百分位数的可信区间估计

百分位数（ｐｅｒｃｅｎｔｉｌｅ）是用于描述计量资料尤其是偏态分布资料极为常用的指标体系。如用于允许区间的估计,变异度的描述,百分位数回归等。但百分位数本身亦存在抽样误差,有必要对其进行区间估计。本文介绍百分位数的ｂｏｏｔｓｔｒａｐ区间估计,并与二项分...     

关于Cox模型的Bootstrap区间估计和假设检验

目的 提出Ｃｏｘ模型参数的Ｂｏｏｔｓｔｒａｐ区间估计和假设检验。方法 通过对样本进行Ｂｏｓｓｔｓｔｒａｐ抽样,构造Ｂｏｓｓｔｓｔｒａｐ区间估计和假设检验３区域。结果 实例分析表明,当再抽样容量较大时,Ｂｏｏｔｓｔｒａｐ区间估计和假设检验与直接对原样本应用正态性得到的结果相差不大,前者在后者周围波动,假检验结果也趋于一致。结论 Ｂｏｓｓｔｓｔｒａｐ区间估计和假设检验在一定程度上可以作为按正态性估计误     

药物溶解参数的Bootstrap方法估计

药物溶解参数的估计过去是采用Ｈａｎｓｅｎ方法进行估计的 ,该法要求药物溶解参数数据模型符合正态分布 ,其理论和计算较为复杂 ,需另写出计算程序方能在计算机上实现其计算过程 ,实际应用困难 ,Ｂｏｏｔｓｔｒａｐ分析方法对模型数据的分布没有严格的规定 ,且在现行的ＳＡＳ统计软件包上较易实现其计算过程 ,但其能否应用于药物溶解参数模型估计。本文的目的就是想以这类研究的一个实际资料 ,探讨Ｂｏｏｔｓｔｒａｐ方法进行参数估计的可行性。资料与方法一、资料来源资料来源于药理学研究中的实例 ,共有 2 6种溶剂条件下的实验数据 ,试作…     

误差为平稳m—相依的线性模型的移动区段再抽样法

引　　言对于一般的线性回归模型Ｙ =Ｘβ ε,假定误差ε独立且服从正态分布 ,才能进行有效的参数区间估计及假设检验 ,当ε的分布未知时 ,若按通常的方法 ,参数的区间估计与假设检验就不稳健 ,1981年Ｆｒｅｅｄ ｍａｎ将Ｂｏｏｔｓｔｒａｐ法应用回归模型 ,提出参数及其方差的Ｂｏｏｔｓｔｒａｐ估计 ,1986年Ｗｕ又进一步加以改进 ,使方差的Ｂｏｏｔｓｔｒａｐ估计达到稳健 ,假设检验也能够顺利实现。然而 ,当误差ε或响应变量序列存在一定的相依关系时 ,上述方法就失效 ,而误差或响应变量序列为相依情形的线性模型是广泛存在的 ,比如目前…     

应用Bootstrap法确定初保评价指标的权重系数

应用Ｂｏｏｔｓｒｔａｐ法,对现有样本进行再抽样,得到Ｂｏｏｔｓｔｒａｐ样本,并计算Ｂｏｏｔｓｔｒａｐ样本特征值及主要分量得分系数,从而可得总体特征值、主分量得分系数的Ｂｏｏｔｓｔｒａｐ估计。可以将主分量得分系数的Ｂｏｏｔｓｔｒａｐ估计作为统一权衡标准,对任何样本指标进行加权压缩,得以若干个主要分量,然后根据所得主分量利用聚类分析的方法对个体分类,达到妆保达标分类评价的目的。本文 可以使现有样本所提     

Bootstrap方法及其在医学统计中的应用

Ｂｏｏｔｓｔｒａｐ方法及其在医学统计中的应用刘勤金丕焕当用样本估计一个总体的某个统计量（如：均数、中位数、相关系数、回归系数等）时总是希望知道这个统计量估计值的准确度（反映准确度的常用指标包括标准差、可信区间等）。如果知道了这个统计量的抽样分布就可以...     

