A simple modeling framework for prediction in the human glucose-insulin system.

Forecasting blood glucose (BG) levels with routinely collected data is useful for glycemic management. BG dynamics are nonlinear, complex, and nonstationary, which can be represented by nonlinear models. However, the sparsity of routinely collected data creates parameter identifiability issues when high-fidelity complex models are used, thereby resulting in inaccurate forecasts. One can use models with reduced physiological fidelity for robust and accurate parameter estimation and forecasting with sparse data. For this purpose, we approximate the nonlinear dynamics of BG regulation by a linear stochastic differential equation: we develop a linear stochastic model, which can be specialized to different settings: type 2 diabetes mellitus (T2DM) and intensive care unit (ICU), with different choices of appropriate model functions. The model includes deterministic terms quantifying glucose removal from the bloodstream through the glycemic regulation system and representing the effect of nutrition and externally delivered insulin. The stochastic term encapsulates the BG oscillations. The model output is in the form of an expected value accompanied by a band around this value. The model parameters are estimated patient-specifically, leading to personalized models. The forecasts consist of values for BG mean and variation, quantifying possible high and low BG levels. Such predictions have potential use for glycemic management as part of control systems. We present experimental results on parameter estimation and forecasting in T2DM and ICU settings. We compare the model's predictive capability with two different nonlinear models built for T2DM and ICU contexts to have a sense of the level of prediction achieved by this model.

Non-stationary phase of the MALA algorithm.

The Metropolis-Adjusted Langevin Algorithm (MALA) is a Markov Chain Monte Carlo method which creates a Markov chain reversible with respect to a given target distribution, π N , with Lebesgue density on R N ; it can hence be used to approximately sample the target distribution. When the dimension N is large a key question is to determine the computational cost of the algorithm as a function of N. The measure of efficiency that we consider in this paper is the expected squared jumping distance (ESJD), introduced in Roberts et al. (Ann Appl Probab 7(1):110-120, 1997). To determine how the cost of the algorithm (in terms of ESJD) increases with dimension N, we adopt the widely used approach of deriving a diffusion limit for the Markov chain produced by the MALA algorithm. We study this problem for a class of target measures which is not in product form and we address the situation of practical relevance in which the algorithm is started out of stationarity. We thereby significantly extend previous works which consider either measures of product form, when the Markov chain is started out of stationarity, or non-product measures (defined via a density with respect to a Gaussian), when the Markov chain is started in stationarity. In order to work in this non-stationary and non-product setting, significant new analysis is required. In particular, our diffusion limit comprises a stochastic PDE coupled to a scalar ordinary differential equation which gives a measure of how far from stationarity the process is. The family of non-product target measures that we consider in this paper are found from discretization of a measure on an infinite dimensional Hilbert space; the discretised measure is defined by its density with respect to a Gaussian random field. The results of this paper demonstrate that, in the non-stationary regime, the cost of the algorithm is of O ( N 1 / 2 ) in contrast to the stationary regime, where it is of O ( N 1 / 3 ) .

Distribution of multidrug-resistant human isolates of MDR-ACSSuT Salmonella Typhimurium and MDR-AmpC Salmonella Newport in the United States, 2003-2005.

PURPOSE: Multidrug-resistant (MDR) Salmonella strains are associated with excess bloodstream infections, hospitalizations, and deaths compared with pansusceptible strains. Bovine products are sometimes a source of MDR Salmonella. To generate hypotheses for regional differences in risk factors for human infection, we analyzed distributions of the two most prevalent MDR Salmonella phenotypes in the United States, 2003-2005: (i) MDR-ACSSuT (resistant to at least ampicillin, chloramphenicol, streptomycin, sulfonamides, and tetracycline) Typhimurium; (ii) MDR-AmpC (resistant to at least ampicillin, chloramphenicol, streptomycin, sulfonamides, tetracycline, amoxicillin/clavulanic acid, and ceftiofur, and with decreased susceptibility to ceftriaxone) Newport. MATERIALS AND METHODS: Participating public health laboratories in all states forwarded every 20th Salmonella isolate from humans to the National Antimicrobial Resistance Monitoring System for Enteric Bacteria for antimicrobial susceptibility testing. Among the serotypes Typhimurium and Newport isolates submitted 2003-2005, pansusceptible, MDR-ACSSuT Typhimurium, and MDR-AmpC Newport were identified. Patterns of resistance, demographic factors, and cattle density were compared across regions. RESULTS: Of 1195 serotype Typhimurium isolates, 289 (24%) were MDR-ACSSuT. There were no significant differences in region, age, or sex distribution for pansusceptible versus MDR-ACSSuT Typhimurium. Of 612 serotype Newport isolates, 97 (16%) were MDR-AmpC, but the percentage of MDR-AmpC isolates varied significantly across regions: South 3%, Midwest 28%, West 32%, and Northeast 38% (p < 0.0001). The South had the lowest percentage of MDR-AmpC Newport isolates and also the lowest density of milk cows. More Newport isolates were MDR-AmpC in the 10 states with the highest milk cow density compared with the remaining states. Overall, 22% of pansusceptible Newport isolates but only 7% of MDR-AmpC Newport isolates were from patients <2 years of age. For both serotypes, MDR phenotypes had less seasonal variation than pansusceptible phenotypes. CONCLUSION: This is the first analysis of the distribution of clinically important MDR Salmonella isolates in the United States. MDR-ACSSuT Typhimurium was evenly distributed across regions. However, MDR-AmpC Newport was less common in the South and in children <2 years of age. Information on individuals' exposures is needed to fully explain the observed patterns.