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