Explicit formulas for a continuous stochastic maturation model. Application to anticancer drug pharmacokinetics/pharmacodynamics

We present a continuous time model of maturation and survival, obtained as the limit of a compartmental evolution model when the number of compartments tends to infinity. We establish in particular an explicit formula for the law of the system output under inhomogeneous killing and when the input follows a time-inhomogeneous Poisson process. This approach allows the discussion of identifiability issues which are of difficult access for finite compartmental models. The article ends up with an example of application for anticancer drug pharmacokinetics/pharmacodynamics.Comment: Revised version, accepted for publication in Stochastic Models (Taylor & Francis

On the strong consistency of asymptotic M-estimators

The aim of this article is to simplify Pfanzagl's proof of consistency for asymptotic maximum likelihood estimators, and to extend it to more general asymptotic M-estimators. The method relies on the existence of a sort of contraction of the parameter space which admits the true parameter as a fixed point. The proofs are short and elementary.Comment: Accepted for publication in Journal of Statistical Planning and Inferenc

Estimation of reference intervals from small samples: an example using canine plasma creatinine

Background: According to international recommendations, reference intervals should be determined from at least 120 reference individuals, which often are impossible to achieve in veterinary clinical pathology, especially for wild animals. When only a small number of reference subjects is available, the possible bias cannot be known and the normality of the distribution cannot be evaluated. A comparison of reference intervals estimated by different methods could be helpful. Objective: The purpose of this study was to compare reference limits determined from a large set of canine plasma creatinine reference values, and large subsets of this data, with estimates obtained from small samples selected randomly. Methods: Twenty sets each of 120 and 27 samples were randomly selected from a set of 1439 plasma creatinine results obtained from healthy dogs in another study. Reference intervals for the whole sample and for the large samples were determined by a nonparametric method. The estimated reference limits for the small samples were minimum and maximum, mean +/-2 SD of native and Box–Cox-transformed values, 2.5th and 97.5th percentiles by a robust method on native and Box–Cox-transformed values, and estimates from diagrams of cumulative distribution functions. Results: The whole sample had a heavily skewed distribution, which approached Gaussian after Box–Cox transformation. The reference limits estimated from small samples were highly variable. The closest estimates to the 1439-result reference interval for 27-result subsamples were obtained by both parametric and robust methods after Box–Cox transformation but were grossly erroneous in some cases. Conclusion: For small samples, it is recommended that all values be reported graphically in a dot plot or histogram and that estimates of the reference limits be compared using different methods

Confidence regions for the multinomial parameter with small sample size

Consider the observation of n iid realizations of an experiment with d>1 possible outcomes, which corresponds to a single observation of a multinomial distribution M(n,p) where p is an unknown discrete distribution on {1,...,d}. In many applications, the construction of a confidence region for p when n is small is crucial. This concrete challenging problem has a long history. It is well known that the confidence regions built from asymptotic statistics do not have good coverage when n is small. On the other hand, most available methods providing non-asymptotic regions with controlled coverage are limited to the binomial case d=2. In the present work, we propose a new method valid for any d>1. This method provides confidence regions with controlled coverage and small volume, and consists of the inversion of the "covering collection"' associated with level-sets of the likelihood. The behavior when d/n tends to infinity remains an interesting open problem beyond the scope of this work.Comment: Accepted for publication in Journal of the American Statistical Association (JASA

Reference values: a review

Reference values are used to describe the dispersion of variables in healthy individuals. They are usually reported as population-based reference intervals (RIs) comprising 95% of the healthy population. International recommendations state the preferred method as a priori nonparametric determination from at least 120 reference individuals, but acceptable alternative methods include transference or validation from previously established RIs. The most critical steps in the determination of reference values are the selection of reference individuals based on extensively documented inclusion and exclusion criteria and the use of quality-controlled analytical procedures. When only small numbers of values are available, RIs can be estimated by new methods, but reference limits thus obtained may be highly imprecise. These recommendations are a challenge in veterinary clinical pathology, especially when only small numbers of reference individuals are available

Limited sampling strategies to estimate glomerular filtration rate in cats with low, normal and high glomerular filtration rates

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Modélisation pharmacocinétique/pharmacodynamique par une approche de population de l'effet du G-CSF chez des patients traités avec du carboplatine

