Three endpoints of in vivo tumour radiobiology and their statistical estimation

Purpose: To review the existing endpoints of tumour growth delay assays in experimental radiobiology with an emphasis on their efficient estimation for statistically significant identification of the treatment effect. To mathematically define doubling time (DT), tumour-growth delay (TGD) and cancer-cell surviving fraction (SF) in vivo using exponential growth and regrowth models with tumour volume measurements obtained from animal experiments. Materials and methods: A statistical model-based approach is used to define and efficiently estimate the three endpoints of tumour therapy in experimental cancer research. Results: The log scale is advocated for plotting the tumour volume data and the respective analysis. Therefore, the geometric mean should be used to display the mean tumour volume data, and the group comparison should be a t -test for the log volume to comply with the Gaussian-distribution assumption. The relationship between cancer-cell SF, TGD and rate of growth is rigorously established. The widespread formula for cell kill is corrected; it has been rigorously shown that TGD is the difference between DTs. The software for the tumour growth delay analysis based on the mixed modeling approach with a complete set of instructions and example can be found on the author's webpage. Conclusions: The existing practice for TGD data analysis from animal experiments suffers from imprecision and large standard errors that yield low power and statistically insignificant treatment effect. This practice should be replaced with a model-based statistical analysis on the log scale. (authors)