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.