Inference for biomedical data by using diffusion models with covariates and mixed effects

TY - JOUR

T1 - Inference for biomedical data by using diffusion models with covariates and mixed effects

AU - Ruse, Mareile Große

AU - Samson, Adeline

AU - Ditlevsen, Susanne

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

KW - Approximate maximum likelihood

KW - Asymptotic normality

KW - Consistency

KW - Covariates

KW - Electroencephalography data

KW - Local asymptotic normality

KW - Mixed effects

KW - Non-homogeneous observations

KW - Random effects

KW - Stochastic differential equations

UR - http://www.scopus.com/inward/record.url?scp=85074618875&partnerID=8YFLogxK

U2 - 10.1111/rssc.12386

DO - 10.1111/rssc.12386

M3 - Journal article

AN - SCOPUS:85074618875

SN - 0035-9254

JO - Journal of the Royal Statistical Society. Series C: Applied Statistics

JF - Journal of the Royal Statistical Society. Series C: Applied Statistics

ER -