方差未知且不等时均数差别Bayes分析的Monte Carlo方法

目的 解决方差未知且不等时总体均值差别的推断问题。方法 根据Ｂａｙｉｓ理论猛士叫体均数差值的后验分布Ｂｅｈｒｅｎｓ－Ｆｉｓｈｅｒ分布，用Ｍｏｎｔｅ Ｃａｒｌｏ模拟方法产生Ｂｅｈｒｅｎｓ－Ｆｉｓｈｅｒ的频数分布进行统计推断。结果 模拟样本足够大时，获得Ｂｅｈｒｅｎｓ－Ｆｉｓｈｅｒ的精确分布、均数差值的置信区间及假设检验结果。结论 与其他Ｂｅｈｒｅｎｓ－Ｆｉｓｈｅｒ分 近似方法结果相同，但本方法不信赖     

关于危险度指标的Bayes统计推断

目的 解决二分类反应资料危险度指标区间估计问题。方法 用Bayes方法进行推断，用MC模拟技术解决统计计算问题。结果 解决了有关的危险度指标的精确估计问题。同时结合有信息先验，提高了估计的精度。结论 危险度指标的Bayes分析与经典方法相比较更精确，更有效。     

用Bootstrap方法计算中位数的可信区间

临床试验中 ,除了需要了解两组观察对象的疗效是否存在差别 ,还希望能了解差别的大小。假设检验能够解决疗效是否存在差别的问题 ,但不能告知差别的实际大小。ＩＣＨＧＣＰ规定 ,在临床试验中 ,除了假设检验的Ｐ值外 ,还需要在统计分析报告中列出统计推断的可信区间。对于正态分布的数据 ,通过均数及标准误能够得到可信区间。但当数据分布未知时 ,此时中位数成为较好的表现数据集中趋势的统计量 ,然而中位数的可信区间的计算是比较困难的。此时 ,Ｂｏｏｔｓｔｒａｐ抽样估计中位数的可信区间成为较好的方法。在某些情况下 ,当有些信息是不可…     

分析季节性波动的新模型（1）

现有的各种季节性统计方法几乎都以正弦曲线作模型，只适应于对称单峰分布且波幅较小的特殊资料，对客观存在的大量不服从这种分布的资料，虽有人作过尝试，但尚未找到合适的统计分析方法。本文提出用混合ｖｏｎ Ｍｉｓｅｓ分布作季节性分析，并推导出估计极大似然参数的搜索迭代法，统计推断采用似然比统计量。模型分析和实验验证都表明：本文方法不仅能用于单峰偏态分布、一般双峰分布的季节性分析，而且对单峰对称分布资料也可     

Intraclass correlation coefficients and bootstrap methods of hierarchical binary outcomes

Intraclass correlation coefficients are designed to assess consistency or conformity between two or more quantitative measurements. When multistage cluster sampling is implemented, no methods are readily available to estimate intraclass correlations of binomial-distributed outcomes within a cluster. Because statistical distribution of the intraclass correlation coefficients could be complicated or unspecified, we propose using a bootstrap method to estimate the standard error and confidence interval within the framework of a multilevel generalized linear model. We compared the results derived from a parametric bootstrap method with those from a non-parametric bootstrap method and found that the non-parametric method is more robust. For non-parametric bootstrap sampling, we showed that the effectiveness of sampling on the highest level is greater than that on lower levels; to illustrate the effectiveness, we analyse survey data in China and do simulation studies.     

Application of the bootstrap procedure provides an alternative to standard statistical procedures in the estimation of the vitamin B-6 requirement.

