MAXIMUM LIKELIHOOD ESTIMATION OF A STOCHASTIC COMPARTMENT MODEL OF CANCER LATENCY - LUNG-CANCER MORTALITY AMONG WHITE FEMALES IN THE UNITED-STATES

Closed form maximum likelihood estimators are derived for a generalization of a model of cancer latency (Tolley, Burdick, Manton, and Stallard, Biometrics35, 1978) by making two assumptions. First it was assumed that the cancer hazard was a constant proportion of the force of mortality within an age interval. Second, it was assumed that the total force of mortality could be estimated externally to the model. With these two conditions it was possible to develop closed form solutions for the MLEs of the parameters of our stochastic compartment model conditional upon the total force of mortality. In addition it was assumed that susceptibility to tumor initiation was gamma distributed over the population of interest. Estimates of the distribution of susceptibility are thus obtained. The model was applied to vital statistics data on deaths due to lung cancer among white females in the U.S. in 1969. A fit was obtained and estimates of latency produced that accord well with clinical and epidemiological findings. Estimates of the parameters of the distribution of susceptibility indicate that the distribution is highly skewed explaining the rather marked downturn in the mortality hazard of lung cancer at advanced ages. © 1979.