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.