The reverse protraction factor in the induction of bone sarcomas in radium-224 patients

More than 50 bone sarcomas have occurred among a collective of about 800 patients who had been injected in Germany after World War II with large activities of radium-224 for the intended treatment of bone tuberculosis and ankylosing spondylitis. In an earlier analysis it was concluded that, at equal mean absorbed doses in the skeleton, patients with longer exposure time had a higher incidence of bone sarcomas. The previous analysis was based on approximations; in particular, it did not account for the varying times at risk of the individual patients. In view of the implications of a reverse protraction factor for basic considerations in radiation protection, the need was therefore felt to reevaluate the data from the continued follow-up by more rigorous statistical methods. A first step of the analysis demonstrates the existence of the reverse dose-rate effect in terms of a suitably constructed rank-order test. In a second step of the analysis it is concluded that the data are consistent with a linear no-threshold dose dependence under the condition of constant exposure time, while there is a steeper than linear dependence on dose when the exposure times increase proportionally to dose. A maximum likelihood fit of the data is then performed in terms of a proportional hazards model that includes the individual parameters, dose, treatment duration, and age at treatment. The fit indicates proportionality of the tumor rates to mean skeletal dose with an added factor (1 + 0.18.tau), where tau is the treatment time in months. This indicates that a protraction of the injections over 15 months instead of 5 months doubles the risk of bone sarcoma