A Bayesian Approach to the Multiplicity Problem for Significance Testing with Binomial Data
Statistical analyses of simple tumor rates from an animal experiment with one control and one treated group typically consist of hypothesis testing of many 2 x 2 tables, one for each tumor type or site. The multiplicity of significance tests may cause excessive overall false-positive rates. This pap...
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| Veröffentlicht in: | Biometrics 1987-06, Vol.43 (2), p.301-311 |
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| container_title | Biometrics |
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| creator | Cliff Y. K. Meng Dempster, Arthur P. |
| description | Statistical analyses of simple tumor rates from an animal experiment with one control and one treated group typically consist of hypothesis testing of many 2 x 2 tables, one for each tumor type or site. The multiplicity of significance tests may cause excessive overall false-positive rates. This paper presents a Bayesian approach to the problem of multiple significance testing. We develop a normal logistic model that accommodates the incidences of all tumor types or sites observed in the current experiment simultaneously as well as their historical control incidences. Exchangeable normal priors are assumed for certain linear terms in the model. Posterior means, standard deviations, and Bayesian P-values are computed for an average treatment effect as well as for the effects on individual tumor types or sites. Model assumptions are checked using probability plots and the sensitivity of the parameter estimates to alternative priors is studied. The method is illustrated using tumor data from a chronic animal experiment. |
| doi_str_mv | 10.2307/2531814 |
| format | Article |
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K. Meng</creatorcontrib><creatorcontrib>Dempster, Arthur P.</creatorcontrib><title>A Bayesian Approach to the Multiplicity Problem for Significance Testing with Binomial Data</title><title>Biometrics</title><addtitle>Biometrics</addtitle><description>Statistical analyses of simple tumor rates from an animal experiment with one control and one treated group typically consist of hypothesis testing of many 2 x 2 tables, one for each tumor type or site. The multiplicity of significance tests may cause excessive overall false-positive rates. This paper presents a Bayesian approach to the problem of multiple significance testing. We develop a normal logistic model that accommodates the incidences of all tumor types or sites observed in the current experiment simultaneously as well as their historical control incidences. Exchangeable normal priors are assumed for certain linear terms in the model. Posterior means, standard deviations, and Bayesian P-values are computed for an average treatment effect as well as for the effects on individual tumor types or sites. Model assumptions are checked using probability plots and the sensitivity of the parameter estimates to alternative priors is studied. The method is illustrated using tumor data from a chronic animal experiment.</description><subject>Analysis of Variance</subject><subject>Animals</subject><subject>Binomials</subject><subject>Biological and medical sciences</subject><subject>Biometrics</subject><subject>Biometry</subject><subject>Carcinogenicity</subject><subject>Carcinogens</subject><subject>Control groups</subject><subject>Diseases of the eye</subject><subject>Drug Evaluation, Preclinical - methods</subject><subject>Maximum likelihood estimation</subject><subject>Maximum likelihood estimators</subject><subject>Medical sciences</subject><subject>Neoplasms, Experimental - pathology</subject><subject>P values</subject><subject>Probability</subject><subject>Radiotherapy. Instrumental treatment. Physiotherapy. Reeducation. Rehabilitation, orthophony, crenotherapy. Diet therapy and various other treatments (general aspects)</subject><subject>Statistical discrepancies</subject><subject>Toxicology</subject><subject>Tumors</subject><issn>0006-341X</issn><issn>1541-0420</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1987</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNp1kF1LwzAUhoMoc07xFwi5ELyqnnw13eU2P2Gi4ATBi5KmyZbRtSXJkP17Kyt65dXh8D68h_MgdE7gmjKQN1QwkhF-gIZEcJIAp3CIhgCQJoyTj2N0EsK6W8cC6AANWAqSAh2izwmeqp0JTtV40ra-UXqFY4PjyuDnbRVdWznt4g6_-qaozAbbxuM3t6yddVrV2uCFCdHVS_zl4gpPXd1snKrwrYrqFB1ZVQVz1s8Rer-_W8wek_nLw9NsMk80YzwmVGVEKT7OSimhKJRMx9YAK22WWg6lIFmppQVDMy0yEIZIMNykoDRQKktgI3S179W-CcEbm7febZTf5QTyHzt5b6cjL_Zkuy02pvzleh1dftnnKmhVWd996MIvJoUAkOIPW4fY-H-vfQPtW3Yr</recordid><startdate>19870601</startdate><enddate>19870601</enddate><creator>Cliff Y. K. 