ArticleRobinson CV, Upton AC.
J Natl Cancer Inst. 1978 May;60(5):995-1007.
The theory of competing risks, extended by the addition of several newly defined estimators, was applied to the analysis of mortality data for acutely X-irradiated, male RF mice, in which the cause of each death was assigned to one of four categories: myeloid leukemia (M), thymic lymphoma (T), lymphosarcoma and reticulum cell sarcoma (L), and all remaining causes (R), Doses from 0 to 450 rads were delivered within two age ranges: A) 5-6 weeks and B) 9-10 weeks, to give 11 treatment groups totaling 2,073 mice. The data were analyzed in terms of: 1) the nonparametric, Kaplan-Meier (K-M) adjusted survival function; 2) its logarithmic transform, the cumulative force of mortality (cumFM) function; 3) a disease model called "early terminating," applied to causes M and T; and 4) a "late-terminating" model, applied to causes L and R. For any given cause and group, two estimators were used, which measured, respectively: a) the relative lateness of the corrected (or adjusted) time course and b) the relative corrected incidence. For causes M and T, these were: a) the mean age of the force of mortality distribution (MAF), or corrected mean latent period; and b) the final cumFM. For causes L and R, the estimators were: a) the adjusted mean age at death (adjMAD), given an upper limit (as %) of adjusted mortality (adjMAD, 50% for L; adjMAD, 100%--the K-M estimator--for R) and b) the cumFM at a cutoff time of 640 days. For causes M and T, the MAF values showed highly significant decreases of the latent periods with dose, through 300 rads. The final cumFM data showed a marked increase of corrected incidence with dose, for both M and T. In addition, the data for cause M were consistent with a three-parameter, leukemogenic cell model that incorporated two opposing radiation effects: leukemogenic cell potentiation and cell killing. For cause R, the adjMAD, 100% data showed a general decrease with dose and considerable scatter. For cause L, the adjMAD, 50% values showed: for treatment A, a gradual decrease with dose through 300 rads; for treatment B, a highly significant drop for 150 rads, with little change for higher doses. The cumFM, 640-day values for both L and R showed a general increase of corrected incidence with dose. The mortality curves for all causes combined showed the expected life shortening, i.e., decreases of the mean age at death with dose, in the 0- to 300-rad range. In addition, the standard deviations of the mortality curves were significantly less for animals irradiated at age range B than at age range A, for each of the doses--150, 300, and 450 rads.