**3. Conclusion**

314 Biomarker

we have included a variation of 25% with the selected three slopes in the simulation model

Nearly all the results were close to the same as in Table 1 when this variation of 25% was included in the exponential function. The false positive (FP) results chanced only a few per cent for the most algorithms and maximum increases in percentages were 4% found at the

Barak

Barak

**Algorithm:**

**Sample 7**

**Algorithm:**

**Sample 7**

algorithms Barak et al. {1} and Tondini & Hayes {2} below 57 U/L after two years.

0 50 100 **Start concentration**

0 50 100 **Start concentration**

percentage positives increasing from 78% to 100%, respectively.

Fig. 7. Impact of biological variation on exponential tumour growth.

Percentage positive patients (POS) as a function of starting concentrations for algorithm Barak et al. {1} after one year. The upper figure shows results from the "normal" rate of increase. The figure below shows results from a modified rate of increase, including biological variation in the exponential function of tumour growth of 25%. For the slowest slope (λ =0.0132) (---o---), the modified slope shows a reduced number of percentage positives from start concentration 0 up to approx 57 U/L TPA with

and compared the results with the results in Table 1.

0

0

20

40

**Percentage positive**

60

80

100

20

40

**Percentage positive**

60

80

100

The start concentration of the biomarker TPA is a very important parameter in the examination of the performance of the algorithm, i.e. time for detection of progression and percentage of false positive results (FP). Start concentrations near cut-off will give more FP in nearly every algorithm – but the algorithms with low FP results also have longer tumour detection time. All the investigated algorithms performed comparable in FP results, when the start concentration was low, i.e. below 57 U/L.

These overall conclusions are relatively identical to the conclusion on results from the same algorithms using biomarker CA 15-3 (Petersen et al., 2011) – this indicates that the relative performance of algorithms is independent of the biomarker.

Differences in biological variation, CVB, have an influence on the performance of nearly all the algorithms. Only the algorithm Molina et al {6} has unchanged results with the different biological variations, CVB, – in other words this algorithm is the most robust against increasing biological variation CVB. Some algorithms show better performance when the biological variation CVB is low. When the biological variation CVB is low the algorithm Söletormos et al. A {3} has the best performance as regards early progression detection and simultaneously low number of FP results.

The biological variation of the tumour growth up to 25% has only a minor influence on the performance of the algorithms and does not chance the overall conclusions.

In a clinical situation the start concentration should be the point for selecting the best algorithm. When the start concentration is near the cut-off, the algorithm Molina et al. {6} could be used to avoid too many FP results. When the start concentration is below 57 U/L, the algorithm Barak et al. {1} could be used to have a short progressive detection time with only few FP results.
