Combining Results of Performance-Based and Informant Test Accuracy Studies: Bayes or Boole?

Since screening and diagnostic tests for dementia do not have perfect accuracy, >1 test is often administered when assessing patients with cognitive complaints. Use of both patient performance tests and informant questionnaires has been recommended. Combination of individual test results may be based on methods originally defined by Thomas Bayes (revision or updating of pretest probabilities to post-test probabilities given the test results) and by George Boole (application of associative "AND" or "OR" operator). This study sought to apply these methods in clinical practice.

Using the dataset of a pragmatic test accuracy study of the Six-Item Cognitive Impairment Test (6CIT) and informant Ascertain Dementia 8 (AD8), post-test probabilities for the combination were calculated using Bayes' formula and compared to Boolean "AND" combination. Combined test sensitivity and specificity was calculated using either Boolean "AND" or "OR" operator and compared to results using equations based on individual test sensitivity and specificity.

Both Bayesian and Boolean methods produced similar improvements from pretest probability (0.288) to combined post-test probability for dementia (≈0.5). Likewise, the 2 different methods for calculating combined sensitivities and specificities gave similar results, with, as anticipated, the "AND" combination improving overall specificity (to ≈0.65) whereas the "OR" combination improved sensitivity (to ≈1.00).

Combination of individual screening test results using Bayesian and Boolean methods is relatively straightforward and may add to clinicians' intuitive judgements when combining test results.