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Asymptotic analysis of reliability measures for an imperfect dichotomous test

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  • Alla Slynko

    (University of Waterloo)

Abstract

To access the reliability of a new dichotomous test and to capture the random variability of its results in the absence of a gold standard, two measures, the inconsistent acceptance probability (IAP) and inconsistent rejection probability (IRP), were introduced in the literature. In this paper, we first analyze the limiting behavior of both measures as the number of test repetitions increases and derive the corresponding accuracy estimates and rates of convergence. To overcome possible limitations of IRP and IAP, we then introduce a one-parameter family of refined reliability measures, $$\Delta (k, s)$$ Δ ( k , s ) . Such measures characterize the consistency of the results of a dichotomous test in the absence of a gold standard as the threshold for a positive aggregate test result varies. Similar to IRP and IAP, we also derive corresponding accuracy estimates and rates of convergence for $$\Delta (k, s)$$ Δ ( k , s ) as the number k of test repetitions increases.

Suggested Citation

  • Alla Slynko, 2022. "Asymptotic analysis of reliability measures for an imperfect dichotomous test," Statistical Papers, Springer, vol. 63(4), pages 995-1012, August.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:4:d:10.1007_s00362-021-01266-9
    DOI: 10.1007/s00362-021-01266-9
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    References listed on IDEAS

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    1. Paul S. Albert, 2007. "Random Effects Modeling Approaches for Estimating ROC Curves from Repeated Ordinal Tests without a Gold Standard," Biometrics, The International Biometric Society, vol. 63(2), pages 593-602, June.
    2. Giorgia Guglielmi, 2020. "Fast coronavirus tests: what they can and can’t do," Nature, Nature, vol. 585(7826), pages 496-498, September.
    3. Peter Politser, 1982. "Reliability, Decision Rules, and the Value of Repeated Tests," Medical Decision Making, , vol. 2(1), pages 47-69, February.
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