An index of parameter reproducibility accounting for estimation uncertainty: theory and case study on β-cell...

Parameter reproducibility is necessary to perform longitudinal studies where parameters are assessed to monitor disease progression or effect of therapy but are also useful in powering the study, i.e., to define how many subjects should be studied to observe a given effect. The assessment of parameter reproducibility is usually accomplished by methods that do not take into account the fact that these parameters are estimated with uncertainty. This is particularly relevant in physiological and clinical studies where usually reproducibility cannot be assessed by multiple testing and is usually assessed from a single replication of the test. Working in a suitable stochastic framework, here we propose a new index (S) to measure reproducibility that takes into account parameter uncertainty and is particularly suited to handle the normal testing conditions of physiological and clinical investigations. Simulation results prove that S, by properly taking into account parameter uncertainty, is more accurate and robust than the methods available in the literature. The new metric is applied to assess reproducibility of insulin sensitivity and β-cell responsivity of a mixed-meal tolerance test from data obtained in the same subjects retested 1 wk apart. Results show that the indices of insulin sensitivity and β-cell responsivity to glucose are well reproducible. We conclude that the oral minimal models provide useful indices that can be used safely in prospective studies or to assess the efficacy of a given therapy.