Parameter Identifiability and Estimation of HIV/AIDS Dynamic Models

We use a technique from engineering (Xia and Moog, in IEEE Trans. Autom. Contr. 48(2):330–336, 2003; Jeffrey and Xia, in Tan, W.Y., Wu, H. (Eds.), Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention, 2005) to investigate the algebraic identifiability of a popular three-dimensional HIV/AIDS dynamic model containing six unknown parameters. We find that not all six parameters in the model can be identified if only the viral load is measured, instead only four parameters and the product of two parameters (N and λ) are identifiable. We introduce the concepts of an identification function and an identification equation and propose the multiple time point (MTP) method to form the identification function which is an alternative to the previously developed higher-order derivative (HOD) method (Xia and Moog, in IEEE Trans. Autom. Contr. 48(2):330–336, 2003; Jeffrey and Xia, in Tan, W.Y., Wu, H. (Eds.), Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention, 2005). We show that the newly proposed MTP method has advantages over the HOD method in the practical implementation. We also discuss the effect of the initial values of state variables on the identifiability of unknown parameters. We conclude that the initial values of output (observable) variables are part of the data that can be used to estimate the unknown parameters, but the identifiability of unknown parameters is not affected by these initial values if the exact initial values are measured with error. These noisy initial values only increase the estimation error of the unknown parameters. However, having the initial values of the latent (unobservable) state variables exactly known may help to identify more parameters. In order to validate the identifiability results, simulation studies are performed to estimate the unknown parameters and initial values from simulated noisy data. We also apply the proposed methods to a clinical data set to estimate HIV dynamic parameters. Although we have developed the identifiability methods based on an HIV dynamic model, the proposed methodologies are generally applicable to any ordinary differential equation systems.     

A Multivariate Method for the Parameter Estimation in Biorhythms

A suitable multivariate method is described for the periodic observations of a group of individuals having comparable periods and amplitudes. Simultaneous confidence region can be obtained for the parameters of the group as a whole instead of an individual. The study of periodic behaviour of a group is more realistic than the study of the behaviour of an individual. An application of human leucocyte counts in microfilariasis (W. bancrofti) infection has been described.     

非线性再生散度随机效应模型的极大似然估计及EM算法

非线性再生散度随机效应模型是指数族非线性随机效应模型和非线性再生散度模型的推广和发展．通过视模型中的随机效应为假想的缺失数据和应用Metropolis-Hastings（MH）算法,提出了模型参数极大似然估计的Monte-Carlo EM（MCEM）算法,并用模拟研究和实例分析说明了该算法的可行性．     

Parameter Estimation for the Compartmental Model

An estimation procedure is obtained for a stochastic compartmental model. Compartmental analysis assumes that a system may be divided into homogeneous components, or compartments. The main theory for the compartmental system was studied by Matis and Hartley (1971) with a discrete population in a steady state. All the transitions among the particles are considered to be stochastic in nature. An estimation procedure, Regular Best Asymptotic Normal (RBAN), discussed by Chiang (1956) is investigated for a stochastic m-compartmental system. The detailed proof of the procedure is provided here. Asymptotic properties for the estimator has been studied and computation has been carried out on our proposed nonlinear model. The downhill simplex search method, originally developed by Nelder and Mead (1965), and applied to minimize our quadratic form is inherently nonlinear in nature, thus avoiding the need to evaluate any derivative for point estimation of the parameters. The procedure applied to an experimental situation involving two compartments gives very encouraging results.     

非线性再生散度随机效应模型的极大似然估计及随机逼近算法

非线性再生散度随机效应模型包括了非线性随机效应模型和指数族非线性随机效应模型等．通过视模型中的随机效应为假想的缺失数据和应用Metropolis-Hastings(简称MH) 算法,提出了模型参数极大似然估计的随机逼近算法．模拟研究和实例分析表明了该算法的可行性．     

Estimation and Tests for Departures from Rao-Structured Covariance Matrices

For linear models, a measure of departure of a variance-covariance matrix from Rao-structure (Rao, 1967) is proposed. Relevant estimation and testing problems are discussed. Illustrative examples are also presented.     

