A survival model and estimation of time to tumor

In this paper we introduce a stochastic model of survival distribution, where the mortality intensity is a function of the accumulated effect of an individual's continuous exposure to toxic material in the environment (absorbing coefficient) and his biological reaction to the toxin absorbed (discharging coefficient). Formulas for the density function, the distribution function, and the expectation of lifetime are presented. The paper also includes special cases where there is a change in exposure level or exposure is discontinued or exposure is discrete in time. The model is then applied to the NCTR's serial sacrifice experimental study on mice fed 2-AAF, including some mice whose feeding was discontinued. The random variable here is the time to tumor. The chi-square test shows a good fit of the model to the data (P = 0.365). In addition to the parameters and their standard errors, estimates are computed for the expectation, variance, and percentiles of time to tumor, and for the age-specific cancer incidence rates. Confidence intervals for the parameters are also given.