Estimation of the random error of binary tests using adaptive polynomials

Abstract

We investigate how to estimate error probabilities for binary measurements and tests when a gold standard is not available. Recent studies have shown that, without a gold standard, the widely used false-acceptance probability ($FAP$) and false-rejection probability ($FRP$) are difficult to estimate. We show by mathematical analysis that this problem is inherent to the unavailability of a gold standard. Instead, the proposed method determines the random components of the error probabilities: the inconsistent acceptance and rejection probabilities $IAP$ and $IRP$. The method is efficient and robust as the number of model parameters is not predetermined but depends on the goodness of fit.

Keywords:

• accuracy of diagnostic tests
• gold standard unavailable
• measurement reliability
• measurement system analysis
• pass/fail-inspection
• semi-nonparametrics

Additional information

Notes on contributors

Thomas S. Akkerhuis

Dr. Akkerhuis is a Statistical Consultant in the Statistics & Data Science team at Shell Global Solutions International. His e-mail address is [email protected].

Jeroen de Mast

Dr. De Mast is Professor in the Department of Statistics and Actuarial Science at the University of Waterloo. His email address is [email protected].

Tashi P. Erdmann

Dr. Erdmann is Manager HR Analytics at Shell International. His email address is [email protected].