The bootstrap procedure is a versatile statistical tool for the estimation of standard errors and confidence intervals. It is useful when standard statistical methods are not available or are poorly behaved, e.g., for nonlinear functions or when assumptions of a statistical model have been violated. Inverse regression estimation is an example of a statistical tool with a wide application in human nutrition. In a recent study, inverse regression was used to estimate the vitamin B-6 requirement of young women. In the present statistical application, both standard statistical methods and the bootstrap technique were used to estimate the mean vitamin B-6 requirement, standard errors and 95% confidence intervals for the mean. The bootstrap procedure produced standard error estimates and confidence intervals that were similar to those calculated by using standard statistical estimators. In a Monte Carlo simulation exploring the behavior of the inverse regression estimators, bootstrap standard errors were found to be nearly unbiased, even when the basic assumptions of the regression model were violated. On the other hand, the standard asymptotic estimator was found to behave well when the assumptions of the regression model were met, but behaved poorly when the assumptions were violated. In human metabolic studies, which are often restricted to small sample sizes, or when statistical methods are not available or are poorly behaved, bootstrap estimates for calculating standard errors and confidence intervals may be preferred. Investigators in human nutrition may find that the bootstrap procedure is superior to standard statistical procedures in cases similar to the examples presented in this paper.     

CONFIDENCE INTERVALS FOR THE LOG-NORMAL MEAN

In this paper we conduct a simulation study to evaluate coverage error, interval width and relative bias of four main methods for the construction of confidence intervals of log-normal means: the naive method; Cox's method; a conservative method; and a parametric bootstrap method. The simulation study finds that the naive method is inappropriate, that Cox's method has the smallest coverage error for moderate and large sample sizes, and that the bootstrap method has the smallest coverage error for small sample sizes. In addition, Cox's method produces the smallest interval width among the three appropriate methods. We also apply the four methods to a real data set to contrast the differences. © 1997 by John Wiley & Sons, Ltd.     

Non‐parametric methods for cost‐effectiveness analysis: the central limit theorem and the bootstrap compared

Cost‐effectiveness analyses (CEA) alongside randomised controlled trials commonly estimate incremental net benefits (INB), with 95% confidence intervals, and compute cost‐effectiveness acceptability curves and confidence ellipses. Two alternative non‐parametric methods for estimating INB are to apply the central limit theorem (CLT) or to use the non‐parametric bootstrap method, although it is unclear which method is preferable. This paper describes the statistical rationale underlying each of these methods and illustrates their application with a trial‐based CEA. It compares the sampling uncertainty from using either technique in a Monte Carlo simulation. The experiments are repeated varying the sample size and the skewness of costs in the population. The results showed that, even when data were highly skewed, both methods accurately estimated the true standard errors (SEs) when sample sizes were moderate to large (n>50), and also gave good estimates for small data sets with low skewness. However, when sample sizes were relatively small and the data highly skewed, using the CLT rather than the bootstrap led to slightly more accurate SEs. We conclude that while in general using either method is appropriate, the CLT is easier to implement, and provides SEs that are at least as accurate as the bootstrap. Copyright © 2009 John Wiley & Sons, Ltd.     

含安慰剂组三臂临床试验基于bootstrap再抽样的非劣效评判

目的探讨含安慰剂组三臂临床试验基于bootstrap再抽样的非劣效评判的方法。方法用Monte Carlo模拟方法,产生服从正态分布、对数正态分布和Gamma分布的随机样本,进行Welch校正t检验法和bootstrap法的α-模拟和power模拟的验证和比较。结果当数据服从正态分布,在样本量较大时,Welch校正t检验法和bootstrap法均表现出较好的统计性能,但当数据呈偏态分布时,Welch校正t检验法的第一类错误率会偏离预先给定的α-水平,而bootstrap法在样本量较大时,第一类错误率基本保持在预先给定的水平。Welch校正t检验法和bootstrap法的power模拟结果基本相同。结论含安慰剂组的三臂临床试验在数据不服从正态分布时,bootstrap法可作为一种有效的非劣效评判方法。     

Methods for testing equality of means of health care costs in a paired design study

