Using a Mixed Effects Model to Estimate Geographic Variation in Cancer Rates
Commonly used methods for depicting geographic variation in cancer rates are based on rankings. They identify where the rates are high and low but do not indicate the magnitude of the rates nor their variability. Yet such measures of variability may be useful in suggesting which types of cancer warr...
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| Veröffentlicht in: | Biometrics 1999-09, Vol.55 (3), p.774-781 |
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| creator | Pennello, Gene A. Devesa, Susan S. Gail, Mitchell H. |
| description | Commonly used methods for depicting geographic variation in cancer rates are based on rankings. They identify where the rates are high and low but do not indicate the magnitude of the rates nor their variability. Yet such measures of variability may be useful in suggesting which types of cancer warrant further analytic studies of localized risk factors. We consider a mixed effects model in which the logarithm of the mean Poisson rate is additive in fixed stratum effects (e.g., age effects) and in logarithms of random relative risk effects associated with geographic areas. These random effects are assumed to follow a gamma distribution with unit mean and variance 1/α, similar to Clayton and Kaldor (1987, Biometrics 43, 671-681). We present maximum likelihood and method-of-moments estimates with standard errors for inference on α-1/2, the relative risk standard deviation (RRSD). The moment estimates rely on only the first two moments of the Poisson and gamma distributions but have larger standard errors than the maximum likelihood estimates. We compare these estimates with other measures of variability. Several examples suggest that the RRSD estimates have advantages compared to other measures of variability. |
| doi_str_mv | 10.1111/j.0006-341X.1999.00774.x |
| format | Article |
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They identify where the rates are high and low but do not indicate the magnitude of the rates nor their variability. Yet such measures of variability may be useful in suggesting which types of cancer warrant further analytic studies of localized risk factors. We consider a mixed effects model in which the logarithm of the mean Poisson rate is additive in fixed stratum effects (e.g., age effects) and in logarithms of random relative risk effects associated with geographic areas. These random effects are assumed to follow a gamma distribution with unit mean and variance 1/α, similar to Clayton and Kaldor (1987, Biometrics 43, 671-681). We present maximum likelihood and method-of-moments estimates with standard errors for inference on α-1/2, the relative risk standard deviation (RRSD). The moment estimates rely on only the first two moments of the Poisson and gamma distributions but have larger standard errors than the maximum likelihood estimates. We compare these estimates with other measures of variability. Several examples suggest that the RRSD estimates have advantages compared to other measures of variability.</description><identifier>ISSN: 0006-341X</identifier><identifier>EISSN: 1541-0420</identifier><identifier>DOI: 10.1111/j.0006-341X.1999.00774.x</identifier><identifier>PMID: 11315006</identifier><identifier>CODEN: BIOMA5</identifier><language>eng</language><publisher>Oxford, UK: Blackwell Publishing Ltd</publisher><subject>Biometrics ; Biometry ; Cancer ; Colorectal Neoplasms - epidemiology ; Delta method ; Epidemiology ; Epidemiology - statistics & numerical data ; Estimation methods ; Geographical variation ; Humans ; Likelihood Functions ; Lymphoma, Non-Hodgkin - epidemiology ; Male ; Maximum likelihood ; Maximum likelihood estimation ; Melanoma - epidemiology ; Method-of-moments ; Models, Statistical ; Mortality ; Neoplasms - epidemiology ; Non Hodgkin lymphoma ; Overdispersion ; Relative risk ; Standard deviation ; Standard error ; Standardized rates ; United States - epidemiology</subject><ispartof>Biometrics, 1999-09, Vol.55 (3), p.774-781</ispartof><rights>Copyright 1999 The International Biometric Society</rights><rights>Copyright International Biometric Society Sep 1999</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c4514-11dbbe5cf2dacbbb26ac4b73d577f91b7576baa3d8f6f43d28bfc92fd53da1703</citedby><cites>FETCH-LOGICAL-c4514-11dbbe5cf2dacbbb26ac4b73d577f91b7576baa3d8f6f43d28bfc92fd53da1703</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/2533603$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/2533603$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,1417,27924,27925,45574,45575,58017,58021,58250,58254</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/11315006$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Pennello, Gene A.</creatorcontrib><creatorcontrib>Devesa, Susan S.</creatorcontrib><creatorcontrib>Gail, Mitchell H.</creatorcontrib><title>Using a Mixed Effects Model to Estimate Geographic Variation in Cancer Rates</title><title>Biometrics</title><addtitle>Biometrics</addtitle><description>Commonly used methods for depicting geographic variation in cancer rates are based on rankings. They identify where the rates are high and low but do not indicate the magnitude of the rates nor their variability. Yet such measures of variability may be useful in suggesting which types of cancer warrant further analytic studies of localized risk factors. We consider a mixed effects model in which the logarithm of the mean Poisson rate is additive in fixed stratum effects (e.g., age effects) and in logarithms of random relative risk effects associated with geographic areas. These random effects are assumed to follow a gamma distribution with unit mean and variance 1/α, similar to Clayton and Kaldor (1987, Biometrics 43, 671-681). We present maximum likelihood and method-of-moments estimates with standard errors for inference on α-1/2, the relative risk standard deviation (RRSD). The moment estimates rely on only the first two moments of the Poisson and gamma distributions but have larger standard errors than the maximum likelihood estimates. We compare these estimates with other measures of variability. Several examples suggest that the RRSD estimates have advantages compared to other measures of variability.