A Stochastic Model of Carcinogenesis and Tumor Size at Detection

This paper discusses the distribution of tumor size at detection derived within the framework of a new stochastic model of carcinogenesis. This distribution assumes a simple limiting form, with age at detection tending to infinity which is found to be a generalization of the distribution that arises in the length-biased sampling. Two versions of the model are considered with reference to spontaneous and induced carcinogenesis; both of them show similar asymptotic behavior. When the limiting distribution is applied to real data analysis its adequacy can be tested through testing the conditional independence of the size, V, and the age, A, at detection given A > t*, where the value of t* is to be estimated from the given sample. This is illustrated with an application to data on premenopausal breast cancer. The proposed distribution offers the prospect of the estimation of some biologically meaningful parameters descriptive of the temporal organization of tumor latency. An estimate of the model stability to the prior distribution of tumor size and some other stability results for the Bayes formula are given.

A Stochastic Model of Carcinogenesis and Tumor Size at Detection

This paper discusses the distribution of tumor size at detection derived within the framework of a new stochastic model of carcinogenesis. This distribution assumes a simple limiting form, with age at detection tending to infinity which is found to be a generalization of the distribution that arises in the length-biased sampling. Two versions of the model are considered with reference to spontaneous and induced carcinogenesis; both of them show similar asymptotic behavior. When the limiting distribution is applied to real data analysis its adequacy can be tested through testing the conditional independence of the size,V,and the age,A,at detection givenA > t*,where the value oft*is to be estimated from the given sample. This is illustrated with an application to data on premenopausal breast cancer. The proposed distribution offers the prospect of the estimation of some biologically meaningful parameters descriptive of the temporal organization of tumor latency. An estimate of the model stability to the prior distribution of tumor size and some other stability results for the Bayes formula are given.

Application of the promotion time cure model with time-changing exposure to the study of HIV/AIDS and other infectious diseases

Infectious diseases are caused by single or successive contacts with pathogens. Nevertheless, contacts with pathogens do not implicate infection. In 1993, Yakovlev et al. proposed a model to study a population of cancer patients with a cured fraction, a well adapted model to describe an infectious disease with a unique infection occasion. Extensions of this model have been proposed in the recent years. We present a mechanistic formulation in the context of infectious diseases with multiple infection occasions. It is a mixture model that enables to study risk factors associated with infection intensity at each infection occasion and factors shortening the delay from exposure to clinical event. Simulations are performed to evaluate the model fitting and two examples are presented for illustration: an analysis of an HIV-1 mother-to-child transmission data set and an analysis of nosocomial urinary tract infections data set.

Heterogeneity and its biodemographic implications for longevity and mortality

In the visible world, heterogeneity typically refers to the differences that exist among individuals in a defined population. These differences can arise from a variety of sources--biological, behavioral and social. Ever since Darwin, scientists have argued over the biological significance of differences observed at the individual, morphological, physiological, genetic, molecular and structural levels. A general consensus has been reached. Heterogeneity is ubiquitous, it is important, and it increases as observations are made at finer levels of biological resolution. Debates over the significance of heterogeneity have emerged once again as biologists and demographers work together in order to create the emerging field of biodemography. For these scientists, the debates center around the relative impact that individual heterogeneity has on population level statistics. It is argued here that in a world where the mortality barriers to long life for individuals have been dramatically weakened, the population consequences of heterogeneity are already visible and will grow in importance as biomedical technologies continue to usher progressively more people into the post-reproductive period of the lifespan.

Parameter estimation in a Gompertzian stochastic model for tumor growth

The problem of estimating parameters in the drift coefficient when a diffusion process is observed continuously requires some specific assumptions. In this paper, we consider a stochastic version of the Gompertzian model that describes in vivo tumor growth and its sensitivity to treatment with antiangiogenic drugs. An explicit likelihood function is obtained, and we discuss some properties of the maximum likelihood estimator for the intrinsic growth rate of the stochastic Gompertzian model. Furthermore, we show some simulation results on the behavior of the corresponding discrete estimator. Finally, an application is given to illustrate the estimate of the model parameters using real data.

A biologically motivated partitioning of mortality

For over a century, actuaries and biologists working independently of each other have presented arguments for why total mortality needs to be partitioned into biologically meaningful subcomponents. These mortality partitions tended to overlook genetic diseases that are inherited because the partitions were motivated by a paradigm focused on aging. In this article, we combine and extend the concepts from these disciplines to develop a conceptual partitioning of total mortality into extrinsic and intrinsic causes of death. An extrinsic death is either caused or initiated by something that orginates outside the body of an individual, while an intrinsic death is either caused or initiated by processes that originate within the body. It is argued that extrinsic mortality has been a driving force in determining why we die when we do from intrinsic causes of death. This biologically motivated partitioning of mortality provides a useful perspective for researchers interested in comparative mortality analyses, the consequences of population aging, limits to human life expectancy, the progress made by the biomedical sciences against lethal diseases, and demographic models that predict the life expectancy of future populations.