Generalized Confidence Intervals and Fiducial Intervals for Some Epidemiological Measures.
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.
The Biostatistics Center, Department of Epidemiology and Biostatistics, The George Washington University, 6110 Executive Blvd., Rockville, MD 20852, USA. ibebu@bsc.gwu.edu.
Ionut
I
Bebu
Department of Biostatistics, Bioinformatics and Biomathematics, Georgetown University, 4000 Reservoir Road, Washington, DC 20057, USA. George.Luta@georgetown.edu.
George
G
Luta
Department of Mathematics and Statistics, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA. mathew@umbc.edu.
Thomas
T
Mathew
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. bagan@idcrp.org.
Brian K
BK
Agan
D016001:Confidence Intervals; D004812:Epidemiologic Methods; D015233:Models, Statistical; D016017:Odds Ratio; D015995:Prevalence; D018401:Sample Size
common odds ratio; fiducial quantity; generalized pivotal quantity; log-binomial model; logistic regression