Giuseppina Albano

Inferring the effect of therapy on tumors showing stochastic Gompertzian growth

The present work deals with a Gompertz-type diffusion process, which includes in the drift term a time-dependent function C(t) representing the effect of a therapy able to modify the dynamics of the underlying process. However, in experimental studies is not immediate to deduce the functional form of C(t) from a treatment protocol. So a statistical approach is proposed in order to estimate this function when a control group and one or more treated groups are observed. In order to validate the proposed strategy a simulation study for several interesting functional forms of C(t) has been carried out. Finally, an application to infer the net effect of cisplatin and doxorubicin+cyclophosphamide in actual murine models is presented.

On the effect of a therapy able to modify both the growth rates in a Gompertz stochastic model

A Gompertz-type diffusion process characterized by the presence of exogenous factors in the drift term is considered. Such a process is able to describe the dynamics of populations in which both the intrinsic rates are modified by means of time-dependent terms. In order to quantify the effect of such terms the evaluation of the relative entropy is made. The first passage time problem through suitable boundaries is studied. Moreover, some simulation results are shown in order to capture the dependence of the involved functions on the parameters. Finally, an application to tumor growth is presented and simulation results are shown.

On the First Exit Time Problem for a Gompertz-Type Tumor Growth

A stochastic model describing tumor growth based on Gompertz law is considered. We pay attention on the tumor size at time detection. We assume the initial state as a random variable since it may suffer from errors due to measurement and diagnostics. The aim of the present work is to study the first exit time problem for the resulting stochastic process. A numerical analysis is also performed for particular choices of the initial distribution.

Estimating and determining the effect of a therapy on tumor dynamics by means of a modified Gompertz diffusion process.

A modified Gompertz diffusion process is considered to model tumor dynamics. The infinitesimal mean of this process includes non-homogeneous terms describing the effect of therapy treatments able to modify the natural growth rate of the process. Specifically, therapies with an effect on cell growth and/or cell death are assumed to modify the birth and death parameters of the process. This paper proposes a methodology to estimate the time-dependent functions representing the effect of a therapy when one of the functions is known or can be previously estimated. This is the case of therapies that are jointly applied, when experimental data are available from either an untreated control group or from groups treated with single and combined therapies. Moreover, this procedure allows us to establish the nature (or, at least, the prevalent effect) of a single therapy in vivo. To accomplish this, we suggest a criterion based on the Kullback-Leibler divergence (or relative entropy). Some simulation studies are performed and an application to real data is presented.

A Wiener-type neuronal model in the presence of exponential refractoriness

An instantaneous return process in the presence of random refractoriness for Wiener model of single neuron activity is considered. The case of exponential distributed refractoriness is analyzed and expressions for output distributions and interspike intervals density are obtained in closed form. A computational study is performed to elucidate the role played by the model parameters in affecting the firing probabilities and the interspike distribution.

On a Non-homogeneous Gompertz-Type Diffusion Process: Inference and First Passage Time

A stochastic diffusion model based on a generalized Gompertz deterministic growth in which the carrying capacity depends on the initial size of the population is considered. The growth parameter of the process is then modified by introducing a time-dependent exogenous term. The first passage time problem is considered and a two-step procedure to estimate the model is proposed. Simulation study is also provided for suitable choices of the exogenous term.

A Sequential Test for Evaluating Air Quality

The present paper provides a simple sequential test for evaluating air quality, to verify a relative higher health risk of some area. The proposed procedure is based on the identification of a Poisson process representing the number of a particular pollutant at day t in a given year. A maximized sequential probability ratio test based on a composite alternative hypothesis has been implemented. The test is performed on emissions of air pollutants in the area of Salerno in which only partial data are available.

Non Linear Time Series Analysis of Air Pollutants with Missing Data

This paper investigates the jointly use of local polynomials and feedforward neural networks for estimating the probability of exceedance of the daily average for \(PM_{10}\) in the presence of missing data. In contrast to other approaches focusing on some assumption on the distribution of \(PM_{10}\), the reconstruction of the unobserved time series is obtained by using a procedure involving two nonparametric steps based on the estimation of the trend-cycle and of the superimposed nonlinear stochastic component of the series. By using Neural Network Sieve Bootstrap, the probability to overcross the limit established by the European Union for \(PM_{10}\) is evaluated at the dates where time series shows missing values. An application to real data is also presented and discussed.

Testing the Weak Form Market Efficiency: Empirical Evidence from the Italian Stock Exchange

This paper investigates the use of feed forward neural networks for testing the weak form market efficiency. In contrast to approaches that compare out-of-sample predictions of non-linear models to those generated by the random walk model, we directly focus on testing for unpredictability by considering the null hypothesis that a given set of past lags has no effect on current returns. To avoid the data-snooping problem the testing procedure is based on the StepM approach in order to control the familiwise error rate. The procedure is used to test for predictive power in FTSE-MIB index of the italian stock market.

Small Sample Analysis in Diffusion Processes: A Simulation Study

In this paper we analyse small sample properties of the ML estimation procedure in Vasicek and CIR models. In particular, we consider short time series, with a length between 20 and 100, typically values observed in finance and insurance contexts. We perform a simulation study in order to investigate which properties of the parameter estimators remain still valid.