LAUSR

In his letter, Prof. Borasi questions (1) whether an exponentially linear decrease of survival as a function of heating time has been proven for hyperthermia (HT) cell survival curves, or whether the linear quadratic (LQ) model [1] would be sufficient to describe such curves, and (2) whether survival data should be weighted by the uncertainty of the data points prior to fitting. We are convinced that weighting clonogenic survival data by the relevant uncertainty in data points is the correct way of fitting. Each data point has its own uncertainty which may be seen as the “quality” of that point. Knowing that there are differences in data quality, these should be accounted for during fitting. Weighting factors should be normalised to the relevant data point in order to account for differences in absolute values. Since our fit was based on a nonlinear least squares fit, weighting factors were also squared. This leads to an overall factor of std(S)/mean(S) (S is the surviving fraction). Uncertainty weighting should not influence the overall shape of the fit if the model used describes the data well, and uncertainties lie within a normal range (i.e. there are no obvious outliers). Figure 1 shows a comparison of weighted vs. unweighted fitting to data from Figure 1 of [2] fitted using the LQ-, and the AlphaR models. Here, we show that, for the data set used, the AlphaR model fit is more robust than that of the LQ-model. Although uncertainty weighting may influence the shape of the LQ fit, this is in its favour since points that are less accurately defined will draw the fit in a direction that does not reflect the underlying individual data points in their totality. In our article [2], we did not conclude that the HT survival data have an exponential asymptote, but presented a model that can describe such behaviour. This is an important difference. Whether the HT survival data allow us to discriminate clearly between a truly exponentially linear model for high thermal doses, or the LQ-model, cannot be answered with certainty. Naturally, models can only be falsified by data, but never be proven. In order to reject a model, such as the LQmodel, a threshold goodness of fit must be defined. Parameters, such as coefficients of determination, will only allow comparison with fits carried out under the same conditions, but it is difficult to decide at which numerical values a fit should be considered inadequate. The AlphaR model is capable of describing both LQ and LQ linear cell survival behaviours, and fits are therefore always equivalent to or superior to the LQ-model fits, while using the same number of free parameters for the HT curves (LQ: a and b, AlphaR: a0 and b). If a LQ fit described the data better, the respective fit with the AlphaR model would be LQ and the parameter a0 would be undeterminable. In our opinion, there are a number of arguments in favour of using the AlphaR model to fit HT survival curves: (1) Traditionally, HT cell survival data has been described using the Arrhenius model [3–6]. This assumes a purely exponentially linear decrease of survival as a function of