Correlation between serial tests made disease probability estimates erroneous

Abstract 

Background

The probability of a disease, given the result of two diagnostic tests, can be calculated by multiplying the odds of disease after the first test by the likelihood ratio of the second test.

Objective

To illustrate the error that occurs when calculating disease probability by combining the results of tests that are correlated.

Methods

Simulation study in which we randomly generated disease status and the results of two binary tests for a range of disease prevalence, test-operating characteristics, and correlation between tests. The primary outcome was the absolute difference between calculated and true probability of disease after two positive tests.

Results

When the tests were correlated, the calculated probability of a disease exceeded the true probability of the disease. With perfect correlation, the true probability of the disease after two positive tests equaled that after a single positive test. Error arising from correlated tests increased as the difference in the calculated probability between the first and second positive tests increased. We noted several combinations of disease prevalence, test-operating characteristics, and test correlation where the absolute difference between calculated and true probability of disease exceeded 25%.

Conclusion

Disease probability is overestimated when the results of correlated tests are combined. Clinicians must consider the correlation between serial tests when calculating the posttest probability.

Keywords: Monte Carlo simulation, Bayesian methods, Serial diagnostic testing, Correlated tests, Likelihood ratio, Pretest probability, Error