Bayesian Cure Rate Modeling of Local Tumor Control: Evaluation in Stereotactic Body Radiation Therapy for Pulmonary Metastases

Abstract

Purpose: Most radiobiological models for prediction of tumor control probability (TCP) do not account for the fact that many events could remain unobserved because of censoring. We therefore evaluated a set of TCP models that take into account this censoring.

Methods and materials: We applied 2 fundamental Bayesian cure rate models to a sample of 770 pulmonary metastasis treated with stereotactic body radiation therapy at German, Austrian, and Swiss institutions: (1) the model developed by Chen, Ibrahim and Sinha (the CIS99 model); and (2) a mixture model similar to the classic model of Berkson and Gage (the BG model). In the CIS99 model the number of clonogens surviving the radiation treatment follows a Poisson distribution, whereas in the BG model only 1 dominant recurrence-competent tissue mass may remain. The dose delivered to the isocenter, tumor size and location, sex, age, and pretreatment chemotherapy were used as covariates for regression.

Results: Mean follow-up time was 15.5 months (range: 0.1-125). Tumor recurrence occurred in 11.6% of the metastases. Delivered dose, female sex, peripheral tumor location and having received no chemotherapy before RT were associated with higher TCP in all models. Parameter estimates of the CIS99 were consistent with the classical Cox proportional hazards model. The dose required to achieve 90% tumor control after 15.5 months was 146 (range: 114-188) Gy10 in the CIS99 and 133 (range: 101-164) Gy10 in the BG model; however, the BG model predicted lower tumor control at long (≳20 months) follow-up times and gave a suboptimal fit to the data compared to the CIS99 model.

Conclusions: Biologically motivated cure rate models allow adding the time component into TCP modeling without being restricted to the follow-up period which is the case for the Cox model. In practice, application of such models to the clinical setting could allow for adaption of treatment doses depending on whether local control should be achieved in the short or longer term.