Estimation of local time-varying reproduction numbers in noisy surveillance data

A valuable metric in understanding local infectious disease dynamics is the local time-varying reproduction number, i.e. the expected number of secondary local cases caused by each infected individual. Accurate estimation of this quantity requires distinguishing cases arising from local transmission from those imported from elsewhere. Realistically, we can expect identification of cases as local or imported to be imperfect. We study the propagation of such errors in estimation of the local time-varying reproduction number. In addition, we propose a Bayesian framework for estimation of the true local time-varying reproduction number when identification errors exist. And we illustrate the practical performance of our estimator through simulation studies and with outbreaks of COVID-19 in Hong Kong and Victoria, Australia. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

The Impact of Exogenous Insulin Input on Calculating Hepatic Clearance Parameters

OBJECTIVE

Model-based metabolic tests require accurate identification of subject-specific parameters from measured assays. Insulin assays are used to identify insulin kinetics parameters, such as general and first-pass hepatic clearances. This study assesses the impact of intravenous insulin boluses on parameter identification precision.

METHOD

Insulin and C-peptide data from two intravenous glucose tolerance test (IVGTT) trials of healthy adults (N = 10 × 2; denoted A and B), with (A) and without (B) insulin modification, were used to identify insulin kinetics parameters using a grid search. Monte Carlo analysis (N = 1000) quantifies variation in simulation error for insulin assay errors of 5%. A region of parameter values around the optimum was identified whose errors are within variation due to assay error. A smaller optimal region indicates more precise practical identifiability. Trial results were compared to assess identifiability and precision.

RESULTS

Trial B, without insulin modification, has optimal parameter regions 4.7 times larger on average than Trial A, with 1-U insulin bolus modification. Ranges of optimal parameter values between trials A and B increase from 0.04 to 0.12 min^-1 for hepatic clearance and from 0.07 to 0.14 for first-pass clearance on average. Trial B's optimal values frequently lie outside physiological ranges, further indicating lack of distinct identifiability.

CONCLUSIONS

A small 1-U insulin bolus improves identification of hepatic clearance parameters by providing a smaller region of optimal parameter values. Adding an insulin bolus in metabolic tests can significantly improve identifiability and outcome test precision. Assay errors necessitate insulin modification in clinical tests to ensure identifiability and precision.

Determining Losses in Jet Injection Subcutaneous Insulin Delivery: A Model-Based Approach

OBJECTIVE

Accurate, safe glycemic management requires reliable delivery of insulin doses. Insulin can be delivered subcutaneously for action over a longer period of time. Needle-free jet injectors provide subcutaneous (SC) delivery without requiring needle use, but the volume of insulin absorbed varies due to losses associated with the delivery method. This study employs model-based methods to determine the expected proportion of active insulin present from a needle-free SC dose.

METHODS

Insulin, C-peptide, and glucose assay data from a frequently sampled insulin-modified oral glucose tolerance test trial with 2U SC insulin delivery, paired with a well-validated metabolic model, predict metabolic outcomes for N = 7 healthy adults. Subject-specific nonlinear hepatic clearance profiles are modeled over time using third-order basis splines with knots located at assay times. Hepatic clearance profiles are constrained within a physiological rate of change, and relative to plasma glucose profiles. Insulin loss proportions yielding optimal insulin predictions are then identified, quantifying delivery losses.

RESULTS

Optimal parameter identification suggests losses of up to 22% of the nominal 2U SC dose. The degree of loss varies between subjects and between trials on the same subject. Insulin fit accuracy improves where loss greater than 5% is identified, relative to where delivery loss is not modeled.

CONCLUSIONS

Modeling shows needle-free SC jet injection of a nominal dose of insulin does not necessarily provide metabolic action equivalent to total dose, and this availability significantly varies between trials. By quantifying and accounting for variability of jet injection insulin doses, better glycemic management outcomes using SC jet injection may be achieved.