Odds ratios from logistic, geometric, Poisson, and negative binomial regression models

Background The odds ratio (OR) is used as an important metric of comparison of two or more groups in many biomedical applications when the data measure the presence or absence of an event or represent the frequency of its occurrence. In the latter case, researchers often dichotomize the count data into binary form and apply the well-known logistic regression technique to estimate the OR. In the process of dichotomizing the data, however, information is lost about the underlying counts which can reduce the precision of inferences on the OR. Methods We propose analyzing the count data directly using regression models with the log odds link function. With this approach, the parameter estimates in the model have the exact same interpretation as in a logistic regression of the dichotomized data, yielding comparable estimates of the OR. We prove analytically, using the Fisher information matrix, that our approach produces more precise estimates of the OR than logistic regression of the dichotomized data. We also show the gains in precision using simulation studies and real-world datasets. We focus on three related distributions for count data: geometric, Poisson, and negative binomial. Results In simulation studies, confidence intervals for the OR were 56–65% as wide (geometric model), 75–79% as wide (Poisson model), and 61–69% as wide (negative binomial model) as the corresponding interval from a logistic regression produced by dichotomizing the data. When we analyzed existing datasets using our approach, we found that confidence intervals for the OR could be up to 64% shorter (36% as wide) compared to if the data had been dichotomized and analyzed using logistic regression. Conclusions More precise estimates of the OR can be obtained directly from the count data by using the log odds link function. This analytic approach is easy to implement in software packages that are capable of fitting generalized linear models or of maximizing user-defined likelihood functions. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Sroka, Christopher J. [verfasserIn] Nagaraja, Haikady N.

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	Binary data Confidence intervals Count data Fisher information Maximum likelihood

Anmerkung:	© The Author(s) 2018

Übergeordnetes Werk:	Enthalten in: BMC medical research methodology - London : BioMed Central, 2001, 18(2018), 1 vom: 20. Okt.
Übergeordnetes Werk:	volume:18 ; year:2018 ; number:1 ; day:20 ; month:10

Links:	Volltext

DOI / URN:	10.1186/s12874-018-0568-9

Katalog-ID:	SPR027375080

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allfields	10.1186/s12874-018-0568-9 doi (DE-627)SPR027375080 (SPR)s12874-018-0568-9-e DE-627 ger DE-627 rakwb eng Sroka, Christopher J. verfasserin (orcid)0000-0002-3049-4684 aut Odds ratios from logistic, geometric, Poisson, and negative binomial regression models 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2018 Background The odds ratio (OR) is used as an important metric of comparison of two or more groups in many biomedical applications when the data measure the presence or absence of an event or represent the frequency of its occurrence. In the latter case, researchers often dichotomize the count data into binary form and apply the well-known logistic regression technique to estimate the OR. In the process of dichotomizing the data, however, information is lost about the underlying counts which can reduce the precision of inferences on the OR. Methods We propose analyzing the count data directly using regression models with the log odds link function. With this approach, the parameter estimates in the model have the exact same interpretation as in a logistic regression of the dichotomized data, yielding comparable estimates of the OR. We prove analytically, using the Fisher information matrix, that our approach produces more precise estimates of the OR than logistic regression of the dichotomized data. We also show the gains in precision using simulation studies and real-world datasets. We focus on three related distributions for count data: geometric, Poisson, and negative binomial. Results In simulation studies, confidence intervals for the OR were 56–65% as wide (geometric model), 75–79% as wide (Poisson model), and 61–69% as wide (negative binomial model) as the corresponding interval from a logistic regression produced by dichotomizing the data. When we analyzed existing datasets using our approach, we found that confidence intervals for the OR could be up to 64% shorter (36% as wide) compared to if the data had been dichotomized and analyzed using logistic regression. Conclusions More precise estimates of the OR can be obtained directly from the count data by using the log odds link function. This analytic approach is easy to implement in software packages that are capable of fitting generalized linear models or of maximizing user-defined likelihood functions. Binary data (dpeaa)DE-He213 Confidence intervals (dpeaa)DE-He213 Count data (dpeaa)DE-He213 Fisher information (dpeaa)DE-He213 Maximum likelihood (dpeaa)DE-He213 Nagaraja, Haikady N. aut Enthalten in BMC medical research methodology London : BioMed Central, 2001 18(2018), 1 vom: 20. Okt. (DE-627)326643818 (DE-600)2041362-2 1471-2288 nnns volume:18 year:2018 number:1 day:20 month:10 https://dx.doi.org/10.1186/s12874-018-0568-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 18 2018 1 20 10
