Quantitative analysis of tumor growth rate and changes in tumor marker level: Specific growth rate versus doubling time

Abstract

Background. Doubling time (DT) of tumor volume has been widely used to estimate the growth rate of tumors. However, DT gives incorrect estimates of the average growth rate of tumors when the uncertainty of growth rate is considerable. Specific growth rate (SGR) is less affected by uncertainties and is a more relevant parameter. Optimized imaging techniques and prolonged interval between observations can reduce the uncertainty of growth rate estimation. DT is also used for defining changes in tumor marker level. The aim of this study was to compare DT and SGR as measures of growth rate when the uncertainty is negligible. Methods. Mathematical analysis and computer simulations were carried out assuming no uncertainty of growth rate estimation. Data from two previously published clinical studies were assessed by both variables. Results. Due to the non-linear relationship between DT and SGR, using these variables does not give similar results. The variation of DT is not uniformly indicating variations of the growth rate. DT largely overestimates the difference in growth rate of slowly growing tumors and underestimates the difference in growth rate of rapidly growing tumors. On the other hand, SGR uniformly indicates the difference between growth rates throughout all ranges. Quantitative analysis of clinical observations can lead to contradictory results depending on the variable used for growth rate. Conclusion. The growth rate of tumor volume should be expressed by SGR, or percentage increase per unit time, regardless of the level of the uncertainty of growth rate estimation. This conclusion is also valid for changes in tumor marker level, whether it is correlated with the growth rate of tumor volume or not.