Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2086403450', 'doi': 'https://doi.org/10.1002/bimj.200610337', 'title': 'Testing the Non‐Unity of Rate Ratio under Inverse Sampling', 'display_name': 'Testing the Non‐Unity of Rate Ratio under Inverse Sampling', 'publication_year': 2007, 'publication_date': '2007-07-10', 'ids': {'openalex': 'https://openalex.org/W2086403450', 'doi': 'https://doi.org/10.1002/bimj.200610337', 'mag': '2086403450', 'pmid': 'https://pubmed.ncbi.nlm.nih.gov/17621387'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1002/bimj.200610337', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S126457381', 'display_name': 'Biometrical Journal', 'issn_l': '0323-3847', 'issn': ['0323-3847', '1521-4036'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320595', 'host_organization_name': 'Wiley', 'host_organization_lineage': ['https://openalex.org/P4310320595'], 'host_organization_lineage_names': ['Wiley'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref', 'pubmed'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5069557245', 'display_name': 'Man‐Lai Tang', 'orcid': 'https://orcid.org/0000-0001-6460-8136'}, 'institutions': [{'id': 'https://openalex.org/I141568987', 'display_name': 'Hong Kong Baptist University', 'ror': 'https://ror.org/0145fw131', 'country_code': 'HK', 'type': 'education', 'lineage': ['https://openalex.org/I141568987']}], 'countries': ['HK'], 'is_corresponding': False, 'raw_author_name': 'Man‐Lai Tang', 'raw_affiliation_strings': ['Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong.'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong.', 'institution_ids': ['https://openalex.org/I141568987']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5000845758', 'display_name': 'Yi Jie Liao', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I178169726', 'display_name': 'Southern Methodist University', 'ror': 'https://ror.org/042tdr378', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I178169726']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Yi Jie Liao', 'raw_affiliation_strings': ['Department of Statistical Science, Southern Methodist University, 3225 Daniel Avenue, P.O. Box 750332, Dallas, Texas 75275-0332, USA.'], 'affiliations': [{'raw_affiliation_string': 'Department of Statistical Science, Southern Methodist University, 3225 Daniel Avenue, P.O. Box 750332, Dallas, Texas 75275-0332, USA.', 'institution_ids': ['https://openalex.org/I178169726']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5088095623', 'display_name': 'Hong Keung Tony Ng', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I178169726', 'display_name': 'Southern Methodist University', 'ror': 'https://ror.org/042tdr378', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I178169726']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Hong Keung Tony Ng', 'raw_affiliation_strings': ['Department of Statistical Science, Southern Methodist University, 3225 Daniel Avenue, P.O. Box 750332, Dallas, Texas 75275-0332, USA.'], 'affiliations': [{'raw_affiliation_string': 'Department of Statistical Science, Southern Methodist University, 3225 Daniel Avenue, P.O. Box 750332, Dallas, Texas 75275-0332, USA.', 'institution_ids': ['https://openalex.org/I178169726']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5025687625', 'display_name': 'Ping Shing Chan', 'orcid': 'https://orcid.org/0000-0002-6983-5845'}, 'institutions': [{'id': 'https://openalex.org/I177725633', 'display_name': 'Chinese University of Hong Kong', 'ror': 'https://ror.org/00t33hh48', 'country_code': 'CN', 'type': 'education', 'lineage': ['https://openalex.org/I177725633']}], 'countries': ['CN'], 'is_corresponding': False, 'raw_author_name': 'Ping Shing Chan', 'raw_affiliation_strings': ['Department of Statistics, Room 109, 1/F, Lady Shaw Building, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong'], 'affiliations': [{'raw_affiliation_string': 'Department of Statistics, Room 109, 1/F, Lady Shaw