Estimating Weekly National Opioid Overdose Deaths in Near Real Time Using Multiple Proxy Data Sources.

Importance: Opioid overdose is a leading public health problem in the United States; however, national data on overdose deaths are delayed by several months or more. Objectives: To build and validate a statistical model for estimating national opioid overdose deaths in near real time. Design, Setting, and Participants: In this cross-sectional study, signals from 5 overdose-related, proxy data sources encompassing health, law enforcement, and online data from 2014 to 2019 in the US were combined using a LASSO (least absolute shrinkage and selection operator) regression model, and weekly predictions of opioid overdose deaths were made for 2018 and 2019 to validate model performance. Results were also compared with those from a baseline SARIMA (seasonal autoregressive integrated moving average) model, one of the most used approaches to forecasting injury mortality. Exposures: Time series data from 2014 to 2019 on emergency department visits for opioid overdose from the National Syndromic Surveillance Program, data on the volume of heroin and synthetic opioids circulating in illicit markets via the National Forensic Laboratory Information System, data on the search volume for heroin and synthetic opioids on Google, and data on post volume on heroin and synthetic opioids on Twitter and Reddit were used to train and validate prediction models of opioid overdose deaths. Main Outcomes and Measures: Model-based predictions of weekly opioid overdose deaths in the United States were made for 2018 and 2019 and compared with actual observed opioid overdose deaths from the National Vital Statistics System. Results: Statistical models using the 5 real-time proxy data sources estimated the national opioid overdose death rate for 2018 and 2019 with an error of 1.01% and -1.05%, respectively. When considering the accuracy of weekly predictions, the machine learning-based approach possessed a mean error in its weekly estimates (root mean squared error) of 60.3 overdose deaths for 2018 (compared with 310.2 overdose deaths for the SARIMA model) and 67.2 overdose deaths for 2019 (compared with 83.3 overdose deaths for the SARIMA model). Conclusions and Relevance: Results of this serial cross-sectional study suggest that proxy administrative data sources can be used to estimate national opioid overdose mortality trends to provide a more timely understanding of this public health problem.

Bayesian functional integral method for inferring continuous data from discrete measurements.

Inference of the insulin secretion rate (ISR) from C-peptide measurements as a quantification of pancreatic ß-cell function is clinically important in diseases related to reduced insulin sensitivity and insulin action. ISR derived from C-peptide concentration is an example of nonparametric Bayesian model selection where a proposed ISR time-course is considered to be a "model". An inferred value of inaccessible continuous variables from discrete observable data is often problematic in biology and medicine, because it is a priori unclear how robust the inference is to the deletion of data points, and a closely related question, how much smoothness or continuity the data actually support. Predictions weighted by the posterior distribution can be cast as functional integrals as used in statistical field theory. Functional integrals are generally difficult to evaluate, especially for nonanalytic constraints such as positivity of the estimated parameters. We propose a computationally tractable method that uses the exact solution of an associated likelihood function as a prior probability distribution for a Markov-chain Monte Carlo evaluation of the posterior for the full model. As a concrete application of our method, we calculate the ISR from actual clinical C-peptide measurements in human subjects with varying degrees of insulin sensitivity. Our method demonstrates the feasibility of functional integral Bayesian model selection as a practical method for such data-driven inference, allowing the data to determine the smoothing timescale and the width of the prior probability distribution on the space of models. In particular, our model comparison method determines the discrete time-step for interpolation of the unobservable continuous variable that is supported by the data. Attempts to go to finer discrete time-steps lead to less likely models.

Autoregulation of free radicals via uncoupling protein control in pancreatic beta-cell mitochondria.

Pancreatic beta-cells sense the ambient blood-glucose concentration and secrete insulin to signal other tissues to take up glucose. Mitochondria play a key role in this response as they metabolize nutrients to produce ATP and reactive oxygen species (ROS), both of which are involved in insulin secretion signaling. Based on data available in the literature and previously developed mathematical models, we present a model of glucose-stimulated mitochondrial respiration, ATP synthesis, and ROS production and control in beta-cells. The model is consistent with a number of experimental observations reported in the literature. Most notably, it captures the nonlinear rise in the proton leak rate at high membrane potential and the increase in this leak due to uncoupling protein (UCP) activation by ROS. The functional forms used to model ROS production and UCP regulation yield insight into these mechanisms, as many details have not yet been unraveled in the experimental literature. We examine short- and long-term effects of UCP activation inhibition and changes in the mitochondrial density on mitochondrial responses to glucose. Results suggest increasing mitochondrial density while decreasing UCP activity may be an effective way to increase glucose-stimulated insulin secretion while decreasing oxidative stress.

