{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:OJ6GN5ZXJ6EGQIC5YLWJCZPTIB","short_pith_number":"pith:OJ6GN5ZX","canonical_record":{"source":{"id":"1111.1210","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-11-04T18:48:43Z","cross_cats_sorted":["stat.AP"],"title_canon_sha256":"822209d36873022250cae1555779cd9f0e56b14cc554759c6d835c815624b919","abstract_canon_sha256":"7ec552cde06c7b17870645891a16ace1c38c24e8caec3e070f27e0428733b472"},"schema_version":"1.0"},"canonical_sha256":"727c66f7374f8868205dc2ec9165f340620e2958e06feec45ee5ec64002e2f53","source":{"kind":"arxiv","id":"1111.1210","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1210","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1210v3","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1210","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"pith_short_12","alias_value":"OJ6GN5ZXJ6EG","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OJ6GN5ZXJ6EGQIC5","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OJ6GN5ZX","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:OJ6GN5ZXJ6EGQIC5YLWJCZPTIB","target":"record","payload":{"canonical_record":{"source":{"id":"1111.1210","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-11-04T18:48:43Z","cross_cats_sorted":["stat.AP"],"title_canon_sha256":"822209d36873022250cae1555779cd9f0e56b14cc554759c6d835c815624b919","abstract_canon_sha256":"7ec552cde06c7b17870645891a16ace1c38c24e8caec3e070f27e0428733b472"},"schema_version":"1.0"},"canonical_sha256":"727c66f7374f8868205dc2ec9165f340620e2958e06feec45ee5ec64002e2f53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:21.851429Z","signature_b64":"6eiVT1PjSf3sqsovVcGECifHRLE9yT3a0K8dIlpcdS/+ZIZNrljPR6ESUti4ndLfYfZOKCpXmql5eVuJ8rzVCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"727c66f7374f8868205dc2ec9165f340620e2958e06feec45ee5ec64002e2f53","last_reissued_at":"2026-05-18T02:54:21.851007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:21.851007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.1210","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CcC4ipVPYFgTHj//S6ZoJ8WimcBWOwakskjgS1OI2UFY5H9DtMi7wBDzo7QO5bV8+QeaCNHxMjEQVZ0al3lFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:15:35.269414Z"},"content_sha256":"e25c4052692ead41122244a9dd2d1b7e86800f8557c58aed3cf86234e7b38214","schema_version":"1.0","event_id":"sha256:e25c4052692ead41122244a9dd2d1b7e86800f8557c58aed3cf86234e7b38214"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:OJ6GN5ZXJ6EGQIC5YLWJCZPTIB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bayesian methods for genetic association analysis with heterogeneous subgroups: From meta-analyses to gene-environment interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.AP"],"primary_cat":"stat.ME","authors_text":"Matthew Stephens, Xiaoquan Wen","submitted_at":"2011-11-04T18:48:43Z","abstract_excerpt":"Genetic association analyses often involve data from multiple potentially-heterogeneous subgroups. The expected amount of heterogeneity can vary from modest (e.g., a typical meta-analysis) to large (e.g., a strong gene--environment interaction). However, existing statistical tools are limited in their ability to address such heterogeneity. Indeed, most genetic association meta-analyses use a \"fixed effects\" analysis, which assumes no heterogeneity. Here we develop and apply Bayesian association methods to address this problem. These methods are easy to apply (in the simplest case, requiring on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1210","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L4WqeajvZu8eresJrljQlBkphnKjDeYqRiH19Kfvqpu/Kztf2R8GppAX0DCFPKbncMycHahFqb279pltTyGXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:15:35.269780Z"},"content_sha256":"b24571a29f0daf555f4cb78d31c6cca16885746a6aedbd4c3c2eeadad4f38657","schema_version":"1.0","event_id":"sha256:b24571a29f0daf555f4cb78d31c6cca16885746a6aedbd4c3c2eeadad4f38657"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OJ6GN5ZXJ6EGQIC5YLWJCZPTIB/bundle.json","state_url":"https://pith.science/pith/OJ6GN5ZXJ6EGQIC5YLWJCZPTIB