Building, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong', 'institution_ids': ['https://openalex.org/I177725633']}]}], 'institution_assertions': [], 'countries_distinct_count': 3, 'institutions_distinct_count': 3, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': {'value': 4120, 'currency': 'USD', 'value_usd': 4120, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 0.452, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 4, 'citation_normalized_percentile': {'value': 0.539482, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 76, 'max': 78}, 'biblio': {'volume': '49', 'issue': '4', 'first_page': '551', 'last_page': '564'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10243', 'display_name': 'Statistical Methods and Bayesian Inference', 'score': 0.9994, 'subfield': {'id': 'https://openalex.org/subfields/2613', 'display_name': 'Statistics and Probability'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T10243', 'display_name': 'Statistical Methods and Bayesian Inference', 'score': 0.9994, 'subfield': {'id': 'https://openalex.org/subfields/2613', 'display_name': 'Statistics and Probability'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T11235', 'display_name': 'Statistical Methods in Clinical Trials', 'score': 0.9987, 'subfield': {'id': 'https://openalex.org/subfields/2613', 'display_name': 'Statistics and Probability'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10845', 'display_name': 'Advanced Causal Inference Techniques', 'score': 0.9948, 'subfield': {'id': 'https://openalex.org/subfields/2613', 'display_name': 'Statistics and Probability'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/wald-test', 'display_name': 'Wald test', 'score': 0.7227401}, {'id': 'https://openalex.org/keywords/nominal-level', 'display_name': 'Nominal level', 'score': 0.6972845}, {'id': 'https://openalex.org/keywords/score-test', 'display_name': 'Score test', 'score': 0.6188792}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.7517405}, {'id': 'https://openalex.org/C203274628', 'wikidata': 'https://www.wikidata.org/wiki/Q748664', 'display_name': 'Wald test', 'level': 3, 'score': 0.7227401}, {'id': 'https://openalex.org/C105795698', 'wikidata': 'https://www.wikidata.org/wiki/Q12483', 'display_name': 'Statistics', 'level': 1, 'score': 0.7083373}, {'id': 'https://openalex.org/C154606282', 'wikidata': 'https://www.wikidata.org/wiki/Q7048579', 'display_name': 'Nominal level', 'level': 3, 'score': 0.6972845}, {'id': 'https://openalex.org/C185429906', 'wikidata': 'https://www.wikidata.org/wiki/Q1130160', 'display_name': 'Estimator', 'level': 2, 'score': 0.6268474}, {'id': 'https://openalex.org/C103463560', 'wikidata': 'https://www.wikidata.org/wiki/Q4456449', 'display_name': 'Score test', 'level': 3, 'score': 0.6188792}, {'id': 'https://openalex.org/C40696583', 'wikidata': 'https://www.wikidata.org/wiki/Q989120', 'display_name': 'Type I and type II errors', 'level': 2, 'score': 0.58897525}, {'id': 'https://openalex.org/C140779682', 'wikidata': 'https://www.wikidata.org/wiki/Q210868', 'display_name': 'Sampling (signal processing)', 'level': 3, 'score': 0.51493293}, {'id': 'https://openalex.org/C207467116', 'wikidata': 'https://www.wikidata.org/wiki/Q4385666', 'display_name': 'Inverse', 'level': 2, 'score': 0.43743107}, {'id': 'https://openalex.org/C199335787', 'wikidata': 'https://www.wikidata.org/wiki/Q743364', 'display_name': 'Negative binomial distribution', 'level': 3, 'score': 0.42680565}, {'id': 'https://openalex.org/C9483764', 'wikidata': 'https://www.wikidata.org/wiki/Q585740', 'display_name': 'Likelihood-ratio test', 'level': 2, 'score': 0.42547446}, {'id': 'https://openalex.org/C19499675', 'wikidata': 'https://www.wikidata.org/wiki/Q232207', 'display_name': 'Monte Carlo method', 'level': 2, 'score': 0.42106354}, {'id': 'https://openalex.org/C87007009', 'wikidata': 'https://www.wikidata.org/wiki/Q210832', 'display_name': 'Statistical hypothesis testing', 'level': 2, 'score': 0.4196626}, {'id': 'https://openalex.org/C44249647', 'wikidata': 