spelling	10.1186/s12874-018-0568-9 doi (DE-627)SPR027375080 (SPR)s12874-018-0568-9-e DE-627 ger DE-627 rakwb eng Sroka, Christopher J. verfasserin (orcid)0000-0002-3049-4684 aut Odds ratios from logistic, geometric, Poisson, and negative binomial regression models 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2018 Background The odds ratio (OR) is used as an important metric of comparison of two or more groups in many biomedical applications when the data measure the presence or absence of an event or represent the frequency of its occurrence. In the latter case, researchers often dichotomize the count data into binary form and apply the well-known logistic regression technique to estimate the OR. In the process of dichotomizing the data, however, information is lost about the underlying counts which can reduce the precision of inferences on the OR. Methods We propose analyzing the count data directly using regression models with the log odds link function. With this approach, the parameter estimates in the model have the exact same interpretation as in a logistic regression of the dichotomized data, yielding comparable estimates of the OR. We prove analytically, using the Fisher information matrix, that our approach produces more precise estimates of the OR than logistic regression of the dichotomized data. We also show the gains in precision using simulation studies and real-world datasets. We focus on three related distributions for count data: geometric, Poisson, and negative binomial. Results In simulation studies, confidence intervals for the OR were 56–65% as wide (geometric model), 75–79% as wide (Poisson model), and 61–69% as wide (negative binomial model) as the corresponding interval from a logistic regression produced by dichotomizing the data. When we analyzed existing datasets using our approach, we found that confidence intervals for the OR could be up to 64% shorter (36% as wide) compared to if the data had been dichotomized and analyzed using logistic regression. Conclusions More precise estimates of the OR can be obtained directly from the count data by using the log odds link function. This analytic approach is easy to implement in software packages that are capable of fitting generalized linear models or of maximizing user-defined likelihood functions. Binary data (dpeaa)DE-He213 Confidence intervals (dpeaa)DE-He213 Count data (dpeaa)DE-He213 Fisher information (dpeaa)DE-He213 Maximum likelihood (dpeaa)DE-He213 Nagaraja, Haikady N. aut Enthalten in BMC medical research methodology London : BioMed Central, 2001 18(2018), 1 vom: 20. Okt. (DE-627)326643818 (DE-600)2041362-2 1471-2288 nnns volume:18 year:2018 number:1 day:20 month:10 https://dx.doi.org/10.1186/s12874-018-0568-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 18 2018 1 20 10
allfields_unstemmed	10.1186/s12874-018-0568-9 doi (DE-627)SPR027375080 (SPR)s12874-018-0568-9-e DE-627 ger DE-627 rakwb eng Sroka, Christopher J. verfasserin (orcid)0000-0002-3049-4684 aut Odds ratios from logistic, geometric, Poisson, and negative binomial regression models 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2018 Background The odds ratio (OR) is used as an important metric of comparison of two or more groups in many biomedical applications when the data measure the presence or absence of an event or represent the frequency of its occurrence. In the latter case, researchers often dichotomize the count data into binary form and apply the well-known logistic regression technique to estimate the OR. In the process of dichotomizing the data, however, information is lost about the underlying counts which can reduce the precision of inferences on the OR. Methods We propose analyzing the count data directly using regression models with the log odds link function. With this approach, the parameter estimates in the model have the exact same interpretation as in a logistic regression of the dichotomized data, yielding comparable estimates of the OR. We prove analytically, using the Fisher information matrix, that our approach produces