{"data":{"deterministic":true,"status":"OK","verdict":"SIMPSONS_REVERSAL","verdictRule":"R4 crude and adjusted effects have opposite signs","confidence":"medium","reasons":[],"claim":"Treatment B causes a higher recovery rate than treatment A.","claimEvaluation":{"direction":"positive","alpha":0.05,"reversalSignificant":false,"crudeSupportsClaim":false,"adjustedSupportsClaim":false,"materialConfounding":true,"changeInEstimateThreshold":0.1},"data":{"rows":74,"completeRows":74,"dropped":0,"treatment":{"name":"treatment","treated":"B","control":"A","nTreated":35,"nControl":39},"outcome":{"name":"success","type":"binary","successValue":"1","failureValue":"0"},"discretization":[]},"dag":{"source":"caller","isAssumption":false,"edges":[{"from":"stone_size","to":"treatment","basis":"caller"},{"from":"stone_size","to":"success","basis":"caller"},{"from":"treatment","to":"success","basis":"caller"}],"unobserved":[],"treatmentOutcomeEdge":true},"identification":{"method":"backdoor","minimalAdjustmentSets":[["stone_size"]],"minimalSetsTruncated":false,"primaryAdjustmentSet":["stone_size"],"frontDoorSets":[],"doNotAdjust":[],"explanation":"The backdoor criterion is satisfied by the primary adjustment set."},"effects":{"scale":"risk_difference","crude":{"meanTreated":0.8285714285714286,"meanControl":0.7948717948717948,"difference":0.0336996336996338,"riskRatio":1.0423963133640555,"oddsRatio":1.2473118279569901,"ci":{"effect":{"lower":-0.15543238488193475,"upper":0.21458333333333296,"valid":500},"riskRatio":{"lower":0.8256048387096775,"upper":1.3036412808172329,"valid":500},"oddsRatio":{"lower":0.33536036036036027,"upper":4.343075684380033,"valid":499}}},"adjusted":{"method":"backdoor","adjustmentSet":["stone_size"],"meanTreated":0.7676426426426427,"meanControl":0.8347193347193347,"difference":-0.06707669207669198,"riskRatio":0.9196416216964163,"oddsRatio":0.6541603880440275,"ci":{"effect":{"lower":-0.26583599671099667,"upper":0.12370126744391434,"valid":500},"riskRatio":{"lower":0.709682667045244,"upper":1.1584163063133892,"valid":500},"oddsRatio":{"lower":0.17212094283328297,"upper":2.7945809276345326,"valid":499}},"positivity":{"supportedRows":74,"unsupportedRows":0,"unsupportedMass":0,"emptyStrata":0,"nearEmptyStrata":0,"minArm":5,"unsupportedMassLimit":0.2}},"bootstrap":{"reps":500,"level":0.95,"status":"OK"},"setAgreement":{"sets":[{"set":["stone_size"],"effect":-0.06707669207669198}],"maxSpread":0}},"tests":{"crude":{"permutation":{"method":"monte_carlo","statistic":0.0336996336996338,"assignments":null,"samples":20000,"pTwoSided":0.7778611069446527,"pOneSided":0.4728263586820659,"mcStdError":0.0029393299002280454,"strataUsed":1},"fisherExact":{"pGreater":0.47267506624589894,"pLess":0.7463212739620166,"pTwoSided":0.7731823619275421,"pObserved":0.21899634020790168}},"adjusted":{"permutation":{"method":"monte_carlo","statistic":-0.06707669207669212,"assignments":null,"samples":20000,"pTwoSided":0.6453677316134193,"pOneSided":0.3158842057897105,"mcStdError":0.0033828111283780602,"strataUsed":2},"mantelHaenszelTest":{"chiSquare":0.09433718535588109,"pValue":0.7587340795279857}}},"stratification":{"byCovariate":[{"covariate":"stone_size","strata":[{"stratum":"stone_size=large","n":34,"nTreated":8,"nControl":26,"support":"ok","sign":-1,"oppositeToCrude":true,"meanTreated":0.625,"meanControl":0.7307692307692307,"difference":-0.10576923076923073,"riskRatio":0.855263157894737,"oddsRatio":0.6140350877192985},{"stratum":"stone_size=small","n":40,"nTreated":27,"nControl":13,"support":"ok","sign":-1,"oppositeToCrude":true,"meanTreated":0.8888888888888888,"meanControl":0.9230769230769231,"difference":-0.03418803418803429,"riskRatio":0.9629629629629629,"oddsRatio":0.6666666666666659}],"strataTruncated":false,"standardized":{"supportedRows":74,"unsupportedRows":0,"unsupportedMass":0,"emptyStrata":0,"nearEmptyStrata":0,"meanTreated":0.7676426426426427,"meanControl":0.8347193347193347,"difference":-0.06707669207669198,"riskRatio":0.9196416216964163,"oddsRatio":0.6541603880440275},"mantelHaenszel":{"oddsRatio":0.6324200913242009,"riskRatio":0.9246607393542349,"riskDifference":-0.0635923768144564,"chiSquare":0.09433718535588109,"pValue":0.7587340795279857}}],"adjustmentSet":{"by":["stone_size"],"strataCount":2,"strata":[{"stratum":"stone_size=large","n":34,"nTreated":8,"nControl":26,"support":"ok","sign":-1,"oppositeToCrude":true,"meanTreated":0.625,"meanControl":0.7307692307692307,"difference":-0.10576923076923073,"riskRatio":0.855263157894737,"oddsRatio":0.6140350877192985},{"stratum":"stone_size=small","n":40,"nTreated":27,"nControl":13,"support":"ok","sign":-1,"oppositeToCrude":true,"meanTreated":0.8888888888888888,"meanControl":0.9230769230769231,"difference":-0.03418803418803429,"riskRatio":0.9629629629629629,"oddsRatio":0.6666666666666659}],"strataTruncated":false,"mantelHaenszel":{"oddsRatio":0.6324200913242009,"riskRatio":0.9246607393542349,"riskDifference":-0.0635923768144564,"chiSquare":0.09433718535588109,"pValue":0.7587340795279857}}},"simpson":{"detected":true,"crudeVsAdjustedReversal":true,"byCovariate":[{"covariate":"stone_size","reversedVsStandardized":true,"allStrataOpposite":true,"strataWithOppositeSign":2,"comparableStrata":2,"standardizedEffect":-0.06707669207669198,"role":"in_adjustment_set"}],"resolution":"adjust_for_valid_set","note":"The crude and the backdoor-adjusted estimate have opposite signs; under the DAG the adjusted one estimates the causal effect."},"dagCheck":{"method":"PC-stable skeleton with G-tests, v-structures and Meek rules R1-R3","status":"OK","alpha":0.01,"tests":4,"edges":[{"a":"treatment","b":"stone_size","orientation":"a-b"}],"vStructures":[],"conflicts":[{"kind":"DAG_IMPLIES_DEPENDENCE_DATA_LACKS","variables":["stone_size","success"],"given":[],"severity":"weak","detail":"stone_size and success are independent given {} in the data, but the DAG leaves them d-connected"},{"kind":"DAG_IMPLIES_DEPENDENCE_DATA_LACKS","variables":["success","treatment"],"given":[],"severity":"weak","detail":"success and treatment are independent given {} in the data, but the DAG leaves them d-connected"}],"strongConflicts":0,"consistent":true},"caveats":["2 weak DAG/data conflicts (the data show no dependence where the DAG draws one, or orient edges against it); low power or cancellation can explain them","the crude and adjusted effects have opposite signs but neither is distinguishable from zero at the chosen alpha"],"assumptions":["The DAG was supplied by the caller and is taken as true.","No unobserved confounders other than those drawn in the DAG.","Consistency and no interference between rows; positivity within the adjustment strata (checked above).","Numeric covariates are discretized into deterministic quantile bins, so confounding within a bin is not removed."],"report":{"summary":"Verdict SIMPSONS_REVERSAL with medium confidence. The unadjusted and adjusted effects have opposite signs (Simpson's paradox); under the assumed DAG the adjusted estimate is the causal one.","findings":["Unadjusted risk difference for treatment on success is 0.034 (95% bootstrap interval -0.155 to 0.215; permutation p = 0.778).","After backdoor adjustment for {stone_size} the risk difference is -0.067 (95% bootstrap interval -0.266 to 0.124; permutation p = 0.645).","The crude and the backdoor-adjusted estimate have opposite signs; under the DAG the adjusted one estimates the causal effect.","2 weak conflicts between the assumed DAG and the independences in the data."],"caveats":["The DAG was supplied by the caller and is taken as true.","No unobserved confounders other