'https://www.wikidata.org/wiki/Q208498', 'display_name': 'Confidence interval', 'level': 2, 'score': 0.18156502}, {'id': 'https://openalex.org/C100906024', 'wikidata': 'https://www.wikidata.org/wiki/Q205692', 'display_name': 'Poisson distribution', 'level': 2, 'score': 0.124595165}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.109233916}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C106131492', 'wikidata': 'https://www.wikidata.org/wiki/Q3072260', 'display_name': 'Filter (signal processing)', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C31972630', 'wikidata': 'https://www.wikidata.org/wiki/Q844240', 'display_name': 'Computer vision', 'level': 1, 'score': 0.0}], 'mesh': [{'descriptor_ui': 'D001699', 'descriptor_name': 'Biometry', 'qualifier_ui': 'Q000379', 'qualifier_name': 'methods', 'is_major_topic': True}, {'descriptor_ui': 'D003627', 'descriptor_name': 'Data Interpretation, Statistical', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': True}, {'descriptor_ui': 'D006330', 'descriptor_name': 'Heart Defects, Congenital', 'qualifier_ui': 'Q000453', 'qualifier_name': 'epidemiology', 'is_major_topic': True}, {'descriptor_ui': 'D007230', 'descriptor_name': 'Infant, Low Birth Weight', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': True}, {'descriptor_ui': 'D018570', 'descriptor_name': 'Risk Assessment', 'qualifier_ui': 'Q000379', 'qualifier_name': 'methods', 'is_major_topic': True}, {'descriptor_ui': 'D001699', 'descriptor_name': 'Biometry', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': False}, {'descriptor_ui': 'D006330', 'descriptor_name': 'Heart Defects, Congenital', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': False}, {'descriptor_ui': 'D006801', 'descriptor_name': 'Humans', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': False}, {'descriptor_ui': 'D007231', 'descriptor_name': 'Infant, Newborn', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': False}, {'descriptor_ui': 'D016013', 'descriptor_name': 'Likelihood Functions', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': False}, {'descriptor_ui': 'D016017', 'descriptor_name': 'Odds Ratio', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': False}, {'descriptor_ui': 'D018570', 'descriptor_name': 'Risk Assessment', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': False}, {'descriptor_ui': 'D012307', 'descriptor_name': 'Risk Factors', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': False}, {'descriptor_ui': 'D018401', 'descriptor_name': 'Sample Size', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': False}, {'descriptor_ui': 'D013223', 'descriptor_name': 'Statistics as Topic', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': False}], 'locations_count': 2, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1002/bimj.200610337', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S126457381', 'display_name': 'Biometrical Journal', 'issn_l': '0323-3847', 'issn': ['0323-3847', '1521-4036'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320595', 'host_organization_name': 'Wiley', 'host_organization_lineage': ['https://openalex.org/P4310320595'], 'host_organization_lineage_names': ['Wiley'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://pubmed.ncbi.nlm.nih.gov/17621387', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306525036', 'display_name': 'PubMed', 'issn_l': None, 'issn': None, 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1299303238', 'host_organization_name': 'National Institutes of Health', 'host_organization_lineage': ['https://openalex.org/I1299303238'], 'host_organization_lineage_names': ['National Institutes of Health'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [{'score': 0.81, 'id': 'https://metadata.un.org/sdg/3', 'display_name': 'Good health and well-being'}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 24, 'referenced_works': ['https://openalex.org/W104186615', 'https://openalex.org/W1964394230', 'https://openalex.org/W1975084993', 