**2.1.4 Algorithms**

Barak et al. {1}:

Two consecutive measurements. The first below and the second above cut-off (Barak et al., 1990).

Tondini & Hayes {2}:

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).

Söletormos et al. A {3}:

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).

Computer Simulation Model System for Interpretation

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Sampling frequency every two months (61 days). Fig. 1B. *Steady-state* and tumour growth graphs.

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state concentrations (-●-) plus 0.95\* eλ\*t U/L.

Fig. 1C**.** Steady-state, tumour growth and resulting graphs.

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and Validation of Algorithms for Monitoring of Cancer Patients by Use of Serial Serum... 299

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Illustration of simulated data for steady-state concentrations (-●-), with a mean concentration 50 U/L, CVB = 24.5% and CVA = 8.5%, and tumours with exponential growth λ = 0.0132 (-■-)), according to 0.95\* eλ\*t U/L. Baseline (starting) concentration 50 U/L and the cut-off concentration, 95 U/L, (- - - -).

**Tumour marker as a function of time**

0 100 200 300 400 500 600 **Time (days)**

Illustration of simulated data for steady-state concentrations (-●-), with a mean concentration 50 U/L, CVB = 24.5% and CVA = 8.5%, and tumour with exponential growth λ = 0.0132 (-■-)),according to 0.95\* eλ\*t U/L. Baseline (starting) concentration for the course is 50 U/L and the cut-off concentration, 95 U/L, (- - - -). Sampling frequency every two months (61 days). The (-○-) graph is the addition result of steady-

**Tumour marker as a function of time**

Chan et al. {4}:

Three consecutive measurements. The last and middle concentrations are both above the cut-off and the first is below the cut-off (Chan et al., 1997).

Söletormos et al. B {5}:

At least three measurements. The last concentration is higher than the penultimate concentration and both are above the cut-off. The penultimate concentration is significantly higher than any previous measurement below the cut-off (Söletormos et al., 1996).

Molina et al. {6}:

Three consecutive measurements. The first concentration is below twice the cut-off (doubling) and the last two are both above twice the cut-off (doubling) (Molina et al., 1995).

Nicolini et al. {7}:

Three consecutive measurements. The first measured concentration is below the cut-off. The middle concentration is above the cut-off and the last measured concentration is >30 % higher than the middle measured concentration (Nicolini et al., 1991).

#### **2.1.5 Methods**

The basic principles and methods have been presented previously (Petersen et al., 2011; Söletormos et al., 2000b), and the basic model and the additional calculations of results for the varying start concentrations of TPA between the cut-off and these initial concentrations are described in detail below.

**Tumour marker as a function of time**

#### Illustration of simulated data for steady-state concentrations (-●-), with a mean concentration 50 U/L, CVB = 24.5% and CVA = 8.5%. Baseline (starting) concentration 50 U/L and the cut-off concentration, 95 U/L, (- - - -). Sampling frequency every two months (61 days).

Fig. 1A. *Steady-state* graph
