 (0.629 to 1.387); modeled 0.967 (0.684 to 1.366); headline allowance 0.699 to 1.354"
   },
   {
    "key": "p2",
    "criterion": "P2 excluding stacks on modeled pre-programme zeros (a and b): allowance intervals overlap",
    "verdict": "PASS",
    "numbers": "P2a 0.894 (0.613 to 1.303); P2b 0.851 (0.514 to 1.409)"
   },
   {
    "key": "p3",
    "criterion": "P3 excluding national-broadcast-only countries: allowance interval overlaps",
    "verdict": "PASS",
    "numbers": "0.993 (0.698 to 1.412) (18 countries)"
   },
   {
    "key": "p4",
    "criterion": "P4 large-jump stacks (dp >= 0.30): allowance interval overlaps",
    "verdict": "PASS",
    "numbers": "0.984 (0.706 to 1.371)"
   },
   {
    "key": "m1",
    "criterion": "M1 intercept CI includes 0 (REML random country intercept)",
    "verdict": "FAIL",
    "numbers": "intercept +0.1802 (95% CI +0.0961 to +0.2644); slope -0.2032; implied r 0.797; country-cluster robust CI +0.0678 to +0.2927; nested country+event RE CI +0.0228 to +0.1744; random-slope CI -0.0153 to +0.2057"
   },
   {
    "key": "m2",
    "criterion": "M2 tertile estimates agree (Cochran Q p > 0.05)",
    "verdict": "PASS",
    "numbers": "T1 0.895, T2 0.910, T3 0.982; Q 0.40 on 2 df, p 0.819"
   },
   {
    "key": "o3",
    "criterion": "O3 no leave-out moves the RR outside the headline allowance interval",
    "verdict": "PASS",
    "numbers": "dropped BRA, USA, GBR, PER, KOR; RR range 0.970 to 0.977; largest move: drop USA -> 0.977"
   }
  ]
 },
 "headline_interval_type": "random_effects",
 "headline_interval": {
  "lo": 0.836147,
  "hi": 1.131335
 },
 "sensitivity_interval": {
  "type": "declared_allowance",
  "lo": 0.69882,
  "hi": 1.353656
 },
 "verdict_re_basis": {
  "criteria": [
   {
    "key": "p1",
    "verdict": "PASS"
   },
   {
    "key": "p2",
    "verdict": "PASS"
   },
   {
    "key": "p3",
    "verdict": "PASS"
   },
   {
    "key": "p4",
    "verdict": "PASS"
   },
   {
    "key": "m1",
    "verdict": "FAIL"
   },
   {
    "key": "m2",
    "verdict": "PASS"
   },
   {
    "key": "o3",
    "verdict": "PASS"
   }
  ],
  "n_pass": 6,
  "n_total": 7,
  "failing": [
   "m1"
  ],
  "same_as_declared": true,
  "note": "P1-P4: subset RE interval overlaps the headline RE interval; O3: leave-out RR inside the headline RE interval; M1 and M2 unchanged"
 },
 "summary": "The work_v5c_v5e headline per-child relative risk is 0.973 (random-effects 95% CI 0.836 to 1.131; the declared-allowance interval, a labelled sensitivity, is 0.699 to 1.354), and 6 of the 7 declared checks pass. The estimate stays in line with the headline when using only measured or only modeled uptake paths, dropping stacks that rest on modeled pre-programme zeros, keeping only countries whose uptake varies within the country, using only large uptake jumps, splitting stacks into thirds by size of uptake jump, and leaving out Brazil, the United States or any of the highest-weight countries. The per-child label is not fully supported by the rule fixed in the entry because the dose-response check fails; this goes into the limitations. In that check the mixture model predicts that stack-level raw steps scale with the uptake jump and are zero when the jump is zero; the fit gives an intercept of +0.180 (95% CI +0.096 to +0.264) and a slope implying r = 0.80, against a pooled per-child estimate of 0.97. (Post hoc: dropping coverage-collapse lead events leaves the intercept at +0.147 (+0.062 to +0.232).) (Post hoc: the slope is not stable to how stack dependence is modelled. With lead events as a second random effect the implied r is 0.96 (0.92 to 0.99) and with country-specific slopes 0.95 (0.79 to 1.12); both intervals include the headline 0.973. The intercept stays positive in the nested model (+0.099, +0.023 to +0.174) and includes 0 only with random slopes.) Across the pooled subsets (measured against modeled paths, pre-zero exclusions, subnational countries, large jumps, outcome systems) the per-child estimates range from 0.82 to 1.11, all with intervals that include 1; the planted x1.25 effect is recovered with attenuation that differs by stratum (see the G table).",
