Formula predicting carcinoma-free probability in rats exposed to carcinogen DMBA

The Weibull distribution is a generalization of the exponential distribution. Pike (Biometrics, 22 (1966) 142-161) used the Weibull distribution in the analysis of carcinogenesis experiments on rats. A formula of conversion that allows mathematical conversion of the Weibull distribution to the generalized lognormal distribution is constructed in this study. This formula is applied to the Pike's data on carcinoma-free probability in rats exposed to carcinogen DMBA. A mathematical model and a computer program previously published by the author are employed in this study. Analysis of the computer-assisted predicted and the Pike's reported data on carcinoma-free probability indicates that a close agreement is present between both data. It seems to the author that a generalized lognormal distribution of the carcinoma-free probability in rats exposed to carcinogen can be derived from the formula of conversion. In addition the generalized lognormal distribution may be proposed as a method of parametric analysis of survival data on estimates by non-parametric product-limit method of Kaplan-Meier in certain biological phenomena.