Parameters Relating to Ultrasensitive Prostate-Specific Antigen Assays

Several recent papers have dealt with the performance of prostate-specific antigen (PSA) assays at very low concentrations (1)(2)(3). In these papers, no less than 5 different parameters have been discussed: the lower limit of detection (LLD), the biological detection limit (BDL), functional sensitivity (FS), the residual cancer detection limit (RCDL), and the minimal detectable concentration (MDC). One may wonder whether such a profusion of terms is meaningful or necessary. However, I believe that, although these parameters are to some extent presented or used as alternatives to each other, fundamental differences exist among them. Here, I aim at distinguishing two groups of parameters, each of which has a specific use. Two types of questions may arise. First, given a certain measured concentration, does this measurement signifies the presence of PSA, as opposed to assay noise? In other words, does the reading of the assay allow to state that the concentration is different from zero? The approach to this question involves statistical inference. First, a distribution of measurements should be obtained (with the same method and under the same conditions) in multiple specimens known to have zero concentration of the analyte. When the analytical signal falls far to the right on the distribution (or to the left for calibration curves with negative slopes), it is unlikely that a sample with actual zero concentration would yield a signal equal to or higher than the one measured. Stated differently, it is thus unlikely that the sample contains no analyte. So, ascertaining the presence of PSA in a clinical sample always and exclusively involves a measurement limit based on the distribution of results from a specimen devoid of analyte. Two parameters qualify as such: the LLD and the RCDL. These differ only in the nature of the blank specimens used: zero calibrators in the case of LLD, and actual clinical samples for the RCDL. In the latter, evidence for the absence of PSA is based on clinical information. In contrast, parameters such as FS, BDL, and MDC do not qualify as limiting values of a zero-sample distribution and therefore cannot be used to judge individual specimens. It is easy to see that FS does not take into account the distribution of null-specimens but only the variability in samples with very low concentrations. The BDL and the MDC do take into account the distribution of values in specimens devoid of analyte but also reflect variability in samples with very low concentrations. A second type of question is, how does a given assay perform at very low concentrations? In this respect, limiting values such as LLD and RCDL reveal only part of the picture, because they relate only to blank specimens. Clinically, it is more relevant to use parameters that in some way reflect precision for specimens with very low concentrations that are different from zero. These include FS, BDL, and MDC. Within this group, however, only MDC is based on firm statistical reasoning: It specifies the concentration that has a certain probability to yield an estimated value above that for blank specimens. In contradistinction, the BDL combines the LLD and variability at low concentrations in an arbitrary way. And by its very definition, FS (the lowest concentration that achieves an interassay CV of <20%) is arbitrary as well. Therefore, although all these parameters reflect various elements of the performance of an assay, only the LLD and the RCDL are useful as guides to test interpretation.