'https://openalex.org/W1982139385', 'https://openalex.org/W1983093461', 'https://openalex.org/W1991632519', 'https://openalex.org/W2004802791', 'https://openalex.org/W2017492627', 'https://openalex.org/W2042732005', 'https://openalex.org/W2051466438', 'https://openalex.org/W2071531714', 'https://openalex.org/W2077348644', 'https://openalex.org/W2078206374', 'https://openalex.org/W2088979439', 'https://openalex.org/W2094806027', 'https://openalex.org/W2122016361', 'https://openalex.org/W2127831140', 'https://openalex.org/W2140048172', 'https://openalex.org/W2141308243', 'https://openalex.org/W2148306011', 'https://openalex.org/W2150290224', 'https://openalex.org/W2159701320', 'https://openalex.org/W2985440518', 'https://openalex.org/W4212786834'], 'related_works': ['https://openalex.org/W4231562469', 'https://openalex.org/W3044716326', 'https://openalex.org/W2566937514', 'https://openalex.org/W2318340221', 'https://openalex.org/W2293342137', 'https://openalex.org/W2141073783', 'https://openalex.org/W2119004137', 'https://openalex.org/W2093700538', 'https://openalex.org/W2075921969', 'https://openalex.org/W2052185453'], 'abstract_inverted_index': {'Inverse': [0], 'sampling': [1, 9, 15], 'is': [2, 27, 148, 171, 191], 'considered': [3], 'to': [4, 153], 'be': [5], 'a': [6, 192, 200, 204], 'more': [7], 'appropriate': [8], 'scheme': [10, 16], 'than': [11], 'the': [12, 22, 60, 86, 131, 140, 155, 164, 178, 185, 197], 'usual': [13], 'binomial': [14], 'when': [17, 21, 30], 'subjects': [18], 'arrive': [19], 'sequentially,': [20], 'underlying': [23], 'response': [24], 'of': [25, 34, 88, 91, 100, 145, 175, 188], 'interest': [26], 'acute,': [28], 'and': [29, 66, 76, 94, 104, 114, 135, 173], 'maximum': [31], 'likelihood': [32, 64], 'estimators': [33], 'some': [35], 'epidemiologic': [36], 'indices': [37], 'are': [38, 79, 118, 127, 138, 182], 'undefined.': [39], 'In': [40, 110], 'this': [41], 'article,': [42], 'we': [43], 'study': [44], 'various': [45], 'statistics': [46, 93], 'for': [47, 81, 120], 'testing': [48], 'non-unity': [49], 'rate': [50, 160], 'ratios': [51], 'in': [52, 98], 'case-control': [53], 'studies': [54], 'under': [55], 'inverse': [56], 'sampling.': [57], 'These': [58], 'include': [59], 'Wald,': [61], 'unconditional': [62], 'score,': [63], 'ratio': [65], 'conditional': [67, 74, 115], 'score': [68, 113, 116], 'statistics.': [69], 'Three': [70], 'methods': [71, 97], '(the': [72], 'asymptotic,': [73], 'exact,': [75], 'Mid-P': [77, 186], 'methods)': [78], 'adopted': [80], 'P-value': [82, 95], 'calculation.': [83], 'We': [84, 195], 'evaluate': [85], 'performance': [87], 'different': [89], 'combinations': [90], 'test': [92, 147, 190], 'calculation': [96], 'terms': [99], 'their': [101, 121, 136], 'empirical': [102], 'sizes': [103, 176], 'powers': [105, 137], 'via': [106], 'Monte': [107], 'Carlo': [108], 'simulation.': [109], 'general,': [111], 'asymptotic': [112], 'tests': [117], 'preferable': [119], 'actual': [122, 156], 'type': [123, 157], 'I': [124, 158], 'error': [125, 159], 'rates': [126], 'well': [128], 'controlled': [129], 'around': [130, 177], 'pre-chosen': [132, 165, 179], 'nominal': [133, 166, 180], 'level,': [134], 'comparatively': [139], 'largest.': [141], 'The': [142], 'exact': [143], 'version': [144, 187], 'Wald': [146, 189], 'recommended': [149], 'if': [150], 'one': [151], 'wants': [152], 'control': [154], 'at': [161], 'or': [162], 'below': [163], 'level.': [167], 'If': [168], 'larger': [169], 'power': [170], 'expected': [172], 'fluctuation': [174], 'level': [181], 'allowed,': [183], 'then': [184], 'desirable': [193], 'alternative.': [194], 'illustrate': [196], 'methodologies': [198], 'with': [199], 'real': [201], 'example': [202], 'from': [203], 'heart': [205], 'disease': [206], 'study.': [207]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2086403450', 'counts_by_year': [{'year': 2015, 'cited_by_count': 1}, {'year': 2014, 'cited_by_count': 1}], 'updated_date': '2024-12-08T23:20:26.031502', 'created_date': '2016-06-24'}