Fitting dynamic models with forcing functions: application to continuous glucose monitoring in insulin therapy.

The artificial pancreas is an emerging technology to treat type 1 diabetes (T1D). It has the potential to revolutionize diabetes care and improve quality of life. The system requires extensive testing, however, to ensure that it is both effective and safe. Clinical studies are resource demanding and so a principle aim is to develop an in silico population of subjects with T1D on which to conduct pre-clinical testing. This paper aims to reliably characterize the relationship between blood glucose and glucose measured by subcutaneous sensor as a major step towards this goal. Blood-and sensor-glucose are related through a dynamic model, specified in terms of differential equations. Such models can present special challenges for statistical inference, however. In this paper we make use of the BUGS software, which can accommodate a limited class of dynamic models, and it is in this context that we discuss such challenges. For example, we show how dynamic models involving forcing functions can be accommodated. To account for fluctuations away from the dynamic model that are apparent in the observed data, we assume an autoregressive structure for the residual error model. This leads to some identifiability issues but gives very good predictions of virtual data. Our approach is pragmatic and we propose a method to mitigate the consequences of such identifiability issues.

Measurement delay associated with the Guardian RT continuous glucose monitoring system.

AIMS: Using compartment modelling, we assessed the time delay between blood glucose and sensor glucose measured by the Guardian RT continuous glucose monitoring system in young subjects with Type 1 diabetes (T1D). METHODS: Twelve children and adolescents with T1D treated by continuous subcutaneous insulin infusion (male/female 7/5; age 13.1 +/- 4.2 years; body mass index 21.9 +/- 4.3 kg/m(2); mean +/- sd) were studied over 19 h in a Clinical Research Facility. Guardian RT was calibrated every 6 h and sensor glucose measured every 5 min. Reference blood glucose was measured every 15 min using a YSI 2300 STAT Plus Analyser. A population compartment model of sensor glucose-blood glucose kinetics was adopted to estimate the time delay, the calibration scale and the calibration shift. RESULTS: The population median of the time delay was 15.8 (interquartile range 15.2, 16.5) min, which was corroborated by correlation analysis between blood glucose and 15-min delayed sensor glucose. The delay has a relatively low intersubject variability, with 95% of individuals predicted to have delays between 10.4 and 24.3 min. Population medians (interquartile range) for the scale and shift are 0.800 (0.777, 0.823) (unitless) and 1.66 (1.47, 1.84) mmol/l, respectively. CONCLUSIONS: In young subjects with T1D, the total time delay associated with the Guardian RT system was approximately 15 min. This is twice that expected on physiological grounds, suggesting a 5- to 10-min delay because of data processing. Delays above 25 min are rarely to be observed.

Examining evidence for neighbourhood variation in the duration of untreated psychosis.

BACKGROUND: Family involvement in help-seeking is associated with a shorter duration of untreated psychoses [DUP], but it is unknown whether neighbourhood-level factors are also important. METHODS: DUP was estimated for all cases of first-episode psychoses identified over 2 years in 33 Southeast London neighbourhoods (n = 329). DUP was positively skewed and transformed to the natural logarithm scale. We fitted various hierarchical models, adopting different assumptions with regard to spatial variability of DUP, to assess whether there was evidence of neighbourhood heterogeneity in DUP, having accounted for a priori individual-level confounders. RESULTS: Neighbourhood-level variation in DUP was negligible compared to overall variability. A non-hierarchical model with age, sex and ethnicity covariates, but without area-level random effects, provided the best fit to the data. DISCUSSION: Neighbourhood factors do not appear to be associated with DUP, suggesting its predictors lie at individual and family levels. Our results inform mental healthcare planning, suggesting that in one urbanised area of Southeast London, where you live does not affect duration of untreated psychosis.

Effects of prolonged fasting and sustained lipolysis on insulin secretion and insulin sensitivity in normal subjects.

Normal beta-cells adjust their function to compensate for any decrease in insulin sensitivity. Our aim was to explore whether a prolonged fast would allow a study of the effects of changes in circulating free fatty acid (FFA) levels on insulin secretion and insulin sensitivity and whether any potential effects could be reversed by the antilipolytic agent acipimox. Fourteen (8 female, 6 male) healthy young adults (aged 22.8-26.9 yr) without a family history of diabetes and a body mass index of 22.6 +/- 3.2 kg/m(2) were studied on three occasions in random order. Growth hormone and FFA levels were regularly measured overnight (2200-0759), and subjects underwent an intravenous glucose tolerance test in the morning (0800-1100) on each visit. Treatment A was an overnight fast, treatment B was a 24-h fast with regular administrations of a placebo, and treatment C was a 24-h fast with regular ingestions of 250 mg of acipimox. The 24-h fast increased overnight FFA levels (as measured by the area under the curve) 2.8-fold [51.3 (45.6-56.9) vs. 18.4 (14.4-22.5) *10(4) micromol/l*min, P < 0.0001], and it led to decreases in insulin sensitivity [5.7 (3.6-8.9) vs. 2.6 (1.3-4.7) *10(-4) min(-1) per mU/l, P < 0.0001] and the acute insulin response [16.3 (10.9-21.6) vs. 12.7 (8.7-16.6) *10(2) pmol/l*min, P = 0.02], and therefore a reduction in the disposition index [93.1 (64.8-121.4) vs. 35.5 (21.6-49.4) *10(2) pmol/mU, P < 0.0001]. Administration of acipimox during the 24-h fast lowered FFA levels by an average of 20% (range: -62 to +49%; P = 0.03), resulting in a mean increase in the disposition index of 31% (P = 0.03). In conclusion, the 24-h fast was accompanied by substantial increases in fasting FFA levels and induced reductions in the acute glucose-simulated insulin response and insulin sensitivity. The use of acipimox during the prolonged fast increased the disposition index, suggesting a partial reversal of the effects of fasting on the acute insulin response and insulin sensitivity.

Cumulative logit models for ordinal data: a case study involving allergic rhinitis severity scores.

Ordered categorical data arise in numerous settings, a common example being pain scores in analgesic trials. The modelling of such data is intrinsically more difficult than the modelling of continuous data due to the constraints on the underlying probabilities and the reduced amount of information that discrete outcomes contain. In this paper we discuss the class of cumulative logit models, which provide a natural framework for ordinal data analysis. We show how viewing the categorical outcome as the discretization of an underlying continuous response allows a natural interpretation of model parameters. We also show how covariates are incorporated into the model and how various types of correlation among repeated measures on the same individual may be accounted for. The models are illustrated using longitudinal allergy data consisting of sneezing scores measured on a four-point scale. Our approach throughout is Bayesian and we present a range of simple diagnostics to aid model building.

The pharmacokinetics of saquinavir: a Markov chain Monte Carlo population analysis.

Saquinavir is an HIV proteinase inhibitor marketed as a treatment for HIV infection. The drug has potent (Ki approximately 0.1 nM) antiviral activity and acts by inhibiting the processing of gag and gag-pol polyproteins, thus blocking the maturation of replicated viral particles. By assuming standard two-compartment disposition kinetics in combination with a variety of absorption processes we have identified two structural models that perform well with respect to describing the pharmacokinetic behavior of saquinavir when administered to healthy human volunteers from various Phase I studies. These structural models have been implemented for population analysis of these Phase I data via the Bayesian Markov chain Monte Carlo approach. We conclude that saquinavir exhibits complex and highly variable behavior, but can be modeled adequately using a two-compartment zero-order absorption model. There is also an indication that saquinavir kinetics may be time-dependent.