Parametric and Non-Parametric Estimation of a Random Diffusion Equation-Based Population Model for Deconvolving Blood/Breath Alcohol Concentration from Transdermal Alcohol Biosensor Data with Uncertainty Quantification*

A population model for the transdermal transport of ethanol from the blood to an alcohol biosensor on the surface of the skin in the form of a random abstract parabolic hybrid system of coupled ordinary and partial differential equations is developed. Linear semigroup theory in a Gelfand triple of Bochner spaces is used to first formulate the model as an equivalent deterministic system in state space form and to then develop a finite dimensional approximation and convergence theory. Both parametric and non-parametric techniques, the method of moments and kernel density estimation, and clinically collected drinking data are used to estimate the distributions of the model’s random parameters. Numerical results demonstrate the efficacy of using our model to 1) deconvolve an estimate of blood alcohol concentration from biosensor measured transdermal alcohol level and 2) quantify the uncertainty in the estimate.