Inference for Biomedical Data by Using Diffusion Models with Covariates and Mixed Effects

Abstract

Summary Neurobiological data such as electroencephalography measurements pose a statistical challenge due to low spatial resolution and poor signal‐to‐noise ratio, as well as large variability from subject to subject. We propose a new modelling framework for this type of data based on stochastic processes. Stochastic differential equations with mixed effects are a popular framework for modelling biomedical data, e.g. in pharmacological studies. Whereas the inherent stochasticity of diffusion models accounts for prevalent model uncertainty or misspecification, random‐effects model intersubject variability. The two‐layer stochasticity, however, renders parameter inference challenging. Estimates are based on the discretized continuous time likelihood and we investigate finite sample and discretization bias. In applications, the comparison of, for example, treatment effects is often of interest. We discuss hypothesis testing and evaluate by simulations. Finally, we apply the framework to a statistical investigation of electroencephalography recordings from epileptic patients. We close the paper by examining asymptotics (the number of subjects going to ∞) of maximum likelihood estimators in multi‐dimensional, non‐linear and non‐homogeneous stochastic differential equations with random effects and included covariates.

Stochastic Models to Qualify Stem Tapers

“…In this study, newly developed stem tapers are defined (as segmented models) by using one or two joining points (a 0 and a 1 ) to weld three stochastic processes, defined by Equations (1), (5), and (9). In the sequel, the fixed effects parameters for the bottom part of a stem are listed by index B, the middle part by index M, and for the top part, they are listed by index T. The stem taper SDE models with two joining points a 0 and a 1 are defined in the following forms, respectively:…”

“…In biological systems, SDEs are used in place of deterministic models, obtained by including a noise term in the ordinary differential equation of the respective deterministic model [7]. The main reason to develop SDE models is the capacity to model highly nonlinear biological dynamic [8,9]. The fundamental advantage of stochastic dynamic models over deterministic models is that they combine both the deterministic and stochastic elements of dynamic systems, where the stochasticity is affected by the outside factors such as weather.…”

Analysis of Longitudinal Forest Data on Individual-Tree and Whole-Stand Attributes Using a Stochastic Differential Equation Model

“…The usefulness of mixed-effect parameters, which account for both fixed and random effects, in tree or stand growth modeling lies in their ability to split the total variation into within and between stands by using fixed and random effects. The stochastic differential mixed-effect models have long been useful tools in medicine and biology for revealing incomplete or inaccurate model kinetics [13,14].…”

Mixingale estimation function for mixed fractional SPDEs with random effect and random sampling

“…Picchini and Forman [54] studied Bayesian inference for stochastic differential equation mixed effects models and applied to tumor xenography. Recently Ruse et al [55] studied inference for biomedical data using diffusion models with covariates and mixed effects.…”