 "a5": {
  "headline": {
   "ok": true,
   "rr": 0.972606,
   "lo": 0.69882,
   "hi": 1.353656,
   "re_lo": 0.836147,
   "re_hi": 1.131335,
   "k_eff": 26.036357,
   "n_countries": 40,
   "n_stacks": 39753,
   "interval_type": "random_effects"
  },
  "p1": {
   "measured": {
    "ok": true,
    "rr": 0.934276,
    "lo": 0.629161,
    "hi": 1.387359,
    "re_lo": 0.717227,
    "re_hi": 1.217009,
    "k_eff": 8.750872,
    "n_countries": 14,
    "n_stacks": 8355
   },
   "modeled": {
    "ok": true,
    "rr": 0.966848,
    "lo": 0.684491,
    "hi": 1.365678,
    "re_lo": 0.806586,
    "re_hi": 1.158952,
    "k_eff": 20.929465,
    "n_countries": 37,
    "n_stacks": 15055
   },
   "mixed": {
    "ok": true,
    "rr": 0.962776,
    "lo": 0.670021,
    "hi": 1.383445,
    "re_lo": 0.778783,
    "re_hi": 1.190239,
    "k_eff": 12.595297,
    "n_countries": 16,
    "n_stacks": 16343
   },
   "q_declared": {
    "Q": 0.043910070467349495,
    "df": 1,
    "p": 0.8340210156895618,
    "I2": 0.0,
    "n_strata": 2
   },
   "q_all3": {
    "Q": 0.04649814249401851,
    "df": 2,
    "p": 0.977019106098237,
    "I2": 0.0,
    "n_strata": 3
   },
   "n_stacks_class": {
    "measured": 8355,
    "modeled": 15055,
    "mixed": 16343
   }
  },
  "p2": {
   "a_unflagged": {
    "ok": true,
    "rr": 0.894079,
    "lo": 0.613295,
    "hi": 1.303414,
    "re_lo": 0.706184,
    "re_hi": 1.131967,
    "k_eff": 13.178411,
    "n_countries": 25,
    "n_stacks": 17247
   },
   "a_flagged": {
    "ok": true,
    "rr": 0.965979,
    "lo": 0.688856,
    "hi": 1.354585,
    "re_lo": 0.817421,
    "re_hi": 1.141535,
    "k_eff": 21.76242,
    "n_countries": 35,
    "n_stacks": 22503
   },
   "b_unflagged": {
    "ok": true,
    "rr": 0.851306,
    "lo": 0.514473,
    "hi": 1.408667,
    "re_lo": 0.565585,
    "re_hi": 1.281366,
    "k_eff": 4.554726,
    "n_countries": 8,
    "n_stacks": 3864
   },
   "b_flagged": {
    "ok": true,
    "rr": 0.973003,
    "lo": 0.699008,
    "hi": 1.354398,
    "re_lo": 0.836233,
    "re_hi": 1.132143,
    "k_eff": 26.03894,
    "n_countries": 40,
    "n_stacks": 35889
   },
   "n_flagged": {
    "a": 22503,
    "b": 35889
   },
   "n_pooled": 39753
  },
  "p3": {
   "subnational": {
    "ok": true,
    "rr": 0.992717,
    "lo": 0.698177,
    "hi": 1.411515,
    "re_lo": 0.818048,
    "re_hi": 1.204683,
    "k_eff": 14.866752,
    "n_countries": 18,
    "n_stacks": 39532
   },
   "national_only": {
    "ok": true,
    "rr": 0.941936,
    "lo": 0.643592,
    "hi": 1.378582,
    "re_lo": 0.73937,
    "re_hi": 1.2,
    "k_eff": 11.371157,
    "n_countries": 22,
    "n_stacks": 221
   },
   "drop_broadcast": {
    "ok": true,
    "rr": 0.985106,
    "lo": 0.705862,
    "hi": 1.374821,
    "re_lo": 0.841903,
    "re_hi": 1.152667,
    "k_eff": 24.055131,
    "n_countries": 38,
    "n_stacks": 39720
   },
   "subnational_countries": [
    "ARG",
    "AUS",
    "BEL",
    "BRA",
    "CAN",
    "COL",
    "CZE",
    "DEU",
    "FIN",
    "FRA",
    "GBR",
    "JPN",
    "KOR",
    "NOR",
    "POL",
    "SWE",
    "TWN",
    "USA"
   ],
   "national_only_countries": [
    "BGD",
    "CHL",
    "DNK",
    "ECU",
    "EST",
    "FSM",
    "GRC",
    "HKG",
    "HUN",
    "IND",
    "ISR",
    "LVA",
    "MEX",
    "MHL",
    "NLD",
    "NZL",
    "PER",
    "PLW",
    "SVK",
    "SVN",
    "TZA",
    "UKR"
   ],
   "broadcast_labelled_countries": [
    "ECU",
    "MEX"
   ]
  },
  "p4": {
   "dp_ge_030": {
    "ok": true,
    "rr": 0.983578,
    "lo": 0.705681,
    "hi": 1.37091,
    "re_lo": 0.842928,
    "re_hi": 1.147697,
    "k_eff": 25.081991,
    "n_countries": 38,
    "n_stacks": 20514
   },
   "dp_lt_030": {
    "ok": true,
    "rr": 0.920963,
    "lo": 0.618999,
    "hi": 1.370232,
    "re_lo": 0.704973,
    "re_hi": 1.203126,
    "k_eff": 9.494654,
    "n_countries": 22,
    "n_stacks": 19177
   },
   "absdp_ge_030": {
    "ok": true,
    "rr": 0.981811,
    "lo": 0.704368,
    "hi": 1.368537,
