The assessment of different methods of data reduction for qualitative assays

An increasing number of biochemical tests for the detection of ailments such as hepatitis, AIDS, listeria poisoning etc are becoming qualitative in nature since the concern is over whether contamination is present or not rather than to what degree it is present. Many tests have an underlying quantitative scale that is dichotomised by the calculation of a detection limit, whereby a result is deemed negative, say, if its assay response is less than the detection limit and positive otherwise. A number of methods have been proposed for determining the detection limit and a few authors have tried to compare some of these methods. To date, as far as we are aware, these comparisons have been neither exhaustive nor conclusive. We propose a comparison criterion based on the false positive and false negative rates and use this criterion to assess five different methods via a simulation study. For the simulation model used, under the conditions imposed, we conclude that a detection limit based on control samples is probably the most efficient. Each method of calculating the detection limit has a coefficient associated with it for determining the exact position of the detection limit. The criteria, to date, for selecting the value of this coefficient seem arbitrary since whole numbers are often quoted, presumably reflecting convenience. Our simulation approach provides a possible method for determining the value of the coefficient which gives rise to a specified false positive or false negative rate.