Parameter Estimation Methods for Chaotic Intercellular Networks

We have investigated simulation-based techniques for parameter estimation in chaotic intercellular networks. The proposed methodology combines a synchronization–based framework for parameter estimation in coupled chaotic systems with some state–of–the–art computational inference methods borrowed from the field of computational statistics. The first method is a stochastic optimization algorithm, known as accelerated random search method, and the other two techniques are based on approximate Bayesian computation. The latter is a general methodology for non–parametric inference that can be applied to practically any system of interest. The first method based on approximate Bayesian computation is a Markov Chain Monte Carlo scheme that generates a series of random parameter realizations for which a low synchronization error is guaranteed. We show that accurate parameter estimates can be obtained by averaging over these realizations. The second ABC–based technique is a Sequential Monte Carlo scheme. The algorithm generates a sequence of “populations”, i.e., sets of randomly generated parameter values, where the members of a certain population attain a synchronization error that is lesser than the error attained by members of the previous population. Again, we show that accurate estimates can be obtained by averaging over the parameter values in the last population of the sequence. We have analysed how effective these methods are from a computational perspective. For the numerical simulations we have considered a network that consists of two modified repressilators with identical parameters, coupled by the fast diffusion of the autoinducer across the cell membranes.     

Parameter Estimation Methods for Single Neuron Models

With the advancement in computer technology, it has become possible to fit complex models to neuronal data. In this work, we test how two methods can estimate parameters of simple neuron models (passive soma) to more complex ones (neuron with one dendritic cylinder and two active conductances). The first method uses classical voltage traces resulting from current pulses injection (time domain), while the second uses measures of the neuron's response to sinusoidal stimuli (frequency domain). Both methods estimate correctly the parameters in all cases studied. However, the time-domain method is slower and more prone to estimation errors in the cable parameters than the frequency-domain method. Because with noisy data the goodness of fit does not distinguish between different solutions, we suggest that running the estimation procedure a large number of times might help find a good solution and can provide information about the interactions between parameters. Also, because the formulation used for the model's response in the frequency domain is analytical, one can derive a local sensitivity analysis for each parameter. This analysis indicates how well a parameter is likely to be estimated and helps choose an optimal stimulation protocol. Finally, the tests suggest a strategy for fitting single-cell models using the two methods examined.     

Estimation and Confidence Intervals for Two-Stage Sample-Size-Flexible Design with LSW Likelihood Approach

Adaptive sample size methods have been a popular topic in the field of clinical trials. There are a few basic requirements for the adaptive methods to be acceptable from the international regulatory viewpoint. All valid methods need to control the overall type-I error rate at the pre-specified level. The rule of the interim and final decisions needs to be explicit and clearly documentable. It is extremely desirable that the method employed also provides estimation of the treatment effect in addition to the significance test. In this paper we describe the point and confidence interval estimation for the likelihood approach of sample-size adaptive design proposed by Li et al. (Biostatistics 3:277–287, 2002, J. Biopharm. Stat. 15:707–718, 2005). We use the median unbiased estimator (Cox and Hinkley, Theoretical Statistics, p. 273, 1974) for estimating the treatment effect and demonstrate that the estimator has small mean squared error compared to the naïve method, and that the confidence interval estimation has correct coverage probability.     

An Improved Parameter Estimation Method for Hodgkin-Huxley Models

We consider whole-cell voltage-clamp data of isolated currents characterized by the Hodgkin-Huxley paradigm. We examine the errors associated with the typical parameter estimation method for these data and show them to be unsatisfactorally large especially if the time constants of activation and inactivation are not sufficiently separated. The size of these errors is due to the fact that the steady-state and kinetic properties of the current are estimated disjointly. We present an improved parameter estimation method that utilizes all of the information in the voltage-clamp conductance data to estimate steady-state and kinetic properties simultaneously and illustrate its success compared to the standard method using simulated data and data from P. interruptus shal channels expressed in oocytes.     

A Novel Nonlinear Parameter Estimation Method of Soft Tissues

The elastic parameters of soft tissues are important for medical diagnosis and virtual surgery simulation. In this study, we propose a novel nonlinear parameter estimation method for soft tissues. Firstly, an in-house data acquisition platform was used to obtain external forces and their corresponding deformation values. To provide highly precise data for estimating nonlinear parameters, the measured forces were corrected using the constructed weighted combination forecasting model based on a support vector machine(WCFM_SVM). Secondly, a tetrahedral finite element parameter estimation model was established to describe the physical characteristics of soft tissues,using the substitution parameters of Young's modulus and Poisson's ratio to avoid solving complicated nonlinear problems. To improve the robustness of our model and avoid poor local minima,the initial parameters solved by a linear finite element model were introduced into the parameter estimation model. Finally, a self-adapting Levenberg–Marquardt(LM) algorithm was presented,which is capable of adaptively adjusting iterative parameters to solve the established parameter estimation model. The maximum absolute error of our WCFM_SVM model was less than 0.03 Newton, resulting in more accurate forces in comparison with other correction models tested.The maximum absolute error between the calculated and measured nodal displacements was less than 1.5 mm, demonstrating that our nonlinear parameters are precise.     

