Optimal Cut-off Point for Interval-scaled Biomarker with Consideration of Utility of Sensitivity and Specificity: An Illustration with HDL and Stroke

Objectives
Population based screening for a chronic disease using an interval scale biomarker is often involved in selecting an optimal cutoff point. Selecting the optimal cut off point is faced with the misclassification between correct decision and alternative decision. The value of screening and selection of an optimal cutoff point depends on personal preference. High density lipoprotein (HDL) is one of protective factors for cerebral infarct. The cut off point of HDL related the outcome of cerebral infarct may vary from individual to individual. In this paper, we aimed to investigate the utility of misclassification by an illustration of the relationship of HDL to cerebral infarct. We also use the clinical model combined with above utility to prove the change of the cut off point of the interval scale biomarkers.

Methods
The study divided to two parts: the first part is that we obtain the utility scores of four scenarios of TP, TN, FP and FN with the relationship of HDL to cerebral infarct.by the standard gamble (SG) and visual analogue scale (VAS) approaches. The second part is that we use Bayes’ minimized cost decision rule and ROC curve method combined with utility scores of above four scenarios to determine the optimal cut-off point of HDL for cerebral infarct.

Results
Of the 69 people who completed the study, 30(43%) were men and 39(57%) were women, the mean age was 37.16±9.99 years old. The utility score of TN among four scenarios were ordered the highest followed by, FP, TP and FN. The utility scores in standard gamble I was 87.53, 81.17, 75.08, 63.06; in standard gamble II was 86.74, 83.64, 80.02, 64.68; in visual analogue scale was 83.17, 74.32, 63.87, 44.16. For personal characteristics, males who have higher income and have habits of smoking and drinking had higher utility of scenarios. The regret between TN and FP was smaller than that between TP and FN.
The results of cut-off value for HDL and Cholesterol performed by Baye’s minimum cost decision rule were that in general population, the cut-off value for HDL and Cholesterol was defined as 40.3 and 252.4 without utility adjustment. The cut-off value for HDL and Cholesterol was defined as 42.5 and 248.6, given utility adjustment from standard gamble I at slope of 31.3. The cut-off value for HDL and Cholesterol was defined as 46.0 and 242.8, given utility adjustment from standard gamble II at slope of 11.9.The cut-off value for HDL and Cholesterol was defined as 43.1 and 247.6, given utility adjustment from visual analogue scale at slope of 26.5. That means utility ratio increases with the level of HDL at decreasing rate and decreases with the level of Cholesterol at decreasing rate.

Conclusion
The utility of TP, TN, FP and FN involved in population-based screening has been measured by using an example of HDL related to cerebral infarct. The considering the utility of FP and FN is meaningful for the selection of a cut off point of a biomarker related to a disease outcome. Besides, Bayes’ minimum cost decision rule was proposed to solve the problem of selecting optimal cutoff point for chronic diseases with interval scale variable.