Une des stratégies pour limiter les neutropénies induites par la chimiothérapie est l utilisation de granulocyte-colony stimulating factor (G-CSF). Nous avons développé, par une approche de population, un nouveau modèle pharmacocinétique/pharmacodynamique capable de décrire la cinétique des neutrophiles des patients traités au carboplatine, qu ils aient ou non reçu du G-CSF. Les simulations réalisées à partir de ce modèle ont montré que le G-CSF n était pas bénéfique chez tous les patients et que la formulation à action longue semblerait plus efficace que les autres formulations. Nous avons également établi des règles de décision permettant d une part de prédire le risque de neutropénie sévère, et d autre part d identifier précocement les patients pour lesquels le G-CSF peut avoir un effet bénéfique.Granulocyte colony-stimulating factor (G-CSF) is often used in cancer patients receiving cytotoxic drugs to prevent or reduce high grade neutropenia. We developed a new population pharmacokinetic/pharmacodynamic model to describe neutrophil time-course in carboplatin-treated patients, whether or not they received G-CSF. Model simulations showed that G-CSF was not as beneficial as expected in some patients and that the onceper- cycle formulation was more efficient than other formulations. Model-based decision rules were also built to anticipate prolonged high grade neutropenia and early identify patients for whom G-CSF was beneficial.TOULOUSE-INP (315552154) / SudocSudocFranceF

A new method for the estimation of variance matrix with prescribed zeros in nonlinear mixed effects models

We propose a new method for the Maximum Likelihood Estimator (MLE) of nonlinear mixed effects models when the variance matrix of Gaussian random effects has a prescribed pattern of zeros (PPZ). The method consists in coupling the recently developed Iterative Conditional Fitting (ICF) algorithm with the Expectation Maximization (EM) algorithm. It provides positive definite estimates for any sample size, and does not rely on any structural assumption on the PPZ. It can be easily adapted to many versions of EM.Comment: Accepted for publication in Statistics and Computin

A new approach for the determination of reference intervals from hospital-based data

Background: Reference limits are some of the most widely used tools in the medical decision process. Their determination is long, difficult, and expensive, mainly because of the need to select sufficient numbers of reference individuals according to well-defined criteria. Data from hospitalized patients are, in contrast, numerous and easily available. Even if all the information required for a direct reference interval computation is usually not available, these data contain information that can be exploited to derive at least rough reference intervals. Methods: In this article, we propose a method for the indirect estimation of reference intervals. It relies on a statistical method which has become a gold-standard in other sciences to separate components of mixtures. It relies on some distributional assumptions that can be checked graphically. For the determination of reference intervals, this new method is intended to separate the healthy and diseased distributions of the measured analyte. We assessed its performance by using simulated data drawn from known distributions and two previously published datasets (from human and veterinary clinical chemistry). Results and discussion: The comparison of results obtained by the new method with the theoretical data of the simulation and determination of the reference interval for the datasets was good, thus supporting the application of this method for a rough estimation of reference intervals when the recommended procedure cannot be used

Why Were More Than 200 Subjects Required to Demonstrate the Bioequivalence of a New Formulation of Levothyroxine with an Old One?

At the request of French Regulatory Authorities, a new formulation of Levothyrox® was licensed in France in 2017, with the objective of avoiding the stability deficiencies of an existing licensed formulation. Before launching the new formulation, an average bioequivalence (ABE) trial was conducted, having enrolled 204 subjects and selected for interpretation a narrow a priori bioequivalence range of 0.90–1.11. Bioequivalence was concluded. In a previous publication, we questioned the ability of an ABE trial to guarantee the switchability within patients of the new and old levothyroxine formulations. It was suggested that the two formulations should be compared using the conceptual framework of individual bioequivalence. The present paper is a response to those claiming that, despite the fact that ABE analysis does not formally address the switchability of the two formulations, future patients will nevertheless be fully protected. The basis for this claim is that the ABE study was established in a large trial and analyzed using a stringent a priori acceptance interval of equivalence. These claims are questionable, because the use of a very large number of subjects nullifies the implicit precautionary intention of the European guideline when, for a Narrow Therapeutic Index drug, it recommends shortening the a priori acceptance interval from 0.80–1.25 to 0.90–1.11