Report a relative proportion of patients ruled-out or ruled-in with a diagnostic test
One measure of the performance of a diagnostic test is the proportion of patients the test stratifies as likely not to have the condition (ruled-out:RO) or to have the condition (ruled-in:RI). This proportion depends on the prevalence of the disease in the cohort. This means that it is not valid to compare tests performed in cohorts with differing prevalences. However, this is exactly what is often done in the discussion section of academic papers. Usually there is a target sensitivity (t_sn) for the test which means that the maximum proportion ruled-out at that sensitivity is:
ROmax=(TN + TP(1/t_sn -1))/(TN + TP/t_sn)
Where TN=True Negative, TP=True Positive. Note for ROmax, there are zero False Positives (FP). Also, in the case where t_sn=1 (False Negatives, FN=0), R0max=1-prevalence.
Similarly, if there is a target specificity (t_sp) the maximum proportion ruled-in is:
RImax=(TP + TN(1/t_sp -1))/(TP + TN/t_sp)
Note, in the case where t_sp=1 (FP=0), RImax=prevalence.
Therefore, to better be able to compare between studies, both the measured proportion of those ruled-out and those ruled-in should be normalised to their maximum possible values:
Adjusted proportion ruled-out = measured proportion ruled-out / ROmax Adjusted proportion ruled-in = measured proportion ruled-in / RImax