We develop a decision-theoretical approach to setting the threshold for a screening procedure that declares each examined subject as a positive or a negative. It is fundamentally different from maximising the Youden index. The method incorporates the consequences of the two kinds of bad decisions (false positives and false negatives) by means of a set of plausible loss functions elicited from a subject-matter expert or committee. We present details for several classes of loss functions and within-group distributions of the outcomes. We outline extensions related to mixture distributions and compositions of loss functions. We illustrate the method on simulated examples and apply it to real datasets. Copyright © 2012 John Wiley & Sons, Ltd.