Beyond Confidence Intervals: Bayesian Credible Intervals - Virginia Henderson International Nursing e-Repository
Beyond Confidence Intervals: Bayesian Credible Intervals
http://hdl.handle.net/10755/163801
Category:AbstractType:PresentationTitle:Beyond Confidence Intervals: Bayesian Credible IntervalsAuthor(s):Lucke, JosephAuthor Details:Joseph Lucke, University of Pittsburgh, School of Nursing, Pittsburgh, Pennsylvania, USA, email: cnrweb@pitt.eduAbstract:Purpose. Nurse researchers and administrators have increasingly advocated statistical methods that provide more information than the significance test. Some authors now recommend that confidence intervals complement or perhaps supplant tests of significance. For a variety of reasons, confidence intervals cannot serve the purposes intended. Fundamentally, confidence intervals cannot be interpreted as probability bounds on an unknown parameter (such as the propensity of infection). However, Bayesian statistical theory provides credible intervals, which yield probability bounds on a parameter. Specific Aim. This study demonstrates the utility of Bayesian estimation of the propensity to acquire nosocomial infections. Framework. Secondary data was obtained from a multi-institutional outcomes database managed by the School of Nursing. The sampling frame consisted of the ICU's of one hospital over 12 months. The data comprised the monthly patient censuses and the number of patients who developed one or more nosocomial infections during their ICU stay. Methods. Standard Bayesian methods for binomial data were used. Let ( denote the propensity of a patient's being nosocomially infected. For each month i = 1,¼, 12, let yi denote the number of infected patients and ni denote the census. Assuming independence, yi | ( ~ binomial((, ni). For (, pi(() = beta((i, (i). The prior distribution of ( was p0(() = beta((0, (0) with (0 = .3 and (0 = .7, generating a diffuse prior. By Bayes's Theorem, (i = (i-1 + yi and (i = (i-1 + ni - yi. Given the pi-1(() for the previous month, the predicted number of infections for the current month is yi* ~ beta-binomial((i-1, (i-1, ni). Results. MonthCensus # ofPropensityCredible IntervalPredicted InfectionsInfectionsLower UpperExpectedUpper0 -- -- .30 .00 .98 -- --1 78 4 .05 .02 .11 23.4 742 77 6 .06 .03 .10 4.0 9... ... ... ... ... ... ... ...11 62 0 .04 .03 .06 2.8 612 60 1 .04 .03 .05 2.5 5 Discussion. Prior to collecting any data, the propensity of infection was posited to have probability .95 of lying between 0 and .98 with a mean of .3. Given the first month's data of 4 infected patients out of 78, the propensity was revised to have probability .95 of lying between.02 and .11 with a mean of .05. The estimated propensities and their 95% credible intervals were continually revised throughout the 12 months as depicted in the table. By the end of 12 months, with 30 infected patients out of 745, the propensity had probability .95 of lying between .03 and .05 with a mean of .04. In no month did the number of infections exceed the 95% predictive upper bound. Implications. In contrast to confidence intervals, 100p% credible intervals have the natural interpretation of "the probability that parameter falls within the interval is p". In addition, credible intervals can be updated over time while retaining previous information. Thus, credible intervals are well suited for outcomes research and evaluation.Repository Posting Date:27-Oct-2011 Date of Publication:27-Oct-2011 Conference Date:2001Conference Name:ENRS 13th Annual Scientific SessionsConference Host:Eastern Nursing Research SocietyConference Location:Atlantic City, New Jersey, USANote:This is an abstract-only submission. If the author has submitted a full-text item based on this abstract, you may find it by browsing the Virginia Henderson Global Nursing e-Repository by author. If author contact information is available in this abstract, please feel free to contact him or her with your queries regarding this submission. Alternatively, please contact the conference host, journal, or publisher (according to the circumstance) for further details regarding this item. If a citation is listed in this record, the item has been published and is available via open-access avenues or a journal/database subscription. Contact your library for assistance in obtaining the as-published article.Full metadata recordDC FieldValue Languagedc.type.categoryAbstracten_US
dc.titleBeyond Confidence Intervals: Bayesian Credible Intervalsen_GB
dc.contributor.authorLucke, Josephen_US
dc.author.detailsJoseph Lucke, University of Pittsburgh, School of Nursing, Pittsburgh, Pennsylvania, USA, email: cnrweb@pitt.eduen_US
dc.identifier.urihttp://hdl.handle.net/10755/163801-
