A nonidentifiability aspect of the two-stage model of carcinogenesis.

This paper discusses identifiability of the two-stage birth-death-mutation model of carcinogenesis. It is shown that the homogeneous version of the model is nonidentifiable; the same is all the more evident for its nonhomogeneous versions. This result implies that the model parameters cannot be uniquely estimated from time-to-tumor observations.

A bivariate limiting distribution of tumor latency time.

The model of radiation carcinogenesis, proposed earlier by Klebanov, Rachev, and Yakovlev [8] substantiates the employment of limiting forms of the latent time distribution at high dose values. Such distributions arise within the random minima framework, the two-parameter Weibull distribution being a special case. This model, in its present form, does not allow for carcinogenesis at multiple sites.

Discrete strategies of cancer post-treatment surveillance. Estimation and optimization problems.

We consider the cancer post-treatment surveillance to be represented by a discrete observation process with a non-zero false-negative rate. Using a simple stochastic model of cancer recurrence derived within the random minima framework, we obtain parametric estimates of both the time-to-recurrence distribution and the probability of false-negative diagnosis. Then assuming the false-negative rate known, we give a nonparametric maximum likelihood estimator for the tumor latency time distribution.

Testing a model of aging in animal experiments.

A stochastic model of aging is developed in terms of accumulation and expression of intracellular lesions caused by environment or intrinsic genetic program. In contrast to the commonly used Gompertz-Makeham approach to the parametric analysis of mortality data, the model yields a hazard function that is bounded from above. For testing the model in experiments aimed at studying animal longevity, a Kolmogorov-type statistical test is presented with regard to the hypothesis involving unknown parameters.

The choice of cancer treatment based on covariate information.

This paper is concerned with methods for choosing optimal treatment for particular patients; the central idea is that information contained in covariates may be useful for this kind of decision making. For each patient estimated conditional survivor functions for each mode of treatment may be compared and the optimal treatment may be defined as the one providing higher predicted survival. Regression survival models form the basis for a pertinent statistical decision rule, and a procedure for retrospective validation of such a rule is given.

A stochastic model of hormesis.

In order to describe the life-prolonging effect of some agents that are harmful at higher doses, ionizing radiations in particular, a stochastic model is developed in terms of accumulation and progression of intracellular lesions caused by the environment and by the agent itself. The processes of lesion repair, operating at the molecular and cellular level, are assumed to be responsible for this hormesis effect within the framework of the proposed model. Properties of lifetime distributions, derived for analysis of animal experiments with prolonged and acute irradiation, are given special attention.

A stochastic model of radiation carcinogenesis: latent time distributions and their properties.

A stochastic model of radiation carcinogenesis is proposed that has much in common with the ideas suggested by M. Pike as early as 1966. The model allows us to obtain a parametric family of substochastic-type distributions for the time of tumor latency that provides a description of the rate of tumor development and the number of affected individuals.

On the optimal policies of cancer screening.

Some problems of optimal screening are considered. A screening strategy is allowed to be nonperiodic. Two approaches to screening optimization are used: the minimum delay time approach and the minimum cost approach.