Understanding the impact of numerical solvers on inference for differential equation models.

Most ordinary differential equation (ODE) models used to describe biological or physical systems must be solved approximately using numerical methods. Perniciously, even those solvers that seem sufficiently accurate for the forward problem, i.e. for obtaining an accurate simulation, might not be sufficiently accurate for the inverse problem, i.e. for inferring the model parameters from data. We show that for both fixed step and adaptive step ODE solvers, solving the forward problem with insufficient accuracy can distort likelihood surfaces, which might become jagged, causing inference algorithms to get stuck in local 'phantom' optima. We demonstrate that biases in inference arising from numerical approximation of ODEs are potentially most severe in systems involving low noise and rapid nonlinear dynamics. We reanalyse an ODE change point model previously fit to the COVID-19 outbreak in Germany and show the effect of the step size on simulation and inference results. We then fit a more complicated rainfall run-off model to hydrological data and illustrate the importance of tuning solver tolerances to avoid distorted likelihood surfaces. Our results indicate that, when performing inference for ODE model parameters, adaptive step size solver tolerances must be set cautiously and likelihood surfaces should be inspected for characteristic signs of numerical issues.

Diabetes and hyperglycemia quality improvement efforts in hospitals in the United States: current status, practice variation, and barriers to implementation.

OBJECTIVE: To determine the status of diabetes and hyperglycemia quality improvement efforts in hospitals in the United States. METHODS: We designed and administered a survey to a convenience sample of hospitals, and the responses were analyzed statistically. RESULTS: We received 269 responses from 1,151 requested surveys. The sample was similar to hospitals in the United States on the basis of hospital type and geographic region (P = no significant difference) but not on the basis of number of beds (P<.001). Among responding hospitals, 39%, 21%, and 15% had fully implemented inpatient diabetes and hyperglycemia quality improvement programs for critically ill, non-critically ill, and perioperative patients, respectively. Moreover, 77%, 44%, and 49% had fully implemented protocols for hypoglycemia, hyperglycemic crises, and diabetic ketoacidosis, respectively. Variations in glucose target ranges were noted. The responding hospitals had no standard biochemical definition of hypoglycemia; 47% defined hypoglycemia as a glucose level