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On inconsistency of the common rate difference estimators from sparse follow-up data

  • Estimation
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Abstract

It has been shown that the unconditional maximum likelihood estimator of the common odds ratio, risk ratio and risk difference parameters are inconsistent in sparse statification. Under a Poisson sparse-data model, the maximum likelihood estimator for the rate difference, which is the difference of the disease incidence rates among the exposed and the unexposed, is also shown to be biased. The sparse-data asymptotic bias of the maximum likelihood estimator is evaluated numerically and compared with that of the weighted least squares estimators.

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References

  • Andersen, E. B. (1970). Asymptotic properties of conditional maximum-likelihood estimators, J. Roy. Statist. Soc. Ser. B, 32, 283–301.

    Google Scholar 

  • Breslow, N. E. (1981). Odds ratio estimators when the data are sparse, Biometrika, 68, 73–84.

    Google Scholar 

  • Breslow, N. E. and Day, N. E. (1987). Statistical Methods in Cancer Research, Vol. 2 — The Design and Analysis of Cohort Studies, Oxford University Press, New York.

    Google Scholar 

  • Greenland, S. (1982). Interpretation and estimation of summary ratios under heterogeneity, Statistics in Medicine, 1, 217–227.

    Google Scholar 

  • Greenland, S. and Robins, J. M. (1985). Estimation of a common effect parameter from sparse follow-up data, Biometrics, 41, 55–68.

    Google Scholar 

  • Grizzle, J. E., Starmer, C. F. and Koch, G. G. (1969). Analysis of categorical data by linear models, Biometrics, 25, 489–504.

    Google Scholar 

  • Rothman, K. J. and Boice, J. D. (1982). Epidemiologic Analysis with a Programmable Calculator, Epidemiology Resources Inc., Boston.

    Google Scholar 

  • Sato, T. (1990). Confidence intervals for effect parameters common in cancer epidemiology, Environmental Health Perspectives, 87, 95–101.

    Google Scholar 

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Author notes

  1. Tosiya Sato

    Present address: The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, 106, Tokyo, Japan

Authors and Affiliations

  1. Department of Epidemiology, School of Health Sciences, University of Tokyo, Hongo, Bunkyo-ku, 113, Tokyo, Japan

    Tosiya Sato

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  1. Tosiya Sato
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Sato, T. On inconsistency of the common rate difference estimators from sparse follow-up data. Ann Inst Stat Math 44, 529–535 (1992). https://doi.org/10.1007/BF00050703

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  • DOI: https://doi.org/10.1007/BF00050703

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