IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v41y2014i2p439-453.html
   My bibliography  Save this article

Hybrid-based confidence intervals for the ratio of two treatment means in the over-dispersed Poisson data

Author

Listed:
  • Krishna K. Saha
  • Roger Bilisoly
  • Darius M. Dziuda

Abstract

In many clinical trials and epidemiological studies, comparing the mean count response of an exposed group to a control group is often of interest. This type of data is often over-dispersed with respect to Poisson variation, and previous studies usually compared groups using confidence intervals (CIs) of the difference between the two means. However, in some situations, especially when the means are small, interval estimation of the mean ratio (MR) is preferable. Moreover, Cox and Lewis [4] pointed out many other situations where the MR is more relevant than the difference of means. In this paper, we consider CI construction for the ratio of means between two treatments for over-dispersed Poisson data. We develop several CIs for the situation by hybridizing two separate CIs for two individual means. Extensive simulations show that all hybrid-based CIs perform reasonably well in terms of coverage. However, the CIs based on the delta method using the logarithmic transformation perform better than other intervals in the sense that they have slightly shorter interval lengths and show better balance of tail errors. These proposed CIs are illustrated with three real data examples.

Suggested Citation

  • Krishna K. Saha & Roger Bilisoly & Darius M. Dziuda, 2014. "Hybrid-based confidence intervals for the ratio of two treatment means in the over-dispersed Poisson data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(2), pages 439-453, February.
  • Handle: RePEc:taf:japsta:v:41:y:2014:i:2:p:439-453
    DOI: 10.1080/02664763.2013.840273
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2013.840273
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/02664763.2013.840273?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Krishna Saha & Sudhir Paul, 2005. "Bias-Corrected Maximum Likelihood Estimator of the Negative Binomial Dispersion Parameter," Biometrics, The International Biometric Society, vol. 61(1), pages 179-185, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mahdi Teimouri, 2022. "bccp: an R package for life-testing and survival analysis," Computational Statistics, Springer, vol. 37(1), pages 469-489, March.
    2. Sileshi, Gudeta & Hailu, Girma & Nyadzi, Gerson I., 2009. "Traditional occupancy–abundance models are inadequate for zero-inflated ecological count data," Ecological Modelling, Elsevier, vol. 220(15), pages 1764-1775.
    3. Seoyun Choe & Hee-Sung Kim & Sunmi Lee, 2020. "Exploration of Superspreading Events in 2015 MERS-CoV Outbreak in Korea by Branching Process Models," IJERPH, MDPI, vol. 17(17), pages 1-14, August.
    4. Mário Castro & Yolanda M. Gómez, 2020. "A Bayesian Cure Rate Model Based on the Power Piecewise Exponential Distribution," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 677-692, June.
    5. Jinfeng Xu & Anthony Kuk, 2015. "On Pooling of Data and Its Relative Efficiency," International Statistical Review, International Statistical Institute, vol. 83(2), pages 309-323, August.
    6. Krishna K. Saha & Debaraj Sen & Chun Jin, 2012. "Profile likelihood-based confidence interval for the dispersion parameter in count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(4), pages 765-783, August.
    7. Dai, Hongsheng & Bao, Yanchun & Bao, Mingtang, 2013. "Maximum likelihood estimate for the dispersion parameter of the negative binomial distribution," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 21-27.
    8. Edwin M.M. Ortega & Gauss M. Cordeiro & Michael W. Kattan, 2012. "The negative binomial--beta Weibull regression model to predict the cure of prostate cancer," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1191-1210, November.
    9. Alex Mota & Eder A. Milani & Jeremias Leão & Pedro L. Ramos & Paulo H. Ferreira & Oilson G. Junior & Vera L. D. Tomazella & Francisco Louzada, 2023. "A new cure rate frailty regression model based on a weighted Lindley distribution applied to stomach cancer data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 883-909, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:japsta:v:41:y:2014:i:2:p:439-453. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.