Translating etiological effect measures into medical test evaluation metrics

Abstract Traditional metrics for medical test evaluation (TE) and etiological evaluation (EE) are often analyzed within separate frameworks. We review these metrics, including recommendations to use less frequently used TE metrics. We propose a novel framework for TE by drawing formal analogies between 2x2 tables in both forward- and backward-directed study designs. The risk (Re) of sickness identified through EE among those exposed to a risk factor in a cohort study is analogous to the sensitivity found through TE. Similarly, the risk among non-exposed individuals in an EE cohort study, the Rne, is analogous to TE’s false-positive fraction (ie, 1 - specificity). The risk ratio, ie, RR = Re / Rne and risk difference of EE, ie, RD = Re - Rne, are analogous to the positive likelihood ratio (plr) and the Youden Index J = sensitivity + specificity-1 of a forward-directed TE (respectively). For backward-directed analysis, we utilize Positive Predictive Value (PPV) and Negative Predictive Value (NPV) to define the Predictive Summary Index (PSI, $\\boldsymbol{\\Psi}$) = PPV + NPV-1 that summarizes the added information obtainable in a backward-directed TE. We identify the Positive Predictive Ratio (PPR) as the TE ratio measure analogous to the plr in EE. Similarly, the Negative Predictive Ratio (NPR) is analogous to the negative likelihood ratio (nlr). Finally, we show that the odds ratios in the forward and backward analyses are identical for both EE and TE, and equal to the analogous ratios of plr/nlr and PPR/NPR. Generic and clinical examples demonstrate the importance of less commonly used measures, PSI, PPR and NPR.