more precise estimates of the OR than logistic regression of the dichotomized data. We also show the gains in precision using simulation studies and real-world datasets. We focus on three related distributions for count data: geometric, Poisson, and negative binomial. Results In simulation studies, confidence intervals for the OR were 56–65% as wide (geometric model), 75–79% as wide (Poisson model), and 61–69% as wide (negative binomial model) as the corresponding interval from a logistic regression produced by dichotomizing the data. When we analyzed existing datasets using our approach, we found that confidence intervals for the OR could be up to 64% shorter (36% as wide) compared to if the data had been dichotomized and analyzed using logistic regression. Conclusions More precise estimates of the OR can be obtained directly from the count data by using the log odds link function. This analytic approach is easy to implement in software packages that are capable of fitting generalized linear models or of maximizing user-defined likelihood functions. Binary data (dpeaa)DE-He213 Confidence intervals (dpeaa)DE-He213 Count data (dpeaa)DE-He213 Fisher information (dpeaa)DE-He213 Maximum likelihood (dpeaa)DE-He213 Nagaraja, Haikady N. aut Enthalten in BMC medical research methodology London : BioMed Central, 2001 18(2018), 1 vom: 20. Okt. (DE-627)326643818 (DE-600)2041362-2 1471-2288 nnns volume:18 year:2018 number:1 day:20 month:10 https://dx.doi.org/10.1186/s12874-018-0568-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 18 2018 1 20 10
allfieldsGer	10.1186/s12874-018-0568-9 doi (DE-627)SPR027375080 (SPR)s12874-018-0568-9-e DE-627 ger DE-627 rakwb eng Sroka, Christopher J. verfasserin (orcid)0000-0002-3049-4684 aut Odds ratios from logistic, geometric, Poisson, and negative binomial regression models 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2018 Background The odds ratio (OR) is used as an important metric of comparison of two or more groups in many biomedical applications when the data measure the presence or absence of an event or represent the frequency of its occurrence. In the latter case, researchers often dichotomize the count data into binary form and apply the well-known logistic regression technique to estimate the OR. In the process of dichotomizing the data, however, information is lost about the underlying counts which can reduce the precision of inferences on the OR. Methods We propose analyzing the count data directly using regression models with the log odds link function. With this approach, the parameter estimates in the model have the exact same interpretation as in a logistic regression of the dichotomized data, yielding comparable estimates of the OR. We prove analytically, using the Fisher information matrix, that our approach produces more precise estimates of the OR than logistic regression of the dichotomized data. We also show the gains in precision using simulation studies and real-world datasets. We focus on three related distributions for count data: geometric, Poisson, and negative binomial. Results In simulation studies, confidence intervals for the OR were 56–65% as wide (geometric model), 75–79% as wide (Poisson model), and 61–69% as wide (negative binomial model) as the corresponding interval from a logistic regression produced by dichotomizing the data. When we analyzed existing datasets using our approach, we found that confidence intervals for the OR could be up to 64% shorter (36% as wide) compared to if the data had been dichotomized and analyzed using logistic regression. Conclusions More precise estimates of the OR can be obtained directly from the count data by using the log odds link function. This analytic approach is easy to implement in software packages that are capable of fitting generalized linear models or of maximizing user-defined likelihood functions. Binary data (dpeaa)DE-He213 Confidence intervals (dpeaa)DE-He213 Count data (dpeaa)DE-He213 Fisher information (dpeaa)DE-He213 Maximum likelihood (dpeaa)DE-He213 Nagaraja, Haikady N. aut Enthalten in BMC medical research methodology London : BioMed Central, 2001 18(2018), 1 vom: 20. Okt. (DE-627)326643818 (DE-600)2041362-2 1471-2288 nnns volume:18 year:2018 number:1 day:20 month:10 https://dx.doi.org/10.1186/s12874-018-0568-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 18 2018 1 20 10
