A method of determining radiation dose-response relationships is presented which does not require combining into the same group members that are affected by different doses. The method is based on hazard theory and is referred to as the hazard-function method or hazard method. The hazard method is employed to resolve dose-response curves for the induction of injury sufficient to cause early mortality from pulmonary injury (mostly from radiation pneumonitis and pulmonary fibrosis) in beagle dogs, after inhalation of relatively insoluble forms of 90Y,90Y, 144Ce or 90Sr and after inhalation of 239Pu02 The dose-response curves appear linear over a large range of doses and appear curvilinear at relatively low doses in some cases. It is demonstrated that the distribution of doses that produce injury to the lung sufficient to cause early mortality is related to the effective half-life of the radioactive material in the lung. The efficiency of low linear energy transfer (LET) radioactive materials in inducing lethal pulmonary injury is shown to decrease as the effective half-life of the material in the lung increases. Dose-RBE (relative biological effectiveness) relationships are presented and a method of correcting for wasted dose is discussed.