**2.2.1 Algorithm {1} Barak et al.**

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

In Fig. 4, the fastest tumour growth (λ = 0.0907) is 100 % percentages positive (POS) after two months for all start concentrations (sample 2), whereas the remaining graphs have almost the same development, with POS increasing from 0% at approximately 57 U/L to approximately 50% POS at 95 U/L. After six months (sample 4), the next lower slope ( λ = 0.0346) reaching 100% POS for all start concentrations, whereas the lowest slope (λ = 0.0132) and *steady-state* (λ = 0.0000) slowly increase to approximately 85% POS near the cut-off of 95 U/L. At ten months (sample 6), the slowest tumour growth has separated from the *steadystate* concentrations, increasing from 0 to 100% POS for starting concentrations between 30 and 70 U/L, and false positive (FP) is still zero up to approximately 57 U/L, but has increased to 97% at 95 U/L.

It is clear from Fig. 4 that true positive (TP) graphs increase with increasing starting concentrations, whereas FP graphs are zero for the low starting concentrations and increase over time for starting concentrations above 57 U/L.

Computer Simulation Model System for Interpretation

"good" POS results for TPA.

**2.2.2 Algorithm {2} Tondini & Hayes** 

and Validation of Algorithms for Monitoring of Cancer Patients by Use of Serial Serum... 305

With the only criterion as crossing the cut-off, the algorithm {1} from Barak et al. is very simple. In this way the time for progression detection is short – however the percentages of FP are unacceptably high - especially with start concentrations near cut-off - i.e. from approx

In comparison with the other algorithms, which all have more restrictive criteria for recording a positive signal (POS) as in progression of tumour growth, the percentage of FP results decreases. Table 1 lists FP after one and two years, and the algorithm Barak et al. {1} has the highest FP (i.e. 98%) rate in 'patients'. However, if the start concentration is below 57 U/L, the algorithm Barak et al. {1} has only few percentages FP (i.e. 3%) and at the same time the fastest detection time for progression. Only Tondini & Hayes {2} has comparable

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

The only difference between algorithm Barak et al. {1} and algorithm Tondini & Hayes {2} is that, in the latter algorithm, the criterion is 25% higher concentration above cut-off compared to the lowest value below cut-off. Many (simulated) patients will be recorded similarly as algorithm Barak et al. {1} - especially with low start concentration. Therefore, the performances of these two algorithms are comparable. Algorithm Tondini & Hayes {2} shows only moderately lower percentages of positives (POS) for the lower tumour growths and the steady-state situation at 6 months, i.e. also slightly lower FP between 55 and 95 U/L

Although there are a few more restrictions in algorithm Tondini & Hayes {2}, the detection time for TP patients is practically the same – however, the percentage of FP is still

At least two measurements. The last measurement is above cut-off and at least 100% higher than any previous measurement below the cut-off (doubling) (Söletormos et al., 1996).

This algorithm is comparable to the algorithm Tondini & Hayes {2}. The only difference is that the increase is not 25% but 100% for the last concentration over cut-off. In other words

The slightly more restrictive criterion with algorithm Söletormos et al. A {3} results in much lower FP signals with start concentrations near cut-off (see Fig. 5). For example the percentages of FP signals are reduced from 98% by algorithm Barak et al. {1} to 32% by algorithm Söletormos et al. A {3} after 1 year just below 95 U/L (cut-off) (see Table 1). However, after 6 months it is not possible to distinguish between the slowest tumour growth and healthy steady-state patients (see Fig. 5). Comparison of the algorithm from Söletormos et al. A {3} with Barak et al. {1} and Tondini & Hayes {2} shows nearly the same results with low start concentrations (below 57 U/L) where all three algorithms have only

57 U/L to cut-off (95 U/L). After 1 year the FP is 98% near the cut-off.

during the first half of the year (compare Fig. 4 and Fig. 5 at sample 4).

unacceptable with start concentrations near cut-off.

**2.2.3 Algorithm {3} Sölétormos et al. A** 

the three first algorithms are very similar.

few FP signals.

Percentage positive (POS) as a function of starting concentration (TPA U/L) for algorithm {1} Barak et al. after 2 months (sample 2), 6 months (sample 4) and 10 months (sample 6). Same slope symbols as in Fig. 2.

Fig. 4. Percentages positive signals at three different times.

With the only criterion as crossing the cut-off, the algorithm {1} from Barak et al. is very simple. In this way the time for progression detection is short – however the percentages of FP are unacceptably high - especially with start concentrations near cut-off - i.e. from approx 57 U/L to cut-off (95 U/L). After 1 year the FP is 98% near the cut-off.

In comparison with the other algorithms, which all have more restrictive criteria for recording a positive signal (POS) as in progression of tumour growth, the percentage of FP results decreases. Table 1 lists FP after one and two years, and the algorithm Barak et al. {1} has the highest FP (i.e. 98%) rate in 'patients'. However, if the start concentration is below 57 U/L, the algorithm Barak et al. {1} has only few percentages FP (i.e. 3%) and at the same time the fastest detection time for progression. Only Tondini & Hayes {2} has comparable "good" POS results for TPA.
