On the effect of confounding in linear regression models: an approach based on the theory of quadratic forms

The main topic of this thesis is confounding in linear regression models. It arises when a relationship between an observed process, the covariate, and an outcome process, the response, is influenced by an unmeasured process, the confounder, associated with both. Consequently, the estimators for the regression coefficients of the measured covariates might be severely biased, less efficient and characterized by misleading interpretations. Confounding is an issue when the primary target of the work is the estimation of the regression parameters. The central point of the dissertation is the evaluation of the sampling properties of parameter estimators. This work aims to extend the spatial confounding framework to general structured settings and to understand the behaviour of confounding as a function of the data generating process structure parameters in several scenarios focusing on the joint covariate-confounder structure. In line with the spatial statistics literature, our purpose is to quantify the sampling properties of the regression coefficient estimators and, in turn, to identify the most prominent quantities depending on the generative mechanism impacting confounding. Once the sampling properties of the estimator conditionally on the covariate process are derived as ratios of dependent quadratic forms in Gaussian random variables, we provide an analytic expression of the marginal sampling properties of the estimator using Carlson’s R function. Additionally, we propose a representative quantity for the magnitude of confounding as a proxy of the bias, its first-order Laplace approximation. To conclude, we work under several frameworks considering spatial and temporal data with specific assumptions regarding the covariance and cross-covariance functions used to generate the processes involved. This study allows us to claim that the variability of the confounder-covariate interaction and of the covariate plays the most relevant role in determining the principal marker of the magnitude of confounding.

Graphene-based bioelectronic interfaces and devices and interpretative models targeting glial cells

Bioelectronic interfaces have significantly advanced in recent years, offering potential treatments for vision impairments, spinal cord injuries, and neurodegenerative diseases. However, the classical neurocentric vision drives the technological development toward neurons. Emerging evidence highlights the critical role of glial cells in the nervous system. Among them, astrocytes significantly influence neuronal networks throughout life and are implicated in several neuropathological states. Although they are incapable to fire action potentials, astrocytes communicate through diverse calcium (Ca2+) signalling pathways, crucial for cognitive functions and brain blood flow regulation. Current bioelectronic devices are primarily designed to interface neurons and are unsuitable for studying astrocytes. Graphene, with its unique electrical, mechanical and biocompatibility properties, has emerged as a promising neural interface material. However, its use as electrode interface to modulate astrocyte functionality remains unexplored. The aim of this PhD work was to exploit Graphene-oxide (GO) and reduced GO (rGO)-coated electrodes to control Ca2+ signalling in astrocytes by electrical stimulation. We discovered that distinct Ca2+dynamics in astrocytes can be evoked, in vitro and in brain slices, depending on the conductive/insulating properties of rGO/GO electrodes. Stimulation by rGO electrodes induces intracellular Ca2+ response with sharp peaks of oscillations (“P-type”), exclusively due to Ca2+ release from intracellular stores. Conversely, astrocytes stimulated by GO electrodes show slower and sustained Ca2+ response (“S-type”), largely mediated by external Ca2+ influx through specific ion channels. Astrocytes respond faster than neurons and activate distinct G-Protein Coupled Receptor intracellular signalling pathways. We propose a resistive/insulating model, hypothesizing that the different conductivity of the substrate influences the electric field at the cell/electrolyte or cell/material interfaces, favouring, respectively, the Ca2+ release from intracellular stores or the extracellular Ca2+ influx. This research provides a simple tool to selectively control distinct Ca2+ signals in brain astrocytes in neuroscience and bioelectronic medicine.