Maximum likelihood estimation of a stochastic compartment model of cancer latency: Lung cancer mortality among white females in the U.S.
✍ Scribed by Kenneth G. Manton; Eric Stallard
- Publisher
- Elsevier Science
- Year
- 1979
- Tongue
- English
- Weight
- 734 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0010-4809
No coin nor oath required. For personal study only.
✦ Synopsis
Closed form maximum likelihood estimators are derived for a generalization of a model of cancer latency (Tolley, Burdick, Manton, and Stallard, Biometrics 35, 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.
I. INTRODUCTI~I~
It is the case that the effects of chronic diseases, such as cancer, on a population are often not well modeled by standard risk assessment procedures. This is because standard risk models (such as the multiple logistic) represent the incidence of the acute phases of the chronic disease process and ignore the processual characteristics of its long-term development. Efforts to model the chronic development of a disease, however, run into the difficulty that often much of the chronic disease process is unobserved. Thus evaluation of the effects of a disease like cancer on a population require the application of specialized techniques to model the disease progression as a partially observed stochastic process.
The specialized techniques for modeling stochastic processes given limited information may generally be referred to as stochastic compartment models. In general these models involve the estimation of the transition parameters of a partially observed stochastic process through the device of developing constraints on the parameters of the process consistent with auxiliary information. The use of stochastic compartment models has received much attention in the recent biological and biostatistical literature. For example, recent applications include the study of cell kinetics (2, 3), environmental safety models (4), stability of the growth of neoplasia (.5), tumor vascularization and growth (6), cancer chemotherapy (7), and cancer