Modeling neural activity with cumulative damage distributions

A New Mixture Model With Cure Rate Applied to Breast Cancer Data

We introduce a new modelling for long-term survival models, assuming that the number of competing causes follows a mixture of Poisson and the Birnbaum-Saunders distribution. In this context, we present some statistical properties of our model and demonstrate that the promotion time model emerges as a limiting case. We delve into detailed discussions of specific models within this class. Notably, we examine the expected number of competing causes, which depends on covariates. This allows for direct modeling of the cure rate as a function of covariates. We present an Expectation-Maximization (EM) algorithm for parameter estimation, to discuss the estimation via maximum likelihood (ML) and provide insights into parameter inference for this model. Additionally, we outline sufficient conditions for ensuring the consistency and asymptotic normal distribution of ML estimators. To evaluate the performance of our estimation method, we conduct a Monte Carlo simulation to provide asymptotic properties and a power study of LR test by contrasting our methodology against the promotion time model. To demonstrate the practical applicability of our model, we apply it to a real medical dataset from a population-based study of incidence of breast cancer in São Paulo, Brazil. Our results illustrate that the proposed model can outperform traditional approaches in terms of model fitting, highlighting its potential utility in real-world scenarios.

Generalised exponential-Gaussian distribution: a method for neural reaction time analysis

Reaction times (RTs) are an essential metric used for understanding the link between brain and behaviour. As research is reaffirming the tight coupling between neuronal and behavioural RTs, thorough statistical modelling of RT data is thus essential to enrich current theories and motivate novel findings. A statistical distribution is proposed herein that is able to model the complete RT's distribution, including location, scale and shape: the generalised-exponential-Gaussian (GEG) distribution. The GEG distribution enables shifting the attention from traditional means and standard deviations to the entire RT distribution. The mathematical properties of the GEG distribution are presented and investigated via simulations. Additionally, the GEG distribution is featured via four real-life data sets. Finally, we discuss how the proposed distribution can be used for regression analyses via generalised additive models for location, scale and shape (GAMLSS).

The Exponential-Centred Skew-Normal Distribution

Data from some research fields tend to exhibit a positive skew. For example, in experimental psychology, reaction times (RTs) are characterised as being positively skewed. However, it is not unlikely that RTs can take a normal or, even, a negative shape. While the Ex-Gaussian distribution is suitable to model positively skewed data, it cannot cope with negatively skewed data. This manuscript proposes a distribution that can deal with both negative and positive skews: the exponential-centred skew-normal (ECSN) distribution. The mathematical properties of the proposed distribution are reported, and it is featured in two non-synthetic datasets.

Statistical modeling of cell-to-cell variability in viral infection during passaging in suspension cell culture: Application in Monte-Carlo simulation

Packaging during the passaging of viruses in cell cultures yields various phenotypes and is regulated by viral protein expression in infected cells. Although such a packaging mechanism has a profound effect in controlling the virus yield, little is known about the underlying statistical models followed by virus packaging and protein expression among cells infected with the virus. A predictive framework combining identification of the probability density function (PDF) based on log-likelihood and using the PDF for Monte-Carlo simulations is developed. The Birnbaum-Saunders distribution was found to be consistent with all three-virus packaging levels, including nucleocapsids/occlusion-derived virus (ODV), ODVs/polyhedra, and polyhedra/cell for both wild-type and genetically modified AcMNPV. Next, it was demonstrated that PDF fitting could be used to compare two viruses having distinctly different genetic configurations. Finally, the identified PDF can be incorporated in RNA synthesis parameters for baculovirus infection to predict the cell-to-cell variability in protein expression using Monte-Carlo simulations. The proposed tool can be used for the estimation of uncertainty in the kinetic parameter and prediction of cell-to-cell variability for other biological systems.

Fatigue-life distributions for reaction time data

The family of fatigue-life distributions is introduced as an alternative model of reaction time data. This family includes the shifted Wald distribution and a shifted version of the Birnbaum-Saunders distribution. Although the former has been proposed as a way to model reaction time data, the latter has not. Hence, we provide theoretical, mathematical and practical arguments in support of the shifted Birnbaum-Saunders as a suitable model of simple reaction times and associated cognitive mechanisms.

The membrane potential process of a single neuron seen as a cumulative damage process

A simple integrate-and-fire mechanism of a single neuron can be compared with a cumulative damage process, where the spiking process is analogous to rupture sequences of a material under cycles of stress. Although in some cases lognormal-like patterns can be recognized in the inter-spike times under a simple integrate-and-fire mechanism, fatigue life models as the inverse Gaussian distribution and the Birnbaum-Saunders distribution (which was recently introduced in the neural activity framework) provide theoretical arguments that make them more suitable for the modeling of the resulting inter-spike times.