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Meng ; Dempster, Arthur P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c334t-2a81aa498d770bba769fe03df86f40d518dc7f0e28c5805e170e4e60ac0227d03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1987</creationdate><topic>Analysis of Variance</topic><topic>Animals</topic><topic>Binomials</topic><topic>Biological and medical sciences</topic><topic>Biometrics</topic><topic>Biometry</topic><topic>Carcinogenicity</topic><topic>Carcinogens</topic><topic>Control groups</topic><topic>Diseases of the eye</topic><topic>Drug Evaluation, Preclinical - methods</topic><topic>Maximum likelihood estimation</topic><topic>Maximum likelihood estimators</topic><topic>Medical sciences</topic><topic>Neoplasms, Experimental - pathology</topic><topic>P values</topic><topic>Probability</topic><topic>Radiotherapy. Instrumental treatment. Physiotherapy. Reeducation. Rehabilitation, orthophony, crenotherapy. Diet therapy and various other treatments (general aspects)</topic><topic>Statistical discrepancies</topic><topic>Toxicology</topic><topic>Tumors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cliff Y. K. Meng</creatorcontrib><creatorcontrib>Dempster, Arthur P.</creatorcontrib><collection>Pascal-Francis</collection><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><jtitle>Biometrics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cliff Y. K. Meng</au><au>Dempster, Arthur P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Bayesian Approach to the Multiplicity Problem for Significance Testing with Binomial Data</atitle><jtitle>Biometrics</jtitle><addtitle>Biometrics</addtitle><date>1987-06-01</date><risdate>1987</risdate><volume>43</volume><issue>2</issue><spage>301</spage><epage>311</epage><pages>301-311</pages><issn>0006-341X</issn><eissn>1541-0420</eissn><coden>BIOMA5</coden><abstract>Statistical analyses of simple tumor rates from an animal experiment with one control and one treated group typically consist of hypothesis testing of many 2 x 2 tables, one for each tumor type or site. The multiplicity of significance tests may cause excessive overall false-positive rates. This paper presents a Bayesian approach to the problem of multiple significance testing. We develop a normal logistic model that accommodates the incidences of all tumor types or sites observed in the current experiment simultaneously as well as their historical control incidences. Exchangeable normal priors are assumed for certain linear terms in the model. Posterior means, standard deviations, and Bayesian P-values are computed for an average treatment effect as well as for the effects on individual tumor types or sites. Model assumptions are checked using probability plots and the sensitivity of the parameter estimates to alternative priors is studied. The method is illustrated using tumor data from a chronic animal experiment.</abstract><cop>Malden, MA</cop><pub>Biometric Society</pub><pmid>3607202</pmid><doi>10.2307/2531814</doi><tpages>11</tpages></addata></record> |
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| ispartof | Biometrics, 1987-06, Vol.43 (2), p.301-311 |
| issn | 0006-341X 1541-0420 |
| language | eng |
| recordid | cdi_crossref_primary_10_2307_2531814 |
| source | MEDLINE; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing |
| subjects | Analysis of Variance Animals Binomials Biological and medical sciences Biometrics Biometry Carcinogenicity Carcinogens Control groups Diseases of the eye Drug Evaluation, Preclinical - methods Maximum likelihood estimation Maximum likelihood estimators Medical sciences Neoplasms, Experimental - pathology P values Probability Radiotherapy. Instrumental treatment. Physiotherapy. Reeducation. Rehabilitation, orthophony, crenotherapy. Diet therapy and various other treatments (general aspects) Statistical discrepancies Toxicology Tumors |
| title | A Bayesian Approach to the Multiplicity Problem for Significance Testing with Binomial Data |
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