ALGORITHM DEVELOPMENT & SOFTWARE DESIGN FOR POPULATION KINETIC ANALYSIS

具体为：1. 开发收敛的数值算法， 种群动力学中参数和非参数估计 分析将在项目2中实施。 2. 具体分析了估计量的统计性质， 目标1：一致性、渐近正态性、渐近置信度 区域和假设检验。 3. 研究估计器的效率和稳健性， 具体目标I通过模拟研究。 对于参数情况，我们将开发四种算法： 最大似然（ML）算法，全局两阶段（GTS）算法， NONMEM型算法和Lindstrom-Bates型算法。 的ML 算法是基于蒙特卡罗积分评估 目标函数 GTS、NONMEM和Lindstrom-Bates类型 算法都是基于扩展最小二乘（ELS）方法。 对于非参数的情况，我们将开发一个Mallet型算法 混合效应模型。 对于参数情况，一致性是一个困难的问题。 一致性意味着估计值收敛于真实值 值作为主题的数量变得任意大。 是 重要的是要注意，原始的估计程序'NONMEM 和Lindstrom-Bates对2个一般非线性模型不一致。 唯一相对于真实参数是一致的算法 values是真正的最大似然算法。 对于ELS类 我们开发的算法，有一个广义的一致性概念， 这意味着估计值收敛到最佳值， 近似模型。 我们将研究所需的理论， 广义一致性和渐近正态性 算法 给出了渐近置信区间和 假设检验将遵循相同的理论。 对于非参数情况，方法的一致性，相对于 模型的真实价值已经确立。 什么 剩下的就是渐近置信度的确定 估计参数的区间，例如均值、中位数、修剪值 目前，这些结果还没有得到的， 非参数情况 我们将使用最大似然理论 在无限维空间中的估计用于此目的。 （无偏）估计量的效率由广义 估计值的方差，Cramer-Rao下限为 最佳 两个估计量的相对效率比较 相应的广义方差。 鲁棒性衡量了 当模型中存在违规时执行算法，和/或 概率分布假设 利用蒙特卡罗方法 模拟研究，这些属性可以研究，而无需 需要1个渐近条件。

The specific are: 1. Develop convergent numerical algorithms for the parametric and nonparametric estimators in population kinetic analysis to be implemented in Project 2. 2. Analyze the statistical properties of the estimators in Specific Aim 1: consistency, asymptotic normality, asymptotic confidence regions and hypothesis testing. 3. Investigate efficiency and robustness of the estimators in Specific Aim I via simulation studies. For the parametric case, we will develop four algorithms: a "true" maximum likelihood (ML) algorithm, a Global Two Stage (GTS) algorithm, a NONMEM type algorithm, and a Lindstrom-Bates type algorithm. The ML algorithm is based on Monte Carlo integration for evaluating the objective function. The GTS, NONMEM, and Lindstrom-Bates type algorithms are all based on the extended least squares (ELS) method. For the nonparametric case, we will develop a Mallet type algorithm for mixed effects models. For the parametric case, consistency is a difficult issue. Consistency means that the estimated values converge to the true values as the number of subjects gets arbitrarily large. It is important to note that the original estimation procedures ot'NONMEM and Lindstrom-Bates are not consistent for 2eneral nonlinear models. The only algorithm that is consistent relative to the true parameter values is the true maximum likelihood algorithm. For the class of ELS algorithms we develop, there is a generalized notion of consistency, which means that the estimated values converge to the values that best approximate the model. We will investigate the required theory for the generalized consistency and asymptotic normality of these algorithms. The formulas for the asymptotic confidence intervals and hypothesis testing will follow from the same theory. For the nonparametric case, the consistency of the method, relative to the true values of the model, has already been established. What remains then is the determination of the asymptotic confidence intervals for estimated parameters such as means, medians, trimmed means, etc. At present these results have not been derived for the nonparametric case. We will use the theory of maximum likelihood estimation in infinite dimensional spaces for this purpose. Efficiency of an (unbiased) estimator is measured by the generalized variance of estimated values, with the Cramer-Rao lower bound being optimal. Relative efficiency of two estimators compares the corresponding generalized variances. Robustness measures how an algorithm performs when there are violations in the model and/or probability distribution assumptions. By utilizing Monte Carlo simulation studies, these properties can be investigated without requiring 1 asymptotic conditions.