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Sample size implications when biases are modelled rather than ignored

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  • Paul Gustafson

Abstract

Summary. Realistic statistical modelling of observational data often suggests a statistical model which is not fully identified, owing to potential biases that are not under the control of study investigators. Bayesian inference can be implemented with such a model, ideally with the most precise prior knowledge that can be ascertained. However, as a consequence of the non‐identifiability, inference cannot be made arbitrarily accurate by choosing the sample size to be sufficiently large. In turn, this has consequences for sample size determination. The paper presents a sample size criterion that is based on a quantification of how much Bayesian learning can arise in a given non‐identified model. A global perspective is adopted, whereby choosing larger sample sizes for some studies necessarily implies that some other potentially worthwhile studies cannot be undertaken. This suggests that smaller sample sizes should be selected with non‐identified models, as larger sample sizes constitute a squandering of resources in making estimator variances very small compared with their biases. Particularly, consider two investigators planning the same study, one of whom admits to the potential biases at hand and consequently uses a non‐identified model, whereas the other pretends that there are no biases, leading to an identified but less realistic model. It is seen that the former investigator always selects a smaller sample size than the latter, with the difference being quite marked in some illustrative cases.

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  • 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.
  • Handle: RePEc:bla:jorssa:v:169:y:2006:i:4:p:865-881
    DOI: 10.1111/j.1467-985X.2006.00436.x
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    References listed on IDEAS

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    1. 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.
    2. Sander Greenland, 2000. "When Should Epidemiologic Regressions Use Random Coefficients?," Biometrics, The International Biometric Society, vol. 56(3), pages 915-921, September.
    3. Sander Greenland, 2001. "Sensitivity Analysis, Monte Carlo Risk Analysis, and Bayesian Uncertainty Assessment," Risk Analysis, John Wiley & Sons, vol. 21(4), pages 579-584, August.
    4. 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.
    5. Paul Gustafson & Nhu D. Le & Refik Saskin, 2001. "Case–Control Analysis with Partial Knowledge of Exposure Misclassification Probabilities," Biometrics, The International Biometric Society, vol. 57(2), pages 598-609, June.
    6. E. Rahme & L. Joseph & T. W. Gyorkos, 2000. "Bayesian sample size determination for estimating binomial parameters from data subject to misclassification," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(1), pages 119-128.
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    Cited by:

    1. Gustafson Paul, 2010. "Bayesian Inference for Partially Identified Models," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-20, March.
    2. P. Gustafson & L. C. McCandless & A. R. Levy & S. Richardson, 2010. "Simplified Bayesian Sensitivity Analysis for Mismeasured and Unobserved Confounders," Biometrics, The International Biometric Society, vol. 66(4), pages 1129-1137, December.
    3. Wang Dongxu & Shen Tian & Gustafson Paul, 2012. "Partial Identification arising from Nondifferential Exposure Misclassification: How Informative are Data on the Unlikely, Maybe, and Likely Exposed?," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-27, November.

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