**2.2.8 Overall results**

The characteristics for the seven algorithms are summarised in Table 1 with the time for 100% true positive results (TP) for each slope of tumour growth, and with percentage false positive (FP) at two years for both start concentrations of 57 U/L and 95 U/L (cut-off).

The two first algorithms (Barak et al. {1} and Tondini & Hayes {2}) in Table 1 show the fastest time to detect 100% positive signals in patients for each of the investigated three slopes. However, these algorithms also show the highest percentage of false positive (FP) signals, both after 1 and 2 years. All the other algorithms also show FP results of lower and varying percentages - except algorithm Molina et al. {6} with zero FP. The algorithm Molina et al. {6} on the other hand also needs the longest time for 100% positive results shared with algorithm Söletormos et al. B {5}. The algorithm Nicolini et al. {7} has partly the same long time, but only at start concentrations below 57 U/L and below 28 U/L for the slopes 0.0346 and 0.0132, respectively. Above these start concentrations, the algorithm Nicolini et al. {7} will never obtain 100% positive results (see also Fig 6). In other words after 14 months the two slowest slopes will "freeze" and have the same results. Only FP percentages will increase slowly.

Overall, all the algorithms are comparable when the start concentrations are below 57 U/l with only few FP results for the algorithms from Barak et al. {1}, Tondini & Hayes {2} and Söletormos et al. A {3}. The other algorithms are even better as regards the percentage of FP results. However, they need longer time for detection of tumour progression.

In the clinical situation, when the TPA start concentration is below 57 U/L, it should be recommended to use the algorithm Barak et al. {1} in order to obtain an early detection of tumour progression. However, when the TPA start concentration is above 57 U/L and up to just below 95 U/L, it should be recommended to use the algorithm Molina et al. {6}– even with a longer detection of tumour progression – in order to avoid any false positive signals.

In a clinical situation using the Nicolini et al. {7} algorithm, several patients with slow tumour growth and with high biomarker (TPA) start concentration near cut-off will never be recorded as positive tumour patients – hopefully treatment action will be taken based on high concentrations or other clinical signals.

In this investigation the performances of the algorithms have been studied using results from the biomarker TPA. The same procedure has been used on the same algorithms with results from the biomarker CA 15-3 (Petersen et al., 2011). The results from these two investigations are very similar. The properties from the algorithms on detection time of progression, the percentages of false positive patients (FP), the dependence on start concentration both near cut-off and approx half cut-off – all the overall characteristic results and figures from each algorithm were relatively identical using different biomarkers, i.e. TPA and CA 15-3.

It has to be underlined that, in this way, the algorithm Nicolini et al. {7} will never achieve 100% POS with start concentrations near cut-off. The 100% POS will only be fulfilled at start

The characteristics for the seven algorithms are summarised in Table 1 with the time for 100% true positive results (TP) for each slope of tumour growth, and with percentage false positive (FP) at two years for both start concentrations of 57 U/L and 95 U/L (cut-off).

The two first algorithms (Barak et al. {1} and Tondini & Hayes {2}) in Table 1 show the fastest time to detect 100% positive signals in patients for each of the investigated three slopes. However, these algorithms also show the highest percentage of false positive (FP) signals, both after 1 and 2 years. All the other algorithms also show FP results of lower and varying percentages - except algorithm Molina et al. {6} with zero FP. The algorithm Molina et al. {6} on the other hand also needs the longest time for 100% positive results shared with algorithm Söletormos et al. B {5}. The algorithm Nicolini et al. {7} has partly the same long time, but only at start concentrations below 57 U/L and below 28 U/L for the slopes 0.0346 and 0.0132, respectively. Above these start concentrations, the algorithm Nicolini et al. {7} will never obtain 100% positive results (see also Fig 6). In other words after 14 months the two slowest slopes will "freeze" and have the same results. Only FP percentages will

Overall, all the algorithms are comparable when the start concentrations are below 57 U/l with only few FP results for the algorithms from Barak et al. {1}, Tondini & Hayes {2} and Söletormos et al. A {3}. The other algorithms are even better as regards the percentage of FP

In the clinical situation, when the TPA start concentration is below 57 U/L, it should be recommended to use the algorithm Barak et al. {1} in order to obtain an early detection of tumour progression. However, when the TPA start concentration is above 57 U/L and up to just below 95 U/L, it should be recommended to use the algorithm Molina et al. {6}– even with a longer detection of tumour progression – in order to avoid any false positive

In a clinical situation using the Nicolini et al. {7} algorithm, several patients with slow tumour growth and with high biomarker (TPA) start concentration near cut-off will never be recorded as positive tumour patients – hopefully treatment action will be taken based on

In this investigation the performances of the algorithms have been studied using results from the biomarker TPA. The same procedure has been used on the same algorithms with results from the biomarker CA 15-3 (Petersen et al., 2011). The results from these two investigations are very similar. The properties from the algorithms on detection time of progression, the percentages of false positive patients (FP), the dependence on start concentration both near cut-off and approx half cut-off – all the overall characteristic results and figures from each algorithm were relatively identical using different biomarkers, i.e.

results. However, they need longer time for detection of tumour progression.

concentrations below 28 U/L, for the two slowest slopes (see footnotes in Table 1)

**2.2.8 Overall results** 

increase slowly.

signals.

TPA and CA 15-3.

high concentrations or other clinical signals.

These results indicate that the relative performance of the investigated algorithms for early detection of tumour progression and avoiding FP results – seems to be independent of the biomarker in the present model and set-up.

It must be underlined that this statement may only be valid based on general considerations. For example biomarkers with relative low *steady-state* variation combined with high rates of tumour increase may change some of the algorithm performances according to the detection time of progression and percentage of FP signals. In this situation the performance from algorithm Nicolini et al. {7} could be better, because start concentration near cut-off may achieve 100% TP signals within an acceptable timeframe compared with a never ending timeframe in this TPA investigation. Nevertheless, the relative information from the algorithms on performance will still stand. In other words - the best ability to detect tumour progression will often be obtained by using the algorithm from Barak et al. {1} and the best ability to get low FP signals will often be obtained by using the algorithm from Molina et al. {6} - and this is noteworthy: independent of the biomarker.
