**3.1 Computer simulations**

A summary of new important conclusions from this investigation:

a. The relative performances of algorithms are independent of the biomarker.

Computer Simulation Model System for Interpretation

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These conclusions are based on computer simulations. In the computer simulations, the *steady-state* variation and the rate of tumour increase (λ = slope) are based on clinical data from the literature and the simulations are based on random counts generated from a Gaussian distribution from the computer multiplied by the parameters borrowed from publications. Furthermore, the cost-price for the clinical investigations compared with computer simulation is enormous and the computer simulation is a convenient, easy and quick method to compare algorithm performances based on the same simulated data-points. Thus, computer simulation should be a tool to select the "right" algorithm before a clinical investigation regarding for example low number of false positive (FP) signals. Computer simulations are thus not a substitute for clinical investigations, but a supplementary tool in helping to interpret biomarker variations and challenge the algorithms with extreme parameters in the model.

Thus, the advantage of computer simulations is that it is relatively easy to vary the parameters in the simulation model and examine the impact on the performances of the algorithms. In this investigation we have investigated these performances under standard conditions as well as under extremes with conditions of varied CVB in *steady-state* and varying slopes of tumour growth. In addition, we have tested the robustness of the algorithms by using extreme values for CVB and we have tested for variation in the exponential slopes of tumour growth.

Parameters which interestingly could also be varied are sampling intervals or the starting points of the exponential tumour growth.

In this study we have chosen a sampling interval of every two months, which is a relevant time schedule for monitoring of patients with breast cancer during follow-up after treatment (Söletormos et al., 2000b). Obviously, a sampling interval of one month could give earlier detection of tumour growth progression. However, in many of the algorithms the number of FP signals will simultaneously increase, and, conversely, longer sampling intervals will reduce FP signals, but true signals will be delayed.

We have chosen arbitrarily the starting point of exponential tumour growth to be 1% of cutoff. The impact on the performances of the algorithms when varying this starting point for the contribution from the growing tumour may be comparable for all the algorithms. If, for example, a starting point of 50% of the cut-off concentration was selected - the time for crossing cut-off would be shortened, so the progression detection time would possibly be earlier, whereas the percentages of FP would be unchanged for all algorithms.

#### **3.2 Future research**

In this investigation, we have investigated and challenged the seven algorithms, but the effect of sampling interval and of the start value of the contribution of marker from the tumour has not been studied. Furthermore, this computer model for simulations can be used for evaluation of other algorithms which can be tested and compared to the existing algorithms, before they are published or introduced in the clinic.
