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Computation of Decision Levels from Differentiated Logistic Regression Probability Curves

Address correspondence to Vincent A. DeBari, Ph.D., School of Graduate Medical Education, Seton Hall University, 400 South Orange Avenue, South Orange, NJ 07079, USA; email debarivi{at}shu.edu.

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 [’(P)] and 2nd ["(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 "(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.

Keywords: Logistic regression, medical decision making, receiver-operator characteristic curves, epidemiology, biostatistics

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