dc.description.abstractPurpose. Nurse researchers and administrators have increasingly advocated statistical methods that provide more information than the significance test. Some authors now recommend that confidence intervals complement or perhaps supplant tests of significance. For a variety of reasons, confidence intervals cannot serve the purposes intended. Fundamentally, confidence intervals cannot be interpreted as probability bounds on an unknown parameter (such as the propensity of infection). However, Bayesian statistical theory provides credible intervals, which yield probability bounds on a parameter. Specific Aim. This study demonstrates the utility of Bayesian estimation of the propensity to acquire nosocomial infections. Framework. Secondary data was obtained from a multi-institutional outcomes database managed by the School of Nursing. The sampling frame consisted of the ICU's of one hospital over 12 months. The data comprised the monthly patient censuses and the number of patients who developed one or more nosocomial infections during their ICU stay. Methods. Standard Bayesian methods for binomial data were used. Let ( denote the propensity of a patient's being nosocomially infected. For each month i = 1,&frac14;, 12, let yi denote the number of infected patients and ni denote the census. Assuming independence, yi | ( ~ binomial((, ni). For (, pi(() = beta((i, (i). The prior distribution of ( was p0(() = beta((0, (0) with (0 = .3 and (0 = .7, generating a diffuse prior. By Bayes's Theorem, (i = (i-1 + yi and (i = (i-1 + ni - yi. Given the pi-1(() for the previous month, the predicted number of infections for the current month is yi* ~ beta-binomial((i-1, (i-1, ni). Results. MonthCensus # ofPropensityCredible IntervalPredicted InfectionsInfectionsLower UpperExpectedUpper0 -- -- .30 .00 .98 -- --1 78 4 .05 .02 .11 23.4 742 77 6 .06 .03 .10 4.0 9... ... ... ... ... ... ... ...11 62 0 .04 .03 .06 2.8 612 60 1 .04 .03 .05 2.5 5 Discussion. Prior to collecting any data, the propensity of infection was posited to have probability .95 of lying between 0 and .98 with a mean of .3. Given the first month's data of 4 infected patients out of 78, the propensity was revised to have probability .95 of lying between.02 and .11 with a mean of .05. The estimated propensities and their 95% credible intervals were continually revised throughout the 12 months as depicted in the table. By the end of 12 months, with 30 infected patients out of 745, the propensity had probability .95 of lying between .03 and .05 with a mean of .04. In no month did the number of infections exceed the 95% predictive upper bound. Implications. In contrast to confidence intervals, 100p% credible intervals have the natural interpretation of "the probability that parameter falls within the interval is p". In addition, credible intervals can be updated over time while retaining previous information. Thus, credible intervals are well suited for outcomes research and evaluation.en_GB
dc.date.available2011-10-27T11:14:04Z-
dc.date.accessioned2011-10-27T11:14:04Z-
Beyond Confidence Intervals: Bayesian Credible Intervals - Virginia Henderson International Nursing e-Repository
Beyond Confidence Intervals: Bayesian Credible Intervals
http://hdl.handle.net/10755/163801
Category:AbstractType:PresentationTitle:Beyond Confidence Intervals: Bayesian Credible IntervalsAuthor(s):Lucke, JosephAuthor Details:Joseph Lucke, University of Pittsburgh, School of Nursing, Pittsburgh, Pennsylvania, USA, email: cnrweb@pitt.eduAbstract:Purpose. Nurse researchers and administrators have increasingly advocated statistical methods that provide more information than the significance test. Some authors now recommend that confidence intervals complement or perhaps supplant tests of significance. For a variety of reasons, confidence intervals cannot serve the purposes intended. Fundamentally, confidence intervals cannot be interpreted as probability bounds on an unknown parameter (such as the propensity of infection). However, Bayesian statistical theory provides credible intervals, which yield probability bounds on a parameter. Specific Aim. This study demonstrates the utility of Bayesian estimation of the propensity to acquire nosocomial infections. Framework. Secondary data was obtained from a multi-institutional outcomes database managed by the School of Nursing. The sampling frame consisted of the ICU's of one hospital over 12 months. The data comprised the monthly patient censuses and the number of patients who developed one or more nosocomial infections during their ICU stay. Methods. Standard Bayesian methods for binomial data were used. Let ( denote the propensity of a patient's being nosocomially infected. For each month i = 1,¼, 12, let yi denote the number of infected patients and ni denote the census. Assuming independence, yi | ( ~ binomial((, ni). For (, pi(() = beta((i, (i). The prior distribution of ( was p0(() = beta((0, (0) with (0 = .3 and (0 = .7, generating a diffuse prior. By Bayes's Theorem, (i = (i-1 + yi and (i = (i-1 + ni - yi. Given the pi-1(() for the previous month, the predicted number of infections for the current month is yi* ~ beta-binomial((i-1, (i-1, ni). Results. MonthCensus # ofPropensityCredible IntervalPredicted InfectionsInfectionsLower UpperExpectedUpper0 -- -- .30 .00 .98 -- --1 78 4 .05 .02 .11 23.4 742 77 6 .06 .03 .10 4.0 9... ... ... ... ... ... ... ...11 62 0 .04 .03 .06 2.8 612 60 1 .04 .03 .05 2.5 5 Discussion. Prior to collecting any data, the propensity of infection was posited to have probability .95 of lying between 0 and .98 with a mean of .3. Given the first month's data of 4 infected patients out