than those drawn in the DAG.","Consistency and no interference between rows; positivity within the adjustment strata (checked above).","Numeric covariates are discretized into deterministic quantile bins, so confounding within a bin is not removed.","2 weak DAG/data conflicts (the data show no dependence where the DAG draws one, or orient edges against it); low power or cancellation can explain them","the crude and adjusted effects have opposite signs but neither is distinguishable from zero at the chosen alpha"],"source":"template"},"translation":null,"audit":{"solver":{"name":"causalReferee","version":"1.0.0"},"inputHash":"0xe755e6914972356ad13ec56f46f41cf1bf84107f7ce81c2d68eec6d5bc5ab1ef","seed":3881166481,"llmCalls":0,"budgets":{"rows":{"used":74,"max":20000},"covariates":{"used":1,"max":12},"bootstrap":{"reps":500,"work":37000,"maxWork":40000000},"permutation":{"exactCap":1000000,"monteCarloSamples":20000,"maxWork":100000000},"pc":{"maxConditioningSet":3,"stepBudget":80000000}},"thresholds":{"alpha":0.05,"unsupportedMassMax":0.2,"changeInEstimate":0.1,"positivityMinArm":5,"minRows":30,"minArm":5}}},"_provenance":{"version":"writerslogic-provenance/1","issuer":"did:web:agents.writerslogic.com","verify":{"endpoint":"POST /api/v1/verify-provenance","did":"did:web:agents.writerslogic.com"},"manifest":{"format":"application/json","instance_id":"xmp:iid:45bebc13-3c03-4b0f-ade7-5d5eb0769d1e","claim_generator_info":[{"name":"WritersLogic x402 Agent Hub","version":"2.0.0"}],"title":"Causal Claim Referee","assertions":[{"label":"c2pa.actions.v2","data":{"actions":[{"action":"c2pa.created","when":"2026-11-04T20:39:35.960Z","softwareAgent":{"name":"writerslogic-agent-hub/causalReferee","version":"2.0.0"},"digitalSourceType":"http://cv.iptc.org/newscodes/digitalsourcetype/algorithmicMedia","parameters":{"endpoint":"POST /api/v1/prove-causality","inputDigest":{"alg":"sha256","hash":"e755e6914972356ad13ec56f46f41cf1bf84107f7ce81c2d68eec6d5bc5ab1ef","canonicalization":"JCS"}}}]}},{"label":"c2pa.hash.data","data":{"alg":"sha256","hash":"ac17728cb56b044311afa5f2eefd8ab58c4a71909e21d5b30b81e5c7f3c48fc5","name":"jcs-canonical-json(data)"}}]},"credential":{"@context":["https://www.w3.org/ns/credentials/v2"],"id":"urn:uuid:f68d8860-9019-4163-b586-e28ae50d7cdc","type":["VerifiableCredential","AgentOutputCredential"],"issuer":"did:web:agents.writerslogic.com","validFrom":"2026-11-04T20:39:35.960Z","credentialSubject":{"id":"urn:sha256:ac17728cb56b044311afa5f2eefd8ab58c4a71909e21d5b30b81e5c7f3c48fc5","agent":"causalReferee","endpoint":"POST /api/v1/prove-causality","outputDigest":{"alg":"sha256","value":"ac17728cb56b044311afa5f2eefd8ab58c4a71909e21d5b30b81e5c7f3c48fc5","canonicalization":"JCS"},"inputDigest":{"alg":"sha256","value":"e755e6914972356ad13ec56f46f41cf1bf84107f7ce81c2d68eec6d5bc5ab1ef","canonicalization":"JCS"},"manifestDigest":{"alg":"sha256","value":"a5802ba139c595c737beea4470f3848e072986dae173900f89c17e79d37ff970","canonicalization":"JCS"},"ingredients":[],"payment":{"scheme":"api-key","network":"eip155:8453","payer":"sample"}},"proof":{"type":"DataIntegrityProof","cryptosuite":"eddsa-jcs-2022","created":"2026-11-04T20:39:35.960Z","verificationMethod":"did:web:agents.writerslogic.com#key-1","proofPurpose":"assertionMethod","proofValue":"z61HhN25jHS2s4CSCEAQYyWUpGgNVkpvFzkainxcVgkiUcn9Q7cD5wi3rjbQGQicXFCQVNmsgkJJXsz2ZKBa4Jfjo"}},"ethSignature":{"type":"EIP-191","signer":"did:pkh:eip155:8453:0x3DBd42560cA7a7E448A2c7DfC9E785526189411f","address":"0x3DBd42560cA7a7E448A2c7DfC9E785526189411f","message":"writerslogic-provenance:d70bf791623953e76009c85817a4df8dc39b36ab59ae50c9c08d732ee5ff93eb","signature":"0xc04cb74c49e6fc52271ac1f74d8b4e2082434e591d1238aba7f5df99389d368c76419362679e86b9007676cc812ad68ee207035ac3a6be9d651b50c27b1e9b281b"}}}