In this paper we propose five new tests for the equality of paired means of health care costs. The first two tests are the parametric tests, a Z-score test and a likelihood ratio test, both derived under the bivariate normality assumption for the log-transformed costs. The third test (Z-score with jack-knife) is a semi-parametric Z-score method, which only requires marginal log-normal assumptions. The last two tests are the non-parametric bootstrap tests: one is based on a t-test statistic, and the other is based on Johnson's modified t-test statistic. We conduct a simulation study to compare the performance of these tests, along with some commonly used tests when the sample size is small to moderate. The simulation results demonstrate that the commonly used paired t-test on the log-scale and the Wilcoxon signed rank for differences of the two original scales can yield type I error rates larger than the preset nominal levels. The commonly used paired t-test on the original data performs well with slightly skewed data, but can yield inaccurate results when two populations have different skewness. The likelihood ratio test, the parametric and semi-parametric Z-score tests all have very good type I error control with the likelihood ratio test being the best. However, the semi-parametric Z-score test requires less distributional assumptions than the two parametric tests. The percentile-t bootstrap test and bootstrapped Johnson's modified t-test have better type I error control than the paired t-test on the original-scale and Johnson's modified t-test, respectively. Combining with the propensity-score method, we can also apply the proposed methods to test the mean equality of two cost outcomes in the presence of confounders. Our two applications are from health services research. In the first one, we want to know the effect of Medicaid reimbursement policy change on outpatient health care costs. The second one is to evaluate the effect of a hospitalist programme on health care costs in an observational study, and the imbalanced covariates between intervention and control patients are taken into account using a propensity score approach.     

Evaluation of old and new tests of heterogeneity in epidemiologic meta-analysis.

The identification of heterogeneity in effects between studies is a key issue in meta-analyses of observational studies, since it is critical for determining whether it is appropriate to pool the individual results into one summary measure. The result of a hypothesis test is often used as the decision criterion. In this paper, the authors use a large simulation study patterned from the key features of five published epidemiologic meta-analyses to investigate the type I error and statistical power of five previously proposed asymptotic homogeneity tests, a parametric bootstrap version of each of the tests, and tau2-bootstrap, a test proposed by the authors. The results show that the asymptotic DerSimonian and Laird Q statistic and the bootstrap versions of the other tests give the correct type I error under the null hypothesis but that all of the tests considered have low statistical power, especially when the number of studies included in the meta-analysis is small (<20). From the point of view of validity, power, and computational ease, the Q statistic is clearly the best choice. The authors found that the performance of all of the tests considered did not depend appreciably upon the value of the pooled odds ratio, both for size and for power. Because tests for heterogeneity will often be underpowered, random effects models can be used routinely, and heterogeneity can be quantified by means of R(I), the proportion of the total variance of the pooled effect measure due to between-study variance, and CV(B), the between-study coefficient of variation.     

Parametric bootstrap and penalized quasi-likelihood inference in conditional autoregressive models

This paper discusses a variety of conditional autoregressive (CAR) models for mapping disease rates, beyond the usual first-order intrinsic CAR model. We illustrate the utility and scope of such models for handling different types of data structures. To encourage their routine use for map production at statistical and health agencies, a simple algorithm for fitting such models is presented. This is derived from penalized quasi-likelihood (PQL) inference which uses an analogue of best-linear unbiased estimation for the regional risk ratios and restricted maximum likelihood for the variance components. We offer the practitioner here the use of the parametric bootstrap for inference. It is more reliable than standard maximum likelihood asymptotics for inference purposes since relevant hypotheses for the mapping of rates lie on the boundary of the parameter space. We illustrate the parametric bootstrap test of the practically relevant and important simplifying hypothesis that there is no spatial autocorrelation. Although the parametric bootstrap requires computational effort, it is straightforward to implement and offers a wealth of information relating to the estimators and their properties. The proposed methodology is illustrated by analysing infant mortality in the province of British Columbia in Canada.     

Bootstrap confidence intervals for cost-effectiveness ratios: some simulation results

Recently, a number of papers have brought up the issue of how to make cost-effectiveness (CE) studies stochastic, i.e. how to obtain confidence intervals for CE ratios. In this note we present a bootstrap procedure for estimating bias-corrected confidence intervals for CE ratios. The bootstrap procedure is tested in a simulation study based on the assumptions made in a recent paper by Wakker and Klaassen in this journal. We test two variants of CE ratio bootstrap confidence intervals. The first is a bootstrap analogue of the parametric method proposed by Wakker and Klaassen which gives results similar to those obtained with the parametric method. However, computing bootstrap confidence intervals directly for the CE ratio produce results closer to the predetermined significance level. © 1998 John Wiley & Sons, Ltd.