of 78, the propensity was revised to have probability .95 of lying between.02 and .11 with a mean of .05. The estimated propensities and their 95% credible intervals were continually revised throughout the 12 months as depicted in the table. By the end of 12 months, with 30 infected patients out of 745, the propensity had probability .95 of lying between .03 and .05 with a mean of .04. In no month did the number of infections exceed the 95% predictive upper bound. Implications. In contrast to confidence intervals, 100p% credible intervals have the natural interpretation of "the probability that parameter falls within the interval is p". In addition, credible intervals can be updated over time while retaining previous information. Thus, credible intervals are well suited for outcomes research and evaluation.Repository Posting Date:27-Oct-2011 Date of Publication:27-Oct-2011 Conference Date:2001Conference Name:ENRS 13th Annual Scientific SessionsConference Host:Eastern Nursing Research SocietyConference Location:Atlantic City, New Jersey, USANote:This is an abstract-only submission. If the author has submitted a full-text item based on this abstract, you may find it by browsing the Virginia Henderson Global Nursing e-Repository by author. If author contact information is available in th
is abstract, please feel free to contact him or her with your queries regarding this submission. Alternatively, please contact the conference host, journal, or publisher (according to the circumstance) for further details regarding this item. If a citation is listed in this record, the item has been published and is available via open-access avenues or a journal/database subscription. Contact your library for assistance in obtaining the as-published article.Full metadata recordDC FieldValue Languagedc.type.categoryAbstracten_US
dc.titleBeyond Confidence Intervals: Bayesian Credible Intervalsen_GB
dc.contributor.authorLucke, Josephen_US
dc.author.detailsJoseph Lucke, University of Pittsburgh, School of Nursing, Pittsburgh, Pennsylvania, USA, email: cnrweb@pitt.eduen_US
dc.identifier.urihttp://hdl.handle.net/10755/163801-
dc.description.abstractPurpose. Nurse researchers and administrators have increasingly advocated statistical methods that provide more information than the significance test. Some authors now recommend that confidence intervals complement or perhaps supplant tests of significance. For a variety of reasons, confidence intervals cannot serve the purposes intended. Fundamentally, confidence intervals cannot be interpreted as probability bounds on an unknown parameter (such as the propensity of infection). However, Bayesian statistical theory provides credible intervals, which yield probability bounds on a parameter. Specific Aim. This study demonstrates the utility of Bayesian estimation of the propensity to acquire nosocomial infections. Framework. Secondary data was obtained from a multi-institutional outcomes database managed by the School of Nursing. The sampling frame consisted of the ICU's of one hospital over 12 months. The data comprised the monthly patient censuses and the number of patients who developed one or more nosocomial infections during their ICU stay. Methods. Standard Bayesian methods for binomial data were used. Let ( denote the propensity of a patient's being nosocomially infected. For each month i = 1,&frac14;, 12, let yi denote the number of infected patients and ni denote the census. Assuming independence, yi | ( ~ binomial((, ni). For (, pi(() = beta((i, (i). The prior distribution of ( was p0(() = beta((0, (0) with (0 = .3 and (0 = .7, generating a diffuse prior. By Bayes's Theorem, (i = (i-1 + yi and (i = (i-1 + ni - yi. Given the pi-1(() for the previous month, the predicted number of infections for the current month is yi* ~ beta-binomial((i-1, (i-1, ni). Results. MonthCensus # ofPropensityCredible IntervalPredicted InfectionsInfectionsLower UpperExpectedUpper0 -- -- .30 .00 .98 -- --1 78 4 .05 .02 .11 23.4 742 77 6 .06 .03 .10 4.0 9... ... ... ... ... ... ... ...11 62 0 .04 .03 .06 2.8 612 60 1 .04 .03 .05 2.5 5 Discussion. Prior to collecting any data, the propensity of infection was posited to have probability .95 of lying between 0 and .98 with a mean of .3. Given the first month's data of 4 infected patients out of 78, the propensity was revised to have probability .95 of lying between.02 and .11 with a mean of .05. The estimated propensities and their 95% credible intervals were continually revised throughout the 12 months as depicted in the table. By the end of 12 months, with 30 infected patients out of 745, the propensity had probability .95 of lying between .03 and .05 with a mean of .04. In no month did the number of infections exceed the 95% predictive upper bound. Implications. In contrast to confidence intervals, 100p% credible intervals have the natural interpretation of "the probability that parameter falls within the interval is p". In addition, credible intervals can be updated over time while retaining previous information. Thus, credible intervals are well suited for outcomes research and evaluation.en_GB
dc.date.available2011-10-27T11:14:04Z-
dc.date.accessioned2011-10-27T11:14:04Z-