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

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 three first algorithms are very similar.

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 few FP signals.

Computer Simulation Model System for Interpretation

Slope 0.0346: 100% at time

100%. 3Only at start concentrations below 28 U/L obtain 100%.

Table 1. Performance results from seven algorithms.

previous measurements below the cut-off (Söletormos et al., 1996).

**2.2.5 Algorithm {5} Sölétormos et al. B** 

months later for all 3 slopes.

0.0907: 100% at time

Algorithm Slope

Barak

Tondini and Hayes {2}

Söletormos

Söletormos

Molina

Nicolini

simulations.

Chan

and Validation of Algorithms for Monitoring of Cancer Patients by Use of Serial Serum... 307

The algorithm Chan et al.{4} appears similar to algorithm Barak et al. {1} with the addition of a confirmation of crossing the cut-off. When the graph is crossing the cut-off (95 U/L) - the next sample should also be above cut-off. In this way the percentage FP signals may be reduced – from 98% FP by algorithm Barak et al. {1} to 64% FP by algorithm Chan et al. {4} after 1 year below 95 U/L. As a consequence - the detection times are correspondingly 2

> False positive below 95 U/L at 1 year

False positive below 95 U/L at 2 years

False positive below 57 U/L at 1 year

False positive below 57 U/L at 2 years

Slope 0.0123: 100% at time

et al. {1} 2 months 6 months 12 months 98% 100% 3% 4%

et al. A {3} 2 months 6 months 14 months 32% 70% 2% 3%

et al. {4} [4 months]1 8 months 14 months 64% 91% 0% 0%

et al. B {5} [4 months]1 8 months 16 months 6% 24% 0% 0%

et al. {6} [4 months]1 8 months 16 months 0% 0% 0% 0%

et al. {7} [4 months]1 [8 months]2[14 months]3 6% 10% 0% 0%

Times for detection of 100 % tumour progression using the different algorithms are listed for three slopes. Percentages of false positive results after 1 and 2 years with TPA start concentrations below 95 U/L and 57 U/L for each algorithm are also listed. All results are generated from 1000 computer

1Three sample points are needed for the algorithm. 2 Only at start concentrations below 57 U/L obtain

At least three measurements. The last measured concentration is higher than the penultimate concentration, both above the cut-off, and higher than the third to last measured concentration. The penultimate concentration is significantly higher than any

In a comparison of algorithm Chan et al. {4} with algorithm Söletormos et al. B {5}, the latter algorithm is much more restrictive in recording positive signals (POS). The last measurement demands an increase compared to the penultimate value – and this

2 months 6 months 12 months 91% 100% 3% 4%

Comparison of the algorithms of algorithm {2} Tondini & Hayes, and algorithm {3} Söletormos et al. A at 6 months (sample 4). Percentage positive (POS) as a function of starting concentration as for Fig. 3. The only difference between the two algorithms is the size of increase after crossing the cut-off, i.e. 25% and 100%, respectively. For symbols see Fig. 3.

Fig. 5. Comparison of two different algorithms.

All three algorithms have also the same tumour detection time – except Söletormos et al. A {3} which has extended the time by two months for the slowest tumour growth (see Table 1).

The next four algorithms presented here - all have a characteristic in common – they all need at least three measurements. As a consequence, the earliest detection time for tumour progression is 4 months. In Table 1, these algorithms are marked with a footnote: 'Three sample points are needed'.

#### **2.2.4 Algorithm {4} Chan et al.**

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

Tondini

**Algorithm:**

**Sample 4**

Sölétormos A

**Algorithm:**

**Sample 4**

0 50 100 **Start concentration**

0 50 100 **Start concentration**

Comparison of the algorithms of algorithm {2} Tondini & Hayes, and algorithm {3} Söletormos et al. A at 6 months (sample 4). Percentage positive (POS) as a function of starting concentration as for Fig. 3. The only difference between the two algorithms is the size of increase after crossing the cut-off, i.e. 25%

All three algorithms have also the same tumour detection time – except Söletormos et al. A {3} which has extended the time by two months for the slowest tumour growth (see Table 1). The next four algorithms presented here - all have a characteristic in common – they all need at least three measurements. As a consequence, the earliest detection time for tumour progression is 4 months. In Table 1, these algorithms are marked with a footnote: 'Three

Three consecutive measurements. The last and penultimate concentrations are both above

the cut-off, and the first measured concentration is below cut-off (Chan et al., 1997).

0

0

and 100%, respectively. For symbols see Fig. 3.

sample points are needed'.

**2.2.4 Algorithm {4} Chan et al.** 

Fig. 5. Comparison of two different algorithms.

20

40

**Percentage positive**

60

80

100

20

40

**Percentage positive**

60

80

100

The algorithm Chan et al.{4} appears similar to algorithm Barak et al. {1} with the addition of a confirmation of crossing the cut-off. When the graph is crossing the cut-off (95 U/L) - the next sample should also be above cut-off. In this way the percentage FP signals may be reduced – from 98% FP by algorithm Barak et al. {1} to 64% FP by algorithm Chan et al. {4} after 1 year below 95 U/L. As a consequence - the detection times are correspondingly 2 months later for all 3 slopes.


1Three sample points are needed for the algorithm. 2 Only at start concentrations below 57 U/L obtain 100%. 3Only at start concentrations below 28 U/L obtain 100%.

Times for detection of 100 % tumour progression using the different algorithms are listed for three slopes. Percentages of false positive results after 1 and 2 years with TPA start concentrations below 95 U/L and 57 U/L for each algorithm are also listed. All results are generated from 1000 computer simulations.

Table 1. Performance results from seven algorithms.
