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Confidence intervals for ratio of two Poisson rates using the method of variance estimates recovery

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  • Hui-Qiong Li
  • Man-Lai Tang
  • Weng-Kee Wong

Abstract

Inference based on ratio of two independent Poisson rates is common in epidemiological studies. We study the performance of a variety of unconditional method of variance estimates recovery (MOVER) methods of combining separate confidence intervals for two single Poisson rates to form a confidence interval for their ratio. We consider confidence intervals derived from (1) the Fieller’s theorem, (2) the logarithmic transformation with the delta method and (3) the substitution method. We evaluate the performance of 13 such types of confidence intervals by comparing their empirical coverage probabilities, empirical confidence widths, ratios of mesial non-coverage probability and total non-coverage probabilities. Our simulation results suggest that the MOVER Rao score confidence intervals based on the Fieller’s theorem and the substitution method are preferable. We provide two applications to construct confidence intervals for the ratio of two Poisson rates in a breast cancer study and in a study that examines coronary heart diseases incidences among post menopausal women treated with or without hormones. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Hui-Qiong Li & Man-Lai Tang & Weng-Kee Wong, 2014. "Confidence intervals for ratio of two Poisson rates using the method of variance estimates recovery," Computational Statistics, Springer, vol. 29(3), pages 869-889, June.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:3:p:869-889
    DOI: 10.1007/s00180-013-0467-9
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    References listed on IDEAS

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    1. Allan Dormer & Guangyong Zou, 2002. "Interval Estimation for a Difference Between Intraclass Kappa Statistics," Biometrics, The International Biometric Society, vol. 58(1), pages 209-215, March.
    2. Ng, H.K.T. & Gu, K. & Tang, M.L., 2007. "A comparative study of tests for the difference of two Poisson means," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3085-3099, March.
    3. Price, Robert M. & Bonett, Douglas G., 2000. "Estimating the ratio of two Poisson rates," Computational Statistics & Data Analysis, Elsevier, vol. 34(3), pages 345-356, September.
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    Cited by:

    1. Guogen Shan, 2016. "Exact sample size determination for the ratio of two incidence rates under the Poisson distribution," Computational Statistics, Springer, vol. 31(4), pages 1633-1644, December.
    2. Malekzadeh, Ahad & Esmaeli-Ayan, Asghar, 2021. "An exact method for testing equality of several groups in panel data models," Statistics & Probability Letters, Elsevier, vol. 177(C).

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