Andrej Y. Yakovlev

Variable selection and pattern recognition with gene expression data generated by the microarray technology.

Lack of adequate statistical methods for the analysis of microarray data remains the most critical deterrent to uncovering the true potential of these promising techniques in basic and translational biological studies. The popular practice of drawing important biological conclusions from just one replicate (slide) should be discouraged. In this paper, we discuss some modern trends in statistical analysis of microarray data with a special focus on statistical classification (pattern recognition) and variable selection. In addressing these issues we consider the utility of some distances between random vectors and their nonparametric estimates obtained from gene expression data. Performance of the proposed distances is tested by computer simulations and analysis of gene expression data on two different types of human leukemia. In experimental settings, the error rate is estimated by cross-validation, while a control sample is generated in computer simulation experiments aimed at testing the proposed gene selection procedures and associated classification rules.

The shape of the hazard function in breast carcinoma: Curability of the disease revisited

The question of curability of breast carcinoma remains controversial. Because the probability of cure essentially is an asymptotic notion, the corresponding estimation problems call for special statistical methods. Such methods should account for an intimate connection between the probability of cure and the shape of the hazard function.

A stochastic model of temporally regulated generation of oligodendrocytes in cell culture

The results of our previous analyses suggest that O-2A progenitor cells become competent for differentiation in vitro after they complete a certain number of critical mitotic cycles. The number of critical cycles varies from clone to clone and should be thought of as a random variable. We propose an approach to the analysis of oligodendrocyte generation in vitro based on a stochastic model allowing for an arbitrary distribution of this random variable with a finite support. When applied to experimental data on clonal growth and differentiation of purified O-2A progenitor cells obtained from optic nerves of 1 and 7 day-old rats, the model provides a good quantitative description not only of the first two moments (mean and variance) of the number of O-2A progenitor cells and oligodendrocytes at different times after the start of experiment, but of the corresponding distributions as well. As our estimates show, there are scarcely any O-2A progenitor cells that divide in vitro more than twice before they acquire the competence for differentiation. Those O-2A cells that have undergone the critical divisions differentiate into an oligodendrocyte in each of the subsequent mitotic cycles with a certain probability. We give estimates of this probability for O-2A cells under different growth conditions. Our analysis suggests that the effect of thyroid hormone is twofold: it reduces the mean duration of the mitotic cycle for progenitor cells, and it increases the probability of their transformation into oligodendrocytes.

Estimation problems associated with stochastic modeling of proliferation and differentiation of O-2A progenitor cells in vitro

Our previous research effort has resulted in a stochastic model that provides an excellent fit to our experimental data on proliferation and differentiation of oligodendrocyte type-2 astrocyte progenitor cells at the clonal level. However, methods for estimation of model parameters and their statistical properties still remain far away from complete exploration. The main technical difficulty is that no explicit analytic expression for the joint distribution of the number of progenitor cells and oligodendrocytes, and consequently for the corresponding likelihood function, is available. In the present paper, we overcome this difficulty by using computer-intensive simulation techniques for estimation of the likelihood function. Since the output of our simulation model is essentially random, stochastic optimization methods are necessary to maximize the estimated likelihood function. We use the Kiefer-Wolfowitz procedure for this purpose. Given sufficient computing resources, the proposed estimation techniques significantly extend the spectrum of problems that become approachable. In particular, these techniques can be applied to more complex branching models of multi-type cell systems with dependent evolutions of different types of cells.

Modeling insight into spontaneous regression of tumors

The phenomenon of spontaneous regression of benign and malignant tumors is well documented in the literature and is commonly attributed to the induction of apoptosis or activation of the immune system. We attempt at evaluating the role of random effects in this phenomenon. To this end, we consider a stochastic model of tumor growth which is descriptive of the fact that tumors are inherently prone to spontaneous regression due to the random nature of their development. The model describes a population of actively proliferating cells which may give rise to differentiated cells. The process of cell differentiation is irreversible and terminates in cell death. We formulate the model in terms of temporally inhomogeneous Markov branching processes with two types of cells so that the expected total number of neoplastic cells is consistent with the observed mean growth kinetics. Within the framework of this model, the extinction probability for proliferating cells tends to one as time tends to infinity. Given the event of nonextinction, the distribution of tumor size is asymptotically exponential. The limiting conditional distribution of tumor size is in good agreement with epidemiologic data on advanced lung cancer.

A random walk model of oligodendrocyte generation in vitro and associated estimation problems

A branching stochastic process proposed earlier to model oligodendrocyte generation by O-2A progenitor cells under in vitro conditions does not allow invoking the maximum likelihood techniques for estimation purposes. To overcome this difficulty, we propose a partial likelihood function based on an embedded random walk model of clonal growth and differentiation of O-2A progenitor cells. Under certain conditions, the partial likelihood function yields consistent estimates of model parameters. The usefulness of this approach is illustrated with computer simulations and data analyses.

Do cells repair precancerous lesions induced by radiation

The most widely accepted point of view is that cells are endowed with the capacity to repair the primary lesions responsible for cancer induction. In radiobiology, this popular belief evolved from experiments of the same type as those that suggested the existence of sublethal radiation damage repair. The central problem with such data is that the cell-killing component of radiation damage may mask the effects associated with repair of precancerous lesions. The challenge is to separate the two processes that contribute to the observed tumor incidence after irradiation. using a recently developed stochastic model of radiation carcinogenesis allowing for cell death, we provide evidence that precancerous lesions are not subject to repair under certain experimental conditions.

Stochastic formulations of a clock model for temporally regulated generation of oligodendrocytes in vitro

It is possible to grow oligodendrocyte type-2 astrocyte (O-2A) progenitor cells in vitro in such a manner that they divide and generate oligodendrocytes with a timing which recapitulates the timing of normal development in vivo. The most widely accepted model of this process assumes a cell-intrinsic biological clock that resides in the O-2A progenitor cell and counts the number of mitotic divisions. The intrinsic clock model, originally proposed in 1985, remains to be the dominant theoretical concept for the analysis of timed differentiation in this cell lineage. In this paper, we proceed from different biologically plausible assumptions to provide a stochastic description of the clock model based on the theory of multitype age-dependent branching processes. This approach makes it possible to interpret the observed pattern of oligodendrocyte generation and its modification in the presence of thyroid hormone in terms of parameters that have a clear biological meaning.

A model of multiple tumorigenesis allowing for cell death: Quantitative insight into biological effects of urethane

This paper considers the utility of a stochastic model of carcinogenesis proposed by Yakovlev and Polig [Math. Biosci. 132 (1996) 1-33] in the analysis of experimental data on multiple tumors induced by chemical carcinogens. The model provides a good description of published data on multiple tumors developing in the lungs of mice in response to different schedules of urethane. The distribution of pulmonary tumor counts appears to be negative binomial for each period of time after exposure to urethane. Our results suggest that the rate of administration of urethane has little effect both on the mean number of initiated cells per unit dose and on the rate of formation of lesions responsible for cell death. As our estimates show, more than 80% of initiated cells die in the course of tumor promotion. The model is robust to variations in the rate of urethane excretion given a fixed total dose of the carcinogen. Some prospects for further development of the model to allow for expansion of promoted cell clones are discussed.

Spline-based estimation of cure rates: An application to the analysis of breast cancer data

This paper considers the utility of spline approximations of the hazard function for estimation of cure rates from survival data. With this approach, it is possible to assess dissimilar effects of various covariates on the probability of tumor cure and on the timing of the endpoint (death, tumor recurrence, etc.) under study. The usefulness of the approach is illustrated with an application to data on survival of patients treated for breast cancer.