Predictive Estimation of Finite Population Mean Using a Product Estimator for Two-Stage Sampling

In an attempt to estimate a finite population mean under the predictive approach described in Basu (1971) through the product method of estimation, we created a new product-type estimator for a two-stage sampling procedure. We also report a simulation study that is made in order to understand better the performance of the new estimator compared to the classical product estimator.     

Parameter Estimation of Fractional-Order Chaotic Systems by Using Quantum Parallel Particle Swarm Optimization Algorithm

Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO) is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm.     

Estimation of a Nonlinear Density-Dependence Parameter for Wild Turkey

Abstract: Although previous research and theory has suggested that wild turkey (Meleagris gallopavo) populations may be subject to some form of density dependence, there has been no effort to estimate and incorporate a density-dependence parameter into wild turkey population models. To estimate a functional relationship for density dependence in wild turkey, we analyzed a set of harvest-index time series from 11 state wildlife agencies. We tested for lagged correlations between annual harvest indices using partial autocorrelation analysis. We assessed the ability of the density-dependent theta-Ricker model to explain harvest indices over time relative to exponential or random walk growth models. We tested the homogeneity of the density-dependence parameter estimates (θ) from 3 different harvest indices (spring harvest no. reported harvest/effort, survey harvest/effort) and calculated a weighted average based on each estimate's variance and its estimated covariance with the other indices. To estimate the potential bias in parameter estimates from measurement error, we conducted a simulation study using the theta-Ricker with known values and lognormally distributed measurement error. Partial autocorrelation function analysis indicated that harvest indices were significantly correlated only with their value at the previous time step. The theta-Ricker model performed better than the exponential growth or random walk models for all 3 indices. Simulation of known parameters and measurement error indicated a strong positive upward bias in the density-dependent parameter estimate, with increasing measurement error. The average density-dependence estimate, corrected for measurement error ranged 0.25 ≤ θC ≤ 0.49, depending on the amount of measurement error and assumed spring harvest rate. We infer that density dependence is nonlinear in wild turkey, where growth rates are maximized at 39-42% of carrying capacity. The annual yield produced by density-dependent population growth will tend to be less than that caused by extrinsic environmental factors. This study indicates that both density-dependent and density-independent processes are important to wild turkey population growth, and we make initial suggestions on incorporating both into harvest management strategies.     

用人工神经网络方法估计Ligistic方程参数

本文提出Logistic方程参数优化估计的人工神经网络方法,并选取一组标样进行具体尝试。结果表明,用这种方法估计Logistic方程参数效果极好。     

Evaluation of Tadalafil Nanosuspensions and Their PEG Solid Dispersion Matrices for Enhancing Its Dissolution Properties

The aim of this work was to prepare and evaluate Tadalafil nanosuspensions and their PEG 4000 solid dispersion matrices to enhance its dissolution rate. Nanosuspensions were prepared by precipitation/ultrasonication technique at 5°C where different stabilizers were screened for stabilization. Nanosuspensions were characterized in terms of particle size and charge. Screening process limited suitable stabilizers into structurally related surfactants composed of a mixture of Tween80 and Span80 at 1:1 ratio (in percent, weight/volume) in adjusted alkaline pH (named TDTSp-OH). The surfactant mixture aided the production of nanosuspensions with an average particle size of 193 ± 8 nm and with short-term stability sufficient for further processing. Solid dispersion matrices made of dried Tadalafil nanosuspensions or dried Tadalafil raw powder suspensions and PEG 4000 as a carrier were prepared by direct compression. Drying was performed via dry heat or via freeze dry. Drug release studies showed that, in general, tablet formulations made of freeze-dried product exhibited faster initial release rates than the corresponding tablets made of oven-dried products which could be attributed to possible larger crystal growth and larger crushing strengths of oven-dried formulations. At best, 60% of drug was released from solid dispersion matrices, while more than 90% of drug was released from TDTSp-OH nanosuspension within the first 5 min. In conclusion, Tadalafil nanosuspensions obtained using a mixed surfactant system provided rapid dissolution rates of Tadalafil that can theoretically enhance its bioavailability.KEY WORDS: nanosuspension, particle size, solid dispersion, stabilizer, tablets, Tadalafil