allfieldsSound	10.1186/s12874-018-0568-9 doi (DE-627)SPR027375080 (SPR)s12874-018-0568-9-e DE-627 ger DE-627 rakwb eng Sroka, Christopher J. verfasserin (orcid)0000-0002-3049-4684 aut Odds ratios from logistic, geometric, Poisson, and negative binomial regression models 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2018 Background The odds ratio (OR) is used as an important metric of comparison of two or more groups in many biomedical applications when the data measure the presence or absence of an event or represent the frequency of its occurrence. In the latter case, researchers often dichotomize the count data into binary form and apply the well-known logistic regression technique to estimate the OR. In the process of dichotomizing the data, however, information is lost about the underlying counts which can reduce the precision of inferences on the OR. Methods We propose analyzing the count data directly using regression models with the log odds link function. With this approach, the parameter estimates in the model have the exact same interpretation as in a logistic regression of the dichotomized data, yielding comparable estimates of the OR. We prove analytically, using the Fisher information matrix, that our approach produces more precise estimates of the OR than logistic regression of the dichotomized data. We also show the gains in precision using simulation studies and real-world datasets. We focus on three related distributions for count data: geometric, Poisson, and negative binomial. Results In simulation studies, confidence intervals for the OR were 56–65% as wide (geometric model), 75–79% as wide (Poisson model), and 61–69% as wide (negative binomial model) as the corresponding interval from a logistic regression produced by dichotomizing the data. When we analyzed existing datasets using our approach, we found that confidence intervals for the OR could be up to 64% shorter (36% as wide) compared to if the data had been dichotomized and analyzed using logistic regression. Conclusions More precise estimates of the OR can be obtained directly from the count data by using the log odds link function. This analytic approach is easy to implement in software packages that are capable of fitting generalized linear models or of maximizing user-defined likelihood functions. Binary data (dpeaa)DE-He213 Confidence intervals (dpeaa)DE-He213 Count data (dpeaa)DE-He213 Fisher information (dpeaa)DE-He213 Maximum likelihood (dpeaa)DE-He213 Nagaraja, Haikady N. aut Enthalten in BMC medical research methodology London : BioMed Central, 2001 18(2018), 1 vom: 20. Okt. (DE-627)326643818 (DE-600)2041362-2 1471-2288 nnns volume:18 year:2018 number:1 day:20 month:10 https://dx.doi.org/10.1186/s12874-018-0568-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 18 2018 1 20 10
language	English
source	Enthalten in BMC medical research methodology 18(2018), 1 vom: 20. Okt. volume:18 year:2018 number:1 day:20 month:10
sourceStr	Enthalten in BMC medical research methodology 18(2018), 1 vom: 20. Okt. volume:18 year:2018 number:1 day:20 month:10
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Binary data Confidence intervals Count data Fisher information Maximum likelihood
isfreeaccess_bool	true
container_title	BMC medical research methodology
authorswithroles_txt_mv	Sroka, Christopher J. @@aut@@ Nagaraja, Haikady N. @@aut@@
publishDateDaySort_date	2018-10-20T00:00:00Z
hierarchy_top_id	326643818
id	SPR027375080
language_de	englisch
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In the latter case, researchers often dichotomize the count data into binary form and apply the well-known logistic regression technique to estimate the OR. In the process of dichotomizing the data, however, information is lost about the underlying counts which can reduce the precision of inferences on the OR. Methods We propose analyzing the count data directly using regression models with the log odds link function. With this approach, the parameter estimates in the model have the exact same interpretation as in a logistic regression of the dichotomized data, yielding comparable estimates of the OR. We prove analytically, using the Fisher information matrix, that our approach produces more precise estimates of the OR than logistic regression of the dichotomized data. We also show the gains in precision using simulation studies and real-world datasets. We focus on three related distributions for count data: geometric, Poisson, and negative binomial. Results In simulation studies, confidence intervals for the OR were 56–65% as wide (geometric model), 75–79% as wide (Poisson model), and 61–69% as wide (negative binomial model) as the corresponding interval from a logistic regression produced by dichotomizing the data. When we analyzed existing datasets using our approach, we found that confidence intervals for the OR could be up to 64% shorter (36% as wide) compared to if the data had been dichotomized and analyzed using logistic regression. Conclusions More precise estimates of the OR can be obtained directly from the count data by using the log odds link function. 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author	Sroka, Christopher J.
