IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v39y2012i11p2453-2473.html
   My bibliography  Save this article

Sample size for estimating a binomial proportion: comparison of different methods

Author

Listed:
  • Luzia Gonçalves
  • M. Rosário de Oliveira
  • Cláudia Pascoal
  • Ana Pires

Abstract

The poor performance of the Wald method for constructing confidence intervals (CIs) for a binomial proportion has been demonstrated in a vast literature. The related problem of sample size determination needs to be updated and comparative studies are essential to understanding the performance of alternative methods. In this paper, the sample size is obtained for the Clopper--Pearson, Bayesian (Uniform and Jeffreys priors), Wilson, Agresti--Coull, Anscombe, and Wald methods. Two two-step procedures are used: one based on the expected length (EL) of the CI and another one on its first-order approximation. In the first step, all possible solutions that satisfy the optimal criterion are obtained. In the second step, a single solution is proposed according to a new criterion (e.g. highest coverage probability (CP)). In practice, it is expected a sample size reduction, therefore, we explore the behavior of the methods admitting 30% and 50% of losses. For all the methods, the ELs are inflated, as expected, but the coverage probabilities remain close to the original target (with few exceptions). It is not easy to suggest a method that is optimal throughout the range (0, 1) for p . Depending on whether the goal is to achieve CP approximately or above the nominal level different recommendations are made.

Suggested Citation

  • Luzia Gonçalves & M. Rosário de Oliveira & Cláudia Pascoal & Ana Pires, 2012. "Sample size for estimating a binomial proportion: comparison of different methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2453-2473, July.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:11:p:2453-2473
    DOI: 10.1080/02664763.2012.713919
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2012.713919
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2012.713919?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. Alan Agresti & Yongyi Min, 2005. "Frequentist Performance of Bayesian Confidence Intervals for Comparing Proportions in 2 × 2 Contingency Tables," Biometrics, The International Biometric Society, vol. 61(2), pages 515-523, June.
    2. Pan, Wei, 2002. "Approximate confidence intervals for one proportion and difference of two proportions," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 143-157, July.
    3. Nandini Dendukuri & Elham Rahme & Patrick Bélisle & Lawrence Joseph, 2004. "Bayesian Sample Size Determination for Prevalence and Diagnostic Test Studies in the Absence of a Gold Standard Test," Biometrics, The International Biometric Society, vol. 60(2), pages 388-397, June.
    4. Liu, W. & Bailey, B. J. R., 2002. "Sample size determination for constructing a constant width confidence interval for a binomial success probability," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 1-5, January.
    5. Vos, Paul W. & Hudson, Suzanne, 2005. "Evaluation Criteria for Discrete Confidence Intervals: Beyond Coverage and Length," The American Statistician, American Statistical Association, vol. 59, pages 137-142, May.
    6. Piegorsch, Walter W., 2004. "Sample sizes for improved binomial confidence intervals," Computational Statistics & Data Analysis, Elsevier, vol. 46(2), pages 309-316, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. M. Rosário Oliveira & Ana Subtil & Luzia Gonçalves, 2020. "Common Medical and Statistical Problems: The Dilemma of the Sample Size Calculation for Sensitivity and Specificity Estimation," Mathematics, MDPI, vol. 8(8), pages 1-17, August.
    2. Luzia Gonçalves & Zélia Santos & Miguel Amado & Daniela Alves & Rui Simões & António Pedro Delgado & Artur Correia & Jorge Cabral & Luís Velez Lapão & Isabel Craveiro, 2015. "Urban Planning and Health Inequities: Looking in a Small-Scale in a City of Cape Verde," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-27, November.

