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Generalized Confidence Intervals and Fiducial Intervals for Some Epidemiological Measures

Author

Listed:
  • Ionut Bebu

    (The Biostatistics Center, Department of Epidemiology and Biostatistics, The George Washington University, 6110 Executive Blvd., Rockville, MD 20852, USA
    These authors contributed equally to this work.)

  • George Luta

    (Department of Biostatistics, Bioinformatics and Biomathematics, Georgetown University, 4000 Reservoir Road, Washington, DC 20057, USA
    These authors contributed equally to this work.)

  • Thomas Mathew

    (Department of Mathematics and Statistics, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA)

  • Brian K. Agan

    (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)

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.

Suggested Citation

  • Ionut Bebu & George Luta & Thomas Mathew & Brian K. Agan, 2016. "Generalized Confidence Intervals and Fiducial Intervals for Some Epidemiological Measures," IJERPH, MDPI, vol. 13(6), pages 1-13, June.
    • Handle: RePEc:gam:jijerp:v:13:y:2016:i:6:p:605-:d:72276
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    References listed on IDEAS

    as
    1. Yang Liu & Jan Hannig, 2016. "Generalized Fiducial Inference for Binary Logistic Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 81(2), pages 290-324, June.
    2. Min-ge Xie & Kesar Singh, 2013. "Confidence Distribution, the Frequentist Distribution Estimator of a Parameter: A Review," International Statistical Review, International Statistical Institute, vol. 81(1), pages 3-39, April.
    3. Zaihra Tasneem & Paul Sudhir, 2010. "Interval Estimation of Some Epidemiological Measures of Association," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-23, October.
    4. Jan Hannig & Hari Iyer & Randy C. S. Lai & Thomas C. M. Lee, 2016. "Generalized Fiducial Inference: A Review and New Results," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1346-1361, July.
    5. Jan Hannig & Thomas C. M. Lee, 2009. "Generalized fiducial inference for wavelet regression," Biometrika, Biometrika Trust, vol. 96(4), pages 847-860.
    6. Xie, Minge & Singh, Kesar & Strawderman, William E., 2011. "Confidence Distributions and a Unifying Framework for Meta-Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 320-333.
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