WHEN TO STOP TESTING. A COEFFICIENT TO MEASURE DIAGNOSTIC STABILITY

Purpose: Parsimonious diagnosis using partial information is potentially efficient and cost-effective.  However, additional information in the form of confirmatory testing may destabilize a diagnosis by casting it into doubt or sufficiently changing the post-test likelihood as to suggest an alternate diagnosis.  Quantifying this risk would enable decision makers to decide when it is acceptable to stop testing.

Methods: Diagnosis is assumed to occur within a Bayesian framework, with predefined numerical diagnostic thresholds.  A likelihood that does not exceed any threshold is considered indeterminate.  A coefficient τ (tau) is defined to quantify 1) the risk of recasting a diagnosis as indeterminate and 2) the risk of crossing an alternate diagnostic threshold.  This coefficient is calculated by examining the entire subset of uncollected information and multiplying the magnitudes of likelihood change by the expected frequency of any given test result.  Any number of sequential tests can be considered; one-level look-ahead is used to illustrate the coefficient.

Results: A common clinical scenario is used to illustrate τ: the diagnosis of pulmonary embolism, using the thresholds suggested by Roy et al: Low Clinical Probability of < 5%, and High Clinical Probability of >85%. Likelihoods between these thresholds would be considered indeterminate. In a potential scenario, the post-test likelihood after a positive venous Doppler ultrasound is 90%, which would ordinarily establish the diagnosis of pulmonary embolism. Consider two additional tests that could recast the diagnosis as indeterminate: V/Q scan (negative LR 0.05) and CT pulmonary angiogram (negative LR 0.11). If each of these gives a negative result 10% of the time, the calculated τ is 9.9. If the post-test likelihood after ultrasound were instead 99%, τ would no longer include the CT pulmonary angiogram result (a negative test would change the likelihood to 91.5%, which remains within the threshold >85%). The calculated τ would then be 1.6.

Discussion: The new coefficient τ has the potential to aid clinical decision makers who are practicing parsimonious diagnosis. The value of τ at which it would be reasonable to stop testing is not explicitly defined and will depend on the hypotheses under consideration. In the example above, τ=9.9 is sufficiently high to warrant further testing, while τ=1.6 is sufficiently low that testing could be stopped.