Linear analysis near a steady-state of biochemical networks: control analysis, correlation metrics and circuit theory.

BACKGROUND: Several approaches, including metabolic control analysis (MCA), flux balance analysis (FBA), correlation metric construction (CMC), and biochemical circuit theory (BCT), have been developed for the quantitative analysis of complex biochemical networks. Here, we present a comprehensive theory of linear analysis for nonequilibrium steady-state (NESS) biochemical reaction networks that unites these disparate approaches in a common mathematical framework and thermodynamic basis. RESULTS: In this theory a number of relationships between key matrices are introduced: the matrix A obtained in the standard, linear-dynamic-stability analysis of the steady-state can be decomposed as A = SRT where R and S are directly related to the elasticity-coefficient matrix for the fluxes and chemical potentials in MCA, respectively; the control-coefficients for the fluxes and chemical potentials can be written in terms of RTBS and STBS respectively where matrix B is the inverse of A; the matrix S is precisely the stoichiometric matrix in FBA; and the matrix eAt plays a central role in CMC. CONCLUSION: One key finding that emerges from this analysis is that the well-known summation theorems in MCA take different forms depending on whether metabolic steady-state is maintained by flux injection or concentration clamping. We demonstrate that if rate-limiting steps exist in a biochemical pathway, they are the steps with smallest biochemical conductances and largest flux control-coefficients. We hypothesize that biochemical networks for cellular signaling have a different strategy for minimizing energy waste and being efficient than do biochemical networks for biosynthesis. We also discuss the intimate relationship between MCA and biochemical systems analysis (BSA).

A stochastic model of oscillatory blood testosterone levels.

A continuous-time, discrete-state stochastic model of testosterone secretion in men is considered. Blood levels of testosterone in men fluctuate periodically with a period of 2-3 h. The deterministic model, on which the stochastic model considered here is based, is well studied and has been shown to have a globally stable fixed point. Thus, no sustained oscillations are possible in the deterministic case. However, the stochastic model does observe periodic, pulsatile behavior. This demonstrates how oscillations can occur due to a switching behavior dependent on the random degradation of testosterone molecules in the system. The Gillespie algorithm is used to simulate the hormone secretion model. Important parameters of the model are discussed and results from the model are compared to experimental observations.

Grand canonical Markov model: a stochastic theory for open nonequilibrium biochemical networks.

In this paper we present the results of a stochastic model of reversible biochemical reaction networks that are being driven through an open boundary, such that the system is interacting with its surrounding environment with explicit material exchange. The stochastic model is based on the master equation approach and is intimately related to the grand canonical ensemble of statistical mechanics. We show that it is possible to analytically calculate the joint probability function of the random variables describing the number of molecules in each state of the system for general linear networks. Definitions of reaction chemical potentials and conductances follow from inherent properties of this model, providing a description of energy dissipation in the system. We are also able to suggest novel methods for experimentally determining reaction fluxes and biochemical affinities at nonequilibrium steady state as well as the overall network connectivity.

Combining flux and energy balance analysis to model large-scale biochemical networks.

Stoichiometric Network Theory is a constraints-based, optimization approach for quantitative analysis of the phenotypes of large-scale biochemical networks that avoids the use of detailed kinetics. This approach uses the reaction stoichiometric matrix in conjunction with constraints provided by flux balance and energy balance to guarantee mass conserved and thermodynamically allowable predictions. However, the flux and energy balance constraints have not been effectively applied simultaneously on the genome scale because optimization under the combined constraints is non-linear. In this paper, a sequential quadratic programming algorithm that solves the non-linear optimization problem is introduced. A simple example and the system of fermentation in Saccharomyces cerevisiae are used to illustrate the new method. The algorithm allows the use of non-linear objective functions. As a result, we suggest a novel optimization with respect to the heat dissipation rate of a system. We also emphasize the importance of incorporating interactions between a model network and its surroundings.