All tests are imperfect: Accounting for false positives and false negatives using Bayesian statistics

Song S Qian; Jeanine M Refsnider; Jennifer A Moore; Gunnar R Kramer; Henry M Streby

doi:10.1016/j.heliyon.2020.e03571

All tests are imperfect: Accounting for false positives and false negatives using Bayesian statistics

Heliyon. 2020 Mar 18;6(3):e03571. doi: 10.1016/j.heliyon.2020.e03571. eCollection 2020 Mar.

Authors

Song S Qian¹, Jeanine M Refsnider¹, Jennifer A Moore², Gunnar R Kramer¹, Henry M Streby¹

Affiliations

¹ Department of Environmental Sciences, University of Toledo, 2801 W. Bancroft Street, MS# 604, Toledo, OH 43606-3390, USA.
² Department of Biology, Grand Valley State University, 3300a Kindschi Hall of Science, Allendale, MI 49401, USA.

Abstract

Tests with binary outcomes (e.g., positive versus negative) to indicate a binary state of nature (e.g., disease agent present versus absent) are common. These tests are rarely perfect: chances of a false positive and a false negative always exist. Imperfect results cannot be directly used to infer the true state of the nature; information about the method's uncertainty (i.e., the two error rates and our knowledge of the subject) must be properly accounted for before an imperfect result can be made informative. We discuss statistical methods for incorporating the uncertain information under two scenarios, based on the purpose of conducting a test: inference about the subject under test and inference about the population represented by test subjects. The results are applicable to almost all tests. The importance of properly interpreting results from imperfect tests is universal, although how to handle the uncertainty is inevitably case-specific. The statistical considerations not only will change the way we interpret test results, but also how we plan and carry out tests that are known to be imperfect. Using a numerical example, we illustrate the post-test steps necessary for making the imperfect test results meaningful.

Keywords: Bayes' rule; Bioinformatics; Conditional probability; Environmental assessment; Environmental risk assessment; Epidemiology; False negative; False positive; Statistics; Uncertainty.