**1. Introduction**

294 Biomarker

Yao, Y., Richman, L., Morehouse, C., de los Reyes, M., Higgs, B. W., Boutrin, A., White, B.,

Young, G. P., & Bosch, L. J. W. (2011). Fecal Tests: From Blood to Molecular Markers. *Current* 

Zheng, P.-P., Luider, T. M., Pieters, R., Avezaat, C. J. J., van den Bent, M. J., Sillevis Smitt, P.

Zhu, W., Qin, W., Atasoy, U., & Sauter, E. R. (2009). Circulating microRNAs in breast cancer

Zhu, W., Qin, W., Bradley, P., Wessel, A., Puckett, C. L., & Sauter, E. R. (2005).

Zubakov, D., Hanekamp, E., Kokshoorn, M., van Ijcken, W., & Kayser, M. (2008). Stable

therapeutic target for psoriasis? *PLoS One*, *3*(7), e2737.

*Neuropathology and Experimental Neurology*, *62*(8), 855-62.

and healthy subjects. *BMC Research Notes*, *2*, 89.

aspirate fluid. *Carcinogenesis*, *26*(1), 145-52.

*Legal Medicine*, *122*(2), 135-42.

*Colorectal Cancer Reports*, *7*(1), 62-70.

Coyle, A., Krueger, J., Kiener, P. A., Jallal, B. (2008). Type I interferon: potential

A. E., & Kros, J. M. (2003). Identification of tumor-related proteins by proteomic analysis of cerebrospinal fluid from patients with primary brain tumors. *Journal of* 

Mitochondrial DNA mutations in breast cancer tissue and in matched nipple

RNA markers for identification of blood and saliva stains revealed from whole genome expression analysis of time-wise degraded samples. *International Journal of* 

> Concentrations of biomarkers for cancers (tumour markers) in plasma vary over time, and the ideal biomarker is a component which reflects the size of the tumour. Optimal interpretation of serial data on biomarkers during monitoring of patients following treatment of malignant disease is therefore vital for early prediction of reappearance of the tumour or metastases. Consequently, an ideal tumour biomarker will signal such reappearance before being detected by other relevant methods. On the other hand any false positive signals which can lead to superfluous investigations and unnecessary anxiety for the patient must be avoided. Because the biomarkers are produced in small amounts and released to plasma during healthy conditions, and because concentrations in plasma vary over time, it is necessary to be able to distinguish between true and false signals when serial measurements after treatment are to be interpreted. Here, different algorithms are proposed in literature, and this chapter deals with validation of some of these algorithms designed for the biomarker TPA (tissue polypeptide antigen) used in follow-up in treated breast tumours.

Computer Simulation Model System for Interpretation

**2.1 Materials and methods** 

**2.1.1 Cut-off**

Bromma, Sweden).

analytical variation, CVA%, is 8.4%.

analytical variation, CVA%, is 8.4%

**2.1.3 Tumour biomarker increase** 

exponential (eλ<sup>t</sup>

**2.1.4 Algorithms** Barak et al. {1}:

Tondini & Hayes {2}:

Söletormos et al. A {3}:

1990).

**2. Interpretation of serial TPA concentrations** 

literature (Söletormos et al., 1996; Söletormos et al., 2000a).

**2.1.2** *Steady-state***, biological and analytical variation** 

analytical variation, CVA%, is 8.4% (Söletormos et al., 2000a).

and 0.0907, respectively (Söletormos et al., 2000a).

percentile has been used with the analytical variation CVA as a constant.

and Validation of Algorithms for Monitoring of Cancer Patients by Use of Serial Serum... 297

The materials were data and parameters for breast cancer patients obtained from the

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,

The variations during the stable period of monitoring breast cancer patients are considered as *steady-state* and expressed as within-subject biological variation (CVB) and analytical variation (CVA) according to Sölétormos et al*.* (2000a). However, the within-subject biological variation, CVB, is not homogeneous. Therefore CVB for 5th, 50th and 95th

For TPA the 50th percentile for within-subject biological variation, CVB%, is 24.5% and

For TPA the 95th percentile of within-subject biological variation, CVB%, is 48.9% and

For TPA the 5th percentile of within-subject biological variation, CVB%, is 8.5% and

The estimated values for the rate of increase (λ) in biomarkers after relapse in women with breast cancer are available (Söletormos et al., 2000a). The increase is assumed to be

Two consecutive measurements. The first below and the second above cut-off (Barak et al.,

At least two measurements. The last measurement is above cut-off and at least 25% higher than any previous measurement below the cut-off concentration (Tondini & Hayes, 1989).

At least two measurements. The last measurement is above cut-off and at least twice

(doubling) of any previous measurement below the cut-off (Söletormos et al., 1996).

) and the λ-values for the 5%, 50%, and 95% percentiles are 0.0132, 0.0346,

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 there are metastases.

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

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

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 reference change value.

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 order to validate the algorithms.
