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Confidence interval construction for disease prevalence based on partial validation series

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  • Tang, Man-Lai
  • Qiu, Shi-Fang
  • Poon, Wai-Yin

Abstract

It is desirable to estimate disease prevalence based on data collected by a gold standard test, but such a test is often limited due to cost and ethical considerations. Data with partial validation series thus become an alternative. The construction of confidence intervals for disease prevalence with such data is considered. A total of 12 methods, which are based on two Wald-type test statistics, score test statistic, and likelihood ratio test statistic, are developed. Both asymptotic and approximate unconditional confidence intervals are constructed. Two methods are employed to construct the unconditional confidence intervals: one involves inverting two one-sided tests and the other involves inverting one two-sided test. Moreover, the bootstrapping method is used. Two real data sets are used to illustrate the proposed methods. Empirical results suggest that the 12 methods largely produce satisfactory results, and the confidence intervals derived from the score test statistic and the Wald test statistic with nuisance parameters appropriately evaluated generally outperform the others in terms of coverage. If the interval location or the non-coverage at the two ends of the interval is also of concern, then the aforementioned interval based on the Wald test becomes the best choice.

Suggested Citation

  • Tang, Man-Lai & Qiu, Shi-Fang & Poon, Wai-Yin, 2012. "Confidence interval construction for disease prevalence based on partial validation series," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1200-1220.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:5:p:1200-1220
    DOI: 10.1016/j.csda.2011.02.010
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    References listed on IDEAS

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    1. Alan Agresti & Yongyi Min, 2001. "On Small-Sample Confidence Intervals for Parameters in Discrete Distributions," Biometrics, The International Biometric Society, vol. 57(3), pages 963-971, September.
    2. Wai-Yin Poon & Hai-Bin Wang, 2010. "Bayesian Analysis of Multivariate Probit Models with Surrogate Outcome Data," Psychometrika, Springer;The Psychometric Society, vol. 75(3), pages 498-520, September.
    3. Nian-Sheng Tang & Man-Lai Tang, 2002. "Exact Unconditional Inference for Risk Ratio in a Correlated 2 × 2 Table with Structural Zero," Biometrics, The International Biometric Society, vol. 58(4), pages 972-980, December.
    4. Ivan S. F. Chan & Nian-Sheng Tang & Man-Lai Tang & Ping-Shing Chan, 2003. "Statistical Analysis of Noninferiority Trials with a Rate Ratio in Small-Sample Matched-Pair Designs," Biometrics, The International Biometric Society, vol. 59(4), pages 1170-1177, December.
    5. Ivan S. F. Chan & Zhongxin Zhang, 1999. "Test-Based Exact Confidence Intervals for the Difference of Two Binomial Proportions," Biometrics, The International Biometric Society, vol. 55(4), pages 1202-1209, December.
    6. Boese, Doyle H. & Young, Dean M. & Stamey, James D., 2006. "Confidence intervals for a binomial parameter based on binary data subject to false-positive misclassification," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3369-3385, August.
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