Compartmental model identification based on an empirical Bayesian approach: the case of thiamine kinetics in rats

Use of prior knowledge and extrapolation in paediatric drug development: A case study with deferasirox

The characterisation of pharmacokinetics, pharmacodynamics and dose-exposure-response relationships requires data arising from well-designed study protocols and a relatively large sample from the target patient population. Such a prerequisite is unrealistic for paediatric rare diseases, where the patient population is often vulnerable and very small. In such cases, different sources of data and knowledge need to be considered to ensure trial designs are truly informative and oncoming data can be analysed efficiently. Here, we use clinical trial simulations to assess the contribution of historical data for (1) the analysis of sparse samples from a limited number of children and (2) the optimisation of study design when an increase in the number of subjects is not feasible. The evaluation of the pharmacokinetics of deferasirox in paediatric patients affected by haemoglobinopathies was used as case study. Our investigation shows that the incorporation of prior knowledge increases parameter precision and probability of successful convergence from only 12% with no priors to 56% and 75% for weakly and highly informative priors, respectively. In addition, results suggest that even when only one sample is collected per subject, as implemented in the original trial and in many other examples in clinical research, there is a 60% probability of biased parameter estimates (>25%). In conjunction with adult prior information and optimisation techniques, the probability of bias could be limited to <20% by increasing the number of samples/subject from 1 to 3. The methodology described here can be easily applied to other studies in small populations.

Stochastic differential equations as a tool to regularize the parameter estimation problem for continuous time dynamical systems given discrete time measurements

In this paper we consider the problem of estimating parameters in ordinary differential equations given discrete time experimental data. The impact of going from an ordinary to a stochastic differential equation setting is investigated as a tool to overcome the problem of local minima in the objective function. Using two different models, it is demonstrated that by allowing noise in the underlying model itself, the objective functions to be minimized in the parameter estimation procedures are regularized in the sense that the number of local minima is reduced and better convergence is achieved. The advantage of using stochastic differential equations is that the actual states in the model are predicted from data and this will allow the prediction to stay close to data even when the parameters in the model is incorrect. The extended Kalman filter is used as a state estimator and sensitivity equations are provided to give an accurate calculation of the gradient of the objective function. The method is illustrated using in silico data from the FitzHugh-Nagumo model for excitable media and the Lotka-Volterra predator-prey system. The proposed method performs well on the models considered, and is able to regularize the objective function in both models. This leads to parameter estimation problems with fewer local minima which can be solved by efficient gradient-based methods.

Reduced sampling schedule for the glucose minimal model: importance of Bayesian estimation

The minimal model (MM) of glucose kinetics during an intravenous glucose tolerance test (IVGTT) is widely used in clinical studies to measure metabolic indexes such as glucose effectiveness (S(G)) and insulin sensitivity (S(I)). The standard (frequent) IVGTT sampling schedule (FSS) for MM identification consists of 30 points over 4 h. To facilitate clinical application of the MM, reduced sampling schedules (RSS) of 13-14 samples have also been derived for normal subjects. These RSS are especially appealing in large-scale studies. However, with RSS, the precision of S(G) and S(I) estimates deteriorates and, in certain cases, becomes unacceptably poor. To overcome this difficulty, population approaches such as the iterative two-stage (ITS) approach have been recently proposed, but, besides leaving some theoretical issues open, they appear to be oversized for the problem at hand. Here, we show that a Bayesian methodology operating at the single individual level allows an accurate determination of MM parameter estimates together with a credible measure of their precision. Results of 16 subjects show that, in passing from FSS to RSS, there are no significant changes of point estimates in nearly all of the subjects and that only a limited deterioration of parameter precision occurs. In addition, in contrast with the previously proposed ITS method, credible confidence intervals (e.g., excluding negative values) are obtained. They can be crucial for a subsequent use of the estimated MM parameters, such as in classification, clustering, regression, or risk analysis.

Nonparametric AUC estimation in population studies with incomplete sampling: a Bayesian approach

The estimation of the AUC in a population without frequent and/or fixed individual samplings is of interest because the number of plasma samples can often be limited due to technical, ethical and cost reasons. Non-linear mixed effect models can provide both population and individual estimates of AUC based on sparse sampling protocols; however, appropriate structural models for the description of the pharmacokinetics are required. Nonparametric solutions have also been proposed to estimate the population AUC and the associated error when particular sampling protocols are adopted. However, they do not estimate the individual AUCs and lack flexibility. Also a semiparametric method has been proposed for addressing the problem of sparse sampling in reasonably well designed studies. In this work, we propose and evaluate a nonparametric Bayesian scheme for AUC estimation in population studies with arbitrary sampling protocols. In the stochastic model representing the whole population, the individual plasma concentration curves and the "mean" population curve are described by random walk processes, allowing the application of the method to the reconstruction of any kind of "regular" curves. Population and individual AUC estimation are performed by numerically computing the posterior expectation through a Markov chain Monte Carlo algorithm.