A survival model for fractionated radiotherapy with an application to prostate cancer

This paper explores the applicability of a mechanistic survival model, base d on the distribution of clonogens surviving a course of fractionated radia tion therapy, to clinical data on patients with prostate cancer. The study was carried out using data on 1100 patients with clinically localized prost ate cancer who were treated with three-dimensional conformal radiation ther apy. The patients were stratified by radiation dose (group 1: <67.5 Gy; gro up 2: 67.5-72.5 Gy; group 3: 72.5-77.5 Gy; group 4: 77.5-87.5 Gy) and progn osis category (favourable, intermediate and unfavourable as defined by pre- treatment PSA and Gleason score). A relapse was recorded when tumour recurr ence was diagnosed or when three successive prostate specific antigen (PSA) elevations were observed from a post-treatment nadir PSA level. PSA relaps e-free survival was used as the primary end point. The model, which is base d on an iterated Yule process, is specified in terms of three parameters: t he mean number of tumour clonogens that survive the treatment, the mean of the progression time of post-treatment tumour development and its standard deviation. The model parameters were estimated by the maximum likelihood me thod. The fact that the proposed model provides an excellent description bo th of the survivor function and of the hazard rate is prima facie evidence of the validity of the model because closeness of the two survivor function s (empirical and model-based) does not generally imply closeness of the cor responding hazard rates. The estimated cure probabilities for the favourabl e group are 0.80, 0.74 and 0.87 (for dose groups 1-3, respectively); for th e intermediate group: 0.25, 0.51, 0.58 and 0.78 (for dose groups 1-4, respe ctively) and for the unfavourable group: 0.0, 0.27, 0.33 and 0.64 (for dose groups 1-4, respectively). The distribution of progression time to tumour relapse was found to be independent of prognosis group but dependent on dos e. As the dose increases the mean progression time decreases (41, 28.5, 26. 2 and 14.7 months for dose groups 1-4, respectively). This analysis confirm s that, in terms of cure rate, dose escalation has a significant positive e ffect only in the intermediate and unfavourable groups. It wits found that progression time is inversely proportional to dose, which means that patien ts recurring in higher dose groups have shorter recurrence times, yet these groups have better survival, particularly long-term. The explanation for t his seemingly illogical observation lies in the fact that less aggressive t umours, potentially recurring after a long period of time, are cured by hig her doses and do not contribute to the recurrence pattern. As it result, pa tients in higher dose groups are less likely to recur: however, if they do, they tend to recur earlier. The estimated hazard rates for prostate cancer pass through a clear-cut maximum, thus revealing a time period with especi ally high values of instantaneous cancer-specific risk; the estimates appea r to be nonproportional across dose strata.