Statistical models for analysing time-to-occurrence data in radiobiology and radiation oncology

Two different methods for analysing late complications data are contrasted and compared. The two methods are the Cox Proportional Hazards model and the Mixture model. The potential limitations of both methods are described together with the circumstances in which one or the other of the methods is preferable. The results from the two methods of analysis will usually be qualitatively similar and frequently quantitatively similar. For estimating the ratio of parameters, such as the alpha/beta ratio if the linear-quadratic model holds, the Cox model is the preferred method. For estimating the proportion with complications by a given follow-up time, the Mixture model is the preferred method. For data, such as from experimental animals, in which there is little censoring during the time period of interest, the Mixture model will usually be the better analysis. In contrast, for data, such as clinical data, in which there is a lot of censoring throughout the time period in which complications occur, the Cox model will usually give a more reliable analysis especially in situations where there are a small number of complications. Both methods are applied to a mouse spinal cord data set and to a clinical head and neck data set. The bias, efficiency, and coverage rate of confidence intervals and robustness of the two methods are compared in a Monte Carlo simulation.