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Int. J. Environ. Res. Public Health 2016, 13(6), 605; doi:10.3390/ijerph13060605

Generalized Confidence Intervals and Fiducial Intervals for Some Epidemiological Measures

1
The Biostatistics Center, Department of Epidemiology and Biostatistics, The George Washington University, 6110 Executive Blvd., Rockville, MD 20852, USA
2
Department of Biostatistics, Bioinformatics and Biomathematics, Georgetown University, 4000 Reservoir Road, Washington, DC 20057, USA
3
Department of Mathematics and Statistics, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA
4
Infectious Disease Clinical Research Program, Department of Preventive Medicine and Biometrics, Uniformed Services University of the Health Sciences, 4301 Jones Bridge Road, Bethesda, MD 20814, USA
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Igor Burstyn
Received: 14 March 2016 / Revised: 3 June 2016 / Accepted: 12 June 2016 / Published: 18 June 2016
(This article belongs to the Special Issue Methodological Innovations and Reflections-1)
View Full-Text   |   Download PDF [344 KB, uploaded 18 June 2016]

Abstract

For binary outcome data from epidemiological studies, this article investigates the interval estimation of several measures of interest in the absence or presence of categorical covariates. When covariates are present, the logistic regression model as well as the log-binomial model are investigated. The measures considered include the common odds ratio (OR) from several studies, the number needed to treat (NNT), and the prevalence ratio. For each parameter, confidence intervals are constructed using the concepts of generalized pivotal quantities and fiducial quantities. Numerical results show that the confidence intervals so obtained exhibit satisfactory performance in terms of maintaining the coverage probabilities even when the sample sizes are not large. An appealing feature of the proposed solutions is that they are not based on maximization of the likelihood, and hence are free from convergence issues associated with the numerical calculation of the maximum likelihood estimators, especially in the context of the log-binomial model. The results are illustrated with a number of examples. The overall conclusion is that the proposed methodologies based on generalized pivotal quantities and fiducial quantities provide an accurate and unified approach for the interval estimation of the various epidemiological measures in the context of binary outcome data with or without covariates. View Full-Text
Keywords: common odds ratio; generalized pivotal quantity; fiducial quantity; log-binomial model; logistic regression common odds ratio; generalized pivotal quantity; fiducial quantity; log-binomial model; logistic regression
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Bebu, I.; Luta, G.; Mathew, T.; Agan, B.K. Generalized Confidence Intervals and Fiducial Intervals for Some Epidemiological Measures. Int. J. Environ. Res. Public Health 2016, 13, 605.

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