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序贯临床试验中次要终点的检验与置信区间AI 解读

In a sequential clinical trial whose stopping rule depends on the primary endpoint, inference on secondary endpoints is an important long-standing problem. Ignoring the possibility of early stopping based on the primary endpoint may result in substantial bias. To address this problem, a commonly used approach is to develop bias correction by estimating the bias in the case of bivariate normal outcomes and appealing to joint asymptotic normality of the statistics associated…

组序贯临床试验设计中的功效、样本量与适应性AI 解读

A class of flexible and asymptotically efficient group sequential designs is developed herein for one-sided and two-sided tests of the parameter of an exponential family. Efficiency is measured in terms of the expected sample size and power function, under prespecified constraints on the maximum sample size and Type I error probability. It is shown how these designs achieve asymptotic efficiency by adapting to the information about the unknown parameter during the course of…

非线性及广义线性混合效应模型的混合估计方法AI 解读

A hybrid method that combines Laplace's approximation and Monte Carlo simulations to evaluate integrals in the likelihood function is proposed for estimation of the parameters in nonlinear mixed effects models that assume a normal parametric family for the random effects. Simulations show that these parametric estimates of fixed effects are close to the nonparametric estimates even though the mixing distribution is far from the assumed normal parametric family. An asymptotic…

非线性混合效应模型中的非参数估计AI 解读

A nonparametric approach is developed herein to estimate parameters in nonlinear mixed effects models. Asymptotic properties of the nonparametric maximum likelihood estimators and associated computational algorithms are provided. Empirical Bayes estimators of functionals of the random effects are also developed. Applications to population pharmacokinetics are given.

自回归参数的固定精度估计AI 解读

For a first order non-explosive autoregressive process with unknown parameter $\beta \in \lbrack -1, 1 \rbrack$, it is shown that if data are collected according to a particular stopping rule, the least squares estimator of $\beta$ is asymptotically normally distributed uniformly in $\beta$. In the case of normal residuals, the stopping rule may be interpreted as sampling until the observed Fisher information reaches a preassigned level. The situation is contrasted with the…

自适应设计与随机逼近AI 解读

When $y = M(x) + \varepsilon$, where $M$ may be nonlinear, adaptive stochastic approximation schemes for the choice of the levels $x_1, x_2, \cdots$ at which $y_1, y_2, \cdots$ are observed lead to asymptotically efficient estimates of the value $\theta$ of $x$ for which $M(\theta)$ is equal to some desired value. More importantly, these schemes make the "cost" of the observations, defined at the $n$th stage to be $\sum^n_1(x_i - \theta)^2$, to be of the order of $\log n$ ins…