    "re_lo": 0.841297,
    "re_hi": 1.145795,
    "k_eff": 25.07142,
    "n_countries": 38,
    "n_stacks": 21033
   },
   "n_dp_ge_030": 20515
  },
  "p5": {
   "k0p70": {
    "k": 0.7,
    "rr": 0.9610966612706386,
    "lo": 0.5993288415872087,
    "hi": 1.541235342286059,
    "re_lo": 0.7744176658842059,
    "re_hi": 1.1927759825195996
   },
   "k0p85": {
    "k": 0.85,
    "rr": 0.9678502668042976,
    "lo": 0.6559953103731041,
    "hi": 1.427958590771591,
    "re_lo": 0.8101545102922272,
    "re_hi": 1.1562413429202103
   },
   "k1p15": {
    "k": 1.15,
    "rr": 0.9761361341137226,
    "lo": 0.7322607572855824,
    "hi": 1.3012328502411803,
    "re_lo": 0.8558934804917158,
    "re_hi": 1.1132714222511315
   },
   "k1p30": {
    "k": 1.3,
    "rr": 0.9788603320213672,
    "lo": 0.7590689898188572,
    "hi": 1.2622931017556607,
    "re_lo": 0.8713997742657277,
    "re_hi": 1.0995728687356698
   },
   "rr_min": 0.9610966612706386,
   "rr_max": 0.9788603320213672,
   "lo_min": 0.5993288415872087,
   "hi_max": 1.541235342286059
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  "m1": {
   "n_stacks": 36117,
   "n_countries": 40,
   "intercept": 0.18024895383257786,
   "lo": 0.09612594409496635,
   "hi": 0.2643719635701894,
   "se": 0.04292069160513309,
   "p": 2.6740845394266853e-05,
   "slope": -0.20316153567216133,
   "slope_lo": -0.21283201978029292,
   "slope_hi": -0.19349105156402974,
   "slope_se": 0.004934011126944753,
   "implied_r": 0.7968384643278387,
   "implied_r_lo": 0.7871679802197071,
   "implied_r_hi": 0.8065089484359702,
   "tau_u": 0.24755788166641915,
   "intercept_includes_0": false,
   "robust": {
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    "lo": 0.06778206890243788,
    "hi": 0.29271583876271784,
    "slope": -0.20316153567216133,
    "slope_lo": -0.329196410290004,
    "slope_hi": -0.07712666105431865,
    "implied_r": 0.7968384643278387,
    "implied_r_lo": 0.670803589709996,
    "implied_r_hi": 0.9228733389456814,
    "intercept_includes_0": false
   },
   "nested_event": {
    "intercept": 0.09859342931138906,
    "lo": 0.02275227209313259,
    "hi": 0.17443458652964555,
    "slope": -0.04078669292753587,
    "slope_lo": -0.07583953480844875,
    "slope_hi": -0.005733851046622981,
    "implied_r": 0.9592133070724641,
    "tau_country": 0.1953406524960629,
    "tau_event": 0.179544774090985,
    "n_events": 397,
    "intercept_includes_0": false
   },
   "ml_comparison": {
    "LR": 14.338228377862833,
    "p": 0.00015273166978493753,
    "aic_with": 108211.61837484938,
    "aic_without": 108223.95660322724,
    "delta_aic_without_minus_with": 12.338228377862833,
    "intercept_model_fits_better": true,
    "implied_r_without_intercept": 0.7976628280761023
   },
   "exact_link": {
    "implied_r": 0.8134222128555927,
    "implied_r_lo": 0.8050718958968147,
    "implied_r_hi": 0.8218134527894297,
    "intercept": 0.17871270829343452,
    "lo": 0.09651387389401228,
    "hi": 0.26091154269285677
   },
   "random_slope": {
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    "lo": -0.015300811860108593,
    "hi": 0.20572615862779517,
    "slope": -0.047673788174229244,
    "slope_lo": -0.21459761645670822,
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    "implied_r": 0.9523262118257707,
    "implied_r_lo": 0.7854023835432917,
    "implied_r_hi": 1.1192500401082497,
    "tau_slope": 0.42990503462811097,
    "intercept_includes_0": true
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   "tau_fixed": {
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    "lo": 0.08345793697286799,
    "hi": 0.1860583663753075,
    "slope": -0.20294327702000037,
    "implied_r": 0.7970567229799996
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   "without_brazil": {
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    "hi": 0.2120745130353135,
    "slope": -0.1052911620618015,
    "implied_r": 0.8947088379381984,
    "n_stacks": 5857,
    "intercept_includes_0": false
   },
   "posthoc": {
    "no_coverage_collapse_leaders": {
