The article considers the diagnostic odds ratio, a special summarising function of specificity and sensitivity for a given diagnostic test, which has been suggested as a measure of diagnostic discriminatory power. In the situation of a continuous diagnostic test a cut-off value has to be chosen and it is a common practice to choose the cut-off value on the basis of the maximised diagnostic odds ratio. We show that this strategy is not to be recommended since it might easily lead to cut-off values on the boundary of the parameter range. This is illustrated by means of some examples. The source of the deficient behaviour of the diagnostic odds ratio lies in the convexity of the log-diagnostic odds ratio as a function of the cut-off value. This can easily be seen in practice by plotting a non-parametric estimate of the log-DOR against the cut-off value. In fact, it is shown for the case of a normal distributed diseased and a normal distributed non-diseased population with equal variances that the log-DOR is a convex function of the cut-off value. It is also shown that these problems are not present for the Youden index, which appears to be a better choice.