    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. M. Rosário Oliveira & Ana Subtil & Luzia Gonçalves, 2020. "Common Medical and Statistical Problems: The Dilemma of the Sample Size Calculation for Sensitivity and Specificity Estimation," Mathematics, MDPI, vol. 8(8), pages 1-17, August.
    2. Frank Tuyl & Richard Gerlach & Kerrie Mengersen, 2008. "Inference for Proportions in a 2 × 2 Contingency Table: HPD or not HPD?," Biometrics, The International Biometric Society, vol. 64(4), pages 1293-1295, December.
    3. Chinyereugo M Umemneku Chikere & Kevin Wilson & Sara Graziadio & Luke Vale & A Joy Allen, 2019. "Diagnostic test evaluation methodology: A systematic review of methods employed to evaluate diagnostic tests in the absence of gold standard – An update," PLOS ONE, Public Library of Science, vol. 14(10), pages 1-25, October.
    4. Hanson, Samuel & Schuermann, Til, 2006. "Confidence intervals for probabilities of default," Journal of Banking & Finance, Elsevier, vol. 30(8), pages 2281-2301, August.
    5. Stamey, James D. & Boese, Doyle H. & Young, Dean M., 2008. "Confidence intervals for parameters of two diagnostic tests in the absence of a gold standard," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1335-1346, January.
    6. Paul Gustafson, 2007. "Measurement error modelling with an approximate instrumental variable," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 797-815, November.
    7. Lei Shi & Hongyuan Sun & Peng Bai, 2009. "Bayesian confidence interval for difference of the proportions in a 2×2 table with structural zero," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(5), pages 483-494.
    8. Sander Greenland, 2005. "Multiple‐bias modelling for analysis of observational data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(2), pages 267-306, March.
    9. Minoda, Yuta & Yanagimoto, Takemi, 2009. "Estimation of a common slope in a gamma regression model with multiple strata: An empirical Bayes method," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4178-4185, October.
    10. Maria Bekker-Nielsen Dunbar & Thomas J R Finnie & Barney Sloane & Ian M Hall, 2019. "Methods for calculating credible intervals for ratios of beta distributions with application to relative risks of death during the second plague pandemic," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-12, February.
    11. Geoffrey Jones & Wesley O. Johnson & Timothy E. Hanson & Ronald Christensen, 2010. "Identifiability of Models for Multiple Diagnostic Testing in the Absence of a Gold Standard," Biometrics, The International Biometric Society, vol. 66(3), pages 855-863, September.
    12. Peng Bai & Wen Gan & Lei Shi, 2011. "Bayesian confidence interval for the risk ratio in a correlated 2 × 2 table with structural zero," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2805-2817, February.
    13. Luai Al-Labadi & Petru Ciur & Milutin Dimovic & Kyuson Lim, 2023. "Assessing Multinomial Distributions with a Bayesian Approach," Mathematics, MDPI, vol. 11(13), pages 1-16, July.
    14. Chris J. Lloyd, 2008. "A New Exact and More Powerful Unconditional Test of No Treatment Effect from Binary Matched Pairs," Biometrics, The International Biometric Society, vol. 64(3), pages 716-723, September.
    15. Alan Agresti & Sabrina Giordano & Anna Gottard, 2022. "A Review of Score-Test-Based Inference for Categorical Data," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 31-48, September.
    16. Li, Huiqiong & Tian, Guoliang & Tang, Niansheng & Cao, Hongyuan, 2018. "Assessing non-inferiority for incomplete paired-data under non-ignorable missing mechanism," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 69-81.
    17. Beavers, Daniel P. & Stamey, James D., 2012. "Bayesian sample size determination for binary regression with a misclassified covariate and no gold standard," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2574-2582.
    18. Paul Gustafson & Sander Greenland, 2006. "The Performance of Random Coefficient Regression in Accounting for Residual Confounding," Biometrics, The International Biometric Society, vol. 62(3), pages 760-768, September.
    19. Paul Vos & Qiang Wu, 2012. "Estimators for the binomial distribution that dominate the MLE in terms of Kullback–Leibler risk," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 359-371, April.
    20. Paul Gustafson, 2006. "Sample size implications when biases are modelled rather than ignored," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(4), pages 865-881, October.

    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:39:y:2012:i:11:p:2453-2473. 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.