Jonathan Jaeger

Bayesian P-spline estimation in hierarchical models specified by systems of affine differential equations

Ordinary differential equations (ODEs) are widely used to model physical, chemical and biological processes. Current methods for parameter estimation can be computationally intensive and/or not suitable for inference and prediction. Frequentist approaches based on ODE-penalized smoothing techniques have recently solved part of these drawbacks. A full Bayesian approach based on ODE-penalized B-splines is proposed to jointly estimate ODE parameters and state functions from affine systems of differential equations. Simulations inspired by pharmacokinetic studies show that the proposed method provides comparable results to methods based on explicit solution of the ODEs and outperforms the frequentist ODE-penalized smoothing approach. The basic model is extended to a hierarchical one in order to study cases where several subjects are involved. This Bayesian hierarchical approach is illustrated on real data for the study of perfusion ratio after a femoral artery occlusion. Model selection is feasible through the analysis of the posterior distributions of the ODE adhesion parameters and is illustrated on a real pharmacokinetic dataset.

Growth and Nutritional Biomarkers of Preterm Infants Fed a New Powdered Human Milk Fortifier: A Randomized Trial

Objectives: The aim of this study was to assess growth and nutritional biomarkers of preterm infants fed human milk (HM) supplemented with a new powdered HM fortifier (nHMF) or a control HM fortifier (cHMF). The nHMF provides similar energy content, 16% more protein (partially hydrolyzed whey), and higher micronutrient levels than the cHMF, along with medium-chain triglycerides and docosahexaenoic acid. Methods: In this controlled, multicenter, double-blind study, a sample of preterm infants ⩽32 weeks or ⩽1500 g were randomized to receive nHMF (n = 77) or cHMF (n = 76) for a minimum of 21 days. Weight gain was evaluated for noninferiority (margin = –1 g/day) and superiority (margin = 0 g/day). Nutritional status and gut inflammation were assessed by blood, urine, and fecal biochemistries. Adverse events were monitored. Results: Adjusted mean weight gain (analysis of covariance) was 2.3 g/day greater in nHMF versus cHMF; the lower limit of the 95% CI (0.4 g/day) exceeded both noninferiority (P < 0.001) and superiority margins (P = 0.01). Weight gain rate (unadjusted) was 18.3 (nHMF) and 16.8 g · kg−1 · day−1 (cHMF) between study days 1 and 21 (D1–D21). Length and head circumference (HC) gains between D1 and D21 were not different. Adjusted weight-for-age z score at D21 and HC-for-age z score at week 40 corrected age were greater in nHMF versus cHMF (P = 0.013, P = 0.003 respectively). nHMF had higher serum blood urea nitrogen, pre-albumin, alkaline phosphatase, and calcium (all within normal ranges; all P ⩽ 0.019) at D21 versus cHMF. Both HMFs were well tolerated with similar incidence of gastrointestinal adverse events. Conclusions: nHMF providing more protein and fat compared to a control fortifier is safe, well-tolerated, and improves the weight gain of preterm infants.

Bayesian penalized smoothing approaches in models specified using differential equations with unknown error distributions

A full Bayesian approach based on ordinary differential equation (ODE)-penalized B-splines and penalized Gaussian mixture is proposed to jointly estimate ODE-parameters, state function and error distribution from the observation of some state functions involved in systems of affine differential equations. Simulations inspired by pharmacokinetic (PK) studies show that the proposed method provides comparable results to the method based on the standard ODE-penalized B-spline approach (i.e. with the Gaussian error distribution assumption) and outperforms the standard ODE-penalized B-splines when the distribution is not Gaussian. This methodology is illustrated on a PK data set.

Effects on Fatty Acid Metabolism of a New Powdered Human Milk Fortifier Containing Medium-Chain Triacylglycerols and Docosahexaenoic Acid in Preterm Infants

Preterm infants require fortification of human milk (HM) with essential fatty acids (FA) to ensure adequate post-natal development. As part of a larger randomized controlled study, we investigated FA metabolism in a subset of 47 clinically stable preterm infants (birth weight ≤1500 g or gestational age ≤32 weeks). Infants were randomized to receive HM supplemented with either a new HM fortifier (nHMF; n = 26) containing 12.5 g medium-chain FA (MCFA), 958 mg linoleic acid (LA), 417 mg α-linolenic acid (ALA), and 157 mg docosahexaenoic acid (DHA) per 100 g of powder (in compliance with the latest guidelines) or a fat-free HMF (cHMF; n = 21). Plasma phospholipid (PL) and triacylglycerol (TAG), and red blood cell phosphatidylcholine (RBC-PC) and phosphatidylethanolamine (RBC-PE) FA profiles were assessed before and after 21 days of feeding. In the nHMF group, significantly increased levels of n-9 monounsaturated fatty acids were observed, formed most likely by elongation and desaturation of dietary saturated fatty acids present in HM. ALA fortification increased ALA assimilation into plasma TAG. Similarly, DHA fortification enriched the DHA content in RBC-PE, which, in this compartment, was not associated with lower arachidonic acid levels as observed in plasma TAG and phospholipids. RBC-PE, a reliable indicator of FA metabolism and accretion, was the most sensitive compartment in this study.

Inference in dynamic systems using B-splines and quasilinearized ODE penalties.

Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one-dimensional dynamic systems. We propose a smoothing approach regularized by a quasilinearized ODE-based penalty. Within the quasilinearized spline-based framework, the estimation reduces to a conditionally linear problem for the optimization of the spline coefficients. Furthermore, standard ODE compliance parameter(s) selection criteria are applicable. We evaluate the performances of the proposed strategy through simulated and real data examples. Simulation studies suggest that the proposed procedure ensures more accurate estimates than standard nonlinear least squares approaches when the state (initial and/or boundary) conditions are not known.