Andrej Yu. Yakovlev

A diversity of responses displayed by a stochastic model of radiation carcinogenesis allowing for cell death

A stochastic model is presented of carcinogenesis induced by irradiation with arbitrary time-dependent dose rate. The key feature of the model is that it allows for radiation-induced cell killing to compete with the process of tumor promotion. Two versions of the model arise when considering target tissues with slow and rapid replacement of damaged cells. These versions show dissimilar shapes of the dose-response curves in the case of short-term exposure. The model provides a natural explanation of the basic experimental findings documented in the radiobiological literature.

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. With this model it is possible to interpret data on tumor incidence in terms of promotion and progression processes. The basic model is developed for a prolonged irradiation at a constant dose rate and includes short-term irradiation as a special case. A limiting form of the latent time distribution for short-term irradiation at high doses is obtained. This distribution arises in the extreme value theory within the random minima framework. An estimate for the rate of convergence to a limiting distribution is given. Based on the proposed latent time distributions, long-term predictions of carcinogenic risk do not call for information about irradiation dose. As shown by computer simulation studies and real data analysis, the parametric estimation of carcinogenic risk appears to be robust to the loss of statistical information caused by the right-hand censoring of time-to-tumor observations. It seems likely that this property, although revealed by means of a purely empirical procedure, may be useful in selecting a model for the practical purpose of risk prediction.

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. The model provides efficient means of interpreting experimental findings, as evidenced by its application to analysis of some published data on the hormetic effects of prolonged irradiation and of procaine on animal longevity.

A distribution of tumor size at detection: an application to breast cancer data.

This paper discusses a method of estimating numerical characteristics of unobservable stages of carcinogenesis from data on tumor size at detection. To this end, a stochastic model of spontaneous carcinogenesis has been developed to allow for a simple pattern of tumor growth kinetics. It is assumed that a tumor becomes detectable when its size attains some threshold level, which is treated as a random variable. The model yields a parametric family of joint distributions for tumor size and age at detection. Some estimation problems associated with the proposed model appear to be tractable. This is illustrated with an application to the statistical analysis of data on primary breast cancer.

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. Both approaches are applied to the analysis of an optimization problem when the natural history of the disease is known and when it is unknown (a minimax problem). The structure of optimal screening policies is investigated as well as the benefit they can provide compared to the periodic screening policy. The detection probability is assumed to depend only on the stage of the disease, though it may not be constant throughout each stage. It is shown that periodic screening appears to be optimal when one has no information on the natural history of the disease, the minimum delay time criterion being used for optimization. Some applications to lung cancer screening are presented.

Queueing models of potentially lethal damage repair in irradiated cells

Some of the ideas arising in queueing theory are applied to describe the repair mechanisms responsible for recovery of cells from potentially lethal radiation damage. Two alternative versions are presented of a queueing model of damage repair after a single dose of irradiation. The first version represents a linear misrepair model, and the second invokes the idea of spontaneous lesion fixation. They are pieced together in the third model, allowing for both mechanisms. The consistency of the proposed models with published experimental data is tested.

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. As shown in the present paper, a natural two-dimensional generalization of the model appears in the form of a Weibull-Marshall-Olkin distribution. Similarly, the study of a randomized version of the model based on the negative binomial minima scheme results in a bivariate Pareto-Marshall-Olkin distribution. In the latter case, an estimate for the rate of convergence to the limiting distribution is given.

COMPUTER SIMULATION OF TUMOR RECURRENCE

Computer simulations have been conducted to provide a realistic model of tumor recurrence in a cancer patient, following treatment. The simulation model incorporates description of the temporal organization of various biological processes underlying tumor development at the cellular level: proliferation, differentiation, death of tumor cells, growth control in neoplastic tissues along with the tumor treatment effect. The prime object of our concern is whether the simple parametric model of tumor recurrence proposed by Hoang et al. [6] allows estimation of actual value of the tumor growth potential. A good fit has been demonstrated of the parametric model when applied to the samples of simulated tumor recurrence times as well as to real data samples of tumor recurrence in breast cancer patients with various regimen of radiotherapy.