     "intercept": 0.14675403135107176,
     "lo": 0.06179240434611159,
     "hi": 0.23171565835603192,
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     "n_stacks": 30732,
     "intercept_includes_0": false
    },
    "no_withdrawal_type_leaders": {
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     "lo": 0.05368266426575405,
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     "slope": -0.13003690641819926,
     "implied_r": 0.8699630935818008,
     "n_stacks": 30649,
     "intercept_includes_0": false
    },
    "dp_positive_only": {
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     "lo": 0.07913453329320642,
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     "slope": -0.16295369125876558,
     "implied_r": 0.8370463087412344,
     "n_stacks": 28238,
     "intercept_includes_0": false
    }
   }
  },
  "m2": {
   "t1": {
    "ok": true,
    "rr": 0.894708,
    "lo": 0.563278,
    "hi": 1.42115,
    "re_lo": 0.625889,
    "re_hi": 1.278985,
    "k_eff": 6.109086,
    "n_countries": 15,
    "n_stacks": 15069
   },
   "t2": {
    "ok": true,
    "rr": 0.909901,
    "lo": 0.619765,
    "hi": 1.335862,
    "re_lo": 0.710745,
    "re_hi": 1.164863,
    "k_eff": 11.856999,
    "n_countries": 23,
    "n_stacks": 11368
   },
   "t3": {
    "ok": true,
    "rr": 0.982316,
    "lo": 0.70432,
    "hi": 1.370037,
    "re_lo": 0.840679,
    "re_hi": 1.147815,
    "k_eff": 24.531009,
    "n_countries": 37,
    "n_stacks": 13246
   },
   "Q": 0.40014280167045113,
   "df": 2,
   "p": 0.8186722971053146,
   "I2": 0.0,
   "n_strata": 3,
   "cuts": [
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   "n_stacks": {
    "T1": 15134,
    "T2": 11369,
    "T3": 13250
   },
   "balanced": {
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     "ok": true,
     "rr": 0.913283,
     "lo": 0.624283,
     "hi": 1.336071,
     "re_lo": 0.717365,
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     "n_stacks": 24194
    },
    "t2": {
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     "n_countries": 33,
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    },
    "t3": {
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     "n_countries": 29,
     "n_stacks": 7090
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    "n_strata": 3,
    "cuts": [
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   }
  },
  "m3": {
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    "exact_rr": 0.9725231166729253,
    "exact_at_loglinear": {
     "0.8": 0.7950874092036194,
     "1.25": 1.2439454699784471,
     "1.5": 1.4779774300511601
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    "exact_re_lo": 0.8329297768478997,
    "exact_re_hi": 1.1295750132535596,
    "exact_lo": 0.6867663621157778,
    "exact_hi": 1.342031746290166,
    "diff_log": -8.522969919770237e-05,
    "weight_share_used": 0.9923963032995065,
    "weighted_mean_dp": 0.6501433890343667,
    "n_stacks": 39753,
    "n_countries": 40
   },
   "p1_measured": {
    "loglinear_rr": 0.9342758854026489,
    "exact_rr": 0.9335904646252914,
    "exact_at_loglinear": {
     "0.8": 0.793144896290176,
     "1.25": 1.2414204354268792,
     "1.5": 1.4687262041587823
    },
    "exact_re_lo": 0.7027426571073009,
    "exact_re_hi": 1.2104570551212321,
    "exact_lo": 0.6023859181845479,
    "exact_hi": 1.3678218024634614,
    "diff_log": -0.0007339077639172825,
    "weight_share_used": 0.9968938454326371,
    "weighted_mean_dp": 0.6583084539584947,
    "n_stacks": 8355,
    "n_countries": 14
   },
   "p1_modeled": {
    "loglinear_rr": 0.9668478643944959,
    "exact_rr": 0.9667098643175572,
    "exact_at_loglinear": {
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     "1.5": 1.4752954737173951
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    "exact_re_lo": 0.8013709743641366,
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   "overall": "NOT FULLY SUPPORTED",
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 },
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