Adapting by calibration the sample size of a phase III trial on the basis of phase II data

The problem of estimating the sample size for a phase III trial on the basis of existing phase II data is considered, where data from phase II cannot be combined with those of the new phase III trial. Focus is on the test for comparing the means of two independent samples. A launching criterion is adopted in order to evaluate the relevance of phase II results: phase III is run if the effect size estimate is higher than a threshold of clinical importance. The variability in sample size estimation is taken into consideration. Then, the frequentist conservative strategies with a fixed amount of conservativeness and Bayesian strategies are compared. A new conservative strategy is introduced and is based on the calibration of the optimal amount of conservativeness – calibrated optimal strategy (COS). To evaluate the results we compute the Overall Power (OP) of the different strategies, as well as the mean and the MSE of sample size estimators. Bayesian strategies have poor characteristics since they show a very high mean and/or MSE of sample size estimators. COS clearly performs better than the other conservative strategies. Indeed, the OP of COS is, on average, the closest to the desired level; it is also the highest. COS sample size is also the closest to the ideal phase III sample size M_I, showing averages and MSEs lower than those of the other strategies. Costs and experimental times are therefore considerably reduced and standardized. However, if the ideal sample size M_I is to be estimated the phase II sample size n should be around the ideal phase III sample size, i.e. n?2M_I/3. Copyright © 2010 John Wiley & Sons, Ltd.     

风险规避情形下第一价格拍卖的非参数估计方法

在拍卖实证研究的大量文献中,越来越多的证据表明投标人更趋向于风险规避,然而目前拍卖计量方法通常只考虑风险中性的情形。针对这一问题,推广了针对第一价格拍卖的非参数估计方法,给出了多个风险规避参数估计量来处理风险规避的情形,并总结了相应的估计过程。为验证估计效果,蒙特卡罗模拟实验被用于进行分析和评价。实验结果表明,无论是对风险规避参数,还是私有估值的估计,总体上都能取得不错的效果,验证了方法的有效性,同时为风险规避参数估计量的选择提供了一些指导性建议。     

Robust Bayesian analysis for parallel system with masked data under inverse Weibull lifetime distribution

Abstract

This paper considers the statistical analysis of masked data in a parallel system with inverse Weibull distributed components under type II censoring. Based on Gamma conjugate prior, the Bayesian estimation as well as the hierarchical Bayesian estimation for the parameters and the reliability function of system are obtained by using the Bayesian theory and the hierarchical Bayesian method. Finally, Monte Carlo simulations are provided to compare the performances of the estimates under different masking probabilities and effective sample sizes.     

Some imputation methods to compensate with non-response for estimation of population mean in two-occasion successive sampling

Abstract

Non-response is an unavoidable phenomenon in almost all sample survey, and if it is not dealt carefully at the very starting of the analysis, results may lead to significant biases in the survey estimates. Keeping these facts in mind and inspired by the work of Singh (2009 Singh, S. 2009. A new method of imputation in survey sampling. Statistics 43 (5):499–511. doi:10.1080/02331880802605114.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), this article suggests some alternative efficient methods to deal with the missing data problems at the beginning of the analysis and proposes estimation procedures of the current population mean in two-occasion successive sampling. The properties of the resultant estimation procedures have been examined and supplemented with empirical studies. Results have been critically analyzed, and recommendations are made to the survey practitioners.     

Distributions minimizing fisher information for scale in kolmogorov neighbourhoods

We construct those distributions minimizing Fisher information for scale in Kolmogorov neighbourhoods K_?(G) = {F|sup_x|F(x) - G(x| ? ?} of d.f.'s G satisfying certain mild conditions. The theory is sufficiently general to include those cases in which G is normal, Laplace, logistic, Student's t, etc. As well, we consider G(x) = 1 - e^-x, ? 0, and correct some errors in the literature concerning this case.     

Analytic Bayesian Solution of the Two-Stage Poisson-Type Problem in Probabilistic Risk Analysis

The basic purpose of probabilistic risk analysis is to make inferences about the probabilities of various postulated events, with an account of all relevant information such as prior knowledge and operating experience with the specific system under study, as well as experience with other similar systems. Estimation of the failure rate of a Poisson-type system leads to an especially simple Bayesian solution in closed form if the prior probability implied by the invariance properties of the problem is properly taken into account. This basic simplicity persists if a more realistic prior, representing order of magnitude knowledge of the rate parameter, is employed instead. Moreover, the more realistic prior allows direct incorporation of experience gained from other similar systems, without need to postulate a statistical model for an underlying ensemble. The analytic formalism is applied to actual nuclear reactor data.     

A Discrete Time Parametric Model for the Analysis of Failure Time Data

This paper introduces a parametric discrete failure time model which allows a variety of smooth hazard function shapes, including shapes which are not readily available with continuous failure time models. The model is easy to fit, and statistical inference is simple. Further, it is readily extended to allow for differences between subjects while retaining the ease of fit and simplicity of statistical inference. The performance of the discrete time analysis is demonstrated by application to several data sets.     

Comparison of a genetic algorithm and simulated annealing in an application to statistical image reconstruction

Genetic algorithms (GAs) are adaptive search techniques designed to find near-optimal solutions of large scale optimization problems with multiple local maxima. Standard versions of the GA are defined for objective functions which depend on a vector of binary variables. The problem of finding the maximum a posteriori (MAP) estimate of a binary image in Bayesian image analysis appears to be well suited to a GA as images have a natural binary representation and the posterior image probability is a multi-modal objective function. We use the numerical optimization problem posed in MAP image estimation as a test-bed on which to compare GAs with simulated annealing (SA), another all-purpose global optimization method. Our conclusions are that the GAs we have applied perform poorly, even after adaptation to this problem. This is somewhat unexpected, given the widespread claims of GAs' effectiveness, but it is in keeping with work by Jennison and Sheehan (1995) which suggests that GAs are not adept at handling problems involving a great many variables of roughly equal influence.We reach more positive conclusions concerning the use of the GA's crossover operation in recombining near-optimal solutions obtained by other methods. We propose a hybrid algorithm in which crossover is used to combine subsections of image reconstructions obtained using SA and we show that this algorithm is more effective and efficient than SA or a GA individually.     

Developments in sample survey theory: An appraisal

Recent developments in sample survey theory include the following topics: foundational aspects of inference, resampling methods for variance and confidence interval estimation, imputation for nonresponse and analysis of complex survey data. An overview and appraisal of some of these developments are presented.     

标准伽玛分布族参数的EB估计的收敛速度

本文构造了标准伽玛分布族参数的EB估计，并给出了该估计的收敛速度。在适当的条件下，该速度可以分别充分接近于1／2和1。