Sieve estimation of constant and time-varying coefficients in nonlinear ordinary differential equation models by considering both numerical error and measurement error

This article considers estimation of constant and time-varying coefficients in nonlinear ordinary differential equation (ODE) models where analytic closed-form solutions are not available. The numerical solution-based nonlinear least squares (NLS) estimator is investigated in this study. A numerical algorithm such as the Runge--Kutta method is used to approximate the ODE solution. The asymptotic properties are established for the proposed estimators considering both numerical error and measurement error. The B-spline is used to approximate the time-varying coefficients, and the corresponding asymptotic theories in this case are investigated under the framework of the sieve approach. Our results show that if the maximum step size of the $p$-order numerical algorithm goes to zero at a rate faster than $n^{-1/(p\wedge4)}$, the numerical error is negligible compared to the measurement error. This result provides a theoretical guidance in selection of the step size for numerical evaluations of ODEs. Moreover, we have shown that the numerical solution-based NLS estimator and the sieve NLS estimator are strongly consistent. The sieve estimator of constant parameters is asymptotically normal with the same asymptotic co-variance as that of the case where the true ODE solution is exactly known, while the estimator of the time-varying parameter has the optimal convergence rate under some regularity conditions. The theoretical results are also developed for the case when the step size of the ODE numerical solver does not go to zero fast enough or the numerical error is comparable to the measurement error. We illustrate our approach with both simulation studies and clinical data on HIV viral dynamics.Comment: Published in at http://dx.doi.org/10.1214/09-AOS784 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Relacorilant, a Selective Glucocorticoid Receptor Modulator in Development for the Treatment of Patients With Cushing Syndrome, Does Not Cause Prolongation of the Cardiac QT Interval

Objective: To assess the effect of relacorilant, a selective glucocorticoid receptor modulator under investigation for the treatment of patients with endogenous hypercortisolism (Cushing syndrome [CS]), on the heart rate–corrected QT interval (QTc). Methods: Three clinical studies of relacorilant were included: (1) a first-in-human, randomized, placebo-controlled, ascending-dose (up to 500 mg of relacorilant) study in healthy volunteers; (2) a phase 1 placebo- and positive-controlled thorough QTc (TQT) study of 400 and 800 mg of relacorilant in healthy volunteers; and (3) a phase 2, open-label study of up to 400 mg of relacorilant administered daily for up to 16 weeks in patients with CS. Electrocardiogram recordings were taken, and QTc change from baseline (ΔQTc) was calculated. The association of plasma relacorilant concentration with the effect on QTc in healthy volunteers was assessed using linear mixed-effects modeling. Results: Across all studies, no notable changes in the electrocardiogram parameters were observed. At all time points and with all doses of relacorilant, including supratherapeutic doses, ΔQTc was small, generally negative, and, in the placebo-controlled studies, similar to placebo. In the TQT study, placebo-corrected ΔQTc with relacorilant was small and negative, whereas placebo-corrected ΔQTc with moxifloxacin positive control showed rapid QTc prolongation. These results constituted a negative TQT study. The model-estimated slopes of the concentration-QTc relationship were slightly negative, excluding an association of relacorilant with prolonged QTc. Conclusion: At all doses studied, relacorilant consistently demonstrated a lack of QTc prolongation in healthy volunteers and patients with CS, including in the TQT study. Ongoing phase 3 studies will help further establish the overall benefit-risk profile of relacorilant.</p

A semiparametric regression cure model with current status data

This paper considers the analysis of current status data with a cured proportion in the population using a mixture model that combines a logistic regression formulation for the probability of cure with a semiparametric regression model for the time to occurrence of the event. The semiparametric regression model belongs to the flexible class of partly linear models that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies were carried out to investigate the performance of the proposed method and the model is fitted to a dataset from a study of calcification of the hydrogel intraocular lenses, a complication of cataract treatment. Copyright 2005, Oxford University Press.

Selection of continuous features based on distribution of objects

A novel feature selection approach is proposed for data space defined over continuous features, which obtains a subset of features,such that it can discriminate class labels of objects and its discriminant ability is not inferior to that of the original features,so to effectively improve the learning performance and intelligibility of the classification model.According to the spatial distribution of objects and their classification labels,a data space with continuous features is partitioned into subspaces,each with a clear edge and a single classification label.Then these labelled subspaces are projected to each continuous feature.The measurement of each feature is estimated for a subspace against all other subspace-projected features by means of statistical significance.Through the construction of a matrix of the measurements of the subspaces by all features,the subspace-projected features are ranked in a descending order based on the discriminant ability of each feature in the matrix.After evaluating a gain function of the discriminant ability defined by the best-so-far feature subset,the resulting feature subset can be incrementally determined. Our comprehensive experiments on the UCI Repository data sets have demonstrated the effectiveness and efficiency of the proposed approach of feature selection

Generalized Ordinary Differential Equation Models

<div><p>Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method. Supplementary materials for this article are available online.</p></div

A Combined Method for Estimating Continuous Runoff by Parameter Transfer and Drainage Area Ratio Method in Ungauged Catchments

Continuous runoff needs to be estimated in ungauged catchments to interpret hydrological phenomena and manage water resources. Researchers have used various methods to estimate runoff in ungauged catchments, but few combined different methods to improve the estimation. A model parameter-based method named the parameter transfer (PT) method and a flow-based method of area ratio (AR) were combined and tested in eight catchments in a lake basin. The performance of the PT method depended on the model simulation and donors, which were related to physical and climate characteristics of the catchments. Two AR methods were compared and the results showed that the standard AR method was suitable in this study area with the area ratio between donor and target ranging from 0.46 to 1.41. ENS and R2 values suggested that the PT method used in this study showed a better result than the AR method in 75% of the considered sites, but the total runoff deviation was lower for the standard AR method than that for the PT method. We used the standard AR method weighted by the PT method, and compared three versions weighted with daily, monthly, and average ENS values of the PT and AR methods and one unweighted version. The results of the combined methods were promising. The version weighted with daily ENS performed best and gave improved R2 and daily ENS values for 75% of the receivers. The unweighted combined method performed stable in all sites. The combined method gave better simulation of daily and monthly continuous runoff in ungauged catchments than each individual method

Building a decentralized industrial alliance with the information system empowered by blockchain

The traditional industrial chain consists of a group of entities that are familiar with each other, and the relationship between the entities is maintained by signing contracts. However, on the one hand, the inability to reach mutual trust between unfamiliar entities limits the collaboration of entities, and on the other hand, most of the profits in the industrial chain are grabbed by the dominant enterprises. In this paper, an information system for collaboration among business entities is developed based on blockchain, based on which a business model called Decentralized Industry Alliance (DIA) is proposed. Transactions and profit distribution in the DIA are executed by smart contracts, which enables unfamiliar entities to trust each other without relying on a third party. Any entity that voluntarily complies with the smart contracts automatically becomes a member of the DIA, thereby promoting the expansion of the industry scale. The smart contracts distribute profits according to each entity’s contribution to the alliance, so as to ensure the fairness of value distribution. A case about the alliance of elderly care industry is carried out, which shows that the DIA achieves rapid expansion on the premise of ensuring fairness. As a general business model in the web 3.0 era, the DIA can be referenced by other industries