The delay before onset of accelerated tumour cell repopulation during radiotherapy: a direct maximum-likelihood analysis of a collection of worldwide tumour-control data.

The worldwide collection of control data for head and neck tumours presented by Withers et al. (Withers, H.R., Taylor, J.M.G. and Maciejewski, B. Acta Oncol. 27: 131-146, 1988) was reanalysed using a model which includes an explicit lag phase before the onset of tumour clonogen repopulation. A direct maximum-likelihood approach was used and the methodology extended to include the computation of profile-likelihood confidence limits. A statistically significant (p = 0.02) lag of 29 days was obtained with 95% confidence limits covering the range 17-31 days. However, the confidence interval was disconnected, and excluded the period 21-23 days. The analysis gave a time factor of 0.66 Gy/day. The mean values confirm the conclusions drawn by the original authors using a two-stage (indirect) method, and the values are similar to those calculated here for another data set comprising 496 patients (lag period = 26 (19-33) days). However, the data set itself is retrospective, and potentially subject to a number of biases. Therefore any clinical conclusions can only be tentative. A new feature of the methodology is the computation of profile-likelihood confidence limits and this will be useful in future direct analyses of clinical data of this type. The more usually computed normal approximation to the confidence limits have been shown to be inadequate in this analysis, and either profile-likelihood limits or likelihood ratio tests must be employed to determine the significance of the model parameters.