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OJ6GN5ZXJ6EGQIC5YLWJCZPTIB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T01:15:35Z","links":{"resolver":"https://pith.science/pith/OJ6GN5ZXJ6EGQIC5YLWJCZPTIB","bundle":"https://pith.science/pith/OJ6GN5ZXJ6EGQIC5YLWJCZPTIB/bundle.json","state":"https://pith.science/pith/OJ6GN5ZXJ6EGQIC5YLWJCZPTIB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OJ6GN5ZXJ6EGQIC5YLWJCZPTIB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OJ6GN5ZXJ6EGQIC5YLWJCZPTIB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7ec552cde06c7b17870645891a16ace1c38c24e8caec3e070f27e0428733b472","cross_cats_sorted":["stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-11-04T18:48:43Z","title_canon_sha256":"822209d36873022250cae1555779cd9f0e56b14cc554759c6d835c815624b919"},"schema_version":"1.0","source":{"id":"1111.1210","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1210","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1210v3","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1210","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"pith_short_12","alias_value":"OJ6GN5ZXJ6EG","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OJ6GN5ZXJ6EGQIC5","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OJ6GN5ZX","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:b24571a29f0daf555f4cb78d31c6cca16885746a6aedbd4c3c2eeadad4f38657","target":"graph","created_at":"2026-05-18T02:54:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Genetic association analyses often involve data from multiple potentially-heterogeneous subgroups. The expected amount of heterogeneity can vary from modest (e.g., a typical meta-analysis) to large (e.g., a strong gene--environment interaction). However, existing statistical tools are limited in their ability to address such heterogeneity. Indeed, most genetic association meta-analyses use a \"fixed effects\" analysis, which assumes no heterogeneity. Here we develop and apply Bayesian association methods to address this problem. These methods are easy to apply (in the simplest case, requiring on","authors_text":"Matthew Stephens, Xiaoquan Wen","cross_cats":["stat.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-11-04T18:48:43Z","title":"Bayesian methods for genetic association analysis with heterogeneous subgroups: From meta-analyses to gene-environment interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1210","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e25c4052692ead41122244a9dd2d1b7e86800f8557c58aed3cf86234e7b38214","target":"record","created_at":"2026-05-18T02:54:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7ec552cde06c7b17870645891a16ace1c38c24e8caec3e070f27e0428733b472","cross_cats_sorted":["stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-11-04T18:48:43Z","title_canon_sha256":"822209d36873022250cae1555779cd9f0e56b14cc554759c6d835c815624b919"},"schema_version":"1.0","source":{"id":"1111.1210","kind":"arxiv","version":3}},"canonical_sha256":"727c66f7374f8868205dc2ec9165f340620e2958e06feec45ee5ec64002e2f53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"727c66f7374f8868205dc2ec9165f340620e2958e06feec45ee5ec64002e2f53","first_computed_at":"2026-05-18T02:54:21.851007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:21.851007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6eiVT1PjSf3sqsovVcGECifHRLE9yT3a0K8dIlpcdS/+ZIZNrljPR6ESUti4ndLfYfZOKCpXmql5eVuJ8rzVCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:21.851429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1210","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e25c4052692ead41122244a9dd2d1b7e86800f8557c58aed3cf86234e7b38214","sha256:b24571a29f0daf555f4cb78d31c6cca16885746a6aedbd4c3c2eeadad4f38657"],"state_sha256":"9107e2351436479967bfab9f0271566dc8b8cb87801e22a8fbe7094f6203ac47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EKtUQn1iwCVP/u0PiU293r0haIchMA8sc9uxHB/vo+4ztmx9ejLuRZ+SOkMgpMoT0gUThjgIQHKhSggqcY71AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T01:15:35.271872Z","bundle_sha256":"45086a91adc570c4c1bd04b92789dab91957a92847395cf27b5407ef915e0c8d"}}