</description><subject>Biometrics</subject><subject>Biometry</subject><subject>Cancer</subject><subject>Colorectal Neoplasms - epidemiology</subject><subject>Delta method</subject><subject>Epidemiology</subject><subject>Epidemiology - statistics & numerical data</subject><subject>Estimation methods</subject><subject>Geographical variation</subject><subject>Humans</subject><subject>Likelihood Functions</subject><subject>Lymphoma, Non-Hodgkin - epidemiology</subject><subject>Male</subject><subject>Maximum likelihood</subject><subject>Maximum likelihood estimation</subject><subject>Melanoma - epidemiology</subject><subject>Method-of-moments</subject><subject>Models, Statistical</subject><subject>Mortality</subject><subject>Neoplasms - epidemiology</subject><subject>Non Hodgkin lymphoma</subject><subject>Overdispersion</subject><subject>Relative risk</subject><subject>Standard deviation</subject><subject>Standard error</subject><subject>Standardized rates</subject><subject>United States - 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epidemiology</topic><topic>Delta method</topic><topic>Epidemiology</topic><topic>Epidemiology - statistics & numerical data</topic><topic>Estimation methods</topic><topic>Geographical variation</topic><topic>Humans</topic><topic>Likelihood Functions</topic><topic>Lymphoma, Non-Hodgkin - epidemiology</topic><topic>Male</topic><topic>Maximum likelihood</topic><topic>Maximum likelihood estimation</topic><topic>Melanoma - epidemiology</topic><topic>Method-of-moments</topic><topic>Models, Statistical</topic><topic>Mortality</topic><topic>Neoplasms - epidemiology</topic><topic>Non Hodgkin lymphoma</topic><topic>Overdispersion</topic><topic>Relative risk</topic><topic>Standard deviation</topic><topic>Standard error</topic><topic>Standardized rates</topic><topic>United States - epidemiology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Pennello, Gene A.</creatorcontrib><creatorcontrib>Devesa, Susan S.</creatorcontrib><creatorcontrib>Gail, Mitchell H.</creatorcontrib><collection>Istex</collection><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Health & Medical Collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Medical Database (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>STEM Database</collection><collection>Public Health Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>Hospital Premium Collection</collection><collection>Hospital Premium Collection (Alumni Edition)</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>Biological Science Collection</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Health Research Premium Collection</collection><collection>Health Research Premium Collection (Alumni)</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Biological Science Collection</collection><collection>Health & Medical Collection (Alumni Edition)</collection><collection>Medical Database</collection><collection>Science Database</collection><collection>Biological Science Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><collection>MEDLINE - Academic</collection><jtitle>Biometrics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Pennello, Gene A.</au><au>Devesa, Susan S.</au><au>Gail, Mitchell H.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Using a Mixed Effects Model to Estimate Geographic Variation in Cancer Rates</atitle><jtitle>Biometrics</jtitle><addtitle>Biometrics</addtitle><date>1999-09</date><risdate>1999</risdate><volume>55</volume><issue>3</issue><spage>774</spage><epage>781</epage><pages>774-781</pages><issn>0006-341X</issn><eissn>1541-0420</eissn><coden>BIOMA5</coden><abstract>Commonly used methods for depicting geographic variation in cancer rates are based on rankings. They identify where the rates are high and low but do not indicate the magnitude of the rates nor their variability. Yet such measures of variability may be useful in suggesting which types of cancer warrant further analytic studies of localized risk factors. We consider a mixed effects model in which the logarithm of the mean Poisson rate is additive in fixed stratum effects (e.g., age effects) and in logarithms of random relative risk effects associated with geographic areas. These random effects are assumed to follow a gamma distribution with unit mean and variance 1/α, similar to Clayton and Kaldor (1987, Biometrics 43, 671-681). We present maximum likelihood and method-of-moments estimates with standard errors for inference on α-1/2, the relative risk standard deviation (RRSD). The moment estimates rely on only the first two moments of the Poisson and gamma distributions but have larger standard errors than the maximum likelihood estimates. We compare these estimates with other measures of variability. Several examples suggest that the RRSD estimates have advantages compared to other measures of variability.</abstract><cop>Oxford, UK</cop><pub>Blackwell Publishing Ltd</pub><pmid>11315006</pmid><doi>10.1111/j.0006-341X.1999.00774.x</doi><tpages>8</tpages></addata></record> |
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| ispartof | Biometrics, 1999-09, Vol.55 (3), p.774-781 |
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| source | MEDLINE; JSTOR Mathematics & Statistics; Access via Wiley Online Library; JSTOR Archive Collection A-Z Listing; Oxford University Press Journals All Titles (1996-Current) |
| subjects | Biometrics Biometry Cancer Colorectal Neoplasms - epidemiology Delta method Epidemiology Epidemiology - statistics & numerical data Estimation methods Geographical variation Humans Likelihood Functions Lymphoma, Non-Hodgkin - epidemiology Male Maximum likelihood Maximum likelihood estimation Melanoma - epidemiology Method-of-moments Models, Statistical Mortality Neoplasms - epidemiology Non Hodgkin lymphoma Overdispersion Relative risk Standard deviation Standard error Standardized rates United States - epidemiology |
| title | Using a Mixed Effects Model to Estimate Geographic Variation in Cancer Rates |
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