Modeling the relationship between radiotherapy delay and cancer outcomes
by
Jon-Paul Voroney
Queen's University Cancer Research Centre, Division of Cancer Care and Epidemiology
Coauthors: William J Mackillop Sarah J Rauth

Background: Worldwide, delay in radiotherapy for cancer allows progression of untreated tumours. The current average delay in Ontario is over 4 weeks. Meta-analyses of retrospective cohorts relate delay of a one month for radiotherapy to a relative risk of 1.15 for local control or survival from head & neck cancer. Paradoxically, in studies that do not adjust for confounding, delay can be associated with better prognosis: more advanced tumours are often preferentially treated first. Treating poor-prognosis patients first is a triaging strategy appropriate for an emergency department, and does not provide a population with as high a cure rate as would a triaging strategy based on priority for those cancer patients who will be most harmed by delay. Objectives: To model the effect of delay in radiotherapy on cancer outcomes, including local control and overall survival, with particular emphasis on data from published series in head & neck cancer. Methods: (1) Meta-analysis of the head & neck cancer literature on the prognostic effect of tumour volume on local control and overall survival in patients treated with radiotherapy, including modeling the functional relationship between volume and radiotherapy outcome. (2) Meta-analysis of radiologic and serologic markers of tumour volume and their time-dependence in untreated patients. (3) Mathematical modeling of the effect of radiotherapy delay on outcomes through combining the prognostic effect of tumour volume and tumour volume doubling times. Results: (1) We pooled results from 55 studies in head & neck cancer, to demonstrate relationships between initial tumour volume, V, and radiotherapy outcomes. The relationship is exponential, exp(-kV), with the rate constant k depending on site, whether primary tumour volume or total tumour volume (including lymph node spread) was measured, and choice of radiotherapy outcome (local control or survival). This is consistent with a Poisson distribution for the fraction of surviving cells after treatment depending linearly on the initial tumour volume. The rate k is also dependent on treatment, surrogates of radioresistance, and the choice of the model relating volume to outcomes e.g. a one-parameter model exp(-kV) versus two-parameter model Aexp(-kV). The prognostic effect of volume is robust- it persists in studies when additional therapy is given to patients with higher tumour volumes. (2) We abstracted data from 100 studies (5702 tumours) on tumour volume doubling times. Doubling time distribution is lognormal within each site. Summary statistics show considerable variation of medians and inter-quartile ranges for doubling times, depending on the primary tumour site, the histologic subtype, and whether the tumour is metastatic or recurrent. For example, primary prostate cancer has a median tumour volume doubling time of 7 years, while a head & neck cancer recurrence has a doubling time of 1 week. (3) Calculation of the effect of treatment delay, using the relationship between outcomes and volume, and tumour volume doubling times is thus possible: for example, for an average head and neck tumour with a volume of 12 cc, volume doubling time of 8 weeks, and dependence of volume on prognosis of exp(-0.03V), the relative risk of 1 month delay is 1.16. An initial cancer local control rate of 70% drops to 60%. Incorporating distributions in population values of model parameters and incorporating a Gompertz or logistic function into modelling tumour growth are refinements that improve modelling for large tumours and long delays. Conclusions: The increased risk of poor outcomes with RT delay is predictable using tumour growth and knowledge of the association between outcomes and tumour volume. We have validated our model of delay in radiotherapy for head & neck cancer, and this model can be tailored to data from particular treatment centres, particular populations, and particular tumours.

Date received: May 14, 2008