Computation of decision levels from differentiated logistic regression probability curves.

The determination of clinical decision levels (DL) or "cut-offs" for laboratory parameters involves the analysis of sensitivity and specificity at varying levels of the predictor variable (PV). Commonly, receiver-operator characteristic (ROC) curves are used for this purpose. However, the association between a binary outcome choice and a continuous PV is often tested for statistical significance by logistic regression (LoRe), which also provides estimates of outcome probability (P) at various levels of the PV. Utilizing a graphical procedure based on the 1st [f'(P)] and 2nd [f"(P)] derivatives of the probability curve, DL were computed for simulated data sets (sims) and for actual data from a case-control study and compared with those obtained from ROC curves. Sims were constructed for 5 sets of two outcomes (n = 50, each outcome) of normally distributed data with progressive overlap and for 2 sets of fewer data (n = 15 and 9 per outcome, respectively). Additionally, data from a study of the relationship between serum Mg+2 concentration and outcomes in chronic obstructive pulmonary disease (COPD) were analyzed. DL from LoRe was taken to be the point where f"(P) = 0. For sims, the DL from LoRe correlated well with the optimum DL from ROC analysis (n = 7; r2 = 0.93; p = 0.0004). DL for Mg+2 in COPD data from LoRe was 0.83 mmol/L compared to mean of 0.82 mmol/L by ROC. These data suggest that, when the strength of association between outcomes and PV is analyzed by LoRe, DL can be determined from the probability curves. Moreover, LoRe may provide a useful method to determine DL with less ambiguity than those obtained from ROC curves, as well as provide measures of dispersion for the DL.