**2.1.1 Cut-off**

296 Biomarker

In contrast to the common statistics used for comparing two or several groups or some distributions, the purpose with the algorithms for bio-markers is to decide at each sampling and measurement time whether there is a reappearance of the tumour and whether or not

Several algorithms to interpret serial measurements of these markers for monitoring have been proposed and used in clinical trials. The simplest algorithm, used by all kit manufactures and included in their inserts, as also published by Barak et al. (1990), is a cutoff which defines relapse when the marker concentration exceeds this concentration. All algorithms include a cut-off, either directly in the interpretation or indirectly as an algorithm to be used either below or above the cut-off value. Some algorithms are based on two measurements (e.g. a minimum and the latest measured value) and crossing of the cut-off limit, while others include rules for the size of a critical difference of 25 % (Tondini & Hayes, 1989) or a doubling (Söletormos et al., 1996) or significant change (Söletormos et al., 1996) according to the reference change value (RCV) concept introduced by (Harris & Yasaka, 1983). An increase of 25% either below or above the cut-off for both measured concentrations (Dinistrian et al., 1991), and also a doubling or significant change when all measurements are above the cut-off value has been proposed (Söletormos et al., 1996). Others are based on three measurements, where the last measurement is a third, confirmatory test for the increase, and these have also been recommended when crossing the cut-off (Chan et al. 1997; Molina et al., 1995; Nicolini et al., 1991; Söletormos et al., 1996), in addition to algorithms where all measurements are below the cut-off (Bonfrer, 1990) as well as for situations where all measurements are above the cut-off (Bonfrer, 1990; Mughal

All these algorithms give different signals for the same monitoring data, and a comparison of outcomes in the form of true positive and false positive results based on computer simulations of relevant monitoring situations has been performed (Söletormos et al., 2000b). These illustrate for each algorithm the advantages in terms of time to detection of reappearance, and disadvantages in the form of false positive signals. The basic biological and clinical data for estimated values of within-subject biological variation of serum-TPA (CVB) during *steady-state* are available (Söletormos et al., 2000a). The rates of exponential increases in serum TPA during tumour growth are based on monitoring data from breast

It has been demonstrated by Iglesias et al*.* (2005) that, for monitoring, the benefit of using the RCV (Harris & Yasaka, 1983) compared to a cut-off depends on the distance between the cut-off and the first measured concentration of the difference between two consecutive measurements to be compared to the RCV. When this distance is small, the probability of crossing the cut-off by the second measurement is higher than the probability of obtaining a significant change between the two measurements. Larger distances speak in favour of the

The purpose of this chapter is to demonstrate the influence of the distance between the cutoff and the initial (baseline) concentration for TPA in serum in a simulation study like the paper on the tumour marker CA 15-3 (Petersen et al., 2011). This is done by challenging the different algorithms, where crossing the cut-off is part of the criterion, by computer simulations of various situations of monitoring breast cancer, imitating various exponential increases corresponding to recurrent cancer and a range of values of biological variation in

there are metastases.

et al., 1983; Söletormos et al., 1996).

cancer patients (Söletormos et al., 2000a).

reference change value.

order to validate the algorithms.

The cut-off concentration for TPA during treatment and follow-up of women with breast cancer is 95 U/L, recommended by the manufacture of the TPA kit (AB Sangtec Medical, Bromma, Sweden).