spellingShingle	Sroka, Christopher J. misc Binary data misc Confidence intervals misc Count data misc Fisher information misc Maximum likelihood Odds ratios from logistic, geometric, Poisson, and negative binomial regression models
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topic_title	Odds ratios from logistic, geometric, Poisson, and negative binomial regression models Binary data (dpeaa)DE-He213 Confidence intervals (dpeaa)DE-He213 Count data (dpeaa)DE-He213 Fisher information (dpeaa)DE-He213 Maximum likelihood (dpeaa)DE-He213
topic	misc Binary data misc Confidence intervals misc Count data misc Fisher information misc Maximum likelihood
topic_unstemmed	misc Binary data misc Confidence intervals misc Count data misc Fisher information misc Maximum likelihood
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title	Odds ratios from logistic, geometric, Poisson, and negative binomial regression models
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title_full	Odds ratios from logistic, geometric, Poisson, and negative binomial regression models
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title_sort	odds ratios from logistic, geometric, poisson, and negative binomial regression models
title_auth	Odds ratios from logistic, geometric, Poisson, and negative binomial regression models
abstract	Background The odds ratio (OR) is used as an important metric of comparison of two or more groups in many biomedical applications when the data measure the presence or absence of an event or represent the frequency of its occurrence. In the latter case, researchers often dichotomize the count data into binary form and apply the well-known logistic regression technique to estimate the OR. In the process of dichotomizing the data, however, information is lost about the underlying counts which can reduce the precision of inferences on the OR. Methods We propose analyzing the count data directly using regression models with the log odds link function. With this approach, the parameter estimates in the model have the exact same interpretation as in a logistic regression of the dichotomized data, yielding comparable estimates of the OR. We prove analytically, using the Fisher information matrix, that our approach produces more precise estimates of the OR than logistic regression of the dichotomized data. We also show the gains in precision using simulation studies and real-world datasets. We focus on three related distributions for count data: geometric, Poisson, and negative binomial. Results In simulation studies, confidence intervals for the OR were 56–65% as wide (geometric model), 75–79% as wide (Poisson model), and 61–69% as wide (negative binomial model) as the corresponding interval from a logistic regression produced by dichotomizing the data. When we analyzed existing datasets using our approach, we found that confidence intervals for the OR could be up to 64% shorter (36% as wide) compared to if the data had been dichotomized and analyzed using logistic regression. Conclusions More precise estimates of the OR can be obtained directly from the count data by using the log odds link function. This analytic approach is easy to implement in software packages that are capable of fitting generalized linear models or of maximizing user-defined likelihood functions. © The Author(s) 2018
abstractGer	Background The odds ratio (OR) is used as an important metric of comparison of two or more groups in many biomedical applications when the data measure the presence or absence of an event or represent the frequency of its occurrence. In the latter case, researchers often dichotomize the count data into binary form and apply the well-known logistic regression technique to estimate the OR. In the process of dichotomizing the data, however, information is lost about the underlying counts which can reduce the precision of inferences on the OR. Methods We propose analyzing the count data directly using regression models with the log odds link function. With this approach, the parameter estimates in the model have the exact same interpretation as in a logistic regression of the dichotomized data, yielding comparable estimates of the OR. We prove analytically, using the Fisher information matrix, that our approach produces more precise estimates of the OR than logistic regression of the dichotomized data. We also show the gains in precision using simulation studies and real-world datasets. We focus on three related distributions for count data: geometric, Poisson, and negative binomial. Results In simulation studies, confidence intervals for the OR were 56–65% as wide (geometric model), 75–79% as wide (Poisson model), and 61–69% as wide (negative binomial model) as the corresponding interval from a logistic regression produced by dichotomizing the data. When we analyzed existing datasets using our approach, we found that confidence intervals for the OR could be up to 64% shorter (36% as wide) compared to if the data had been dichotomized and analyzed using logistic regression. Conclusions More precise estimates of the OR can be obtained directly from the count data by using the log odds link function. This analytic approach is easy to implement in software packages that are capable of fitting generalized linear models or of maximizing user-defined likelihood functions. © The Author(s) 2018
abstract_unstemmed	Background The odds ratio (OR) is used as an important metric of comparison of two or more groups in many biomedical applications when the data measure the presence or absence of an event or represent the frequency of its occurrence. In the latter case, researchers often dichotomize the count data into binary form and apply the well-known logistic regression technique to estimate the OR. In the process of dichotomizing the data, however, information is lost about the underlying counts which can reduce the precision of inferences on the OR. Methods We propose analyzing the count data directly using regression models with the log odds link function. With this approach, the parameter estimates in the model have the exact same interpretation as in a logistic regression of the dichotomized data, yielding comparable estimates of the OR. We prove analytically, using the Fisher information matrix, that our approach produces more precise estimates of the OR than logistic regression of the dichotomized data. We also show the gains in precision using simulation studies and real-world datasets. We focus on three related distributions for count data: geometric, Poisson, and negative binomial. Results In simulation studies, confidence intervals for the OR were 56–65% as wide (geometric model), 75–79% as wide (Poisson model), and 61–69% as wide (negative binomial model) as the corresponding interval from a logistic regression produced by dichotomizing the data. When we analyzed existing datasets using our approach, we found that confidence intervals for the OR could be up to 64% shorter (36% as wide) compared to if the data had been dichotomized and analyzed using logistic regression. Conclusions More precise estimates of the OR can be obtained directly from the count data by using the log odds link function. This analytic approach is easy to implement in software packages that are capable of fitting generalized linear models or of maximizing user-defined likelihood functions. © The Author(s) 2018
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title_short	Odds ratios from logistic, geometric, Poisson, and negative binomial regression models
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